Thought Experiments

When you are always bored with anything you understand, you will gravitate towards ideas which are impossible to understand – aka nonsense! Thought experiments provide a wealth of nonsense like Epiminides’ paradox, the crocodile dilema, and just about anything that Einstein said. These paradoxes arise when you do not think outside of the box which defines them. That is their sole heuristic purpose, but they are frequently mis-used.

When the paradoxes of the theory of relativity are taught as ‘fact’, students are given a feeling that they have learned something when they haven’t actually learned anything. They are given a false confidence in their understanding of a counter-intuitive logic puzzle composed of imaginary situations while gaining no understanding of the subtleties required for the application of the theory to real data.

All that the student has learned from these paradoxes is how to feel clever while being gullible, how to throw his common sense in the trash, and how to abandon himself to faith in a model. In a fit of doublespeak, teachers even tell their students that despite the fact that the paradoxes demonstrate a contradiction with common sense, they are not really paradoxes.

Relativity is not the only lesson of physics in which this subversion of common sense is encouraged. Consider the simple example of a man dropping a ball as he runs along a street.

Image result for physics mazur make believe
Mazur: Make-believe world of real-world physics

If you ask physicists if the ball falls straight down or if it follows a curved trajectory, they all say curved, while if you ask non-physicists which trajectory closely conforms to reality, they mostly answer straight.

Who is right? The non-physicists were actually more right by saying straight. The ball doesn’t drop exactly straight down, but the curve of the trajectory is so small that one can’t see it or measure it. A curved trajectory would only be appropriate if the man is as fast a cheetah or on the moon.

In this example, physicists believe in the model they have learned more than they believe their daily experience with gravity.

Next, consider quantum mechanics. Physics teachers tell their students that there are old models of atoms which are incorrect because our new mathematical models require the counter-intuitive interpretation that particles literally exist as a cloud of probabilities until they are measured. This sort of statement is actually false because there are many ways to describe a quantum system and, given certain interpretations, the older models are often consistent with the newer models making them superior with respect to qualitative explanatory power and with respect to quantitative predictive power.

In this example, instead of straightforward explanations which suffice for most situations, physicists prefer counter-intuitive, literal interpretations which detach the student from a kinematic sense of motion and time.

Taken altogether, I see three examples in which physics teachers encourage myopia with overly-literal instruction which encourages detachment from reality: paradoxes in relativity, everyday physics, and quantum uncertainty.

The result of this system of instruction is so extreme that there are whole branches of physics today that either have no connection to experimental reality (string theory, loop quantum gravity, etc) or they draw inferences which go far beyond what the experimental data suggests. Gell-Mann’s nuclear model with quarks is a good example of this.

One of the hallmarks of cultish thinking is a gradual abandonment of common sense and people who leave a cult leader often describe it as a sort of ‘snap’ in which their long-suppressed, old identity suddenly re-emerges and recognizes all of the nonsense that they have absorbed throughout their indoctrination. These people simply stand up one day and walk away from the cult, re-emerging into the world like a person reborn as their old self. Academia has many of the hallmarks of a cult with respect to the rituals and sacrifices required for acceptance and this is something of which both parents and students should be well aware.

Children’s minds are softened for indoctrination by educational materials on the internet and in the classroom that tell them that relativity is paradoxical, but that the paradoxes are not really paradoxical, or something like that. They watch videos of relativistic trains going into tunnels and ladders going into barns and they either develop a feeling of confusion or a sense of pride over their comprehension of something abstract and counter-intuitive, but this sense of comprehension is often very misleading.

Section 1: anthropomorphizing particles

To demonstrate how one constructs an illusion of comprehension, consider the simplest possible description of relativity:

Alice and Bob are particles.

Bob walks into a bar holding a clock and a meter stick and runs back and forth past the bartender at close to the speed of light. This is as fast as he can run. Alice, the bartender, says, “Your clock is slow and your meter stick is short, see, look”, and she holds up her own clock and meter stick. Bob is running up and down the bar and says, “No, your clock is slow and your meter stick is short!”

That is special relativity.

Seriously.

Both statements about the meter sticks and clocks are true while Bob is passing by Alice, but every time Bob turns around at the end of the bar, Alice’s clock runs faster than Bob’s. They jump into a car and Alice ties a blindfold around Bob’s eyes. Alice steps on the gas, accelerating the car. Bob asks her, “Are we going uphill?” Alice answers, “Wouldn’t you like to know.”

