Doesn't rotation cause a problem in relativity?

Question

Imagine you are in a closed rotating spaceship. You could tell exactly how fast you are rotating, and by deduction from the ship dimensions and forces, you could tell your absolute velocity. Or have I missed something?

By the way it's spinning fast enough that you are pinned to the wall and you can measure the force as you spin round.

It's the rotation that I'm vexed by. Why should you be able to tell you are rotating, but you obviously can as you are pinned to the wall?

Dr Spocks answer is truly very interesting and explains something I could never fathom about the laser gyroscopes that are used in aircraft. To the other responders, I must say I used the term 'absolute velocity' to describe an idea I knew did not fit with relativity. So why local inertial space should appear to be fixed in orientation? But that's another question!

Answer 1

The answer is NO! And, perhaps astonishingly, local "absolute rotation" can be measured and used for practical purposes.

This is not only an interesting question, the point you raise is in fact the basis of, yes, being able to tell whether you're in a space ship rotating with respect to local inertia space!

You didn't actually specify, originally, how "you could tell exactly how fast you are rotating." But let me tell you how it's done in practice (if with a certain amount of idealization), without needing to look outside the spacecraft! [Added later: What's more, with modern laser technology, this works for astonishingly small amounts of rotation, far less than would "pin you against the wall," or that indeed could be measured by mere mechanical or dynamical means.]

Imagine a series of little mirrors stuck onto the inside of a circular spaceship These form a circular reflecting track around which beams of laser light can be sent at a shallow angle to each mirror.

Initially, the spaceship isn't rotating with respect to inertial space. Two laser beams sent around this reflecting track in opposite directions will come back to the initial point at the same time, and with the same frequencies that they started out with.

Now imagine that the spaceship rotates around an axis perpendicular to this circular track. Now, when the two beams are sent in opposite directions, one beam encounters mirrors with a component of rotational speed toward it. So in their own rest frame, these mirrors receive, and then reflect onward, slightly blue-shifted radiation! This keeps happening for every successive reflection, resulting in a NET BLUE-SHIFT by the time it gets back to its "starting point." ALSO, since its "starting point" is in fact coming toward it at the end, having been "moving forward to it circularly" all along, THIS beam is received EARLY by comparison with that in the stationary situation.

Conversely, the beam sent in the other direction is always encountering receding mirrors; its radiation is RED-SHIFTED and arrives LATE at the moving "starting point."

A definite prediction can be made for each of these two observable consequences of "absolute rotation" (frequency shifts and time separations, after returning to their "starting point" as far as the ship is concerned). These TWO independently measurable effects act as a valuable check on each other.

I first encountered this idea in a somewhat obscure review article that mentioned "X's suggestion for determining absolute rotation" some decades earlier. Casual though the reference was, the mention was enough to enable me to see the basic idea behind it. It blew me away, and I excitedly discussed it shortly afterwards in a corridor with a grad. student who I knew would be equally intrigued by the idea. As we were talking about it, a know-it-all physicist who is always making pompous pronouncements passed by, snorting that what we were discussing was "absolutely imposible because it violates the basic assumption of special relativity --- you simply can't measure an absolute velocity." (He was, in fact, confusing linear with rotational velocity, as I'm afraid you did in your own statement of the "problem.")

BUT IT DOESN'T --- one ISN'T finding one's "velocity with respect to absolute space." One IS finding out that one is ROTATING with respect to local inertial space, AND THAT IS FINE AND ALLOWED. Indeed, even Newton knew that "non-rotating frames" were in some sense "preferred", as the free motion of particles appear to be perfectly straight lines only in a NON-ROTATING FRAME.

Some time after the above encounter, I came upon an article describing how devices based on the above physical realization of the older suggestion now help ensure that things like GPS satellites are not rotating (which would throw the system off). They are an essential part of that technology! You can imagine with what pleasure I dumped a copy of that article on the know-it-all's desk.

(The person concerned thinks of himself as one of the world's if not THE top world's top expert on certain matters of relativity and cosmology, etc. I find it very amusing that he has not the slightest intuition about unconventional but basically simple applications of relative motion like this.)

Live long and prosper.

POSTSCRIPTS:

1. To emphasize the point I've now also put in square brackets near the start, this is currently the most accurate way we have, technologically, of measuring the MINUTEST degree of absolute rotation. It's far more sensitive than anything based on dynamical effects like "centrifugal" or "Coriolis forces."

2. My account above addresses a number of points that puzzle some of the other responders.

Answer 2

No the center of gravity is in the spaceship and there is no relative motion. Compare to a plane trip. When you take off the gravity force is still between the ground surface and the plane seat, therefore you have a point of refence. When the plane in in full flight but not accelorating you feel no force on your seat and can easily walk around. This applies more so in space due to less outside gravity affecting the ship then in an airpplane.

Answer 3

"absolute velocity"? what is that..in any case
if you're inside the spaceship,
you're going the same velocity as the spaceship, otherwise
you'd be quickly thru the side of the spaceship.

You can detect the forces due to changes in velocity, i.e.
the rotation. But then you'll just know about the rotation.
Not about the issue of you moving at 25,000 mph into
the center of the sun :)

Answer 4

If you are in a CLOSED rotating spaceship, what evidence do you have of your rotation?

For example, imagine you are in a room with no windows. What evidence do you have that the earth is rotating?

Now imagine that the the earths gravity is greatly increased. You will be pinned to the floor, on the inside of the earths rotation .

You have no evidence of rotation and there for can not calculate velocity.

Answer 5

everyday relativity ties area with time as a around imaginary volume called manifold. everyday Relativity field equation tutor the make up of Newton Gravity consistent for susceptible fields. whether; the sphere Equation of everyday relativity ,basically will possibly not rather carry in terms of an electrostatic gravity consistent for the solid fields interior the atomic factors. that are micro systems. possibly Newton Gravity consistent could basically prepare to the macro international yet is a distinctive fee interior the micro Quantum international. Einstein did attempt to discover a relationship that would tie the micro to the macro as a function of a greater everyday field Equation,whether, his outcomes have been inconclusive. Why a spiral galaxy has palms shifting outward on the same time as the regulations of Gravity could reason it to spiral inwardly could have some thing to do with preserving gravitational equilibrium,

Answer 6

no problem. and no. you could tell nothing of your orientation if you are not able to observe (or be observed by) another who is oriented otherwise. if that is your question. your misunderstanding may have something to do with your belief in an absolute velociity. there is no such concept to relativity.

Answer 7

Ahh but can you tell how much your rotation is pulling the universe around with you?

Answer 8

You are accelerating. Spinning like you describe is acceleration. Hence you can feel the force.