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If a rocket in space fires its thrusters, it is propelled forwards as per the laws of motion. This can be measured by its position relative to other bodies in the universe.

Hypothetically if there was a universe that was completely empty except for the rocket and it then fired its thrusters, surely the same forces would apply (even if its movement could not be measured). Just because we can’t measure an event, is that the same thing as saying that it never happened? Is it correct to say that the rocket didn’t move?

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    $\begingroup$ "Rocket" might not be a good choice in your question. You want to ask about absolute velocity, while rocket leaves gas (exhaust) behind, and people will be quick to point out you can use those as reference frames. Try to come up with something that moves without creating new objects. $\endgroup$ – Double Vision Stout Fat Heavy Jun 10 at 3:00
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    $\begingroup$ @DoubleVisionStoutFatHeavy I believe you'll have some trouble coming up with an example. $\endgroup$ – knzhou Jun 11 at 8:27
  • $\begingroup$ @knzhou : A windowless elevator attached to a long cable that is accelerated in the usual way. This is not a new thought experiment. $\endgroup$ – Eric Towers Jun 11 at 21:50

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Within the context of Newtonian mechanics, there's a simple answer: velocities are not absolute, but differences in velocities are. So you can state that acceleration occurs unambiguously.

In special relativity, this is a bit more complicated because of relativistic velocity addition, but all observers can unambiguously compute a "proper" acceleration for every object, which is the acceleration in that object's momentary rest frame.

In fact, the same logic still works in general relativity; acceleration is unambiguous even in a universe without matter. However, in certain philosophical stances inspired by general relativity, the question is trickier because one might take a hardline Machian position, where motion should only be defined in relation to other matter. But in this case you can still answer the question because there is motion relative to the exhaust.

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    $\begingroup$ This, I think, is the best way to think about it. Relative velocity is what to focus on. $\endgroup$ – CCTO Jun 10 at 13:42
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    $\begingroup$ It's also important that even in general relativity, acceleration is absolute (if you define it correctly). See also physics.stackexchange.com/questions/173 $\endgroup$ – WorldSEnder Jun 10 at 20:04
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    $\begingroup$ This should be the accepted answer. $\endgroup$ – gented Jun 11 at 8:26
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    $\begingroup$ I'd be careful of motion relative to exhaust; you can build a photon drive that only uses light, and the light remains traveling at c regardless of how "fast" you are going, and the photons (with nothing to interact with) instantly leave your light cone once they leave the body of the space ship. $\endgroup$ – Yakk Jun 11 at 15:52
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    $\begingroup$ @Azzinoth You are completely right, I edited. $\endgroup$ – knzhou Jun 24 at 13:11
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A rocket's thrusters function by ejecting reaction mass (exhaust). You can measure the movement of the rocket by its distance from its reaction mass. The rocket moves relative to its reactant.

You can say the rocket didn't move, but not because it can't be measured. The center of mass of a rocket-reactant system* never goes anywhere—not even in our universe**—because the force of the rocket on its reactant is equal and opposite to the force of the reactant on the rocket. In this sense, the rocket-reactant system's center of mass is unaffected by the thrusters because the thrusters are internal to the system in question.

* Edited for clarity.

** Unless acted upon by an outside force.

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    $\begingroup$ What are you talking about? Of course the rockets center of mass will move. The particles it exhausts need not be of comparable weight to the rocket. As a counter example, consider an air filled rocket that propels itself by a pressure difference between the outside, and the air within the container. Once the pressure difference has been equalized, the rocket toy will not weigh significantly less, but it will have moved a great distance. $\endgroup$ – user400188 Jun 10 at 0:53
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    $\begingroup$ @user400188 Conservation of linear momentum. Nothing can change the center of mass of a system without an outside force. $\endgroup$ – Draconis Jun 10 at 3:08
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    $\begingroup$ @Draconis thank you for reminding me. Sorry for the mistake Isusr $\endgroup$ – user400188 Jun 10 at 4:09
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    $\begingroup$ I downvoted because this answer fails to distinguish between the rocket (a largely solid entity that gets into orbit) and the exhaust gas (other stuff which is left behind as the rocket accelerates). If you use the word 'rocket' to mean 'solid thing plus all the stuff it ejected' then you can say its centre of mass didn't move, but this is mere word-trickery. Redefining words away from their natural meaning should be announced up-front and justified. Otherwise it merely encourages confusion and meaningless debate. $\endgroup$ – Andrew Steane Jun 10 at 10:28
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    $\begingroup$ @JohnDvorak, the OP asked explicitly in a completely empty space. No earth, no other planets or stars. $\endgroup$ – Mayou36 Jun 10 at 19:17
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how can we say a rocket accelerates in empty space ?

