# Thought Experiments

### About the project

Science is always telling stories. Whether in the creation myths, of evolution or the Big Bang, or in the 'eureka moments' of science history, narrative just as much as metaphor is a key tool in the scientist's surprisingly literary toolkit. Perhaps the most interesting use of story is the thought experiment, the intuition pump, that draws on the most instinctive impulses of the human imagination to crack otherwise perplexing philosophical problems. From Newton's Bucket, to Maxwell's Demon, from Einstein's Lift to Schrodinger's Cat, all are examples of 'fiction' being used at the highest level, not just to explain, but to deduce, to prove.For this project Comma is asking authors to create stories in which a fictional character learns (or reads, relates, stumbles upon, refers to, or teaches) a thought experiment from the history science (see list), as a seemingly incidental plot point which subtly/gently/almost accidentally allows for metaphoric parallels to be drawn with the wider human 'story' that character finds him/herself in.

The format will be the same as Comma's previous science-into-fiction commissions. The scientists will propose thought experiments first - between 3 and 5 each (thought experiments that they personally regard as vital in the development of their particular field and that they're happy to expound upon till the cows come home). These will then go on a list and the authors will pick them on a first-come-first served basis. The authors will then meet the scientist that proposed their thought experiment, and the scientist will inform, consult and science-check the story as it progresses and write a short, accessible afterword to the finished product.

### THOUGHT EXPERIMENTS

**1. Schrodinger's Cat**

This thought experiment neatly illustrates just how very strange and counter-intuitive quantum physics is. Imagine a steel box, impervious to the outside world. Inside it is a cat, and a small phial of deadly cat-poison. Connected to the phial is a piece of radioactive material, and a detector which will give a positive signal, and release the poison, on detecting radiation. (This is why it is best kept as a thought experiment!) The box is sealed. The radiation, and thus the cat's survival or death, are random. Common sense tells us if we open the box, the cat is either alive or dead inside the box, and that's what we'll see when we open the lid. In quantum physics though, according to our viewpoint, the cat is simultaneously alive and dead before we look to make sure. We only know once we open the lid, at which point we've forced the cat to be one or the other.

This scenario was invented when quantum physics was being developed at the start of the twentieth century. It encapsulates all the philosophical problems involved in trying to understand what quantum physics tell us. How can something be alive and dead at the same time? How can an observer influence reality just by looking at it? Does an impartial reality exist? And its fascinating quantum physics gives us one of the most fundamental viewpoints we have, and we are still trying to make sense of the way it forces us to see the universe.

Consultant Scientist: TARA SHEARS.

**2. Twin Paradox**

This thought experiment shows us the bizarre nature of space and time, as described by Einstein's theories of relativity. In relativity, space and time are deeply connected, and are not absolute. They both change depending on your viewpoint, although you have to find a pretty extreme situation to notice this, and this is why a thought experiment is a good way of illustrating it.

Imagine two twins. One stays on Earth, the other is jettisoned out into space on a rocket to explore the solar system. The astro-twin is moving extremely fast compared to their sibling, and in special relativity, to their twin on Earth watching them, this means that the astro-twin time appears to be slowed down (literally, if you could see their watch, it would tick slower). To the astro-twin, their sibling is moving just as fast but in the other direction, and the Earth-twin time is slowed down compared to them. Strange. So what happens when astro-twin completes their circuit of the solar system and comes back to land? Which twin is younger?

It's a paradox that needs general relativity to resolve, because this explains how time changes as the astro-twin is accelerated into space and decelerated back again. Once you do this, you find that time has genuinely moved in a different way to the astro-twin, and the astro-twin is younger than their sibling. This might sound odd, and is, but it is true, and we need to use this time-bending behaviour of relativity to keep GPS working.

Consultant Scientist: TARA SHEARS.

**3. Ladder Paradox**

Einstein's special relativity illustrates the inter-connection of space and time, and shows us how to relate the time and space experienced by observers moving at different speeds to each other. Someone travelling fast will experience distances shortening and time lengthening with respect to someone standing still. This can often be really confusing.

In this thought experiment you must imagine a ladder moving fast into a barn that is shorter than the ladder. The faster the ladder moves, the shorter it gets, so if it moves fast enough it should be able to fit inside the barn. At least, that's from the barn's point of view. From the ladder's point of view it is stationary with a mad barn rushing towards it. This moving barn is shortened, so there is no way that the ladder will ever fit. How can both be true?