That is general relativity.

Seriously.

That story accurately represents Einstein’s relativity and it certainly sounded simple, but something about it should bother you. A child might feel stupid for not understanding the strange story whereas a wise, old grandma might recognize that when something doesn’t compute, the storyteller is at fault, not the listener. Physics tends to get this backwards.

Let’s try to tell the same story with different words and see if it makes more sense.

  • You and your friend are each holding onto a long rope.
  • You shake your end of the rope up and down and your friend sets up a metronome to match your frequency.
  • You start moving away from her and she says that your frequency has gotten slower than the metronome.
  • You move towards her and she says that your frequency has gotten faster than the metronome.

That is time dilation (stretching and contracting). It is merely an illusion created by your changing position relative to your friend. In real relativity experiments, you are replaced by an oscillating particle.

Length contraction is also a direct result of changing position. If you are moving, when you look out of your window and see everything streaking past, you realize that your body would look streaked out relative to everything at rest. When your body streaks out, the distance between the particles in your body gets larger. Alternatively, one could describe your particles as contracted instead of saying that the space between your particles has expanded. Electrically, since all of your particles are charged, these two conditions must be equivalent.

A beam of light which travels alongside you and makes an optical replica of your body would record that your body’s length is the same as it was before you started moving. A scientist would then conclude that your particles have gotten very short – like pancakes.

Once you understand that only particles length contract and that macroscopic objects never length contract, then you will see that anyone who talks about trains contracting and fitting in short tunnels is talking nonsense – unless she understands that the trains and tunnels are used to symbolize the behavior of individual particles.

The takeaway from this section is – be wary of people who speak of particles as though they are people or macroscopic objects.

Section 2: Twin Paradox

Everybody has seen science fiction movies featuring time travel and we are given a sense that it is a scientific possibility. Popular science shows tell us that if you had a pair of twins and launched one of them to Alpha Centauri, when the space-bound twin returned to earth, he would be much younger than his earthbound counterpart.

You need to know that this is not science. This is bad science fiction.

We have no evidence that such things happen to macroscopic objects like people yet somehow this picture has made it into mainstream academic discourse and physics students accept it as a fact of reality. I think (hope) that future generations will laugh about this.

If the calculation is done properly, one sees that while the travelling twin is journeying through the stars, he ages at a different rate from the warped perspective of the earth twin. However, by the time the traveller gets back home to meet his earthbound twin, time has caught up with him and they are the same age.

Depending on our preference for special or general relativity, we can disagree about when and how the travelling twin ages from the perspective of the earthbound twin. Does he age all at once when the space ship turns around to head home (no preferred reference frame)? Does he age gradually throughout the journey (preferred reference frame)? But we can agree that when you throw a ball up into the air and catch it, it only momentarily feels heavier than the ball you didn’t throw. I think that travelling twins work the same way. The travelling twin only momentarily appears to be younger than the earth twin.

This isn’t what all of the math implies —or is it?

About the math, one can say several things that are conceptually inconsistent yet geometrically possible:

  • General relativity: every time the space traveller accelerates, time slows for him relative to the earth.
  • Special relativity: while he travels away from and towards the earth, his clock is running slowly.
  • Absolute space is a clock: the further away from earth he gets, the slower his clock is relative to the earth.

These three things can’t all be true at the same time unless you say that they are all different ways of saying the same thing – which is what most people say because they are intellectual cowards.

In the general relativity interpretation, each time the astronaut accelerates towards earth, she is lighter relative to on earth and time slows for her. Each time she accelerates away from earth, she is heavier relative to on earth and time speeds up for her. So, time speeds, slows, slows, and speeds as she lands on earth – only there is nothing in the calculation so-far which explicitly describes the final acceleration. When a mathematician forgets about the final acceleration, you end up with an old twin meeting a young twin at the end of the journey.

In the special relativity interpretation, an astronaut’s clock will tick more slowly relative to the earthling’s clock throughout the journey and when the astronaut arrives back home, she will be younger than her earth twin. Unfortunately, special relativity does not tell us how to calculate the effect of acceleration, so a mathematician will often skip that step and we will end up with a young twin meeting an old twin at the end of the journey.

In the absolute space interpretation, the earthling measures the oscillations of a laser beam clock sent to earth from the spaceship and the wavelength lengthens as the astronaut travels away, and it shortens when she returns. While she is on the distant planet, the clock still appears to be a bit slow because the light loses a bit of energy and the wavelength lengthens when it traverses vast distances. The person on Earth doesn’t predict any sort of paradox involving old twins and young twins because the apparent changes in clock speed were clearly illusions caused by motion through space.