According to third Newton law, body in a rocket will experience pseudo-force with direction opposite to that of rocket acceleration. That is - rocket acceleration will induce body weight which can be observed / measured : enter image description here

It's much like water "feels" centrifugal force. What you actually will not be able to distinguish is that if rocket flies with acceleration OR if it has already landed at some planet given that astronauts were sleeping in a journey and no windows to see planet surface and rocket's dashboard is broken showing false acceleration. It is a direct conclusion of Equivalence principle.

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Acceleration and relative velocities

An absolute velocity can not be measured, that's correct. But an absolute acceleration can. E.g. with a simple scale.

Measuring the acceleration, you can know your velocity. This is a system that is e.g. already since long time used in airplanes known as inertial navigation system.

There is the other part, the relative velocity, as already mentioned in other answers: while the absolute velocity is not measurable, differences are. And in this case the difference to the exhaust of the rocket can be measured.

Relative velocities are the only ones that actually matter.

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  • $\begingroup$ Distance to emitted photons cannot be measured. So with a photon drive does your answer change? $\endgroup$ – Yakk Jun 11 at 16:06
  • $\begingroup$ Why not? I know the position of a star and can measure it's photons. Since I am here and the star is there, I know the distance. If you refer to "cannot be measured by the emitter only without any additional tools (like photon detectors placed somewhere away", then I agree. Sure, it's not just velocity in the case of a photon, you take it's wavelength and energy conservation. $\endgroup$ – Mayou36 Jun 11 at 21:17
  • $\begingroup$ there is nothing else in the universe. I guess you could drop a mirror and fire photons at it. $\endgroup$ – Yakk Jun 11 at 22:36
  • $\begingroup$ @Yakk yes, but then again a mirror is another object. So I would leave it as: in principle the relative exhaust velocity can even be measured with a photon drive. Practically, to be slightly picky, if there is nothing else in the universe, neither the photons nor any other exhaust can be measured (you won't even see it, there is no light). Measurement equipment allowed -> relative distances works. No "external" equipment -> acceleration only measurable (inside rocket a scale is available I guess). Do you agree? $\endgroup$ – Mayou36 Jun 12 at 8:28
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If we set up the universe using Newton's mechanics, we can get a (mostly useless) definition of absolute velocity from the big bang itself. If momentum is conserved while energy is not (which it cannot be), absolute velocity is defined from the big bang's initial reference frame.

We can do the same in general relativity for some sets of initial conditions but not others, but there is no simple proof for this because conservation of momentum and conservation of energy are linked in general relativity. In all of the ones for which this works, the absolute velocity is equivalent to the velocity of the cosmic background radiation.

Rockets accelerate by pushing mass out the back. The weak forces resulting from CMB interaction are negligible for any reasonable rocket, therefore if fired in deep space, the reasonable reference frame is the initial frame of the rocket, and there is no change to position of the center of mass of rocket + exhaust. As we should expect from this, engine efficiency is exponential with engine exhaust velocity.

So, the effective answer to your question is "we don't care". The laws of physics from the time of Newton never really cared what the effective frame is. If you take the laws of physics and take the limit* as $c$ goes to infinity, Newton's mechanics drop out again.

*Yes I know taking the limit of a constant makes no mathematical sense. What we're looking for is reintroducing Newton's assumption that the speed of light is too large to matter for anything else.

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    $\begingroup$ I don't see a big bang in the OP's described universe? $\endgroup$ – Yakk Jun 11 at 17:03
  • $\begingroup$ @Yakk: I also do not see anything in it to make Noether's theorem on momentum not apply. $\endgroup$ – Joshua Jun 12 at 0:13
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if it is a universe with the same dimensions and physical laws as our own, then the rocket would move per action and reaction, whether or not there was any other mass or energy in the universe. Then the rocket would be moving away from the gasses it expelled.

