albert einstein thought experiments

Albert Einstein used to ponder these 5 mind-melting questions for fun. Can you figure them out?

• Albert Einstein was well known for his thought experiments involving complex scientific ideas.
• Often he used real-world examples that helped non-scientists grasp his theories of relativity.
• He started pondering one of them, about chasing a beam of light through space, when he was 16.

Albert Einstein , one of the greatest minds of the 20th century, forever changed the landscape of science by introducing revolutionary concepts that shook our understanding of the physical world.

One of Einstein's most defining qualities was his remarkable ability to conceptualize complex scientific ideas by imagining real-life scenarios. He called these scenarios Gedankenexperiments , which is German for thought experiments.

Despite the name, Einstein's mental exercises incorporated data from actual experiments.

Here are a few thought experiments that demonstrate some of Einstein's most groundbreaking discoveries, including his special and general theories of relativity .

What would happen if you chased a beam of light as it moved through space?

Einstein started wondering about this when he was just 16 years old. 

If you could somehow catch up to the light and travel as fast as it is going, Einstein reasoned, you would be able to observe the light frozen in space. But since he knew light was a wave composed of changing magnetic and electric fields, it couldn't truly be still.   

"One sees in this paradox the germ of the special relativity theory is already contained," Einstein wrote in his " Autobiographical Notes ." This "special" theory applies to certain relationships between space and time, and he further explored it with another thought experiment involving trains and light.

Can 2 people experience the exact same event differently? 

Imagine you're standing on a train while your friend is standing outside the train, watching it pass by. If lightning struck near both ends of the train, your friend would see both bolts flash at the same time.

But on the train, you are closer to the bolt of lightning you're moving toward. So you see this lightning first because the light has a shorter distance to travel.

The setup for this experiment is a bit complicated and involves angled mirrors and poles. But the result is that time behaves differently for someone moving than for someone standing still. 

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It cemented Einstein's belief that time and space are relative and simultaneity — two events happening at the same time — depends on your perspective. This is a cornerstone of Einstein's special theory of relativity.

How does your space-traveling twin age compared to you?

Let's say you have a twin who was born at almost the exact same time as you.

But almost immediately, your twin boards a spaceship and launches into space to travel through the universe at nearly the speed of light. 

Since, according to Einstein's special theory of relativity, time moves slower the closer you reach the speed of light, your twin in the spaceship would age more slowly.

When the spaceship landed back on Earth, you would be celebrating your 65th birthday, while your twin hadn't even turned 10 yet, based on an estimation from Omni Calculator.

Is your elevator accelerating or floating in space?

Imagine you are in a windowless elevator, unable to see what's happening outside. Without visual cues, you don't know if you're in a stationary elevator on Earth or in space being hauled upwards. Gravity's tug and upward acceleration in zero gravity both pull you to the floor.  

The physics of both events is the same, Einstein decided, based on the "principle of equivalence." Similarly, if your elevator were to plummet far and fast, you would float as though you were in space.

Now consider Einstein's previous assertion that time and space are relative. If motion can affect time and space (like with the train experiment) and gravity and acceleration behave the same, that means gravity can actually affect time and space. 

If you put a bowling ball on a trampoline, it will depress the fabric. Place marbles close by, and they will roll toward the ball. Objects with huge mass can affect space-time in a similar way. 

The ability of gravity to warp space-time is a key part of Einstein's general theory of relativity, which he published a decade after the special theory and expanded upon it.

Can particles communicate faster than the speed of light?

Einstein wasn't the biggest cheerleader for quantum theory. In fact, he argued back and forth with physicist Niels Bohr over certain occurrences that he believed violated fundamental laws of physics.

One of Einstein's thought experiments had to do with quantum entanglement, which he called " spooky action at a distance ."

Imagine you have a two-sided coin that you can easily split in half. You flip the coin. Without looking at the outcome, you hand one side to your friend and keep the other side for yourself. Then your friend gets on a rocket ship and travels across the universe.

When you look at your coin, you see you're holding the heads side of the coin. Instantly you know that your friend, who is billions of light years away, has the tails side.

Einstein's version of this thought experiment is more complicated than coins and involves entangled particles that share a wave function. Both particles have the potential to be in two possible states, spin up and spin down. Measuring one gives you information about the other, no matter how far apart they are.

It's a bit like if your half of the coin was neither heads nor tails until you looked at it. Since the coin wasn't double-sided, you know your friend has tails when you have heads. But Einstein thought particles behaved more like real coins. They had some inherent property that made them "spin up" or "spin down" all along.

Other scientists have proven him wrong in the decades since. In 2022, three physicists won the Nobel Prize for demonstrating spooky action at a distance.

Watch: Physicist breaks down the science behind 10 iconic Marvel scenes

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September 1, 2015

Lost in Thought—How Important to Physics Were Einstein’s Imaginings?

Einstein’s thought experiments left a long and somewhat mixed legacy of their own

By Sabine Hossenfelder

Gedankenexperiment , German for “thought experiment,” was Albert Einstein’s famous name for the imaginings that led to his greatest breakthroughs in physics. He traced his realization of light’s finite speed—the core idea of special relativity—to his teenage daydreams about riding beams of light. General relativity, his monumental theory of gravitation, has its origins in his musings about riding up and down in an elevator. In both cases, Einstein crafted new theories about the natural world by using his mind’s eye to push beyond the limitations of laboratory measurements.

Einstein was neither the first nor the last theorist to do this, but his remarkable achievements were pivotal in establishing the gedankenexperiment as a cornerstone of modern theoretical physics. Today physicists regularly use thought experiments to formulate new theories and to seek out inconsistencies or novel effects within existing ones.

But the modern embrace of thought experiments raises some uncomfortable questions. In the search for a grand unified theory that would wed the small-scale world of quantum mechanics with Einstein’s relativistic description of the universe at large, the most popular current ideas are bereft of observational support from actual experiments. Can thought alone sustain them? How far can we trust logical deduction? Where is the line between scientific intuition and fantasy? Einstein’s legacy offers no certain answers: On one hand, his reliance on the power of thought was a spectacular success. On the other, many of his best-known thought experiments were based on data from real experimentation, such as the classic Michelson-Morley experiment that first measured the constancy of the speed of light. Moreover, Einstein’s fixation on that which can be measured at times blinded him to deeper layers of reality—although even his mistakes in thought experiments contributed to later breakthroughs.

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Here we will walk through some of Einstein’s most iconic thought experiments, highlighting how they succeeded, where they failed and how they remain vital to questions now at the frontiers of theoretical physics.

The Windowless Elevator

In his thought experiments, Einstein’s genius was in realizing which aspects of experience were essential and which could be discarded. Consider his most famous one: the elevator thought experiment, which he began devising in 1907. Einstein argued that inside a windowless elevator, a person cannot tell whether the elevator is at rest in a gravitational field or is instead being hauled up with constant acceleration. He then conjectured that the laws of physics themselves must be identical in both situations. According to this “principle of equivalence,” locally (in the elevator), the effects of gravitation are the same as those of acceleration in the absence of gravity. Converted into mathematical equations, this principle became the basis for general relativity. In other words, the elevator thought experiment motivated Einstein to make the daring intellectual leap that ultimately led to his greatest achievement, his geometric description of gravity.

Credit: Nigel Holmes

Spooky Action

Later in his career, Einstein fought hard against the tenets of quantum mechanics, particularly the uncertainty principle, which dictates that the more you know about one aspect of a fundamental particle, such as its position, the less you can know about another, related aspect of that particle, such as its momentum—and vice versa. Einstein thought that the uncertainty principle was a sign that quantum theory was deeply flawed.

During a years-long exchange with Danish quantum theorist Niels Bohr, Einstein conceived of a series of thought experiments meant to demonstrate that it is possible to violate the uncertainty principle, but Bohr dissected every one of them. This exchange bolstered Bohr’s conviction that quantum uncertainty was a fundamental aspect of nature. If not even the great Einstein could devise a way to precisely measure both the position and the momentum of a particle, then certainly there must be something to the uncertainty principle!

In 1935, along with his colleagues Boris Podolsky and Nathan Rosen, Einstein published what was meant to be his most potent critique of the uncertainty principle. Perhaps because Podolsky, not Einstein, drafted the actual text of the paper, this Einstein-Podolsky-Rosen (EPR) thought experiment was presented not as an easy-to-imagine scenario of boxes, clocks and light beams but as an abstract series of equations describing interactions between two generalized quantum systems.

The simplest version of the EPR experiment studies the paradoxical behavior of “entangled” particles—pairs of particles that share a common quantum state. It unfolds as follows: Imagine an unstable particle with a spin of zero decaying into two daughter particles, which speed off in opposite directions. (Spin is a measure of a particle’s angular momentum, but counterintuitively, it has little to do with a particle’s rate of rotation.) Conservation laws dictate that the spins of those two daughter particles must add up to zero; one particle, then, could possess a spin value of “up,” and the other could have a spin value of “down.” The laws of quantum mechanics dictate that in the absence of measurement, neither of the particles possesses a definite spin until one of the two speeding entangled particles is measured. Once a measurement of one particle is made, the state of the other changes instantaneously , even if the particles are separated by vast distances!

Einstein believed this “spooky action at a distance” was nonsense. His own special theory of relativity held that nothing could travel faster than light, so there was no way for two particles to communicate with each other instantaneously from opposite sides of the universe. He suggested instead that the measurement outcomes must be determined prior to measurement by “hidden variables” that quantum mechanics failed to account for. Decades of discussion followed until 1964, when physicist John Stewart Bell developed a theorem quantifying exactly how the information shared between entangled particles differs from the information that Einstein postulated would be shared through hidden variables.

Since the 1970s lab experiments with entangled quantum systems have repeatedly confirmed that Einstein was wrong, that quantum particles indeed share mutual information that cannot be accounted for by hidden variables. Spooky action at a distance is real, but experiments have demonstrated that it cannot be used to transmit information faster than light, making it perfectly consistent with Einstein’s special relativity. This counterintuitive truth remains one of the most mysterious conundrums in all of physics, and it was Einstein’s stubborn, mistaken opposition that proved crucial to confirming it.

Alice and Bob

Today some of the most significant thought experiments in physics explore how to reconcile Einstein’s clockwork, relativistic universe with the fuzzy uncertainties inherent to quantum particles.

Consider, for instance, the widely discussed black hole information paradox. If you combine general relativity and quantum field theory, then you find that black holes evaporate, slowly radiating away their mass because of quantum effects. You also find that this process is not reversible: regardless of what formed the black hole, the evaporating black hole always produces the same featureless bath of radiation from which no information about its contents can be retrieved. But such a process is prohibited in quantum theory, which states that any occurrence can, in principle, be reversed in time. For instance, according to the laws of quantum mechanics, the leftovers of a burned book still contain all the information necessary to reassemble that book even though this information is not easily accessible. Not so for evaporating black holes. And so we arrive at a paradox, a logical inconsistency. A union of quantum mechanics and general relativity tells us that black holes must evaporate, but we conclude that the result is incompatible with quantum mechanics. We must be making some mistake—but where?

The thought experiments created to explore this paradox typically ask us to imagine a pair of observers, Bob and Alice, who share a pair of entangled particles—those spooky entities from the EPR experiment. Alice jumps into the black hole, carrying her particle with her, whereas Bob stays outside and far away with his. Without Alice, Bob’s particle is just typical, with a spin that might measure up or down—the information that it once shared with its entangled partner is lost, along with Alice.

