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I have learnt that if we are travelling in space we have no way to tell if we are moving towards something or if it is the something that is moving towards us; to either object they judge that they are still and the thing is just coming at them.

Did I learn it wrong, or is this really how physics go?

If it is, how is it that we cannot just ‘probe’ ourselves to promptly find out our ‘absolute motion’?

For example if we have a known amount of fuel that can be burnt to go from zero to one length per time, or ‘increase our kinetic energy by one’, and we see a planet ahead that from our frame of reference seems to be moving towards us at ‘one length per time’ as we are still; and for good measure let us also suppose we have another mass identical to us near us that is also still in relation to us. Then as we burn that fuel the planet should change from one to two lengths per time while the other mass formerly in our still frame should become negative one length by going backwards in relation to us. But would not that only happen if we were truly still? By doing so we would know that we cannot now possible be ‘still’ and further that the fuel spent cannot possible correspond to that acceleration of the planet that is an increase in kinetic energy many orders above that fuel energy; we know that it is us who accelerated from zero to one, that the planet indeed has that one length per time towards us and that the mass left behind is truly still because we can attribute it only to ourselves – if the planet seems to accelerate by merely around zero dot forty two and the companion go backwards with that same magnitude then we know that the planet was still all along and that both masses were moving towards the still planet at one length per time, and that now we are moving at the velocity of the root of two as that is the only valid conclusion that matches our observation of the total kinetic energy after that perturbation with us having now two total kinetic energy as one unit was added to our motion so that the proportion of the change in velocity by burning some fuel to the total kinetic energy of the system tell us the magnitude of the motion of every body in it as one giant coherent frame no matter from which point it is so analysed giving a single ‘true’ result without the need to ‘translate’ every ‘possible frame’, which are actually impossible and wrong interpretations since they disagree on the total kinetic energy of the system, to any other.

Where does this thought experiment fail?

And if it does not fail then is it not impossible to hold any ‘still frame’ as ‘valid’ and that since we can probe for the exact relation of the magnitude of motion of every body then would we not also be aware of our motion and thus measure light in relation to us as any other moving body of non-constant speed, merely as much faster or slower as the sum of ours velocity and its?

Thanks for your time in reading through all of that; and for simplicity you can answer just where exactly the thought experiment falls apart.

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  • $\begingroup$ Planet and you moved to the left at speed 100 km/s. Then you slowed down. That is an alternative theory. $\endgroup$
    – stuffu
    Jul 29, 2023 at 2:51
  • $\begingroup$ But is not that case trivial? If I am moving to -1 that example would measure the same thing, but it would mean I actually stopped rather than being still before. But then the second burn would be different; on the first case it would show the proportion to kinetic energy '1 to 2', but on the -1 case it would once again show the same change from 0 to 1. So repeated 'probes' would give me the different proportions; -100 to -99 to -100 and -111 kinetic energy on your case would all give different changes for that same equal amount of fuel, which rate is proportional to that total velocity. $\endgroup$
    – Bedengus
    Jul 29, 2023 at 9:03
  • $\begingroup$ @Bedengus your question is not actually a duplicate of this question physics.stackexchange.com/questions/287101/… so I am not marking it as a duplicate. But that other question answers the misunderstanding that produced this question. Please read it and the answers. I think it will give you the concepts you need to resolve your question here $\endgroup$
    – Dale
    Jul 29, 2023 at 15:49
  • $\begingroup$ I have read them, @Dale, but I do not see how they are related. He is asking 'why going from 1m/s to 2m/s costs more energy than going from 0m/s to 1m/s when the change is 1m/s in both?'. On my question I am already assuming 2m/s is four times the energy of 1m/s; and my doubt is about how the change caused by a 1J increase in the KE does not forces us 'out of the frame' by analysing how the change in velocity shows the total KE of the body. $\endgroup$
    – Bedengus
    Jul 29, 2023 at 17:16
  • $\begingroup$ @Bedengus that is the same physics. It is a different question but the same physics $\endgroup$
    – Dale
    Jul 29, 2023 at 17:22

3 Answers 3

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Well, acceleration is not relative, so if you burn fuel to increase your speed by a metre per second, you know that if you were still beforehand you won't be now. However, there are two other points to consider. The first is that you have no way of knowing whether, in an absolute sense, you were still beforehand. The second, and more important point, is that there is no absolute motion- you can only define motion relative to something else, and what you chose as your baseline is arbitrary. For example, we usually treat the ground as the frame against which we define speed, but the Earth, as you know, is moving around the Sun, which is turn is moving relative to the rest of our galaxy. So in summary you can only define speed relative to some inertial frame; which frame you pick is entirely up to you; given that, you are always free to pick your rest frame as your baseline.

When you say you are 'still', that is relative too. It just means that you are not moving relative to whichever frame of reference you are using. Again you are always free to pick your own rest frame, so you can always consider yourself, by definition, to be still if you are coasting inertially.

