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Here's a thought experiment: suppose I'm in a large box in space without windows or sensors, and I fire a laser in 6 different directions and measure the redshift along each direction. Could that data could then be used to determine my absolute velocity? Note that I'm talking about absolute velocity here, not velocity with respect to anything.

knzhou
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justin
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  • To clarify, by absolute velocity, are you referring to the velocity with respect to a fixed point in the box? Also, is 'your' velocity a significant fraction of the speed of light? –  Jun 10 '18 at 14:15
  • No, by absolute velocity I mean with respect to the entire universe. In this thought experiment, we could make my space-box velocity be 60 mph or 0.6c, I don't have enough knowledge to know if that matters. – justin Jun 10 '18 at 14:53
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    $\uparrow$ Absolute velocity wrt. what part of the entire universe? – Qmechanic Jun 11 '18 at 14:07

5 Answers5

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A red or blue shift is created when the light source is moving relative to the detector. In your thought experiment, you emit light and you receive it, so there is no red or blue shift. For your idea to work, light must be emitted not by you, but by the universe equally in all directions. Such emission is known as Cosmic Microwave Background. By measuring its redshift in different directions you can find that we are moving with the speed of 368 kilometers per second toward the Great Attractor. (CMBR dipole anisotropy).

You can obtain a similar result by measuring the average redshift of distant stars.

Also, hypothetically, in a closed non expanding universe, it would be possible to define your speed relative to the universe without CMB or starlight, but by measuring the time for light to make a trip around the universe. However, it would take a very long time.

safesphere
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  • Does that imply that general relativity does not apply in a closed non expanding universe? – kasperd Jun 10 '18 at 20:32
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    @kasperd No, there is no conflict with general relativity. This only means that the Lorentz invariance of special relativity is globally broken in a closed universe. This is not unusual though, because Lorentz invariance is a local concept and is broken globally in any gravitational field. – safesphere Jun 10 '18 at 22:29
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    It should also be noted that this isn't strictly absolute velocity either - it just seems to be the closest thing we have. We couldn't tell if all the "universe" was moving 100 Mm/s to the "left" when the CMB was emitted - it would look the same to us. The main benefit of CMB as the "reference frame" is that it seems to be pretty darn isotropic - so at least it's likely that other observers in different parts of our observable universe will mostly agree with our measurements (adjusting for the subjective simultaneity etc., of course). – Luaan Jun 11 '18 at 05:35
  • @Luaan Your comment implies a difference between absolute and relative velocities. However, velocity is relative by nature. There is no such thing as absolute velocity (it would be gauge invariant like the electric potential - only a difference is measurable). If an observer is alone in the empty flat universe, his speed is not a meaningful concept. So, "if all the 'universe' was moving", has no physical meaning (unless you mean a part of the universe, which case is likely to be ruled out by symmetry). – safesphere Jun 11 '18 at 05:56
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    No, my comment says the same thing as yours - there is no absolute velocity (to the best of our knowledge). – Luaan Jun 11 '18 at 07:04
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Your proposal is almost exactly the Michelson-Morley experiment, done in 1887.

It compared the speed of light in perpendicular directions, in an attempt to detect the relative motion of matter through the stationary luminiferous aether ("aether wind"). The result was negative.

enter image description here

Eric Duminil
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  • Nice explanation. Is this the Michelson & Morley expected result in the case the platform is moving toward the right? – dan May 28 '23 at 16:04
  • @dan: The right gif displays what was expected: The whole experiment is moving along the horizontal axis, and was expected to separate the light. It didn't happen, and the left gif is what happened, even though the Earth is rotating around the sun at ~30km/s, or around the galaxy at ~600km/s. – Eric Duminil May 28 '23 at 18:03
  • If the move is along the horizontal axis, then it's the red photon which would "theoretically" make a longer path and thus arrive after the blue one. Which tool did you use to make such animations? – dan May 28 '23 at 18:08
  • @dan : In wrong theory, if the mirror moved at the same speed as the blue photon, the photon would never reach the mirror, right? Sorry, it was 5 years ago, I don't remember where I found the animation. – Eric Duminil May 28 '23 at 20:15
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No, you can't. If no information can leak through the walls of the box you can only determine your velocity / position / &c with respect to the box.

You can determine if the box is rotating or accelerating, and if it is large enough (or you have good enough instruments) you can determine if it is in a gravitational field.

  • Am I misunderstanding redshift? I assume you're saying if I'm traveling v in one direction, there won't be any measurable redshift along or against that direction? what if v = 0.8c? Thanks – justin Jun 10 '18 at 13:50
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    @justin yes, you are misunderstanding it. EM redshift ist only observable if emmiter and detector have a relative speed to each other (its dufferent from acustical redshift) – lalala Jun 10 '18 at 16:41
  • To bei fair: you ciuld determine absolut rotation (e.g. sagnac experiment) – lalala Jun 10 '18 at 16:42
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  1. there is no absolute velocity compared to the universe as you say. You can only have velocity relative to an object (except in a closed universe as per the comment)

  2. EM waves become redshifted, because when they travel towards us from a far away receding galaxy, they will eventually be traveling through a region of space where there is no matter (between galaxy clusters), and in that region of space, space itself is expanding. When the EM wave travels through expanding space, the wavelength of the wave gets stretched, and the frequency becomes smaller, the wave gets redshifted.