Bob and Alice play a central role in one of the most popular proposed solutions to the paradox, called black hole complementarity. Proposed in 1993 by Leonard Susskind, Lárus Thorlacius and John Uglum, all then at Stanford University, black hole complementarity rests on Einstein’s golden rule for a gedankenexperiment: a strict focus on that which can be measured. Susskind and his colleagues postulated that the information falling in with Alice must come out later with the evaporating black hole’s radiation. This scenario would usually create another inconsistency because quantum mechanics allows only pair-wise entanglement with one partner at a time, a property called monogamy of entanglement. That is, if Bob’s particle is entangled with Alice’s, it cannot be entangled with anything else. But black hole complementarity requires that Bob’s particle be entangled with Alice’s and with the radiation the black hole later emits even though this violates monogamy. At first sight, then, black hole complementarity seems to exchange one inconsistency with another.

But like a perfect crime, if no one actually witnesses this inconsistency, perhaps it can subvert nature’s otherwise strict laws. Black hole complementarity relies on the argument that it is physically impossible for any observer to see Alice and Bob’s entangled particles breaking the rules.

To envision how this perfect quantum-mechanical crime could unfold, imagine a third observer, Charlie, hovering near the black hole, keeping an eye on Alice and Bob. He watches as Bob stays outside and as Alice falls in, measuring the black hole’s emitted radiation all the while. In theory, information encoded in that radiation could tip off Charlie that Bob and Alice had violated the monogamy of their entanglement. To know for certain, however, Charlie would have to compare his observations not only with Bob’s measurement but also with Alice’s— inside the black hole. So he must hover at the horizon, measure the emitted radiation, then jump in to tell Alice what he has found. Amazingly enough, Susskind and Thorlacius showed that no matter how hard Charlie tries, it is impossible for him to enter the black hole and compare his information with Alice’s before they are both torn apart by tidal forces. Their grisly fate suggests no violations of quantum mechanics can ever be measured by anybody around a black hole, and so theorists can commit this crime against nature with impunity.

Suffice it to say, not all theorists are convinced that this argument is valid. One criticism of black hole complementarity is that it might violate Einstein’s equivalence principle—the one that grew out of his elevator thought experiment. Einstein’s general relativity predicts that just as the elevator’s passenger cannot distinguish between gravity and acceleration, an observer crossing a black hole’s horizon should not notice anything unusual; there is no way an observer can tell that he or she has slipped past the point of no return.

Now let us return to the entanglement of Alice and Bob. If the radiation that Bob sees from far outside the hole contains all the information that we thought vanished with Alice behind the horizon, then this radiation must have been emitted with an extremely high energy; otherwise it would not have escaped the strong gravitational pull near the horizon. This energy is high enough to vaporize any infalling observer before he or she slips past the black hole’s horizon. In other words, black hole complementarity implies that black holes have a “firewall” just outside the horizon—and yet the firewall directly contradicts the predictions of Einstein’s equivalence principle.

At this point, we have ventured deep into the realm of theory. Indeed, we might never know the solutions to these puzzles. But because those solutions could lead to an understanding of the quantum nature of space and time, these puzzles are, for better or worse, some of the most vibrant areas of research in theoretical physics. And it all goes back to Einstein’s musings about falling elevators.

Sabine Hossenfelder is a physicist and research fellow at the Frankfurt Institute for Advanced Studies in Germany. She currently works on dark matter and the foundations of quantum mechanics.

Einstein’s Relativity Explained in 4 Simple Steps

The revolutionary physicist used his imagination rather than fancy math to come up with his most famous and elegant equation.

Albert Einstein’s theory of relativity is famous for predicting some really weird but true phenomena, like astronauts aging slower than people on Earth and solid objects changing their shapes at high speeds.

But the thing is, if you pick up a copy of Einstein’s original paper on relativity from 1905, it’s a straightforward read. His text is plain and clear, and his equations are mostly just algebra—nothing that would bother a typical high-schooler.

That’s because fancy math was never the point for Einstein. He liked to think visually, coming up with experiments in his mind’s eye and working them around in his head until he could see the ideas and physical principles with crystalline clarity. (Read “ 10 Things You (Probably) Didn’t Know About Einstein. ”)

To bring his process to life, National Geographic created an interactive version of one of Einstein’s most famous thought experiments : a parable about lightning strikes as seen from a moving train that shows how two observers can understand space and time in very different ways.

Here’s how Einstein got started on his thought experiments when he was just 16, and how it eventually led him to the most revolutionary equation in modern physics.

1895: Running Beside a Light Beam

By this point, Einstein’s ill-disguised contempt for his native Germany’s rigid, authoritarian educational methods had already gotten him kicked out of the equivalent of high school, so he moved to Zurich in hopes of attending the Swiss Federal Institute of Technology (ETH). (Also see “ Why the FBI Kept a 1,400-Page File on Einstein .”)

First, though, Einstein decided to put in a year of preparation at a school in the nearby town of Aarau—a place that stressed avant garde methods like independent thought and visualization of concepts. In that happy environment, he soon he found himself wondering what it would be like to run alongside a light beam.

Einstein had already learned in physics class what a light beam was: a set of oscillating electric and magnetic fields rippling along at 186,000 miles a second, the measured speed of light. If he were to run alongside it at just that speed, Einstein reasoned, he ought to be able to look over and see a set of oscillating electric and magnetic fields hanging right next to him, seemingly stationary in space.

Yet that was impossible. For starters, such stationary fields would violate Maxwell’s equations, the mathematical laws that codified everything physicists at the time knew about electricity, magnetism, and light. The laws were (and are) quite strict: Any ripples in the fields have to move at the speed of light and cannot stand still—no exceptions.

Worse, stationary fields wouldn’t jibe with the principle of relativity, a notion that physicists had embraced since the time of Galileo and Newton in the 17th century. Basically, relativity said that the laws of physics couldn’t depend on how fast you were moving; all you could measure was the velocity of one object relative to another.

But when Einstein applied this principle to his thought experiment, it produced a contradiction: Relativity dictated that anything he could see while running beside a light beam, including the stationary fields, should also be something Earthbound physicists could create in the lab. But nothing like that had ever been observed.

This problem would bug Einstein for another 10 years, all the way through his university work at ETH and his move to the Swiss capital city of Bern, where he became an examiner in the Swiss patent office. That’s where he resolved to crack the paradox once and for all.

1904: Measuring Light From a Moving Train

It wasn’t easy. Einstein tried every solution he could think of, and nothing worked. Almost out of desperation, he began to consider a notion that was simple but radical. Maybe Maxwell’s equations worked for everybody, he thought, but the speed of light was always constant.

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When you saw a light beam zip past, in other words, it wouldn’t matter whether its source was moving toward you, away from you, or off to the side, nor would it matter how fast the source was going. You would always measure that beam’s velocity to be 186,000 miles a second. Among other things, that meant Einstein would never see the stationary, oscillating fields, because he could never catch the light beam.

This was the only way Einstein could see to reconcile Maxwell’s equations with the principle of relativity. At first, though, this solution seemed to have its own fatal flaw. Einstein later explained the problem with another thought experiment: Imagine firing a light beam along a railroad embankment just as a train roars by in the same direction at, say, 2,000 miles a second.

Someone standing on the embankment would measure the light beam’s speed to be the standard number, 186,000 miles a second. But someone on the train would see it moving past at only 184,000 miles a second. If the speed of light was not constant, Maxwell’s equations would somehow have to look different inside the railway carriage, Einstein concluded, and the principle of relativity would be violated.

This apparent contradiction left Einstein spinning his wheels for almost a year. But then, on a beautiful morning in May 1905, he was walking to work with his best friend Michele Besso, an engineer he had known since their student days in Zurich. The two men were talking with about Einstein’s dilemma, as they often did. And suddenly, Einstein saw the solution. He worked on it overnight, and when they met the next morning, Einstein told Besso, “Thank you. I’ve completely solved the problem.”

May 1905: Lightning Strikes a Moving Train

Einstein’s revelation was that observers in relative motion experience time differently: it’s perfectly possible for two events to happen simultaneously from the perspective of one observer, yet happen at different times from the perspective of the other. And both observers would be right.

Einstein later illustrated this point with another thought experiment. Imagine that you once again have an observer standing on a railway embankment as a train goes roaring by. But this time, each end of the train is struck by a bolt of lightning just as the train’s midpoint is passing. Because the lightning strikes are the same distance from the observer, their light reaches his eye at the same instant. So he correctly says that they happened simultaneously.

Meanwhile, another observer on the train is sitting at its exact midpoint. From her perspective, the light from the two strikes also has to travel equal distances, and she will likewise measure the speed of light to be the same in either direction. But because the train is moving, the light coming from the lightning in the rear has to travel farther to catch up, so it reaches her a few instants later than the light coming from the front. Since the light pulses arrived at different times, she can only conclude the strikes were not simultaneous—that the one in front actually happened first.

In short, Einstein realized, simultaneity is what’s relative. Once you accept that, all the strange effects we now associate with relativity are a matter of simple algebra.

Einstein dashed off his ideas in a fever pitch and sent his paper in for publication just a few weeks later. He gave it a title—“ On the Electrodynamics of Moving Bodies ”—that spoke to his struggle to reconcile Maxwell’s equations with the principle of relativity. And he concluded it with a thank you to Besso (“I am indebted to him for several valuable suggestions”) that guaranteed his friend a touch of immortality.

September 1905: Mass and Energy

That first paper wasn’t the end of it, though. Einstein kept obsessing on relativity all through the summer of 1905, and in September he sent in a second paper as a kind of afterthought.

It was based on yet another thought experiment. Imagine an object that’s sitting at rest, he said. And now imagine that it spontaneously emits two identical pulses of light in opposite directions. The object will stay put, but because each pulse carries off a certain amount of energy, the object’s energy content will decrease.

Now, said Einstein, what would this process look like to a moving observer? From her perspective, the object would just keep moving in a straight line while the two pulses flew off. But even though the two pulses’ speed would still be the same—the speed of light—their energies would be different: The pulse moving forward along the direction of motion would now have a higher energy than the one moving backward.

With a little more algebra, Einstein showed that for all this to be consistent, the object not only had to lose energy when the light pulses departed, it had to lose a bit of mass, as well. Or, to put it another way, mass and energy are interchangeable.

Einstein wrote down an equation that relates the two. Using today’s notation, which abbreviates the speed of light using the letter c , he produced easily the most famous equation ever written: E = mc 2 .

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Relativity: The Thought Experiments Behind Einstein's Theory

Paul Sutter is an astrophysicist at The Ohio State University and the chief scientist at COSI science center . Sutter is also host of " Ask a Spaceman " and " Space Radio ," and leads AstroTours around the world. Sutter contributed this article to  Space.com's Expert Voices: Op-Ed & Insights .

Albert Einstein's theory of general relativity is a monumental achievement of human ingenuity, creativity and perseverance — to say the least.