Finally, you're confused about kinetic energy, as that is frame dependent too. Imagine you are in an empty room. You can perform a little experiment to use up some fuel and use it to propel a little model car, and you can figure out who much energy you've used up and relate it to the resulting speed of the car. Well, you can do exactly the same calculation if the room is a cabin on a moving ship, or the first class lounge of a cruising jumbo jet etc etc. If your perform the experiment on the jumbo jet, but baseline all the calculations in the ground frame, you'll find that it all becomes more complicated. If burning a fixed amount of fuels increases the speed of the car by a metre per second, then in the frame in which the car started at rest, the increase in KE of the car is 0.5 times the car's mass. On the other hand, if the experiment is in a jumbo jet travelling at 100m per second, you'll find that the car's speed after burning the fuel is 101m per second relative to they ground, and the increase in KE is much much larger in the ground frame. There's nothing 'wrong' with that, you just have to correct for the fact that if you model the experiment in the ground frame, you have to take into account the fact that accelerating the car imparts a tiny recoil to the jumbo jet, and then all the energy gains and losses balance again.

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  • $\begingroup$ Then that amount of fuel that increases the car from zero to one is the same required to to produce a change 201 times larger, both accelerating the car to 101 and somehow also pushing the jet back too? Would it not take a lot more fuel to accomplish that effect? If an observer saw a fuel equivalent to 1J change the little car velocity from 100 to 101 than he can be sure he is the one moving at 100 and the car went from still to 1; if the car was at 100 then the seen 1J of fuel would change its velocity much less, wouldn't then by that proportion its 'actual velocity' be known? $\endgroup$
    – Bedengus
    Jul 29, 2023 at 12:45
  • $\begingroup$ No, you need to think about it a little harder. The recoil of the jumbo happens regardless of which frame you pick. In the initial jumbo frame, the change in the jumbo's KE owing to the recoil is so small as to be totally negligible, so all the energy in the spent fuel can be equated with a small KE increase for the car. In the ground frame, the KE lost by the jumbo owing to the recoil is much bigger, so now the energy conservation equation is that the energy of the spent fuel is a much bigger increase in the KE of the car less a non-negligible drop of KE of the jumbo. $\endgroup$ Jul 29, 2023 at 13:38
  • $\begingroup$ There is no 'actual' velocity. $\endgroup$ Jul 29, 2023 at 13:39
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To start, "if we have a known amount of fuel that can be burnt to go from zero to one length per time" is already a frame-dependent statement. When we say "all inertial frames are equivalent", this says that you cannot perform any experiment on your spaceship to tell whether or not you are "moving" at 0 lengths per time to 1 length per time (say with respect to someone observing from Earth).

I also think the confusion here is differentiating between instantaneous inertial frames of reference, which are local, and time-extended non inertial frames. The period of acceleration experienced by the ship is the latter case, in which case the principle of relativity does not hold - acceleration is absolute (in the Newtonian sense) with respect to inertial frames. The problem occurs, however, once you "stabilize" to your new inertial frame - it is at this point that the principle of relativity holds, and you cannot perform an experiment to tell that you are moving towards the planet. The most you can say as someone on the ship is that at some point you increased your velocity towards the planet, but this does not define an absolute notion of "who is moving towards whom."

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  • $\begingroup$ Thank you for the answer. But how is the energy released by the fuel a frame-dependent thing? $\endgroup$
    – Bedengus
    Jul 29, 2023 at 0:11
  • $\begingroup$ The energy released by the fuel is frame-independent as all observers agree on the rest mass energy of the fuel, but the contribution of that energy release to the change in velocity is frame-dependent. This is a relativistic effect, and you can think of it in the case of an observer traveling close to light speed in the opposite direction of the ship. If the energy release contributed the same to the velocity increase as it did to an observer on Earth, the ship's speed could exceed light-speed in such a frame, which is impossible. $\endgroup$
    – x32vertigo
    Jul 29, 2023 at 0:39
  • $\begingroup$ If they all agree on the energy, is that not that known increase in 'kinetic energy'? With any arbitrary amount of fuel I divide it in equal parts. I burn the first and set whatever observed change to be that 'zero to one' base. Would not the subsequent burn of the equal amount of fuel then give me that exact proportion mentioned of the 'actual kinetic energy' as everyone sees the same fuel changing the speed less at some exact proportion to the previous change? $\endgroup$
    – Bedengus
    Jul 29, 2023 at 8:55
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    $\begingroup$ @Bedengus that isn’t how rockets work. They are based on conservation of momentum. Their energy efficiency changes dramatically. See physics.stackexchange.com/questions/287101/… $\endgroup$
    – Dale
    Jul 29, 2023 at 11:52
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Rockets are weird. Every identical burn causes identical acceleration. So can't have a velocity meter.

Cars are weird in a different way. Acceleration depends on how fast wheels turn. How fast wheels turn at some velocity through space depends on the velocity of the planet that the car is on. So can't have a velocity meter, unless velocity of the planet is known.

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