This is resolved when you remember to also change the time that the ladder and barn experience - once you do this too, there's no paradox. This thought experiment, although slightly crazy, illustrates that time is not absolute, that it runs at different rates for measurements taken at different speeds. And because of this, there is no absolute simultaneity in the universe. Everyone is on a slightly different clock. Although odd, this seems to be true. We even take these effects into account in my experiment, at the Large Hadron Collider where particles move so close to the speed of light that these effects are large if we didn't, we wouldn't be able to make sense of what happens there.

Consultant Scientist: TARA SHEARS.

**4. Newton's Cannonball & the invention of satellites**

Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his 1728 book A Treatise of the System of the World. In this experiment Newton visualizes a cannon on top of a very high mountain.

If there were no forces of gravitation or air resistance, then the cannonball should follow a straight line away from Earth, in the direction that it was fired.

(i) If a gravitational force acts on the cannon ball, it will follow a different path depending on its initial velocity. (1 If the speed is low, it will simply fall back on Earth, for example horizontal speed of 0 to 7000 m/s for Earth

(ii) If the speed is the orbital speed at that altitude it will go on circling around the Earth along a fixed circular orbit just like the moon, for example horizontal speed of at approximately 7300 m/s for Earth

(iii) If the speed is higher than the orbital velocity, but not high enough to leave Earth altogether (lower than the escape velocity) it will continue revolving around Earth along an elliptical orbit, for example horizontal speed of 7300 to approximately 10000 m/s for Earth.

(iv) If the speed is very high, it will indeed leave Earth, for example horizontal speed of approximately greater than 10 000 m/s for Earthg

There's a great illustration from his â€œA Treatise of the system of the worldâ€ in which he envisaged satellites.

See here. A good connection to Jodrell is that we tracked the first actual satellite Sputnik I (well the rocket that carried it) in 1957.

Consultant: Dr TIM O'BRIEN

**5. Galileo's Leaning Tower of Pisa experiment.**

A research colleague Steve Shore who works on novae (with me occasionally) at the University of Pisa recreated this (although people think it probably never actually happened in the first place!) - watch this.

More here. Consultant: Dr TIM O'BRIEN

**6. Newton's Bucket**

Isaac Netwon in his argument with Gotfried Leibniz, via his student Samuel Clarke, argued for the existence of 'absolute space' - a concept of space that survives even if there are no objects in that space. Even in an empty universe, Newtwon argued, space would persist.

He argued this conceptually, with the help of a simple bucket.

In 1715 and 1716, a supporter and student of Isaac Newton, called Samuel Clarke, engaged in a famous correspondence with Netwon's arch adversary Gottfried Wilhem von Leibniz (a German counterpart to Newton's genius who, a few years earlier, had miraculously invented the idea of calculus

*simultaneously*with Netwon, working on the other side of Europe. Many believe Clarke's letters were overseen by Newton himself, and represent a direct face-off between the two world intellects of the day. In this correspondence, Leibniz and Clarke advocated conflicting interpretations of what space and time actually are: Leibniz was a relationist, believing space was only a series of relations between specific non-identical objects, and likewise time only a series of relations between non-identical events. Clarke on the other hand (and by implication Newton) believed that time would exist even if in a universe in which nothing happened, where there were no events, no changes. And likewise space would exist if you removed all the objects from it. Even in empty space, there is still space. Newton, through Clarke, presented a final thought experiment that he believed proved this idea of 'Absolute Space'. He imagined a universe which was completely empty except for a single, symmetrical bucket (with outwardly sloping sides), half-filled with water. Assuming this was still effectively an empty universe, with no objects elsewhere, he argued that the surface of water would have to 'decide' to be either flat (implying the bucket was not spinning around its axis), or concave (implying through centrifugal forces that bucket was spinning). But spinning relative to what? On he horizontal plane, the bucket represents a point in an otherwise empty space. Hence, Newton's bucket idea suggests that basic forces and the behaviour of mass needs an absolute space to be 'projected' around it, in order for these forces and masses to be able to work as we understand them.

More here and here.

Consultant: DR JUHA SAATSI.

