Hypothetical question: I wake up to find myself on a spaceship. There is no one else. The ship is silent and the engines are dead.
As far as I can see through the porthole, there is nothing to see. I rig up a photon detector and a gravitational wave detector (dont ask me how). They both report no hits at all. There is no light, no interstellar medium, no gravitating bodies (within limits of detection, at least).
This is a depressing situation, but the scientist in me is morbidly curious to know just one thing: am I moving or stationary w.r.t the space I am suspended in? Can I answer this question without an external frame of reference?
If I am moving, I must have momentum and kinetic energy. Can I measure these - without reference to any external frame of reference - and thereby conclude I am in motion (or not), with a particular speed? (Crudely, what I am asking is, is it possible to rig up a device that tells me you have this many joules of kinetic energy, so you must be moving at 98% the speed of light?)
What else could I do to answer my question conclusively? Technology is no constraint. The nanobots are be able to rig up cool devices and sensors on demand.
Relies to the effect of “this is the dumbest question ever” will gracefully accepted (and ignored). Thanks!
You could detect acceleration is some crude way but I’m pretty sure if your just talking about movement you have to ask if you’re moving with respect to some other object, I mean the frames of reference are all relative, no?
As HMHW pointed out, all (linear) motion is relative, and that the laws of physics behave the same way as long as you aren’t under acceleration. An implication is that there is no absolute notion of momentum or kinetic energy. In one reference frame you’re motionless, with zero kinetic energy, while in a frame (even just an imaginary one) moving at 99% of the speed of light, you have massive kinetic energy. Each observer sees the same behavior even though they disagree on the amount of energy in the universe.
Since you have a portholes, theoretically, you could measure your motion relative to the cosmic background radiation (by observing different temperatures for the background in different directions). This is cheating, of course, since you said you wanted a method that didn’t rely on an external reference - but I wanted to point out that even though you can’t see anything macroscopic out the porthole, the cosmic background radiation is still there.
I thought so, but as it turns out, I was probably wrong. The explanations surpass my understanding, but I believe the predominant interpretation is that if there is only one object in the universe, it by definition isn’t rotating. There will be no (apparent) centrifugal forces at the skin.
If you fire rockets to make it rotate, then it’s no longer a single object in the universe, and the rotation will be with respect to the exhaust of the retros. If you spin a mass inside, causing the rest to rotate the opposite way, no doubt you’ll get the same kind of effect.
Hopefully, someone like Chronos or Astymptotically Fat who actually has a clue what they’re talking about will be by to clarify.
[ol]
[li]There are some reference frames that can, using only local measurements of inertial forces, be determined to be non-rotating.[/li][li]In those reference frames, the distant bodies in the universe are non-rotating.[/li][/ol]
Are connected somehow, because the local inertial frames are somehow being determined by the bulk behaviour of distant matter through some physical law. I.e. if we magically caused all the distant galaxies to start spinning around us, we would start to feel centrifugal forces here.
My understanding is that in advanced GR there are some hints that this is true (e.g. frame dragging) but it is undetermined whether GR actually implies Mach’s Principle.
I deeply resent the idea that I know what I’m talking about!
As leachim says this is Mach’s principle. It has the status of being an idea that a lot physicists really like, but there aren’t really any theories worth talking about that are truly 100% Machian (i.e. all inertial effects are due to interactions between matter). Despite the fact that Einstein obviously held Mach’s principle in high esteem, general relativity is not Machian. Whether an observer feels inertial forces in relativity is related to geodesics which are defined locally. I.e. you don’t need to look at the whole of space to decide which inertial forces someone feels in GR.
I had assumed he and his ship weren’t the only thing in the universe, just that he couldn’t detect anything else. I had briefly considered that if he were inside a cavity in a large spinning mass, that frame dragging could give a false* reading of his spin. But then, Andy L’s CMB measurement would fail as well, so at least I’m not alone.
false relative to far away from the spinning mass. I’ll let pedants argue whether the “true” non-spinning frame is with or without compensating for the frame dragging effect.
This invites one of the simplest possible physical experiments: put a piece of trash out the airlock. Now there are two objects in the universe. If the piece of trash moves away from the ship…the ship must have been rotating.
I was told, way back in college, that the full Relativistic equations describing a cosmos have only been solved for certain simplified “universes.” One was the universe containing only one object (a point mass.) Another was a cosmos completely filled with a “fog” of matter, spread out perfectly smoothly (i.e., infinitely divisible – not even protons, just pure abstract infinitesimal matter.)