While one might reasonably argue that there were several people on the planet in the early 20th century who were as brilliant as Einstein, nobody could think the same way he did. His seven-year journey to develop a new theory of gravity was filled with leap after startling intuitive leap — with pregnant pauses in between as he worked out the consequences of those new thoughts. And the result of all that labor was our modern understanding of how gravity works, unchanged in the century since Einstein. [ Einstein's Theory of General Relativity: A Simplified Explanation ]

Let's a take a peek into the mind of a true gravitational master. 

Free, free falling

Einstein's first insight into the nature of gravity was to put a new twist on an old idea. In Isaac Newton's original mathematical description of gravity ("OG"?), there's an odd coincidence when it comes to the concept of "mass." In one famous equation, F = ma, mass is your inertia — how much oomph it takes to shove you along. In Newton's other equation on gravity, mass is more like gravitational charge — the level of attraction you might feel toward the Earth, for example.

Objects with twice the mass feel twice the attraction toward the Earth, and should therefore fall twice as quickly. But years back, Galileo Galilei had conclusively shown that they don't: Neglecting air resistance, all objects fall at the same rate regardless of their mass.

Thus for Newton's theory to work, inertial mass had to be the same as gravitational mass, but only by sheer coincidence: there was no reason for this equality to hold. For an object with twice the mass, the Earth may pull on it twice as strongly, but this is perfectly canceled out by the fact that it's now twice as hard to get the object moving. Inertial and gravitational masses move in perfect lockstep.

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This odd correspondence had long been a puzzle in gravitational circles, but in 1907, Einstein took it one step further. The physicist imagined what would happen if you were to fall from a great height. Again neglecting air resistance, your inertial and gravitational masses would cancel, making you feel perfectly weightless, as if there were no gravity at all. But zero-gravity environments are precisely the playground of Special Relativity, the theory he had cooked up just a couple years prior that wove our conceptions of space and time into the unified fabric of spacetime.

To Einstein, this was a major clue. Lurking in the shadows of gravity was his precious special relativity and the essential concept of space-time, and what made that realization possible was the elevation of the equivalence between inertial and gravitational masses into a fundamental principle, rather than the awkward afterthought it had been.

Up, up, and away

Then, Einstein took it another step further. Suppose that in the middle of the night, we relocated your bedroom to the interior of a rocket, launched the craft into space (you're a heavy sleeper) and sent it flying away with the engines purring, providing a constant 1 g acceleration, the same acceleration you would feel on the Earth. 

Let's further assume that the rocket is perfectly quiet, so there's no immediate giveaway that you're on that spaceship. Unless you looked outside and noticed that only a worryingly thin piece of glass separated you from the vacuum of space, you would have no idea that you were part of some grotesque science experiment.

Drop an apple — it falls to the floor. Drop a jug of milk — it falls to the floor at the exact same rate. From outside the spaceship, it's easy to see why: The apple and milk aren't really moving, but the rocket is accelerating forward, "meeting" the dropped items. If we removed the floor altogether, the apple and milk would simply stay put as the rocket zoomed away.

But inside the rocket ,you would just think it's normal gravity: Objects are falling, as they are wont to do, and all at the same rate.

The implication is clear (or at least, it was clear to Einstein): Gravity causes acceleration, and acceleration causes gravity. They are absolutely identical.

Round and round we go

Einstein had to make one more big leap to get us to modern gravity. It's such a big leap that he spent five years just tinkering around with the implications of gravity = acceleration before he could make the next jump. And to do it, you could almost say, he had to think in circles.

Imagine a specially designed merry-go-round, with all the horses lined up nose to tail, forming a perfect circle around the perimeter. Now, accelerate the ride such that it's rotating at close to the speed of light. What happens?

Let's assume, first of all, that the ride can actually stay together. As the horses pass in front of your view, they appear shorter. Why? At those speeds, Einstein's special relativity teaches us that moving objects contract along their direction of motion.

That means the horses aren't perfectly nose-to-tail anymore; you can squeeze more seats into a rotating ride than you could in a stationary one. But the total width of the ride hasn't changed; the entire ride isn't powering across your field of view, so you don’t observe any relativistic length-contraction funny business to the entire structure, just to the horses as they pass by. This combination means that our old familiar relationship between diameter and circumference (C = pi * d) no longer applies to the rotating ride.

The geometry that describes this relationship simply isn't the normal Euclid-derived stuff that we were taught in high school. It's non-Euclidean, or the geometry of curved spaces.

Supreme general

So here are the puzzle pieces that Einstein had in 1912: a) Space-time must be involved somehow, b) acceleration and gravity are intimately linked, and c) some accelerations need to be described by curved geometries.

While it's easy enough for us, a hundred years later, to simply say, "Gravity is the curvature of space-time," it took Einstein another two years of feverish work to make all the mathematical pieces fit and give us what we know as general relativity.

Learn more by listening to the episode "Seriously, What Is Gravity? (Part 1)" on the "Ask A Spaceman" podcast, available on iTunes and on the web at http://www.askaspaceman.com . Thanks to Andrew P., Joyce S., @Luft08, Ben W., Ter B., Colin E., Christopher F., Maria A., Brett K., bryguytheflyguy, @MarkRiepe, Kenneth L., Allison K., Phil B. and @shrenic_shah for the questions that led to this piece! Ask your own question on Twitter using #AskASpaceman or by following Paul @PaulMattSutter and facebook.com/PaulMattSutter . Follow us @Spacedotcom , Facebook and Google+ . Original article on Space.com .

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

Paul M. Sutter is an astrophysicist at SUNY Stony Brook and the Flatiron Institute in New York City. Paul received his PhD in Physics from the University of Illinois at Urbana-Champaign in 2011, and spent three years at the Paris Institute of Astrophysics, followed by a research fellowship in Trieste, Italy, His research focuses on many diverse topics, from the emptiest regions of the universe to the earliest moments of the Big Bang to the hunt for the first stars. As an "Agent to the Stars," Paul has passionately engaged the public in science outreach for several years. He is the host of the popular "Ask a Spaceman!" podcast, author of "Your Place in the Universe" and "How to Die in Space" and he frequently appears on TV — including on The Weather Channel, for which he serves as Official Space Specialist.

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• 25 April 2024
• Correction 25 April 2024

‘Shut up and calculate’: how Einstein lost the battle to explain quantum reality

• Jim Baggott 0

Jim Baggott is a science writer based in Cape Town, South Africa. He is co-author with John Heilbron of Quantum Drama .

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For entangled particles, a change in one instantly affects the other, no matter how far apart they are. Credit: Volker Steger/SPL

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Quantum mechanics is an extraordinarily successful scientific theory, on which much of our technology-obsessed lifestyles depend. It is also bewildering. Although the theory works, it leaves physicists chasing probabilities instead of certainties and breaks the link between cause and effect. It gives us particles that are waves and waves that are particles , cats that seem to be both alive and dead, and lots of spooky quantum weirdness around hard-to-explain phenomena, such as quantum entanglement.

Myths are also rife. For instance, in the early twentieth century, when the theory’s founders were arguing among themselves about what it all meant, the views of Danish physicist Niels Bohr came to dominate. Albert Einstein famously disagreed with him and, in the 1920s and 1930s, the two locked horns in debate . A persistent myth was created that suggests Bohr won the argument by browbeating the stubborn and increasingly isolated Einstein into submission. Acting like some fanatical priesthood, physicists of Bohr’s ‘church’ sought to shut down further debate. They established the ‘Copenhagen interpretation’, named after the location of Bohr’s institute, as a dogmatic orthodoxy.

My latest book Quantum Drama , co-written with science historian John Heilbron, explores the origins of this myth and its role in motivating the singular personalities that would go on to challenge it. Their persistence in the face of widespread indifference paid off, because they helped to lay the foundations for a quantum-computing industry expected to be worth tens of billions by 2040.

John died on 5 November 2023 , so sadly did not see his last work through to publication. This essay is dedicated to his memory.

Foundational myth

A scientific myth is not produced by accident or error. It requires effort. “To qualify as a myth, a false claim should be persistent and widespread,” Heilbron said in a 2014 conference talk. “It should have a plausible and assignable reason for its endurance, and immediate cultural relevance,” he noted. “Although erroneous or fabulous, such myths are not entirely wrong, and their exaggerations bring out aspects of a situation, relationship or project that might otherwise be ignored.”

Does quantum theory imply the entire Universe is preordained?

To see how these observations apply to the historical development of quantum mechanics, let’s look more closely at the Bohr–Einstein debate. The only way to make sense of the theory, Bohr argued in 1927, was to accept his principle of complementarity. Physicists have no choice but to describe quantum experiments and their results using wholly incompatible, yet complementary, concepts borrowed from classical physics.

In one kind of experiment, an electron, for example, behaves like a classical wave. In another, it behaves like a classical particle. Physicists can observe only one type of behaviour at a time, because there is no experiment that can be devised that could show both behaviours at once.

Bohr insisted that there is no contradiction in complementarity, because the use of these classical concepts is purely symbolic. This was not about whether electrons are really waves or particles. It was about accepting that physicists can never know what an electron really is and that they must reach for symbolic descriptions of waves and particles as appropriate. With these restrictions, Bohr regarded the theory to be complete — no further elaboration was necessary.

Such a pronouncement prompts an important question. What is the purpose of physics? Is its main goal to gain ever-more-detailed descriptions and control of phenomena, regardless of whether physicists can understand these descriptions? Or, rather, is it a continuing search for deeper and deeper insights into the nature of physical reality?

Einstein preferred the second answer, and refused to accept that complementarity could be the last word on the subject. In his debate with Bohr, he devised a series of elaborate thought experiments, in which he sought to demonstrate the theory’s inconsistencies and ambiguities, and its incompleteness. These were intended to highlight matters of principle; they were not meant to be taken literally.

Entangled probabilities

In 1935, Einstein’s criticisms found their focus in a paper 1 published with his colleagues Boris Podolsky and Nathan Rosen at the Institute for Advanced Study in Princeton, New Jersey. In their thought experiment (known as EPR, the authors’ initials), a pair of particles (A and B) interact and move apart. Suppose each particle can possess, with equal probability, one of two quantum properties, which for simplicity I will call ‘up’ and ‘down’, measured in relation to some instrument setting. Assuming their properties are correlated by a physical law, if A is measured to be ‘up’, B must be ‘down’, and vice versa. The Austrian physicist Erwin Schrödinger invented the term entangled to describe this kind of situation.

How Einstein built on the past to make his breakthroughs

If the entangled particles are allowed to move so far apart that they can no longer affect one another, physicists might say that they are no longer in ‘causal contact’. Quantum mechanics predicts that scientists should still be able to measure A and thereby — with certainty — infer the correlated property of B.

But the theory gives us only probabilities. We have no way of knowing in advance what result we will get for A. If A is found to be ‘down’, how does the distant, causally disconnected B ‘know’ how to correlate with its entangled partner and give the result ‘up’? The particles cannot break the correlation, because this would break the physical law that created it.

Physicists could simply assume that, when far enough apart, the particles are separate and distinct, or ‘locally real’, each possessing properties that were fixed at the moment of their interaction. Suppose A sets off towards a measuring instrument carrying the property ‘up’. A devious experimenter is perfectly at liberty to change the instrument setting so that when A arrives, it is now measured to be ‘down’. How, then, is the correlation established? Do the particles somehow remain in contact, sending messages to each other or exerting influences on each other over vast distances at speeds faster than light, in conflict with Einstein’s special theory of relativity?