  3. your only option would be (since you don't want to measure your speed compared to the box) to compare your speed relative to the EM waves you are emitting. But the problem with EM waves is exactly that no matter your own speed, if you are emitting EM waves, they will still seem to be traveling with speed c relative to you.

  4. Now you could try to release beacons, then try to use EM waves to measure the distance between beacons and the time elapsed between their release, and divide length with time and get your past speed, and assume you are not accelerating, and so get your constant speed, but that could only work if you were traveling with small speeds and not close to the speed of light. Of course in this case you would not measure your speed relative to the universe but to the actual beacons, and even then you could only tell acceleration and not speed. You could set up the beacons so that you have 0 acceleration and constant velocity. But still you would not know your velocity because there is nothing to measure it relative to. And then there is the case about the problem with time. Your time seems normal to you. But relative to what? You could use photon clocks. But even then, distance and time (you use those to calculate speed) are relative to other places in the universe where there are different gravitational fields.

Árpád Szendrei
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  • Could you clarify how exactly you would "release" beacons and how they would help you measure your speed relative to the universe? This seems flawed. Also, your #1 conceptually is not true in a closed universe. – safesphere Jun 10 '18 at 16:37
  • Dear safesphere, we are living in a infinite universe (or at least not closed) to our best knowledge, but I will edit my answer. To releasing beacons, at slow speeds (not close to c) the EM waves as radio signals can pop back from the beacons and will tell you the distance between them with simple triangle theory (OK not so simple) but it would still work. Now of course, this would not measure your speed compared to the universe, but to the actual beacons. – Árpád Szendrei Jun 10 '18 at 16:45
  • Please see this here: https://physics.stackexchange.com/questions/292206/explanation-on-how-cant-we-really-use-rindler-metric-on-twin-parad-and-that-yo/292226#292226 – Árpád Szendrei Jun 10 '18 at 16:45
  • Please see CR Drost's answer. – Árpád Szendrei Jun 10 '18 at 16:47
  • I see. The beacons would help measuring your acceleration, not speed. So they are irrelevant to this question. – safesphere Jun 10 '18 at 17:06
  • The beacons (at least 2) can be used to measure your speed too. But in this case, it is enough to measure your acceleration to be 0, so your speed constant. Even then, your speed will be measured relative to the beacons, and the beacons are moving too (since you released them while moving with constant speed). But you are right in the part where you say that nonetheless, measuring your speed compared to the universe is still not possible in an infinite universe. – Árpád Szendrei Jun 10 '18 at 17:17
  • A "beacon" can not be used to measure your speed relative to anything but the beacon itself. Suppose you are in a space ship that happens to be coasting (i.e., unaccelerated) past the Solar System at half the speed of light. If stick your arm out the window holding a "beacon" in your hand, and you simply let go of it, then an hour later, or a year later or however long you wish to wait, when you look out the window, the beacon still will be right there, where you can reach your arm out and grab hold of it again. – Solomon Slow Jun 10 '18 at 18:58
  • If you throw the beacon with velocity $\vec{v}$ relative to your non-accelerating ship, then for as long as you are able to observe it and measure its velocity, you will measure its velocity to be $\vec{v}$. The only thing you can learn by observing it is how hard, and in which direction (relative to your ship) you threw it. – Solomon Slow Jun 10 '18 at 19:05
  • Dear James, you are correct, the only thing here that is being measured the acceleration to be 0. So you have a constant velocity. But still you cannot measure your velocity compared to the universe, as you say. Please see this link and CR Drost's answer. The beacons are used to measure in this case 0 acceleration, because as you say, if the beacon is just let go, and stays there forever (moves together with us), and the second beacon does the same, then you have 0 acceleration. – Árpád Szendrei Jun 10 '18 at 22:08
  • https://physics.stackexchange.com/questions/292206/explanation-on-how-cant-we-really-use-rindler-metric-on-twin-parad-and-that-yo/292226#292226 – Árpád Szendrei Jun 10 '18 at 22:08
  • But I will edit my answer. – Árpád Szendrei Jun 10 '18 at 22:15
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No. Assuming you're traveling at a constant speed, your box is an inertial frame of reference. By definition, you cannot determine whether an inertial frame of reference is stationary or moving - let alone the speed of movement. [1]

To my understanding, in most cases red shift occurs because the light source is moving relative to the observer - Doppler effect.[2] Think of your example in terms of Doppler shift of the train horn. For simplicity, let's assume the train is moving at the constant speed. You will notice the change in horn pitch if you're standing on the platform as the train passes you by. The passenger on train, on the other hand, won't hear it. This is because external observer is hearing the sound waves from a different inertial frame of reference. The passenger is, however, in the same inertial frame as the source of sound waves, the horn.

vedran
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