Why is a thought experiment a valid way to prove anything?

Isn't a thought experiment as subjective as you could make science be? Is it that since it is impossible with our current methods, we are simply skipping too many hurdles that would have to first be passed in order to satisfy minimal scientific method steps?

I understand that in order to prompt further investigation you would need to first have a model and that such model would first have to be proven, but there seems to be a bit of the: "Nobody can prove this or that thought experiment wrong" or "Nobody can argue anything against that thought experiment" that seems to validate a theory more than objective experimentation after a clinical hypothesis that delivers a more scientific approach to our methodologies. In other words, how is it that a thought experiment is even called an experiment, because in reality it should be classified more as a form of belief or a primordial idea that could drive further research.

I would just like to know if anyone cares to explain.

Thank you!

You are hung up on the word "experiment." Thought experiments are not replacements for empirical experiments, nor were they ever claimed to be.

A thought experiment starts with assumptions about the laws of physics ("the speed of light is constant," "$F = ma$," etc.) and derives conclusions from these assumptions, analytically. The conclusions are necessarily as true as the hypotheses that went into the thought experiment.

That is, thought experiments are part of the theoretical side of physics, where we say things like "given theory $T$ and setup $S$, result $R$ logically follows." The empirical side comes in afterward, where it sets up $S$ and observes whether or not $R$ holds. If $R$ does not empirically follow from $S$, we have evidence against $T$. Empirical physics also plays a role beforehand, where it gathers evidence in favor of $T$.

You can no more argue against a thought experiment than you can argue against a mathematical proof, assuming it is free of logical flaws. You can argue that the input theory $T$ isn't physical (something you can't really do in math), but a proper thought experiment that shows $S \stackrel{T}{\Rightarrow} R$ cannot be doubted in that $S$ really does imply $R$ in physical theory $T$.

• What happens if your premises for S and T are both based on the wrong interpretation of reality and you come to R. To you it will be right, but since S and T are false, your R will be false too, even though you will apparently have created an entirely positive proof of R? Nov 30, 2014 at 2:32
• The thought experiment doesn't prove $R$ in some sense of absolute truth, it only proves that $R$ follows from $S$ and $T$. You are always free to doubt that $R$ holds in the real world, but you have to simultaneously doubt that $T$ and/or $S$ accurately describe the world.
– user10851
Nov 30, 2014 at 2:37
• Well, I would say that if either S or T are in doubt, your entire thought experiment is forfeit... Nov 30, 2014 at 3:35
• No, you're missing the whole point. The thought experiment is never supposed to deliver absolute truth. It provides a way of going from (possibly flawed) theory $T$ to observable consequence $R$. Problems with $R$ imply problems with $T$ (think logical contrapositive), and that's the whole point. The experiment provides a way to test the validity of $T$ by producing a testable $R$.
– user10851
Nov 30, 2014 at 3:40
• No. Many consequences of relativity follow from thought experiments. But the axioms do not. Things like time dilation logically, necessarily follow from the axioms of relativity, as illustrated by thought experiments, so if you believe in the axioms you must believe in all their consequences. Because all the consequences we've enumerated have been verified many times over in experiment, we generally believe the axioms, but we aren't logically required to believe in them.
– user10851
Nov 30, 2014 at 4:11

Let's be specific. I don't believe Galileo ever dropped two balls from the Leaning Tower of Pisa. It was a thought experiment.

Suppose you believe a 1 lb iron object will fall slower than a 2 lb one, but that two 1 lb iron objects would fall at the same speed as a single 1 lb iron object.

OK, take a 2 lb iron ball. It falls at a certain speed. Now, you take a very fine saw and cut it almost in half, so it is two 1 lb iron objects, held together by a very very fine thread of material, no stronger than a wisp of spider web.

Now you drop it. Does it fall at the rate of a 2 lb object, or at the rate of two 1 lb objects?

Or, to put it another way, suppose you drop the two 1 lb objects next to each other. They fall together at the 1 lb speed. On the way down, the tiny spider you didn't notice joins the two with a bit of web. This makes it one object. Does it suddenly speed up to the 2 lb speed?

Obviously the 1 lb speed and the 2 lb speed have to be the same. So that contradicts your original belief.

That's what a thought experiment is. Now, you could actually try it, but in the mean-time you've got a pretty good reason to doubt your original belief.

• I wouldn't doubt or believe more because of a thought experiment, I would like to prove my hypothesis first, before it becomes a dogma that cannot be undone by any proof and which even stigmatizes anyone who differs. Nov 30, 2014 at 2:36
• Galileo did, however roll a heck of a lot of balls down ramps. That is he had already done the investigation in slightly less ideal conditions. Nov 30, 2014 at 3:23
• And lets not forget about 45 degree angled ramps... Of course Galileo dropped stuff from towers, he was a true scientist! I just wish I saw the same rigor in some areas... hence my question. Nov 30, 2014 at 3:36
• @Albalma: I agree - dogmas and stigmas are bad things. I'm in favor of skepticism. Not only questioning of positive results, but questioning of negative results. A perfect example is "cold fusion". If on the other hand you're talking about global warming, skepticism is a good thing, but using it as an excuse to do nothing and just let the hammer fall is poor wisdom. Nov 30, 2014 at 14:06
• I would completely agree, but then there is a lot more solidity in the evidence behind global warming (even though it has been really chilly). There is no dispute our polar caps are under producing ice and not reaching the levels and latitudes they used to before. There is proof of the amounts of CO2 and methane in ancient ice layers. However, as far as I know, we have little evidence to provide about something like accelerating a body near the speed of light. Just saying that we are too young as a species to pretend we know so much as we do. Dec 2, 2014 at 1:14