The alternative possibility, equally discomforting to contemplate, is that the entangled particles do not actually exist independently of each other. They are ‘non-local’, implying that their properties are not fixed until a measurement is made on one of them.

Both these alternatives were unacceptable to Einstein, leading him to conclude that quantum mechanics cannot be complete.

Niels Bohr (left) and Albert Einstein. Credit: Universal History Archive/Universal Images Group via Getty

The EPR thought experiment delivered a shock to Bohr’s camp, but it was quickly (if unconvincingly) rebuffed by Bohr. Einstein’s challenge was not enough; he was content to criticize the theory but there was no consensus on an alternative to Bohr’s complementarity. Bohr was judged by the wider scientific community to have won the debate and, by the early 1950s, Einstein’s star was waning.

Unlike Bohr, Einstein had established no school of his own. He had rather retreated into his own mind, in vain pursuit of a theory that would unify electromagnetism and gravity, and so eliminate the need for quantum mechanics altogether. He referred to himself as a “lone traveler”. In 1948, US theoretical physicist J. Robert Oppenheimer remarked to a reporter at Time magazine that the older Einstein had become “a landmark, but not a beacon”.

Prevailing view

Subsequent readings of this period in quantum history promoted a persistent and widespread suggestion that the Copenhagen interpretation had been established as the orthodox view. I offer two anecdotes as illustration. When learning quantum mechanics as a graduate student at Harvard University in the 1950s, US physicist N. David Mermin recalled vivid memories of the responses that his conceptual enquiries elicited from his professors, whom he viewed as ‘agents of Copenhagen’. “You’ll never get a PhD if you allow yourself to be distracted by such frivolities,” they advised him, “so get back to serious business and produce some results. Shut up, in other words, and calculate.”

The spy who flunked it: Kurt Gödel’s forgotten part in the atom-bomb story

It seemed that dissidents faced serious repercussions. When US physicist John Clauser — a pioneer of experimental tests of quantum mechanics in the early 1970s — struggled to find an academic position, he was clear in his own mind about the reasons. He thought he had fallen foul of the ‘religion’ fostered by Bohr and the Copenhagen church: “Any physicist who openly criticized or even seriously questioned these foundations ... was immediately branded as a ‘quack’. Quacks naturally found it difficult to find decent jobs within the profession.”

But pulling on the historical threads suggests a different explanation for both Mermin’s and Clauser’s struggles. Because there was no viable alternative to complementarity, those writing the first post-war student textbooks on quantum mechanics in the late 1940s had little choice but to present (often garbled) versions of Bohr’s theory. Bohr was notoriously vague and more than occasionally incomprehensible. Awkward questions about the theory’s foundations were typically given short shrift. It was more important for students to learn how to apply the theory than to fret about what it meant.

One important exception is US physicist David Bohm’s 1951 book Quantum Theory , which contains an extensive discussion of the theory’s interpretation, including EPR’s challenge. But, at the time, Bohm stuck to Bohr’s mantra.

The Americanization of post-war physics meant that no value was placed on ‘philosophical’ debates that did not yield practical results. The task of ‘getting to the numbers’ meant that there was no time or inclination for the kind of pointless discussion in which Bohr and Einstein had indulged. Pragmatism prevailed. Physicists encouraged their students to choose research topics that were likely to provide them with a suitable grounding for an academic career, or ones that appealed to prospective employers. These did not include research on quantum foundations.

These developments conspired to produce a subtly different kind of orthodoxy. In The Structure of Scientific Revolutions (1962), US philosopher Thomas Kuhn describes ‘normal’ science as the everyday puzzle-solving activities of scientists in the context of a prevailing ‘paradigm’. This can be interpreted as the foundational framework on which scientific understanding is based. Kuhn argued that researchers pursuing normal science tend to accept foundational theories without question and seek to solve problems within the bounds of these concepts. Only when intractable problems accumulate and the situation becomes intolerable might the paradigm ‘shift’, in a process that Kuhn likened to a political revolution.

Do black holes explode? The 50-year-old puzzle that challenges quantum physics

The prevailing view also defines what kinds of problem the community will accept as scientific and which problems researchers are encouraged (and funded) to investigate. As Kuhn acknowledged in his book: “Other problems, including many that had previously been standard, are rejected as metaphysical, as the concern of another discipline, or sometimes as just too problematic to be worth the time.”

What Kuhn says about normal science can be applied to ‘mainstream’ physics. By the 1950s, the physics community had become broadly indifferent to foundational questions that lay outside the mainstream. Such questions were judged to belong in a philosophy class, and there was no place for philosophy in physics. Mermin’s professors were not, as he had first thought, ‘agents of Copenhagen’. As he later told me, his professors “had no interest in understanding Bohr, and thought that Einstein’s distaste for [quantum mechanics] was just silly”. Instead, they were “just indifferent to philosophy. Full stop. Quantum mechanics worked. Why worry about what it meant?”

It is more likely that Clauser fell foul of the orthodoxy of mainstream physics. His experimental tests of quantum mechanics 2 in 1972 were met with indifference or, more actively, dismissal as junk or fringe science. After all, as expected, quantum mechanics passed Clauser’s tests and arguably nothing new was discovered. Clauser failed to get an academic position not because he had had the audacity to challenge the Copenhagen interpretation; his audacity was in challenging the mainstream. As a colleague told Clauser later, physics faculty members at one university to which he had applied “thought that the whole field was controversial”.

Aspect, Clauser and Zeilinger won the 2022 physics Nobel for work on entangled photons. Credit: Claudio Bresciani/TT News Agency/AFP via Getty

However, it’s important to acknowledge that the enduring myth of the Copenhagen interpretation contains grains of truth, too. Bohr had a strong and domineering personality. He wanted to be associated with quantum theory in much the same way that Einstein is associated with theories of relativity. Complementarity was accepted as the last word on the subject by the physicists of Bohr’s school. Most vociferous were Bohr’s ‘bulldog’ Léon Rosenfeld, Wolfgang Pauli and Werner Heisenberg, although all came to hold distinct views about what the interpretation actually meant.

They did seek to shut down rivals. French physicist Louis de Broglie’s ‘pilot wave’ interpretation, which restores causality and determinism in a theory in which real particles are guided by a real wave, was shot down by Pauli in 1927. Some 30 years later, US physicist Hugh Everett’s relative state or many-worlds interpretation was dismissed, as Rosenfeld later described, as “hopelessly wrong ideas”. Rosenfeld added that Everett “was undescribably stupid and could not understand the simplest things in quantum mechanics”.

Unorthodox interpretations

But the myth of the Copenhagen interpretation served an important purpose. It motivated a project that might otherwise have been ignored. Einstein liked Bohm’s Quantum Theory and asked to see him in Princeton in the spring of 1951. Their discussion prompted Bohm to abandon Bohr’s views, and he went on to reinvent de Broglie’s pilot wave theory. He also developed an alternative to the EPR challenge that held the promise of translation into a real experiment.

Befuddled by Bohrian vagueness, finding no solace in student textbooks and inspired by Bohm, Irish physicist John Bell pushed back against the Copenhagen interpretation and, in 1964, built on Bohm’s version of EPR to develop a now-famous theorem 3 . The assumption that the entangled particles A and B are locally real leads to predictions that are incompatible with those of quantum mechanics. This was no longer a matter for philosophers alone: this was about real physics.

It took Clauser three attempts to pass his graduate course on advanced quantum mechanics at Columbia University because his brain “kind of refused to do it”. He blamed Bohr and Copenhagen, found Bohm and Bell, and in 1972 became the first to perform experimental tests of Bell’s theorem with entangled photons 2 .

How to introduce quantum computers without slowing economic growth

French physicist Alain Aspect similarly struggled to discern a “physical world behind the mathematics”, was perplexed by complementarity (“Bohr is impossible to understand”) and found Bell. In 1982, he performed what would become an iconic test of Bell’s theorem 4 , changing the settings of the instruments used to measure the properties of pairs of entangled photons while the particles were mid-flight. This prevented the photons from somehow conspiring to correlate themselves through messages or influences passed between them, because the nature of the measurements to be made on them was not set until they were already too far apart. All these tests settled in favour of quantum mechanics and non-locality.

Although the wider physics community still considered testing quantum mechanics to be a fringe science and mostly a waste of time, exposing a hitherto unsuspected phenomenon — quantum entanglement and non-locality — was not. Aspect’s cause was aided by US physicist Richard Feynman, who in 1981 had published his own version of Bell’s theorem 5 and had speculated on the possibility of building a quantum computer. In 1984, Charles Bennett at IBM and Giles Brassard at the University of Montreal in Canada proposed entanglement as the basis for an innovative system of quantum cryptography 6 .

It is tempting to think that these developments finally helped to bring work on quantum foundations into mainstream physics, making it respectable. Not so. According to Austrian physicist Anton Zeilinger, who has helped to found the science of quantum information and its promise of a quantum technology, even those working in quantum information consider foundations to be “not the right thing”. “We don’t understand the reason why. Must be psychological reasons, something like that, something very deep,” Zeilinger says. The lack of any kind of physical mechanism to explain how entanglement works does not prevent the pragmatic physicist from getting to the numbers.

Similarly, by awarding the 2022 Nobel Prize in Physics to Clauser, Aspect and Zeilinger , the Nobels as an institution have not necessarily become friendly to foundational research. Commenting on the award, the chair of the Nobel Committee for Physics, Anders Irbäck, said: “It has become increasingly clear that a new kind of quantum technology is emerging. We can see that the laureates’ work with entangled states is of great importance, even beyond the fundamental questions about the interpretation of quantum mechanics.” Or, rather, their work is of great importance because of the efforts of those few dissidents, such as Bohm and Bell, who were prepared to resist the orthodoxy of mainstream physics, which they interpreted as the enduring myth of the Copenhagen interpretation.

The lesson from Bohr–Einstein and the riddle of entanglement is this. Even if we are prepared to acknowledge the myth, we still need to exercise care. Heilbron warned against wanton slaying: “The myth you slay today may contain a truth you need tomorrow.”

Nature 629 , 29-32 (2024)

doi: https://doi.org/10.1038/d41586-024-01216-z

Updates & Corrections

Correction 25 April 2024 : An earlier version of this Essay misnamed the Institute for Advanced Study.

Einstein, A., Podolsky, B. & Rosen, N. Phys. Rev. 47 , 777–780 (1935).

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Freedman, S. J. & Clauser, J. F. Phys. Rev. Lett. 28 , 938–941 (1972).

Bell, J. S. Phys. Phys. Fiz. 1 , 195–200 (1964).

Aspect, A., Dalibard, J. & Roger, G. Phys. Rev. Lett. 49 , 1804–1807 (1982).

Feynman, R. P. Int . J. Theor. Phys. 21 , 467–488 (1982).

Bennett, C. H. & Brassard, G. in Proc. IEEE Int. Conf. on Computers, Systems and Signal Processing 175–179 (IEEE, 1984).

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10 Things Einstein Got Right

One hundred years ago, on May 29, 1919, astronomers observed a total solar eclipse in an ambitious effort to test Albert Einstein’s general theory of relativity by seeing it in action. Essentially, Einstein thought space and time were intertwined in an infinite “fabric,” like an outstretched blanket. A massive object such as the Sun bends the spacetime blanket with its gravity, such that light no longer travels in a straight line as it passes by the Sun.