7.

**Einstein's Elevator and the Equivalence Principle**

Imagine you are in an elevator or, more precisely, in what looks like an elevator cabin from the inside, and that you are isolated from the outside world. If you pick up an object and let it drop, it falls down to the floor, in exactly the way you would expected given your experiences here on Earth. Does that mean the elevator is indeed situated in a gravitational field like that of the Earth?

Not necessarily. Theoretically, you could be in deep space, far away from all significant mass concentrations and their gravitational influence. The room you are in could be a cabin aboard a rocket (or somekind of 'spacelift') - as long as the rocket engines work at exactly the right rate to accelerate the rocket at 9.81 meters per square second.

Conversely, imagine you're floating freely inside the elevator. Around you, other objects are floating, as well, and you feel totally weightless. Does that mean you are far away from all gravitational influences, far away from all stars, planets and other massive bodies, somewhere in deep space?

Again, not necessarily. You and the elevator could be in the gravitational field of a mass, for instance that of the Earth, as long as the elevator was in free fall.

Einstein postulated that this thought experiment holds true for any physical measurements at all: no experiment, no clever exploitation of the laws of physics, he claimed, can tell us whether we are in a gravitational field or simply accelerating in free space.

Consultant: DR MICHELA MASSIMI.

**8. The EPR Paradox**

According to quantum mechanics, under some conditions, a pair of quantum systems may be described by a single wave function (i.e. they are 'entangled'). Imagine, say, an electron and a positron created by a single event, one flying off in one direction, and the other flying off in the other direction. To preserve spin, one will have a quantum spin pointing in one direction and the other will have a spin pointing in the opposite direction. Although we don't know which, in either case, until one of them is measured.

Quantum Uncertainty tells us that physical quantities come in pairs which are called 'conjugate quantities' (e.g. position and momentum). When one is measured the other becomes undetermined.

In 1935 Albert Einstein, and his colleagues Boris Podolsky and Nathan Rosen, conceived a thought experiment that they claimed showed the incompleteness of Quantum Mechanics. Imagine two entangled particles (like the electron and positron described above, created by the same single event). Let's call them as A and B. EPR pointed out that measuring a quantity of a particle A will cause the conjugated quantity of particle B to become undetermined, even if there was no contact, no classical disturbance. Put another way, if we allow the electron and positron to fly out to the far ends of the universe, and THEN measure the spin of one of them (it points 'up', say), we immediately know the other particle at the other end of the universe has a spin pointing down. This means the wave function has collapsed across the breadth of the universe, instantaneously, measuring a particle at one side of the universe has 'effected' another particle at the other side of the universe instantaneously.

EPR concluded: either there was some interaction between the particles (instantaneous, i.e. faster than the speed of light, contradicting relativity), or the information about the outcome of all possible measurements was already present in both particles (a hidden variables theory). As the former contradicted relativity, the latter must be the case. QM had failed to explain and include all the information - there were still some hidden variables.

Consultant: DR MICHELA MASSIMI.

**9. The Halting Problem**

In computability theory, the halting problem can be stated as follows: "Given a description of an arbitrary computer program, decide whether the program finishes running or continues to run forever". This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever.

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, what became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.

More about the Turing Machine solution here and the original Halting Problem here.

Consultant: Dr MARTYN AMOS

**10. The Infinite Monkey Typing Pool**

The thought experiment of the infinite monkeys is well known. If we take a bunch of monkeys and lock them in a room with some typewriters, they will, by randomly hitting they keys, eventually produce a play by Shakespeare. At first sight, for them to write Romeo and Juliet seems fairly preposterous, as surely they would merely type random sequences of letters, but the point of the thought experiment is to understand probabilities, and probabilities with respect to the age of the universe. The probability of a monkey typing Romeo and Juliet is very small indeed but the chance of it occuring during the life of the universe is small but not equal to zero.

Consultant: Dr ROBERT APPLEBY

**11. The Chinese Room**

The Chinese room is a thought experiment presented by John Searle.[1] It supposes that there is a program that gives a computer the ability to carry on an intelligent conversation in written Chinese. If the program is given to someone who speaks only English to execute the instructions of the program by hand, then in theory, the English speaker would also be able to carry on a conversation in written Chinese. However, the English speaker would not be able to understand the conversation. Similarly, Searle concludes, a computer executing the program would not understand the conversation either. More about the Chinese Room here.