The conclusion is that if the mathematician skips the last step of the general relativity calculation, then the result will agree with the naive special relativity calculation without acceleration. If the mathematician includes the last step of the general relativity calculation, then the result will agree with the absolute space interpretation and disagree with the special relativity calculation.

In the naive, pop-sci interpretation of the math, time within the astronaut’s body is slowed when she arrives on Earth and there is nothing describing how it speeds back up to match the clocks around her. I don’t think that time can stay slowed down for her indefinitely. If time is slowed for her, then the particles in her body are cold and have to heat back up. In other words, her internal clock has to speed back up to the normal earth rate and that is the info which is missing in pop-sci interpretations of the math of relativity and it is the reason that the image of an old twin meeting a young twin is wrong.

For a less-wrong science fiction picture, when the younger twin descends to earth, she is momentarily younger but time quickly catches up with her. Since she is made of probabilistic, quantum things, she would appear in the sky as a youthful, muon mist and slowly solidify on the ground as an old, electron woman.

Section 3: ladders don’t length contract

The train-tunnel or barn-ladder paradox is a thought experiment in which relativistic length contraction is applied to macroscopic objects which are moving at close to the speed of light. Students are taught that in the moving ladder reference frame, the ladder fits in the garage and in the stationary reference frame, it doesn’t. The garage sees a short ladder and the ladder sees a short garage. Then they tell the students that this is not paradoxical because the math makes sense.

Perhaps we should hold ourselves to a higher standard in which both the math and the interpretation of the math must make sense.

One can either accept the strange implications of the math for macroscopic objects OR one can say, “Hey, we’ve never measured relativistic effects for macroscopic objects like ladders, so maybe we shouldn’t imagine that there are such effects, or, at the very least, we shouldn’t imagine that such effects could be observed by looking at the system from the side -as the drawings imply.”

  • We can measure that clocks in planes run slowly compared to clocks on earth, but these clocks are just made up of oscillating atoms and this doesn’t tell us anything about length contraction of a macroscopic object.
  • We can measure relativistic effects for small things like particle bunches and what we see there is that the length contraction and time dilation effects only apply on the individual particle level, not on a collective level.

I know this because when you accelerate a bunch of electrons to near the speed of light, the bunch doesn’t get shorter, but the fields from the individual electrons do get shorter/weaker in the direction in which they are accelerated. We know this happens because the longitudinal forces between charges get smaller when the electrons are going faster. This happens because the electric field of each particle transforms from a sphere (at rest) into a pancake (going fast).

See, for example, Wiedemann’s Introduction to Accelerator Physics

The bunch as observed by an electrode or antenna will look shorter after acceleration, and this seems like a contradiction to what I just wrote unless you consider that this doesn’t mean that the bunch actually got shorter, the fields just got pancaked so that the image of those fields on the electrode is shorter.

It may also seem confusing that when fast moving charged particles encounter a series of magnets which cause them to wiggle up and down in their trajectory, the magnets look like they have a longitudinal separation of a few Angstroms- from the longitudinal perspective of the fast-moving particles, while from our perspective, the magnets are several centimeters long.

How is this consistent with my initial claim that the contraction only happens on the level of the individual particle fields, not as a collective effect? Here, the magnets didn’t really contract – the magnet’s particle’s fields only contracted in the eyes of the electron bunch because the bunch spent less time interacting with those fields. The magnets didn’t contract in any sense that I can think of.

So, if you are passing me by with your ladder at the speed of light, I don’t think, “gee, your ladder looks short!” No. You and your ladder look quite normal. But, if I could look at you through a microscope, I would say, “My goodness, your particles look frozen and very short – like pancakes!” You would look at your own particles through your microscope and say, “I don’t know what you are talking about, everything looks normal to me.”

As you carry your ladder through the barn while looking straight ahead, you would think the barn was very short because your particles are contracted and that froze your clock, but if you turned your head to the side to take a picture of the barn while you were in it, you would think it was just as long as I think it is. To me, that distinction is what the relativity of simultaneity is all about.

Section 4: spinning wheels don’t get smaller

We can extend this logic to the Ehrenfest paradox and thereby resolve the confusion over the proper radius of a spinning object – In contrast to Einstein’s confusing musings, the radius of a spinning object does not change due to relativistic effects because the relativistic effects are operating on an individual particle level, not as a collective effect.