This means the apparent positions of background stars seen close to the Sun in the sky — including during a solar eclipse — should seem slightly shifted in the absence of the Sun, because the Sun’s gravity bends light. But until the eclipse experiment, no one was able to test Einstein’s theory of general relativity, as no one could see stars near the Sun in the daytime otherwise.

The world celebrated the results of this eclipse experiment — a victory for Einstein, and the dawning of a new era of our understanding of the universe.

General relativity has many important consequences for what we see in the cosmos and how we make discoveries in deep space today. The same is true for Einstein's slightly older theory, special relativity, with its widely celebrated equation E= mc 2 . Here are 10 things that result from Einstein’s theories of relativity:

1. Universal Speed Limit

Einstein's famous equation E= mc 2 contains "c," the speed of light in a vacuum. Although light comes in many flavors – from the rainbow of colors humans can see to the radio waves that transmit spacecraft data – Einstein said all light must obey the speed limit of 186,000 miles (300,000 kilometers) per second. So, even if two particles of light carry very different amounts of energy, they will travel at the same speed.

This has been shown experimentally in space. In 2009, NASA's Fermi Gamma-ray Space Telescope detected two photons at virtually the same moment , with one carrying a million times more energy than the other. They both came from a high-energy region near the collision of two neutron stars about 7 billion years ago. A neutron star is the highly dense remnant of a star that has exploded. While other theories posited that space-time itself has a " foamy " texture that might slow down more energetic particles, Fermi's observations found in favor of Einstein.

2. Strong Lensing

Just like the Sun bends the light from distant stars that pass close to it, a massive object like a galaxy distorts the light from another object that is much farther away. In some cases, this phenomenon can actually help us unveil new galaxies. We say that the closer object acts like a “lens,” acting like a telescope that reveals the more distant object. Entire clusters of galaxies can be lensed and act as lenses, too.

When the lensing object appears close enough to the more distant object in the sky, we actually see multiple images of that faraway object. In 1979, scientists first observed a double image of a quasar, a very bright object at the center of a galaxy that involves a supermassive black hole feeding off a disk of inflowing gas. These apparent copies of the distant object change in brightness if the original object is changing, but not all at once, because of how space itself is bent by the foreground object’s gravity.

Sometimes, when a distant celestial object is precisely aligned with another object, we see light bent into an “Einstein ring” or arc. In this image from NASA’s Hubble Space Telescope , the sweeping arc of light represents a distant galaxy that has been lensed, forming a “smiley face” with other galaxies.

3. Weak Lensing

When a massive object acts as a lens for a farther object, but the objects are not specially aligned with respect to our view, only one image of the distant object is projected. This happens much more often. The closer object’s gravity makes the background object look larger and more stretched than it really is. This is called “weak lensing.”

Weak lensing is very important for studying some of the biggest mysteries of the universe: dark matter and dark energy. Dark matter is an invisible material that only interacts with regular matter through gravity, and holds together entire galaxies and groups of galaxies like a cosmic glue. Dark energy behaves like the opposite of gravity, making objects recede from each other. Three upcoming observatories -- NASA’s Wide Field Infrared Survey Telescope , WFIRST, mission, the European-led Euclid space mission with NASA participation, and the ground-based Large Synoptic Survey Telescope --- will be key players in this effort. By surveying distortions of weakly lensed galaxies across the universe, scientists can characterize the effects of these persistently puzzling phenomena.

Gravitational lensing in general will also enable NASA’s James Webb Space telescope to look for some of the very first stars and galaxies of the universe.

4. Microlensing

So far, we’ve been talking about giant objects acting like magnifying lenses for other giant objects. But stars can also “lens” other stars, including stars that have planets around them. When light from a background star gets “lensed” by a closer star in the foreground, there is an increase in the background star’s brightness . If that foreground star also has a planet orbiting it, then telescopes can detect an extra bump in the background star’s light, caused by the orbiting planet. This technique for finding exoplanets, which are planets around stars other than our own, is called “microlensing.”

NASA’s Spitzer Space Telescope , in collaboration with ground-based observatories, found an “iceball” planet through microlensing. While microlensing has so far found less than 100 confirmed planets, WFIRST could find more than 1,000 new exoplanets using this technique.

5. Black Holes

The very existence of black holes, extremely dense objects from which no light can escape, is a prediction of general relativity. They represent the most extreme distortions of the fabric of space-time, and are especially famous for how their immense gravity affects light in weird ways that only Einstein’s theory could explain.

In 2019 the Event Horizon Telescope international collaboration, supported by the National Science Foundation and other partners, unveiled the first image of a black hole’s event horizon , the border that defines a black hole’s “point of no return” for nearby material. NASA's Chandra X-ray Observatory , Nuclear Spectroscopic Telescope Array (NuSTAR) , Neil Gehrels Swift Observatory, and Fermi Gamma-ray Space Telescope all looked at the same black hole in a coordinated effort, and researchers are still analyzing the results.

6. Relativistic Jets

This Spitzer image shows the galaxy Messier 87 (M87) in infrared light, which has a supermassive black hole at its center. Around the black hole is a disk of extremely hot gas, as well as two jets of material shooting out in opposite directions . One of the jets, visible on the right of the image, is pointing almost exactly toward Earth. Its enhanced brightness is due to the emission of light from particles traveling toward the observer at near the speed of light, an effect called “relativistic beaming.” By contrast, the other jet is invisible at all wavelengths because it is traveling away from the observer near the speed of light. The details of how such jets work are still mysterious, and scientists will continue studying black holes for more clues.

7. A Gravitational Vortex

Speaking of black holes, their gravity is so intense that they make infalling material “wobble” around them. Like a spoon stirring honey, where honey is the space around a black hole, the black hole’s distortion of space has a wobbling effect on material orbiting the black hole. Until recently, this was only theoretical. But in 2016, an international team of scientists using European Space Agency's XMM-Newton and NASA’s Nuclear Spectroscopic Telescope Array (NUSTAR) announced they had observed the signature of wobbling matter for the first time. Scientists will continue studying these odd effects of black holes to further probe Einstein’s ideas firsthand.

Incidentally, this wobbling of material around a black hole is similar to how Einstein explained Mercury’s odd orbit. As the closest planet to the Sun, Mercury feels the most gravitational tug from the Sun, and so its orbit’s orientation is slowly rotating around the Sun, creating a wobble.

8. Gravitational Waves

Ripples through space-time called gravitational waves were hypothesized by Einstein about 100 years ago, but not actually observed until recently. In 2016, an international collaboration of astronomers working with the Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors announced a landmark discovery: This enormous experiment detected the subtle signal of gravitational waves that had been traveling for 1.3 billion years after two black holes merged in a cataclysmic event. This opened a brand new door in an area of science called multi-messenger astronomy, in which both gravitational waves and light can be studied.

For example, NASA telescopes collaborated to measure light from two neutron stars merging after LIGO detected gravitational wave signals from the event, as announced in 2017. Given that gravitational waves from this event were detected mere 1.7 seconds before gamma rays from the merger, after both traveled 140 million light-years, scientists concluded Einstein was right about something else: gravitational waves and light waves travel at the same speed.

9. The Sun Delaying Radio Signals

Planetary exploration spacecraft have also shown Einstein to be right about general relativity. Because spacecraft communicate with Earth using light, in the form of radio waves, they present great opportunities to see whether the gravity of a massive object like the Sun changes light’s path.

In 1970, NASA’s Jet Propulsion Laboratory announced that Mariner VI and VII, which completed flybys of Mars in 1969, had conducted experiments using radio signals — and also agreed with Einstein. Using NASA’s Deep Space Network (DSN) , the two Mariners took several hundred radio measurements for this purpose. Researchers measured the time it took for radio signals to travel from the DSN dish in Goldstone, California, to the spacecraft and back. As Einstein would have predicted, there was a delay in the total roundtrip time because of the Sun’s gravity. For Mariner VI, the maximum delay was 204 microseconds, which, while far less than a single second, aligned almost exactly with what Einstein’s theory would anticipate.

In 1979, the Viking landers performed an even more accurate experiment along these lines. Then, in 2003 a group of scientists used NASA’s Cassini Spacecraft to repeat these kinds of radio science experiments with 50 times greater precision than Viking. It’s clear that Einstein’s theory has held up!

10. Proof from Orbiting Earth

In 2004, NASA launched a spacecraft called Gravity Probe B specifically designed to watch Einstein’s theory play out in the orbit of Earth. The theory goes that Earth, a rotating body, should be pulling the fabric of space-time around it as it spins, in addition to distorting light with its gravity.

The spacecraft had four gyroscopes and pointed at the star IM Pegasi while orbiting Earth over the poles. In this experiment, if Einstein had been wrong, these gyroscopes would have always pointed in the same direction. But in 2011, scientists announced they had observed tiny changes in the gyroscopes’ directions as a consequence of Earth, because of its gravity, dragging space-time around it.

Bonus: Your GPS!

Speaking of time delays, the GPS (global positioning system) on your phone or in your car relies on Einstein’s theories for accuracy. In order to know where you are, you need a receiver – like your phone, a ground station and a network of satellites orbiting Earth to send and receive signals. But according to general relativity, because of Earth’s gravity curving spacetime, satellites experience time moving slightly faster than on Earth. At the same time, special relativity would say time moves slower for objects that move much faster than others.

When scientists worked out the net effect of these forces, they found that the satellites’ clocks would always be a tiny bit ahead of clocks on Earth. While the difference per day is a matter of millionths of a second, that change really adds up. If GPS didn’t have relativity built into its technology, your phone would guide you miles out of your way!

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Thought Experiment: How Einstein Solved Difficult Problems

Thought experiments are a classic tool used by many great thinkers. They enable us to explore impossible situations and predict their implications and outcomes. Mastering thought experiments can help you confront difficult questions and anticipate (and prevent) problems .

The purpose of a thought experiment is to encourage speculation, logical thinking and to change paradigms. Thought experiments push us outside our comfort zone by forcing us to confront questions we cannot answer with ease. They demonstrate gaps in our knowledge and help us recognize the limits of what can be known.

“All truly wise thoughts have been thought already thousands of times; but to make them truly ours, we must think them over again honestly, until they take root in our personal experience.” Johann Wolfgang von Goethe

Famous thought experiments

Thought experiments have a rich and complex history, stretching back to the ancient Greeks and Romans.

An early example of a thought experiment is Zeno’s narrative of Achilles and the tortoise, dating to around 430 BC. Zeno’s thought experiments aimed to deduce first principles through the elimination of untrue concepts.

In one instance, the Greek philosopher used it to ‘prove’ motion is an illusion. Known as the dichotomy paradox, it involves Achilles racing a tortoise. Out of generosity, Achilles gives the tortoise a 100m head start. Once Achilles begins running, he soon catches up on the head start. However, by that point, the tortoise has moved another 10m. By the time he catches up again, the tortoise will have moved further. Zeno claimed Achilles could never win the race as the distance between the pair would constantly increase.

Descartes conducted a thought experiment, doubting the existence of everything he could until there was nothing left he could doubt.  Descartes could doubt everything except for the fact that he could doubt. His process left us with the philosophical thought experiment of ‘a brain in a vat’.