Consultant: Dr MARTYN AMOS

**12. Quantum Suicide**

Unlike the Schrodinger's cat thought experiment which used poison gas and a radioactive decay trigger, this version involves a life-terminating device and a device that measures the spin value of protons. Every 10 seconds, the spin value of a fresh proton is measured. Conditioned upon that quantum bit, the weapon is either deployed, killing the experimenter, or it makes an audible "click" and the experimenter survives.

The theories are distinctive from the point of view of the experimenter only; their predictions are otherwise identical.

The probability of surviving the first iteration of the experiment is 50%, under both interpretations, as given by the squared norm of the wavefunction. At the start of the second iteration, if the Copenhagen interpretation is true, the wavefunction has already collapsed, so if the experimenter is already dead, there's a 0% chance of survival. However, if the many-worlds interpretation is true, a superposition of the live experimenter necessarily exists, regardless of how many iterations or how improbable the outcome. Barring life after death, it is not possible for the experimenter to experience having been killed, thus the only possible experience is one of having survived every iteration.

This conundrum is also closely related to the 'Unexpected Hanging' paradox, see below.

Consultant:

**13. The Unexpected Hanging**

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.

Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.

He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.

The next week, the executioner knocks on the prisoner's door at noon on Wednesday, which, despite all the above, was an utter surprise to him. Everything the judge said came true.

Consultant:

**14.Einstein's Lift**

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**15.The Sticky Beard Argument**

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**16.The ABC Universe**

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**17.Wigner's Friend**

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**18.The Monkey and Hunter**

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*ALREADY TAKEN*

**A. Maxwell's Demon**

Created by the physicist James Clerk Maxwell, this is a thought experiment devised to "show that the Second Law of Thermodynamics has only a statistical certainty". It hypothetically describes how the Second Law of thermodymanics (also known as the Law of Entropy - that entropy always increases) might be broken: A container of gas molecules at equilibrium is divided into two parts by an insulated wall, with a door that can be opened and closed by a very small agent, that came to be called "Maxwell's demon". The demon opens the door to allow only the faster than average molecules to flow through to a favored side of the chamber, and only the slower than average molecules to the other side, causing the favored side to gradually heat up while the other side cools down, thus decreasing entropy.

See more here.

Consultant: Dr ROBERT APPLEBY

B.

**Laplace's Demon**

The laws of classical mechanics, as written down by people like Newton, Lagrange and others, gives us a framework to calculate the future motion of bodies or particles if we know the current position and speed of the particle. Laplace's demon (although there isn't really a demon!) takes this idea and confronts head-on the ideas of determinism and free will. Laplace stated that, if we believe classical mechanics, we can know the past and future positions and speeds of all atoms in the universe provided we know their positions and speeds at some point in time. In essence it means the universe is somehow clockwork and the state of the universe (and hence us) is pre-determined for all time. This is clearly a very profound statement, and one incompatible with quantum mechanics. Where does it leave personal choice?

"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.", Pierre Simon Laplace, A Philosophical Essay on Probabilities.

Consultant: Dr ROBERT APPLEBY

C.

**Galileo's Ship**

Common sense seems to tell against the idea that the Earth moves. How could it? We experience things as being at rest. And if we drop an object from a tower it lands directly below the tower. How can that be if the earth rotates? Galileo found himself confronted with such objections and devised the following thought experiment to counter them:

"Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butteries, and other small animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals y with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still." (Dialogue Concerning the Two Chief World Systems).

The thrust of the argument is of course that the earth is like the ship! It is moving and yet the effects of this motion are not observable. This is a powerful idea against the claim that common sense tells us that the Earth has to be stationary. In fact, we can have all the elements of common sense physics without being committed to a stationary Earth!

Consultant: Dr Roman Frigg

D.

**Einstein Riding on a Wave**

At the age of 16, Einstein imagined chasing after, or riding, a beam of light and asked wondered what he could see, what the world looked like at that speed. Years later this daydream - or thought experiment - played a memorable role in the development of his special special theory of relativity. More here.

Consultant: DR MICHELA MASSIMI.

Supported by the Institute of Physics.

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