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Thought experiments have played a starring role in physics. They seem, sometimes, to pluck knowledge out of thin air. This is the starting point for my discussion this week with the philosopher Harald Wiltsche: what are thought experiments?

How do they function — are they platonic laboratories with no moorings in observations or a way of supercharging our reasoning about phenomena?

What do they deliver? Much emphasis has been put on the paradigm-shattering insights of Einstein where thought experiments appear like midwives in the production of new theories. But they can also function in explaining those theories, in ensuring they are understood.

This leads to the question: what is understanding? Harald argues that it’s the ability to manipulate or deploy knowledge backed up by a mental model. He reasons that thought experiments can help us to make sense of the abstraction of mathematical models.

We discuss many topics: the mathematization of science with Galileo, where thought experiments go wrong, transcendental arguments, the links between Husserl and Mach — it was the latter’s emphasis on grounding physics in phenomenona that inspired the phenonomenological tradition in philosophy.

While there are many notes we touch on, the theme that we dance to is this: there are lots of forms of reasoning that can work well within physics and we need equal pluralism in our philosophy of science to understand the its startling, uncanny success in modeling nature.

Notes

• Harald’s website haraldwiltsche.com is a great way to access his papers
• Some ones to highlight from our discussion: his paper on thought experiments and science fiction is here, on a phenomenological approach to Wigner’s conundrum of the “unreasonable effectiveness of mathematics”, and the introduction to Phenomenological Approaches to Physics by Harald and Philipp Berghofer
• @haraldwiltsche on Twitter

How well does ChatGPT do with thought experiments?

Pretty well.

This question came up when discussing understanding. Large language models are certainly adept at manipulating symbols in ways that sound convincingly human, but how well do they in reasoning (or appearing to reason) about physics?

I go through two sets of prompts here, the second — where I prompt it with a thougth experiment that gets increasingly bizarre — is the more intriguing. It’s possible in all of these cases that a similar experiment has somewhere been discussed and ChatGPT is esstially parroting someone else’s understanding, however, the setup is rather complex: a helicopter magnetically levitating a butterfly in a plastic plane — has that really been dicussed before? I think one is forced to concede that it appears to have a good grasp of the physics.

Asking ChatGPT (GPT4) to think up a thought experiment

User Can you construct a thought experiment to explore the issue of whether space is absolute or relative, the ingredients in the experiment are two brass balls, scissors and a ribbon

ChatGPT
Absolutely, let’s consider a thought experiment, that could potentially show how to understand the difference between the concepts of absolute and relative space.

First, let’s define these terms for clarity:

Absolute Space: This refers to the Newtonian concept of space, which exists independently and objectively, as an unchangeable and infinite background where all physical events occur.

Relative Space: This refers to the Einsteinian concept of space, where space doesn’t exist independently of the things within it. Instead, space and time are interwoven into a four-dimensional fabric known as spacetime, and the presence of mass and energy can distort this spacetime fabric. This is the basis of Einstein’s theory of General Relativity.

Now, let’s proceed to the thought experiment:

Imagine you’re in a spaceship with no windows, floating in deep space, far away from any celestial bodies. In this spaceship, you have two brass balls, a ribbon, and a pair of scissors.

You tie the two balls together with the ribbon and hang them in the middle of your spaceship. Since you’re in deep space with no other forces acting on your spaceship, the balls just float there, not moving relative to the spaceship.

Experiment 1: Now, you give your spaceship a slight spin. After a while, you notice that the balls are now rotating around the center of the spaceship, the ribbon taut, maintaining a fixed distance from each other due to the centrifugal force caused by the rotation of the spaceship. In this case, from the perspective of Newton’s absolute space, you’ve imparted a rotation on the spaceship, and the balls are simply responding to this by moving in a circle.

Experiment 2: Now, imagine an alternate scenario where your spaceship remains stationary, but all the universe around it starts to spin instead. According to the principle of relativity, you wouldn’t be able to tell the difference between these two situations from inside the spaceship. The balls would behave in exactly the same way, spinning around the center due to what appears to be the centrifugal force. However, this time, according to the relative space concept of Einstein’s General Relativity, the mass-energy of the universe spinning around the spaceship would distort the spacetime around it, creating a frame-dragging effect which leads to the balls’ circular movement.

This experiment illustrates that whether space is absolute or relative can dramatically change our interpretation of the same phenomena. Although this is just a thought experiment and not a practical one (we can’t spin the entire universe), it highlights the difference between the Newtonian concept of absolute space and the Einsteinian concept of relative space.