In the 17th century, Galileo used thought experiments to affirm his theories. One example is his thought experiment involving two balls (one heavy, one light) which are dropped from the Leaning Tower of Pisa. Prior philosophers had theorized the heavy ball would land first. Galileo claimed this was untrue, as mass does not influence acceleration.

According to Galileo’s early biography (written in 1654), he dropped two objects from the Leaning Tower of Pisa to disprove the gravitational mass relation hypothesis. Both landed at the same time, ushering in a new understanding of gravity. It is unknown if Galileo performed the experiment itself, so it is regarded as a thought experiment, not a physical one.

In 1814, Pierre Laplace explored determinism through ‘Laplace’s demon.’ This is a theoretical ‘demon’ which has an acute awareness of the location and movement of every single particle in existence. Would Laplace’s demon know the future? If the answer is yes, the universe must be linear and deterministic. If no, the universe is nonlinear and free will exists.

In 1897, the German term ‘Gedankenexperiment’ passed into English and a cohesive picture of how thought experiments are used worldwide began to form.

Albert Einstein used thought experiments for some of his most important discoveries. The most famous of his thought experiments was on a beam of light, which was made into a brilliant children’s book . What would happen if you could catch up to a beam of light as it moved he asked himself? The answers led him down a different path toward time, which led to the special theory of relativity.

Natural tendencies

In On Thought Experiments , 19th-century Philosopher and physicist Ernst Mach writes that curiosity is an inherent human quality. Babies test the world around them and learn the principle of cause and effect. With time, our exploration of the world becomes more and more in depth. We reach a point where we can no longer experiment through our hands alone. At that point, we move into the realm of thought experiments.

Thought experiments are a structured manifestation of our natural curiosity about the world.

Mach writes:

Our own ideas are more easily and readily at our disposal than physical facts. We experiment with thought, so as to say, at little expense. It shouldn’t surprise us that, oftentime, the thought experiment precedes the physical experiment and prepares the way for it… A thought experiment is also a necessary precondition for a physical experiment. Every inventor and every experimenter must have in his mind the detailed order before he actualizes it.

Mach compares thought experiments to the plans and images we form in our minds before commencing an endeavor. We all do this — rehearsing a conversation before having it, planning a piece of work before starting it, figuring out every detail of a meal before cooking it. Mach views this as an integral part of our ability to engage in complex tasks and to innovate creatively.

According to Mach, the results of some thought experiments can be so certain that it is unnecessary to physically perform it. Regardless of the accuracy of the result, the desired purpose has been achieved.

“It can be seen that the basic method of the thought experiment is just like that of a physical experiment, namely, the method of variation. By varying the circumstances (continuously, if possible) the range of validity of an idea (expectation) related to these circumstances is increased.” Ernst Mach

Thought experiments in philosophy

Thoughts experiments have been an integral part of philosophy since ancient times. This is in part due to philosophical hypotheses often being subjective and impossible to prove through empirical evidence.

Philosophers use thought experiments to convey theories in an accessible manner. With the aim of illustrating a particular concept (such as free will or mortality), philosophers explore imagined scenarios. The goal is not to uncover a ‘correct’ answer, but to spark new ideas.

An early example of a philosophical thought experiment is Plato’s Allegory of the Cave , which centers around a dialogue between Socrates and Glaucon (Plato’s brother.)

A group of people are born and live within a dark cave. Having spent their entire lives seeing nothing but shadows on the wall, they lack a conception of the world outside. Knowing nothing different, they do not even wish to leave the cave. At some point, they are led outside and see a world consisting of much more than shadows.

Plato used this thought experiment to illustrate the incomplete view of reality most of us have. Only by learning philosophy, Plato claimed, can we see more than shadows.

Upon leaving the cave, the people realize the outside world is far more interesting and fulfilling. If a solitary person left, they would want others to do the same. However, if they return to the cave, their old life will seem unsatisfactory. This discomfort would become misplaced, leading them to resent the outside world. Plato used this to convey his (almost compulsively) deep appreciation for the power of educating ourselves. To take up the mantle of your own education and begin seeking to understand the world is the first step on the way out of the cave.

Moving from caves to insects, here’s a thought experiment from 20th-century philosopher Ludwig Wittgenstein.

Imagine a world where each person has a beetle in a box. In this world, the only time anyone can see a beetle is when they look in their own box. As a consequence, the conception of a beetle each individual has is based on their own. It could be that everyone has something different, or that the boxes are empty, or even that the contents are amorphous.

Wittgenstein uses the ‘Beetle in a Box’ thought experiment to convey his work on the subjective nature of pain. We can each only know what pain is to us, and we cannot feel another person’s agony. If people in the hypothetical world were to have a discussion on the topic of beetles, each would only be able to share their individual perspective. The conversation would have little purpose because each person can only convey what they see as a beetle. In the same way, it is useless for us to describe our pain using analogies (‘it feels like a red hot poker is stabbing me in the back’) or scales (‘the pain is 7/10.’)

Thought experiments in science

Although empirical evidence is usually necessary for science, thought experiments may be used to develop a hypothesis or to prepare for experimentation. Some hypotheses cannot be tested (e.g, string theory) – at least, not given our current capabilities.Theoretical scientists may turn to thought experiments to develop a provisional answer, often informed by Occam’s razor .

In a paper entitled Thought Experimentation of Presocratic Philosophy , Nicholas Rescher writes:

In natural science, thought experiments are common. Think, for example, of Einstein’s pondering the question of what the world would look like if one were to travel along a ray of light. Think too of physicists’ assumption of a frictionlessly rolling body or the economists’ assumption of a perfectly efficient market in the interests of establishing the laws of descent or the principles of exchange, respectively.

In a paper entitled Thought Experiments in Scientific Reasoning , Andrew D. Irvine explains that thought experiments are a key part of science. They are in the same realm as physical experiments. Thought experiments require all assumptions to be supported by empirical evidence. The context must be believable, and it must provide useful answers to complex questions. A thought experiment must have the potential to be falsified .

Irvine writes:

Just as a physical experiment often has repercussions for its background theory in terms of confirmation, falsification or the like, so too will a thought experiment. Of course, the parallel is not exact; thought experiments…no do not include actual interventions within the physical environment.

In Do All Rational Folks Think As We Do? Barbara D. Massey writes:

Often critique of thought experiments demands the fleshing out or concretizing of descriptions so that what would happen in a given situation becomes less a matter of guesswork or pontification. In thought experiments we tend to elaborate descriptions with the latest scientific models in mind…The thought experiment seems to be a close relative of the scientist’s laboratory experiment with the vital difference that observations may be made from perspectives which are in reality impossible, for example, from the perspective of moving at the speed of light…The thought experiment seems to discover facts about how things work within the laboratory of the mind.

“We live not only in a world of thoughts, but also in a world of things. Words without experience are meaningless.” Vladimir Nabokov

Biologists use thought experiments, often of the counterfactual variety. In particular, evolutionary biologists question why organisms exist as they do today. For example, why are sheep not green? As surreal as the question is, it is a valid one. A green sheep would be better camouflaged from predators. Another thought experiment involves asking: why don’t organisms (aside from certain bacteria) have wheels? Again, the question is surreal but is still a serious one. We know from our vehicles that wheels are more efficient for moving at speed than legs, so why do they not naturally exist beyond the microscopic level?

Psychology and Ethics — The Trolley Problem

Picture the scene. You are a lone passerby in a street where a tram is running along a track. The driver has lost control of it. If the tram continues along its current path, the five passengers will die in the ensuing crash. You notice a switch which would allow the tram to move to a different track, where a man is standing. The collision would kill him but would save the five passengers. Do you press the switch?

The Trolley Problem was first suggested by philosopher Phillipa Foot, and further considered extensively by philosopher Judith Jarvis Thompson. Psychologists and ethicists have also discussed the trolley problem at length, often using it in research. It raises many questions, such as:

• Is a casual observer required to intervene?
• Is there a measurable value to human life? I.e. is one life less valuable than five?
• How would the situation differ if the observer were required to actively push a man onto the tracks rather than pressing the switch?
• What if the man being pushed were a ‘villain’? Or a loved one of the observer? How would this change the ethical implications?
• Can an observer make this choice without the consent of the people involved?

Research has shown most people are far more willing to press a switch than to push someone onto the tracks. This changes if the man is a ‘villain’- people are then far more willing to push him. Likewise, they are reluctant if the person being pushed is a loved one.

The trolley problem is theoretical, but it does have real world implications. As we move towards autonomous vehicles, there may be real life instances of similar situations. Vehicles may be required to make utilitarian choices – such as swerving into a ditch and killing the driver to avoid a group of children.

The Infinite Monkey Theorem and Mathematics

“Ford!” he said, “there’s an infinite number of monkeys outside who want to talk to us about this script for Hamlet they’ve worked out.” Douglas Adams, The Hitchhiker’s Guide to the Galaxy

In Fooled By Randomness , Nassim Taleb writes:

If one puts an infinite number of monkeys in front of (strongly built) typewriters, and lets them clap away, there is a certainty that one of them will come out with an exact version of the ‘Iliad.’ Upon examination, this may be less interesting a concept than it appears at first: Such probability is ridiculously low. But let us carry the reasoning one step beyond. Now that we have found that hero among monkeys, would any reader invest his life’s savings on a bet that the monkey would write the ‘Odyssey’ next?

The infinite monkey theorem is intended to illustrate the idea that any issue can be solved through enough random input, in the manner a drunk person arriving home will eventually manage to fit their key in the lock even if they do it without much finesse. It also represents the nature of probability and the idea that any scenario is workable, given enough time and resources.

To learn more about thought experiments, and other mental models, check out our book series, The Great Mental Models .

These 5 Crazy Thought Experiments Show How Einstein Formed His Revolutionary Hypotheses

Albert Einstein , one of the greatest minds of the 20th century, forever changed the landscape of science by introducing revolutionary concepts that shook our understanding of the physical world.

One of Einstein's most defining qualities was his remarkable ability to conceptualise complex scientific ideas by imagining real-life scenarios. He called these scenarios " Gedankenexperiments ", which is German for "thought experiments".

Here are a few thought experiments that demonstrate some of Einstein's most ground-breaking discoveries.

Imagine you're chasing a beam of a light.

This is something Einstein  started thinking about when he was just 16 years old . What would happen if you chased a beam of light as it moved through space?

If you could somehow catch up to the light, Einstein reasoned, you would be able to observe the light frozen in space. But light can't be frozen in space, otherwise it would cease to be light.

Eventually Einstein realised that light cannot be slowed down and must always be moving away from him at the speed of light. Therefore something else had to change. Einstein eventually realised that time itself had to change, which laid the groundwork for his  special theory of relativity .

Imagine you're standing on a train.

Imagine you're standing on a train while your friend is standing outside the train, watching it pass by. If lightning struck on both ends of the train, your friend would see both bolts of lightning strike at the same time.

But on the train, you are closer to the bolt of lightning that the train is moving toward. So you see this lightning first because the light has a shorter distance to travel.

This thought experiment showed that time moves differently for someone moving than for someone standing still, cementing Einstein's belief that time and space are relative and simultaneity doesn't exist. This is a cornerstone in Einstein's special theory of relativity.

Imagine you have a twin in a rocket ship.

This thought experiment is a well-known variation of Einstein's light-clock thought experiment, which has to do with the passage of time.

