Relativity of bodies in motion in space

Question

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.

Answer 1

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.

Answer 2

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."

Answer 3

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.