Is this still true? (Was it true back then?) With better computers and better math in general, have more of these relativistic universe-equations been solved?
The metric which describes the geometry of spacetime is fundamentally smooth (infinitely differentiable) and as there is a strict link between the distribution of matter in spacetime and it’s geometry any matter in the spacetime must be described using the continuum approximation and it’s distribution can’t be discontinuous or have any other features which would lead the metric not to be smooth. This means for example general relativity can’t describe the boundary between the matter contained in a star and the vacuum surrounding it (though in practice there are techniques for matching interior fluid solutions with exterior vacuum solutions, but this has to be done ‘by hand’ and there are certain pitfalls involved)
A seeming counter example (though not necessarily the only apparent counterexample of this type) to this would be vacuum solutions (solutions devoid of matter) which describe black holes where there seems to exist a singularity in the equations describing a point in space where all the matter is contained. However the singularity, mathematical speaking, is not a point or set of points on the spacetime manifold.
One could argue that Mach’s principle isn’t even properly a question of science, since there is no way, even in principle, to conduct the experiment. Personally, I think that it adds nothing but unneeded complication, and so ought to be ignored.
Thanks for all the responses so far. A couple of clarifications about my OP:
My ship is NOT the only object in the Universe - I am just stranded in a emptier-than-average region of intergalactic space.
Will I be able to measure CMB temperature fluctuations while travelling at a trivial fraction of light-speed, such as say 50 mps? Can I accurately calculate motion vectors with this information? (Assume the measurement itself is not a problem with the tools I have.)
The question was not meant to explore GR/SR, but as a practical problem that may arise during space travel. I need to fire my side-thrusters to turn around, and for that I need to know how fast I am moving in a given direction, so I will not be smashed to a pulp on the hull.
If this helps: suppose I see a star or galaxy millions of light-years away, can I use this object to measure my own velocity vectors? The reference frame I need to use is an imaginary point ‘pinned’ to the surface of the fabric of space I am suspended in.
In principle, maybe, but our current best estimate has an error bar of +/- 900 meters/second. Without gaps in your CMB measurement (since you’re not in the middle of a galaxy), it’s possible your error bars would be smaller, but I would think not by much.
You could look at the star’s spectrum, and get your radial component of velocity relative to that. That’s only one of three velocity components, and you wouldn’t know the star’s motion relative to the CMB. ETA: I should add that the frame of reference at rest relative to the CMB is really the only way you have of defining “the surface of the fabric of space I am suspended in”. Other than that, you could use any inertial frame you want. They’d all be just as good.
What makes you think that will be a problem? If you are using your maneuvering thrusters to change the direction your ship is facing, the forces you experience during the process will be the same no matter how fast you are traveling relative to some arbitrary reference frame.
I think this shows that you still aren’t really getting the point. There is no stationary reference frame that can be pinned to the fabric of space. According to relativity, all reference frames are equal, there’s no one point that you can call stationary. This is not a matter of measurement, it’s a matter of how the universe works. You can call a distant star or galaxy stationary, or measure you apparent movement relative to the cosmic background radiation, but these are still just arbitrary reference frameworks of convenience.
Not sure, but IIRC GENERAL relativity fails when the frame of reference is accelerating. Rotation is acceleration, so general relativity assertions should fail at this point; you cannot assert that there is no “centrifugal force” detectable. Unless the roating frame is incredibly large, you can detect the coriolis “force” of rotation.
Yes, the speed of light is the same in every direction no matter how you measure it. This is the mathematical basis on which GR’s time dilation and relative directional shrinking happen, depending on frame of reference.
You are only moving wrt other objects.
Measuring kinetic energy would be relative to some other frame of reference. I.e. the entire world is rotating, going around the sun, and in motion with respect to local neighbourhood, spiral arm of the galaxy, and flying away from he Big Bang… but when I bump into you, we do not disintegrate in a burst of energy, because relative to each other we are not travelling more than a few feet per second.
OTOH, if I smack into an incoming meteor in Siberia, things will be different because relative motion is much much higher. So the only valid way to determine kinetic energy is relative motion compared to some other object. Different comparison object, different speeds, different kinetic energy.
It’s only kinetic energy because somehow, some way, you and the other object obtained your relative motion by the expenditure of energy by you or the other object.
General relativity works fine with acceleration (including rotating coordinate systems). It’s special relativity that can’t handle it. The treatment of acceleration is really the core principle behind GR; that gravity is exactly the same kind of force as centrifugal or Coriolis forces (i.e., in a curved coordinate system, objects will appear to be subject to accelerating forces).