Let's say  you have a twin, born at almost the exact same time as you . But the moment your twin is born, he or she gets placed in a spaceship and launched into space to travel through the universe at nearly the speed of light. 

According to Einstein's special theory of relativity, you and your twin would age differently. Since time moves slower the closer that you get to the speed of light, your twin would age more slowly.

When the spaceship lands back on Earth, you might be trying to sort out your retirement, while your twin is just trying to get through puberty.

Imagine you're standing in a box.

Imagine you are  floating in a box, unable to see what's happening outside of the box . Suddenly, you drop to the floor. So what happened? Is the box being pulled down by gravity? Or is the box being accelerated by a rope yanking it upward?

The fact that these two effects would produce the same results led Einstein to the conclusion that there is no difference between gravity and acceleration - they are the same thing.

Now consider Einstein's previous assertion that time and space are not absolute. If motion can affect time and space, and gravity and acceleration are the same thing, that means gravity can actually affect time and space.

The ability of gravity to warp spacetime is a huge part of Einstein's general theory of relativity .

Imagine you're tossing a two-sided coin.

Einstein wasn't the biggest cheerleader for quantum theory. In fact, he was always coming up with thought experiments to try to disprove it. But it was these thought experiments that challenged the pioneers of quantum theory to perfect it down to its finest details.

One of Einstein's thought experiments had to do with  quantum entanglement , which Einstein liked to call "spooky action at a distance".

Imagine you have a two-sided coin that can easily be split in half. You flip the coin and, without looking, hand one side to your friend and keep the other side for yourself. Then your friend gets on a rocket ship and travels across the universe.

Then you look at your coin. You see that in your hand you're holding the heads side of the coin and instantaneously you know that your friend, who is billions of light years away from you at this point, is holding the tails side.

If you think of the sides of these coins as indeterminate, changing back and forth between heads and tails until the point in time that you look at one, then the coins can circumvent the speed of light, instantaneously affecting each other regardless of how many light years separate them.

This article was originally published by Business Insider .

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Chasing a Beam of Light: Einstein's Most Famous Thought Experiment

John D. Norton Department of History and Philosophy of Science University of Pittsburgh, Pittsburgh PA 15260 Homepage: www.pitt.edu/~jdnorton This page (with animated figures) is available at www.pitt.edu/~jdnorton/goodies

Einstein recalled how, at the age of 16, he imagined chasing after a beam of light and that the thought experiment had played a memorable role in his development of special relativity. Famous as it is, it has proven difficult to understand just how the thought experiment delivers its results. It fails to generate serious problems for an ether based electrodynamics. I propose a new way to read it that fits it nicely into the stages of Einstein's discovery of special relativity. It shows the untenability of an "emission" theory of light, an approach to electrodynamic theory that Einstein considered seriously and rejected prior to his breakthrough of 1905.

For more details, see: "Chasing the Light: Einstein's Most Famous Thought Experiment," prepared for Thought Experiments in Philosophy, Science and the Arts , eds., James Robert Brown, Mélanie Frappier and Letitia Meynell, Routledge. Download. Sections 5-6 of "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905," Archive for History of Exact Sciences , 59 (2004), pp. 45­105. Download .

1. The Puzzle

How could we be anything but charmed by the delightful story Einstein tells in his Autobiographical Notes of a striking thought he had at the age of 16? While recounting the efforts that led to the special theory of relativity, he recalled

"...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained."

The thought is simplicity itself. Here is light, a waveform propagating at c:

If the young Einstein were to chase after it at c, he would catch up with the wave and be moving with it, like a surfer riding the wave. He would see a frozen lightwave.

The untenability of that thought led to the downfall of the great achievement of nineteenth century physics, the ether, which then provided the basis for all electromagnetic theory.

The trouble is that it is quite unclear just how this thought creates difficulties for the ether. Einstein gave three reasons and each of them could be answered readily by an able ether theorist.

So what are we to make of the thought experiment? Perhaps it is no more than the recording of the visceral hunches of a precocious 16 year old who did not even study Maxwell's theory until two years later. This is a possibility we cannot rule out. If it is correct, then we need not puzzle any further over how the thought experiment works, for there is little more to be found that illuminates Einstein's pathway to special relativity.

But then we must ask why the thought experiment merits pride of place in Einstein's defining autobiography? Does it have a cogency that extends beyond Einstein's final high school year? That Einstein mentions Maxwell's equations in the thought experiment suggests their relevance to the operation of the thought experiment and thus that this operation was pertinent to Einstein's later thought, after he had learned Maxwell's equations.

While we cannot know on the evidence available if the thought experiment truly had cogency beyond the mullings of Einstein's 16th year, we can ask if there are plausible accounts of Einstein's pathway to special relativity in which the thought experiment figures more significantly.

2. A Proposed Solution

There is a way of understanding how the thought experiment could have a significance that extended well beyond the confines of Einstein's final year at high school. The key is not to relate the thought experiment to ether theories of electromagnetism. Rather, we know that Einstein devoted some effort during the years leading up to his discovery of 1905, to so-called "emission" theories of light and electromagnetism. Einstein eventually found such theories objectionable and untenable.

I propose that Einstein's thought experiment provided an especially cogent way of formulating those objections and thereby supported Einstein in his final decision: it give up an emission theory in favor of retaining the celebrated Maxwell-Lorentz theory, but with a radically altered theory of space and time.

3. An Emission Theory of Light and Electromagnetism

On many later occasions, Einstein recalled that, prior to his discovery of special relativity, he had investigated emission theories, indicating a similarity in his approach to that used by Walter Ritz. In the then standard electrodynamics of Maxwell and Lorentz, electromagnetic action always propagated at c with respect to the ether . The simplest example was the propagation of a lightwave. But it held equally for the action of one charge upon another. It was this fact that made it seem impossible to conform the principle of relativity to electromagnetism. The ether supplied a preferred state of rest essential to the theory, but incompatible with the idea that all inertial states of motion are equivalent.

So Ritz in 1908, and Einstein sometime before 1905, tried to modify electromagnetic theory in such a way that electromagnetic effects are always propagated at c with respect to the source of the effect . If such a theory could be found, it would no longer require an ether state of rest and it would reasonable to expect that it could conform to the principle of relativity.

The animation below displays the difference . On the left, in the Maxwell-Lorentz theory, electromagnetic action propagates from a fixed point in the ether. So when two charges moving together act on each other, the source of the effect felt by one is a fixed point in the ether left behind by the moving source. Since the effect propagates from a point left behind by the moving charges, an observer moving with the charges can use this fact to determine that the charges are moving.

On the right, we see the corresponding process in a modified "emission" theory, such as devised by Ritz and Einstein. The motion of the source is added to the propagating effect. So now the effect propagates isotropically from a point that moves with the source. To see this, notice how the expanding spherical shells remain centered on the moving positive charge that is their source, just as would happen if the two charges were at rest. The propagation of electromagnetic effects can no longer be used by observers moving with the two charges to detect their absolute motion; the principle of relativity is no longer threatened .

The simplest electromagnetic action is the propagation of light. So in this theory, the velocity of the emitter--the source--is added to the velocity of the light emitted. For this reason it is known as an "emission" theory.

Promising as this must initially have seemed to an Einstein intent on restoring the principle of relativity, the emission theory was ultimately rejected by Einstein. His later correspondence and papers are littered with remarks on the problems the theory faced. Two will return as our story unfolds.

- In a letter to Paul Ehrenfest of June 1912 (and elsewhere), Einstein remarked that an emission theory ran afoul of an elementary result of optics: the physical state of a ray of light is determined completed by its intensity and color (and polarization). - In an interview with R. S. Shankland in the 1950s, Einstein remarked that the theory could not be formulated as a local field theory that is, in terms of differential equations.

In a local field theory, we reconstruct how a field evolves over time by taking its state at one instant and consulting the theory's differential field equations. These equations take the present state of the fields and tell us how rapidly they are changing. From these rates of change we can then infer the states of the field at future times. (A similar analysis tells us how the field will alter at different parts of space.)

4. Einstein's Thought Experiment in the Context of an Emission theory of Light

Let us now return to Einstein's thought experiment and imagine that its target has become an emission theory of light. We immediately see that the three objections Einstein's reports present serious obstacles to an emission theory. Let us take the three objections in order.

1. The first objection was that we don't actually experience frozen light. That is a puzzle in an emission theory of light. We must presume that there are light sources with all sorts of velocities around us. A light source moving rapidly away from us will emit a lightwave that propagates slowly with respect to us. The most extreme case is of light source moving away from us at c. That source will leave a frozen light wave behind in space, as the animation shows:

So, if an emission theory is the correct theory of light, we should expect eventually to run into frozen lightwaves, emitted by rapidly receding sources. But we experience no such thing.

2. The second objection was that frozen light was incompatible with Maxwell's equations. Why should this be a problem for an emission theory when such a theory does not employ Maxwell's equations? It will be a problem, but it takes a few steps to arrive at the conclusion. First note that an emission theory allows frozen light in ordinary circumstances; we don't need to be moving at c to find it. That means that a frozen light wave must be a part of electrostatics and magnetostatics, the theories of static electric and magnetic fields. Now Maxwell's electrodynamics evolved over the course of half a century and built on a long series of experiments in electricity and magnetism. An emission theory must adjust the theory, but it cannot alter it too radically on pain of incompatibility with those experiments. The one part of Maxwell's theory that seems most secure is its simplest part, its treatment of static electric and magnetic fields. So we would expect a successful emission theory to agree with Maxwell's theory in this simplest and most secure part.

Now we have a problem: An emission theory allows the existence of frozen light waves. But the emission theory must agree closely with the treatment of static fields in Maxwell's theory and Maxwell's theory does not admit the static fields that corresponds to frozen light waves.

3. In his third objection, Einstein lamented for the observer catching the light beam, "...For how should the first observer know or be able to determine , that he is in a state of fast uniform motion?" Of course, in the context of an emission theory, the "state of fast uniform motion" must be read as "fast uniform motion with respect to the source of the light."

At first it is not clear why it should matter at all whether the observer catching the light beam can make this judgment. It turns out to be important if the overall emission theory of light is to be deterministic ; that is, if the present state of fields and the like in space are to be able to determine how they will develop in the future. Einstein's worry is that determinism will fail. To see why, imagine that you are an observer given a waveform, but all you know of it is its state at the present instant.

Would you be able to tell whether the waveform is one that is frozen in space;

or whether it is one that is propagating past you?

Both are possible in an emission theory. Which is the case depends upon your velocity with respect to the light's source. If you are moving at c with respect to the source, the wave is frozen. If you are at rest with respect to the source, the wave is propagating at c.

Can you tell which case you have by merely looking at the waveform at an instant? You cannot. Einstein's earlier remark about light is now decisive. A light wave is fully characterized by its color, intensity and polarization and both cases agree on these properties. The waveform has no property at an instant that would enable you to tell what its future time development would be. This is indeterminism. The present state of the wave does not determine its future time development.

While this circumstance might just be just an odd incompleteness of our knowledge, it becomes a crisis if we imagine that we are not human observers but the differential equations of a local field theory. For, as we saw above, a basic function of those field equations is to take the present state of the fields and from them infer the rates of change of the field. Those rates of change then determine the time development of the waveform--whether it propagates or not and how fast it propagates. This essential function will not be possible in an emission theory, for the instantaneous state of the lightwave does not determine the rates of change of the field.

