# Can we really not tell if we are moving?

It has been a while since I've thought about physics, however, I remember something about how if you are on a train with no windows that is going perfectly straight and is perfectly smooth, there is no experiment that you could perform to prove that you are in motion or at rest. So I have a couple of questions related to this.

1. Is this still held to be true? I was just wondering if anything in physics has come to light since I learned about this (about 10 years ago) that would allow an observer on the train to tell if they are moving.

2. If this is true, why couldn't you accelerate a particle in different directions to a certain mass and measure how much energy it took to get it up to that mass. If you were moving in any direction, wouldn't you measure less energy in your direction of travel?

3. Would having an outside observer affect the aforementioned experiment in any way?

• I don't quite understand what you mean by "Is this still held to be true?" Are you asking about the possibility of the validity of that statement somehow changing over time? Or are you asking if presently accepted theories say that the symmetry is broken under certain circumstances? – user191954 Aug 19 '18 at 15:58
• @Chair I was just wondering if anything in physics has come to light since I learned about this (about 10 years ago) that would allow an observer on the train to tell if they are moving. – CumminUp07 Aug 19 '18 at 16:01
• @CumminUpo7 AFAIK, nope. But perhaps you could make question 1 a little bit more specific by including the stuff from your comment? – user191954 Aug 19 '18 at 17:20

Yes, it is held to be true, both in Galilean and Einsteinian relativity.

If you did the experiment you described you would discover that there was no difference based on direction in the energy it took to accelerate something to a given velocity.

If there was an observer compared to whom you are moving, then, as speeds approach that of light, they would observe different things than you would observe. Perfectly symmetrically, if you observed them doing the same experiments you would differ about things in the same way they do, because neither of you has any basis to assume that you are in some privileged 'rest frame' since such a thing does not exist(*). In particular you and the observer will differ about lengths & times in such a way as to make the laws of physics be the same to both of you.

The way that you differ in what you observe as speeds approach $c$ is described by special relativity, and it's exactly this kind of reconciliation between all observers measuring the speed of light to be the same in all directions and observers moving relative to each other that gave rise to this theory.

(*) No privileged rest frame exists according to the best theories we have, which theories have been very extensively tested. This does not mean it is absolutely impossible that someone will find that one, in fact, does exist, but this seems absurdly unlikely.

• Re, "...an observer compared to whom you are moving...would observe different things than you..." But, in either case, each observer's version of the events and measurements would be entirely consistent with the known laws of physics. – Solomon Slow Aug 19 '18 at 16:12
• I realize that accelerating something to a given velocity would be the same, that's why I was wondering about accelerating it to a given mass. Because relative to anything on the outside of the train the particle would would be moving faster in your direction of travel and therefore have a higher mass in your direction of travel even though the measured velocity would be the same. – CumminUp07 Aug 19 '18 at 16:19
• @CumminUp07, Yes. Relative to an observer who is standing by the side of the tracks, the lengths, and the masses, and the time intervals all would appear to be different from what you measure on-board the train. Those differences are necessary to uphold the Principle of Relativity, which says that you both should see the experiment obey the same laws of physics. But for you, on board the train, if you don't look out the window, you have no way of knowing that there is an outside observer or, that you are moving with respect to that observer. – Solomon Slow Aug 19 '18 at 16:25
• @jameslarge Thank you, I think what I was missing was that masses could be measured differently by different observers, but that makes sense now. – CumminUp07 Aug 19 '18 at 16:38
• @jameslarge: yes, of course. I've edited my answer slightly to add this explicitly. – tfb Aug 19 '18 at 17:15