This should become more obvious when you think about the charge density in a closed loop of electric current. The loop of wire in which the current flows does not get smaller, the particles within the loop get squished like pancakes. When their fields are squished, they stick out further from the wire and that is why loops of current carrying wires have stronger magnetic fields around them than wires without current.

Section 5: spaceship paradox

The same way of thinking resolves Bell’s spaceship paradox: what happens to the distance between two spaceships after they accelerate? If the spaceships length contract, then a string connecting them would snap after they both accelerate. That isn’t how any other physical system behaves, so it must be a paradox unless you realize that the paradox disappears if you only apply length contraction to individual particles and not to macroscopic objects.

You can take this logic into the domain of the neutron star and imagine that the charged particles propagating around the surface of the star have fields like pancakes facing in the direction of their propagation. This reduces the repulsive forces between the particles in the direction which is tangential to the surface of the star. Such a reduction contributes to the stability of the star. You can model this particle beam with the concept of tunes in a giant synchrotron.

For a different and, according to what I just wrote, wrong explanation watch some YouTube videos or listen to a lousy professor. Some are good, some are bad.

Section 6: muons and the atmosphere

One also frequently finds mistakes in physics texts about muons and time dilation.

Many people know the story of how a cosmic ray muon streaking through the atmosphere has a short lifetime in its rest frame, but it has a longer lifetime in the earth frame because it is moving at such a high velocity.

Pedagogically, this example is turned around to demonstrate length contraction by saying that from the muon’s perspective, the earth’s atmosphere is length contracted and because it doesn’t have to interact with as much atmosphere, that is why it lasts for longer in the earth’s frame of reference than it would’ve without special relativity.

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html

I have no issue with the description in terms of particle lifetime, but based on what I know about particle bunches in accelerator physics, the description in terms of distance is wrong in a fundamental way: there is no situation where a muon observer looks at a train of atmospheric particles stretching from the surface of earth to the stratosphere and concludes that the train has gotten shorter after it has been accelerated.

The distance between two points is defined by the speed of light and nothing about motion changes that. A light year is a light year and it is associated with a fixed distance in meters. The distance from the muon to the earth and the distance from the earth to the muon are the same. This makes statements about a contracted atmosphere sound preposterous.

It would be better to tell students that from the muon’s perspective, the reason that the particle lives longer in the earth’s atmosphere when it is traveling quickly is because the atmospheric particles appear individually pancaked (length contracted) to the fast-moving muon and this reduces the amount of time that the muon interacts with each atmospheric particle. The reduced interaction time makes the decay likelihood lower than if it had interacted with non-contracted atmospheric particles.

The important takeaway is that the length contraction of the atmosphere is not a literal contraction of the distance between the earth’s surface and the muon. It is only a contraction of the fields of the atmospheric particles and this contraction reduces the amount of time that the muon interacts with each atmospheric particle. Of course, from an absolute perspective, the atmospheric particle didn’t actually contract, it only appeared to contract from the perspective of the muon.

The alternative to thinking about squished particles in a fast-moving object is to imagine that the object has been streaked out such that the space between the particles has expanded within the moving object’s rest frame. But for the muon story, this streaked out picture leads to paradoxes in which the earth’s atmosphere stretches out past the moon. In the streaked out picture, the muon looks at the atmosphere moving toward him and imagines what the atmosphere would look like in its rest frame and the muon sees that the atmospheric particles would be spherical, and the aetheric fluid flowing around them is practically stopped because it has become extremely thin and less viscous due to being so spread out. This leads to the fluid interacting with the muon much more weakly than it would’ve had it not been so stretched out.

This description has two layers of abstraction instead of one.

  • One layer: I see a muon moving towards me and I say it looks contracted and has a slow clock. The muon looks at me and says that my particles look contracted and have a slow clock.
  • Two layers: I see the muon coming towards me and I imagine that if it were frozen in time, it would look temporally streaked out in space, but its field would be spherical, not contracted. The muon sees the earth’s atmosphere coming towards it and it imagines that if the earth’s atmosphere were frozen in time, it would look streaked out in space with larger distances between atmospheric particles with spherical, not contracted, fields.

I think that the two layer explanations are unnecessary (they do not add predictive power) and they should be thrown in the trash because they only serve to make things seem more complicated than they really are.