User
If a butterfly is inside a plane, but flying — so not on the seats — does the plane need to generate more thrust to maintain altitude than if the butterfly were absent?

Asking ChatGPT (GPT4) to reason through a thought experiment

ChatGPT
The plane doesn’t need to generate any additional thrust to maintain altitude whether a butterfly is flying or resting within the airplane cabin. This is due to the principle of conservation of momentum.

In the closed system of the airplane, the mass and the momentum are conserved. This means that the butterfly’s presence, flight, or rest doesn’t change the total momentum of the plane. When the butterfly is flying, it pushes air downwards to generate lift. The air pushes back on the butterfly, but it also pushes (very slightly) on the plane. The sum of these forces and reactions remains constant, so no extra thrust from the plane’s engines is necessary to maintain altitude.

In other words, when the butterfly takes off from a perch inside the airplane, it imparts a slight force to the airplane in the opposite direction. But as it flies around, all the movements it makes, the flapping of its wings, the changes in direction, etc., just redistribute the mass and momentum within the plane. The net effect on the plane is zero.

The situation would be the same whether the object in question is a butterfly, a bird, or a passenger walking down the aisle. As long as the action takes place within the closed system of the plane, it won’t affect the thrust needed to maintain the plane’s altitude or direction.

User
But if the butterfly were absent, wouldn’t the plane weigh less and therefore less thrust would be required?

ChatGPT
You are correct that if the butterfly were not present at all, the total weight of the airplane would be marginally less by the weight of the butterfly. The plane would therefore need a tiny amount less lift to maintain altitude, and consequently a tiny amount less thrust to maintain a particular speed.

However, once the butterfly is on board the plane, whether it is flying within the cabin or resting doesn’t affect the thrust required to maintain the plane’s altitude. This is because the weight of the plane system (including the butterfly, passengers, seats, etc.) is the same whether the butterfly is in flight or at rest.

In simpler terms, the energy required to lift the butterfly against gravity is still accounted for within the closed system of the plane, whether the butterfly is using its own wings to stay aloft or if it’s sitting on a seat.

So, to summarize, the plane does weigh less if the butterfly isn’t there at all, which would mean slightly less thrust is required. However, if the butterfly is present in the plane, whether it’s flying or not doesn’t make a difference to the thrust required.

User
What happens if the inside of the plane were a vacuum and the butterfly could levitate (perhaps magnetically) inside the plane, would it contribute to the weight of the plane’s contents then?

ChatGPT
Your scenario is a fascinating one. If we’re assuming the butterfly can somehow levitate magnetically, in a vacuum, inside the plane, then the answer to your question is yes, the butterfly still contributes to the total weight of the plane.

In this case, even if the butterfly is levitating, it doesn’t escape the pull of gravity. The butterfly still has mass, and the Earth’s gravity still acts on it, exerting a force (its weight). That gravitational force doesn’t disappear when it levitates; instead, it’s just counterbalanced by another force (in this case, a magnetic one).

This means that the butterfly’s weight still contributes to the overall weight of the plane. So if the butterfly weren’t present at all, the plane would be marginally lighter by the weight of the butterfly, regardless of whether it’s levitating or not.

The important point here is that gravity acts on all mass, regardless of its state or position. A levitating object in a gravitational field is still subject to gravity and still contributes to the total weight of the system it’s part of.

User
What if the plane were made of plastic, and the magnetic force holding the butterfly in place was one due to a helicopter flying above the plane, would it still contribute to the weight of the plane and thus lead the plane to require a tiny amount more thrust than if the butterfly were absent?

ChatGPT
If the magnetic force attracting the butterfly is not coming from the plane itself, but from an external source like a helicopter above it, then the situation changes.

In this case, the force that’s supporting the levitating butterfly is not being applied by the plane, but by the helicopter. So, the weight of the butterfly (which is the force of gravity acting on its mass) is essentially being “transferred” to the helicopter, not the plane.

Therefore, in this specific scenario, the butterfly’s weight would not contribute to the total weight of the airplane while it’s levitating. As a result, the plane would not require more thrust to maintain altitude than if the butterfly were completely absent.

However, remember that this situation is based on quite a few assumptions that would be very difficult to realize in the real world, and it doesn’t take into account other potential factors that could affect the plane’s flight.