Hence , thanks to Einstein's thought experiment, we infer that an emission theory cannot be formulated as a local field theory.

We can summarize the problems brought by Einstein's thought experiment to an emission theory:

5. Conclusion

When Einstein abandoned an emission theory of light, he had also to abandon the hope that electrodynamics could be made to conform to the principle of relativity by the normal sorts of modifications to electrodynamic theory that occupied the theorists of the second half of the 19th century. Instead Einstein knew he must resort to extraordinary measures. He was willing to seek realization of his goal in a re-examination of our basic notions of space and time. Einstein concluded his report on his youthful thought experiment:

"One sees that in this paradox the germ of the special relativity theory is already contained. Today everyone knows, of course, that all attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of time, or of simultaneity, was rooted unrecognized in the unconscious. To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem."

Copyright John D. Norton, December 2004. Rev. February 15, 2005. Reformatted April 14, 2005 on a transatlantic flight returning to Pittsburgh from the Israel Academy of Science and Humanities conference on Einstein.

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Part of the Einstein exhibition.

Light section of exhibition AMNH; Photo Studio

In 1905, nearly a decade after this first "thought experiment," Einstein answered these questions with his Special Theory of Relativity. The theory, which revolutionized our understanding of time and space, is based on Einstein's astonishing recognition that light always travels at a constant speed, regardless of how fast you're moving when you measure it. Einstein's explorations into the fundamental properties of light also laid the groundwork for his most impressive achievement, the General Theory of Relativity.

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Gedankenexperiment

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• University of Pittsburgh - Chasing a Beam of Light: Einstein's Most Famous Thought Experiment
• The Encyclopedia of Science Fiction - Thought Experiment
• Stanford Encyclopedia of Philosophy - Thought Experiments
• Nature - Renninger’s Gedankenexperiment, the collapse of the wave function in a rigid quantum metamaterial and the reality of the quantum state vector

Gedankenexperiment , term used by German-born physicist Albert Einstein to describe his unique approach of using conceptual rather than actual experiments in creating the theory of relativity .

For example, Einstein described how at age 16 he watched himself in his mind’s eye as he rode on a light wave and gazed at another light wave moving parallel to his. According to classical physics , Einstein should have seen the second light wave moving at a relative speed of zero. However, Einstein knew that Scottish physicist James Clerk Maxwell ’s electromagnetic equations absolutely require that light always move at 3 × 10 8 metres (186,000 miles) per second in a vacuum . Nothing in the theory allows a light wave to have a speed of zero. Another problem arose as well: if a fixed observer sees light as having a speed of 3 × 10 8 metres per second, whereas an observer moving at the speed of light sees light as having a speed of zero, it would mean that the laws of electromagnetism depend on the observer. But in classical mechanics the same laws apply for all observers, and Einstein saw no reason why the electromagnetic laws should not be equally universal. The constancy of the speed of light and the universality of the laws of physics for all observers are cornerstones of special relativity .

Einstein used another Gedankenexperiment to begin building his theory of general relativity . He seized on an insight that came to him in 1907. As he explained in a lecture in 1922:

I was sitting on a chair in my patent office in Bern. Suddenly a thought struck me: If a man falls freely, he would not feel his weight. I was taken aback. This simple thought experiment made a deep impression on me. This led me to the theory of gravity.

Einstein was alluding to a curious fact known in English physicist Sir Isaac Newton ’s time: no matter what the mass of an object, it falls toward Earth with the same acceleration (ignoring air resistance) of 9.8 metres (32 feet) per second squared. Newton explained this by postulating two types of mass: inertial mass, which resists motion and enters into his general laws of motion , and gravitational mass, which enters into his equation for the force of gravity . He showed that, if the two masses were equal, then all objects would fall with that same gravitational acceleration.

Einstein, however, realized something more profound. A person standing in an elevator with a broken cable feels weightless as the enclosure falls freely toward Earth. The reason is that both he and the elevator accelerate downward at the same rate and so fall at exactly the same speed; hence, short of looking outside the elevator at his surroundings, he cannot determine that he is being pulled downward. In fact, there is no experiment he can do within a sealed falling elevator to determine that he is within a gravitational field. If he releases a ball from his hand, it will fall at the same rate, simply remaining where he releases it. And if he were to see the ball sink toward the floor, he could not tell if that was because he was at rest within a gravitational field that pulled the ball down or because a cable was yanking the elevator up so that its floor rose toward the ball.

Einstein expressed these ideas in his deceptively simple principle of equivalence, which is the basis of general relativity: on a local scale—meaning within a given system, without looking at other systems—it is impossible to distinguish between physical effects due to gravity and those due to acceleration.

In that case, continued Einstein’s Gedankenexperiment , light must be affected by gravity. Imagine that the elevator has a hole bored straight through two opposite walls. When the elevator is at rest, a beam of light entering one hole travels in a straight line parallel to the floor and exits through the other hole. But if the elevator is accelerated upward, by the time the ray reaches the second hole, the opening has moved and is no longer aligned with the ray. As the passenger sees the light miss the second hole, he concludes that the ray has followed a curved path (in fact, a parabola).

If a light ray is bent in an accelerated system, then, according to the principle of equivalence, light should also be bent by gravity, contradicting the everyday expectation that light will travel in a straight line (unless it passes from one medium to another). If its path is curved by gravity, that must mean that “straight line” has a different meaning near a massive gravitational body such as a star than it does in empty space. This was a hint that gravity should be treated as a geometric phenomenon.

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Thought Process

Yes, his great breakthroughs came from visual experiments performed in his head rather than the lab. They were called Gedankenexperiment -- thought experiments. At age 16, he tried to picture in his mind what it would be like to ride alongside a light beam. If you reached the speed of light, wouldn't the light waves seem stationery to you? But Maxwell's famous equations describing electromagnetic waves didn't allow that. He knew that math was the language nature uses to describe her wonders, so he could visualize how equations were reflected in realities. So for the next ten years he wrestled with this thought experiment until he came up with the special theory of relativity.

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Learn How to Think Like Einstein

Albert Einstein is widely considered one of the smartest people who ever lived, significantly impacting our understanding of the world around us. His General Theory of Relativity has redefined what we know about space and time and is one of the pillars of modern physics. What’s also remarkable about Einstein’s achievements is that they relied largely on his mental powers and the intricacy of his imagination. He was able to discern and relate very complex scientific concepts to everyday situations. His thought experiments, that he called Gedankenexperiments in German, used conceptual and not actual experiments to come up with groundbreaking theories.

CHASING A BEAM OF LIGHT

One of Einstein’s most famous thought experiments took place in 1895, when he was just 16. The idea came to him when he ran away from a school he hated in Germany and enrolled in an avant-garde Swiss school in the town of Aarau that was rooted in the educational philosophy of Johann Heinrich Pestalozzi, which encouraged visualizing concepts.

Einstein called this thought experiment the “ germ of the special relativity theory. ” What he imagined is this scenario – you are in a vacuum, pursuing a beam of light at the speed of light – basically going as fast as light. In that situation, Einstein thought, that light should appear stationary or frozen, since both you and the light would be going at the same speed. But this was not possible in direct observation or under Maxwell’s equations,  the fundamental mathematics that described what was known at the time about the workings of electromagnetism and light. The equations said that nothing could stand still in the situation Einstein envisioned and would have to move at the speed of light – 186,000 miles per second.

Artists pose in a laser projection entitled ‘Speed of Light’ at the Bargehouse on March 30, 2010 in London, England.  (Photo by Peter Macdiarmid/Getty Images)

Here’s how Einstein expanded on this in his Autobiographical Notes :

“If I pursue a beam of light  with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell’s equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained.”

The tension between what he conceived of in his mind and the equations bothered Einstein for close to a decade and led to further advancements in his thinking.

LIGHTNING STRIKING A MOVING TRAIN

A 1905 thought experiment laid another cornerstone in Einstein’s special theory of relativity. What if you were standing on a train, he thought, and your friend was at the same time standing outside the train on an embankment, just watching it go by. If at that moment, lightning struck both ends of the train, it would look to your friend that it struck both of them at the same time.

But as you are standing on the train, the lighting that the train is moving towards would be closer to you. So you would see that one first. It is, in other words, possible for one observer to see two events happening at once and for another to see them happening at different times.

“Events that are simultaneous with reference to the embankment are not simultaneous with respect to the train,” wrote Einstein. 

The contradiction between how time moves differently for people in relative motion, contributed to Einstein’s realization that time and space are relative.

Lightning strikes during a thunderstorm on July 6, 2015 in Las Vegas, Nevada. (Photo by Ethan Miller/Getty Images)

MAN IN FALLING ELEVATOR

Another thought experiment led to the development of Einstein’s General Theory of Relativity by showing that gravity can affect time and space. Here’s how he described it happened:

“I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me,” he remembered. “If a person falls freely, he will not feel his own weight.” He later called it “the happiest thought in my life.”

A 1907 thought experiment expanded on this idea. If a person was inside an elevator-like “chamber” with no windows, it would not be possible for that person to know whether he or she was falling or pulled upward at an accelerated rate. Gravity and acceleration would produce similar effects and must have the same cause, proposed Einstein. 

“The effects we ascribe to gravity and the effects we ascribe to acceleration are both produced by one and the same structure,” wrote Einstein.

One consequence of this idea is that gravity should be able to bend a beam of light – a theory confirmed by a 1919 observation by the British astronomer Arthur Eddington. He measured how a star’s light was bend by the sun’s gravitational field.

THE CLOCK PARADOX AND THE TWIN PARADOX

In 1905, Einstein thought – what if you had two clocks that were brought together and synchronized. Then one of them was moved away and later brought back. The traveling clock would now lag behind the clock that went nowhere, exhibiting evidence of time dilation – a key concept of the theory of relativity.

“ If at the points A and B of K there are clocks at rest which, considered from the system at rest, are running synchronously, and if the clock at A is moved with the velocity v along the line connecting B, then upon arrival of this clock at B the two clocks no longer synchronize but the clock that moved from A to B lags behind the other which has remained at B,“ wrote Einstein. 

This idea was expanded upon to human observers in 1911 in a follow-up thought experiment by the French physicist Paul Langevin. He imagined two twin brothers – one traveling to space while his twin stays on Earth. Upon return, the spacefaring brother finds that the one who stayed behind actually aged quite a bit more than he did.

Einstein solved the clocks paradox by considering acceleration and deceleration effects and the impact of gravity as causes of the for the loss of synchronicity in the clocks. The same explanation stands for the differences in the aging of the twins.

Time dilation has been abundantly demonstrated in atomic clocks, when one of them was sent on a space trip or by comparing clocks on the space shuttle that ran slower than reference clocks on Earth.

How can you utilize Einstein’s approach to thinking in your own life? For one – allow yourself time for introspection and meditation. It’s equally important to be open to insight wherever or whenever it might come. Many of Einstein’s key ideas occurred to him while he was working in a boring job at the patent office. The elegance and the scientific impact of the scenarios he proposed also show the importance of imagination not just in creative pursuits but in endeavors requiring the utmost rationality. By precisely yet inventively formulating the questions within the situations he conjured up, the man who once said “imagination is more important than knowledge” laid the groundwork for the emergence of brilliant solutions, even if it would come as a result of confronting paradoxes.