Thought Experiments

[heiwos]

Einstein. Thought experiments are predictions only, and should not be mistaken for conclusions.

Thought experiments are not just predictions. They can make valid conclusions. Wikipedia has it right here:

 

From Thought Experiment:

 

In terms of their theoretical consequences, thought experiments generally:

 

- challenge (or, even, refute) a prevailing theory, often involving the device known as reductio ad absurdum,

- confirm a prevailing theory,

- establish a new theory, or

- simultaneously refute a prevailing theory and establish a new theory through a process of mutual exclusion.

[iNow]

Your thought experiment still must translate into reality or it is nonsense, regardless what wikipedia says.

[heiwos]

It's not my thought experiment. I'm just making a side point about thought experiments in general.

[swansont]

It's not my thought experiment. I'm just making a side point about thought experiments in general.

 

Do you have an example where a thought experiment has refuted an existing theory?

 

If the theory is self-consistent, it can't contradict itself. So if the theory predicts that under a set of conditions A, that B will occur, you can't set up a thought experiment where you start with A and the outcome isn't B. That can only occur if you've made an error. All you have done is math. The twins paradox is an example here — you have a contradiction, but it turns out you've violated a condition of special relativity when you have the acceleration.

 

Now, you can certainly do a thought experiment where your set of conditions predicts that C will occur. But then you must look at an actual physical situation to see if C, in fact, occurred. It has to be something that actually happens, or is empirically known not to happen, that is your basis for comparison. And then it's a prediction, not just a thought experiment, and you still have to make sure you've set the problem up properly if you find a discrepancy between prediction and outcome.

[heiwos]

Do you have an example where a thought experiment has refuted an existing theory?

Yes, the blog we've discussed elsewhere seems to do that.

 

If the theory is self-consistent, it can't contradict itself.

Yes, because "self-consistent" is synonymous with "doesn't contradict itself".

 

So if the theory predicts that under a set of conditions A, that B will occur, you can't set up a thought experiment where you start with A and the outcome isn't B. That can only occur if you've made an error.

True when the theory is self-consistent, otherwise false.

 

The twins paradox is an example here — you have a contradiction, but it turns out you've violated a condition of special relativity when you have the acceleration.

I agree that the twin paradox doesn't show a problem with SR.

 

Now, you can certainly do a thought experiment where your set of conditions predicts that C will occur. But then you must look at an actual physical situation to see if C, in fact, occurred. It has to be something that actually happens, or is empirically known not to happen, that is your basis for comparison. And then it's a prediction, not just a thought experiment, and you still have to make sure you've set the problem up properly if you find a discrepancy between prediction and outcome.

This looks fine to me.

 

A thought experiment that claims to show that a theory is self-inconsistent cannot be refuted by simply assuming that the theory is self-consistent and then making the tautology, "If the theory is self-consistent, it can't contradict itself." That’s just ignoring a challenge to the theory (it's not good science). If the thought experiment is invalid, then there must be a mistake in it that can be pointed out. For example, the twin paradox contains a mistake.

[swansont]

Not finding a mistake, especially when the thought experiment lacks rigor, is not the same thing as not containing a mistake.

[heiwos]

You didn't specify the axioms on which your point is based. "Rigor" has different meanings to different people. Some people may want a claim to specify all the axioms on which it depends, even ones like x=x, otherwise they'll dismiss the claim as being insufficiently rigorous. It can get silly.

 

From The Barefoot Bum: Thought Experiments (boldface mine):

 

...three very important thought experiments: the Brownian Ratchet, Einstein's Box and the EPR Argument. In all of these cases, the original argument proposes a contradiction in the formulated laws of physics, the Brownian Ratchet in thermodynamics, and Einstein's Box and the ERP argument in quantum mechanics. In the first two cases, the apparent contradiction was resolved by discovering non-obvious lack of rigor in the thought experiment, and the paradox resolved.

 

We see here that if lack of rigor is a problem, it can be pointed out as a mistake. So it wouldn't be good science to dismiss a thought experiment due to an unspecified lack of rigor.

[swansont]

We see here that if lack of rigor is a problem, it can be pointed out as a mistake. So it wouldn't be good science to dismiss a thought experiment due to an unspecified lack of rigor.

 

What? It's not good science to ask for a rigorous treatment of the thought experiment? Your examples contradict this — apparent paradoxes resolved when more rigor was applied.

[heiwos]

That's not what I said. Asking for more rigor of the thought experiment is different than dismissing it due to an unspecified lack of rigor. Yet asking for more rigor becomes silly at some point, like demanding that all axioms be stated, even x=x, so asking for more rigor can be tantamount to conveniently finding a "problem" where no problem exists. That's obviously not good science, which explains why the apparent paradoxes that were resolved when more rigor was applied were not dismissed due to lack of rigor until that lack was found.

[swansont]

That's not what I said. Asking for more rigor of the thought experiment is different than dismissing it due to an unspecified lack of rigor. Yet asking for more rigor becomes silly at some point, like demanding that all axioms be stated, even x=x, so asking for more rigor can be tantamount to conveniently finding a "problem" where no problem exists. That's obviously not good science, which explains why the apparent paradoxes that were resolved when more rigor was applied were not dismissed due to lack of rigor until that lack was found.

 

They were not accepted as correct, either. One needs sufficient rigor to determine that lack of rigor is not a problem.

[heiwos]

It may be obvious to a reasonable person that the thought experiment is sufficiently rigorous. For example, a reasonable person doesn't need to see the thought experiment include the axiom x=x to be convinced that it's sufficiently rigorous.

[DJBruce]

I hate to go against the all knowing Wikipedia but in my opinion normally a thought experiment brings a new a idea that can either eventually be proven true and become a theory or can be proven false and die.

 

But I think it is rare that a thought experiment alone becomes a theory.