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from whatever i have read this is a fundamental open q. properties of space and time are not known in an "empty" universe and hence concept of motion is not clearly understood. you might want to read about spinning water bucket thought experiment

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I will firstly answer in the context of relativity. The proper acceleration, meaning the acceleration as measured in the reference frame of the rocket, which is related to the "force" felt by the rocket, is independent of its velocity (relative to any other observer). However the rocket's acceleration as measured in other reference frames does depend on the relative velocity: $\vec a' = \vec a/\gamma^3$, where $\gamma := (1-(v/c)^2)^{-1/2}$ is the Lorentz factor. Hence other frames measure a lower acceleration for the rocket. The "$\vec a$" terms are accelerations in space (3-accelerations) to be precise; also this simple formula applies only when the relative velocity lines up with the acceleration direction (again, I mean in space only). Tsamplaris 2010 is a nice reference, see $\S7.2$.

To take a very different perspective, from philosophy of physics and Newtonian gravity, you can actually define or interpret "acceleration" as relative if you really want to. (I mention this as a curiosity only, and if the reader is pragmatic or prefers a simple answer then ignore this and just say "acceleration is absolute".) John Norton, in a 1995 article subtitled "Acceleration is relative", writes

Relativity of Acceleration

The decomposition of gravitational free fall into an inertial trajectory and a gravitational deflection is conventional; we are free to divide free fall motion into any combination of inertial motion and gravitational deflection we please, as long as the latter corresponds to a gravitational potential satisfying Poisson's equation.

Presumably this could be extended to the rocket example here.

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The instant your rocket begins to accelerate, the space it’s in is no longer “empty except for the rocket”. Because you now also have the rocket’s reaction mass, and that gives you something else against which its movement can be measured.

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You got "movement" and "acceleration" mixed up.

"Movement" (in free-fall), i.e. velocity, cannot be measured without outside references. Movement is always in relation to something else.

But acceleration, i.e. the changing of velocity, can readily be measured without outside references.

So you can't tell whether a rocket is moving or not if you have no reference, but you can very easily measure if it is accelerating, by how much, and in which direction.

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  • $\begingroup$ Movement in free-fall is acceleration, not velocity, because free-fall generally refers to falling under the influence of gravity in the absence of other forces. In the absence of other forces, you cannot measure this acceleration without outside references. It might be worth clarifying that measuring acceleration doesn't really work if it's due to gravity. $\endgroup$ – JMac Jun 12 at 11:17
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Without an Ether, there can be no absolute velocity.

That's the gist of it. It's for this reason that Einstein stated, "space without ether is unthinkable".

Unfortunately, he was voted down by his peers as this went against everything he said in his theory of spacial relativity. Einstein realized his mistake, but by then, his theory had taken on a life of its own.

OH yeah, back to the question. Tie a Lazer pointer to a light fitting, pointing straight down. Mark the spot. If the dot moves, you're accelerating in the opposite direction.

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    $\begingroup$ "Without an Ether, there can be no absolute velocity." Nope! Correct statement: without an Ether we cannot observe the definition of absolute velocity experimentally. $\endgroup$ – Joshua Jun 9 at 18:40
  • $\begingroup$ @Joshua we can never observe it. Observations are always subjective. All motion is relative for a subjective observer. $\endgroup$ – zane scheepers Jun 9 at 19:14
  • $\begingroup$ Two words: CMB frame. Whether we can find the absolute frame by a sufficient degree of cunning, and whether the laws of physics care are two different questions. $\endgroup$ – Joshua Jun 9 at 19:16
  • $\begingroup$ Technically, that's 4 words. Secondly, how would you know if the entire universe, including the CBM background, isn't moving uniformly through space? $\endgroup$ – zane scheepers Jun 9 at 19:22
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    $\begingroup$ Here's the full text. As far as I can tell, what Einstein's calling the "gravitational ether" there is what we would call the "spacetime metric" now. $\endgroup$ – Michael Seifert Jun 10 at 14:33

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