The takeaway from this is that the math can still turn out to be correct even if the heuristic is wrong and your theory can still be wrong if it has a bad heuristic.

Section 8: temperature

After a beam of particles is accelerated, it looks colder from the perspective of the lab, as in, the particles don’t move much relative to one another.

Likewise, a muon decaying into an electron can be thought of as a particle going through different phases of matter, like solid, liquid, and gas. The faster it moves, the longer it stays solid and cold.

This leads to a paradox because relativity tells us that if the muon looks cold to us, then we must also look cold to the muon. This contradicts common sense because if a sensor is colder than its surroundings, it should automatically measure warmth.

The physics contradicts intuition and many physicists are content to accept such a contradiction and move on.

I am not such a physicist.

The situation loses its paradoxical nature if you consider that temperature can be positive and negative about absolute zero – the coldest temperature possible. Yet if we only ever talk about the absolute value of the temperature, then relativity will suggest paradoxical situations with respect to temperature.

If an absolute perspective allows us to see that particles in relative motion are positive cold vs. negative cold, a simple change of scale produces a result consistent with the hot vs. cold psychological intuition, thereby removing the contradiction with the relativistic intuition imposed by the condition that the speed of light cannot be exceeded.

Section 9: relativistic mass

The alternative to thinking about how the temperature approaches absolute zero as the energy of a relativistic object increases is to talk about an increase of “relativistic mass” as an object’s velocity increases. For some reason, this terminology has gone out of fashion and students are told that thinking about relativistic mass will confuse them. I find that the opposite is the case. You will get confused if you do not think in terms of relativistic mass.

This becomes clear when you learn that when particle beams are accelerated, they get stiffer, as in harder to bend with magnets. This stiffness can be interpreted as an increase in the relativistic mass of the particles or as an increase in the energy of the particles.

The only difference between the two linguistic approaches is that one is given in terms of a concrete thing that you can see and feel (mass) and the other is given in terms of an abstract concept (energy) about which most people have no intuition. There isn’t really any reason for the present-day fashion of ranting and raving about relativistic mass being a terrible, misleading concept.

The property which increases exponentially is the resistance of space to motion. The massive object is made up of moving space and moving space cannot move at more than the speed of light. The internal motion of the mass at rest tells you how close to the speed of light you can get before the internal motion breaks apart.

Section 10: illusions and reality

In this post, I’ve explored eight different situations in which a literal interpretation of the mathematics leads to counter-intuitive or paradoxical results. Instead of insisting that because the math works out, the situations cannot be considered to be paradoxical, as is the custom in the present-day physics community, I have insisted that we should demand that of our interpretation of the math does not contradict our basic understanding of reality.

Reality is our daily experience of how the world works and illusion is something that contradicts out daily experience but which can be explained with a deeper understanding of the tricks reality can play.

In the case of a particle which appears to length contract because it is traveling at a high rate of speed, we might say that the contraction was an illusion, but if that is the case, that illusion has real physical consequences in terms of the magnetic field of the particle. Thus, it makes sense to describe length contraction of particles as a feature of reality whereas the paradoxes which result from this contraction are an illusion caused by a poor choice of the words used to interpret the mathematics.

Section 10: the speed of light

So far, I’ve stuck to the convention that the speed of light is constant while length and time change, but it is also possible to derive all of physics by starting with the assumption that the speed of light changes but time and length are constant. The convention you choose determines what you think of as reality and what you think of as an illusion.

When you decide that the speed of light is constant and time literally dilates, you end up talking about an expanding universe and galaxies full of dark matter. You end up having to explain the contradiction that, in such a framework, stars are moving away from each other at faster than the speed of light.

When you decide that time is an absolute and the speed of light is just a geometric convention which changes depending on relative speed or gravity, then you find that the universe is not expanding and that there is no dark matter. You end up having to speculate about light gradually losing energy in a non-quantum mechanical fashion as it travels over vast distances.

The difference is therefore just a matter of word choice, but one description sounds more mysterious and full of illusions and paradoxes than the other.

[This was composed from posts I made on quora.com]

Categories Relativity, Science

11 thoughts on “Thought Experiments

  1. Dear Kirsten,

    Your physics related articles are inspiring me to write about how well they dovetail with what I call Neoclassical Physics and Quantum Gravity.

    Your Gell-Man quarks reference led to a train of thought I wrote about here: https://johnmarkmorris.com/2019/10/14/kirsten-hacker-thought-experiments/

    Best,
    Mark

    Liked by 1 person

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