The role of SR in a 2d universe

[tommac]

If I had a simple universe that lived in 2 d, lets say on the surface of a frictionless record player with the table spinning. And all of the objects on the surface of the record were spinning around due to say the spin of a BH in the center. If a 2d spaceship were to travel in the direction against the spin, everything in the universe would be travelling towards the spaceship. Is the velocity of the spaceship limited because the rest of the universe is moving towards it?

[antoniseb]

I'm not sure your analogy of the frictionless record player makes much sense. Why would things that the 2d spaceship had just passed be considered to be moving toward the spaceship, and how is SR coming in to any of this?

[WayneFrancis]

I'm not sure you question is clearly stated. Are you trying to get around the speed limit of c by having the objects within the universe orbit something and adding to your speed. Much like if you drive a car at 60km/hr towards another car driving at you at 60km/hr that you'd crash at 120km/hr? If so then no....just as having 2 ships travelling towards each other each thinking they are travelling at .6c would not have them observe each other approaching each other at faster then the speed of light.

[tommac]

I'm not sure your analogy of the frictionless record player makes much sense. Why would things that the 2d spaceship had just passed be considered to be moving toward the spaceship, and how is SR coming in to any of this?

Well lets say a treadmill ... if everything else is moving toward us ... does that somehow limit our velocity in that direction?

I guess what I am trying to figure out is if one can tell the difference if an observer is moving towards everything else or if everything else is moving towards the observer. Lets say everything is moving at us at near the speed of light from one direction, then wouldnt SR limit my movement towards them to prevent the relative speed between the two of us to be greater than the speed of light?

[NEOWatcher]

At those velocities speed and acceleration IS NOT LINEAR. I believe that has been pointed out to you many times in the past.
No, you cannot tell the difference between who's moving towards whom.

[WayneFrancis]

Oh wait that is maths....

[tommac]

At those velocities speed and acceleration IS NOT LINEAR. I believe that has been pointed out to you many times in the past.
No, you cannot tell the difference between who's moving towards whom.

So if a 2d universe moved like a record baby ... would I be able to travel in the direction of the turn of the record and towards the center easier than I would towards the edge of the record ( where it spins faster ) and against the record?

The reason I am asking all of this is our Universe was rotating what would we expect to see in 3d?

[NEOWatcher]

Since that comment was mine, let me try to stumble through as a non-expert speculation.

Since this analogy infers to me a rotating universe, then the space-time would have to rotate with it to prevent any speed of light issues. There are many problems with this concept that I'll let others comment on before I stick my foot in my mouth. Also; I can't see a 2d rotation applying to a 3d universe because of rotation needing an axis that would be difficult to explain away with the uniform observations in all directions.

So; If the analogy can somehow be made, then my answer would be "no". Direction wouldn't make any difference because you are in a rotating space-time.

[tommac]

then the space-time would have to rotate with it to prevent any speed of light issues.

What do you mean by space-time rotating?

Can space-time rotate without having any mass or energy in it ( other than a lone observer ) ?

[Ken G]

The reason I am asking all of this is our Universe was rotating what would we expect to see in 3d?

That is a tough question. It was held by Mach that if the whole universe was rotating, we would not expect to see anything-- we'd have no way of knowing it rotated. Indeed, that means the entire proposition is nonsensical from a physics standpoint-- in physics there is "no such thing" as a rotating universe, because motion is relative. General relativity attempted to incorporate this property, but it is still debated if it succeeded or not. What is not open to debate is that we see no evidence of universe rotation-- to some, that's because it doesn't rotate, to others, it is an indication of the correctness of Mach's principle.

[Andrew D]

What do you mean by space-time rotating?

Can space-time rotate without having any mass or energy in it ( other than a lone observer ) ?

The coordinates of space-time itself would have to rotate, i.e. the coordinates we assign would have some axis of rotation. However, as we would be embedded in those coordinates, then we would not observe any rotation. For example, if I went out into my garden and started walking circles, I could define a coordinate system in which I was walking in a straight line and the universe was rotating around an axis at the center of my circle. My friend sitting on the ground would observe no such rotation.

Sure, space time can rotate without anything in it. Imagine an observer spinning around in this empty space. Since he is the only thing in it, a claim that it is rotating around him is just as valid as the claim that he is spinning within a static coordinate system.

Now for your original question: The spaceship on the space record player would be limited by the speed of light in its coordinate system. None of the objects flying past an astronaut in the ship would ever move at the speed of light relative to him, regardless of the speed he is moving around the center.

[tommac]

The coordinates of space-time itself would have to rotate.

That was the point sort of ... Wouldnt the coordinates be based on the stars and galaxies that would be rotating?

[tommac]

That is a tough question. It was held by Mach that if the whole universe was rotating, we would not expect to see anything-- we'd have no way of knowing it rotated. Indeed, that means the entire proposition is nonsensical from a physics standpoint-- in physics there is "no such thing" as a rotating universe, because motion is relative. General relativity attempted to incorporate this property, but it is still debated if it succeeded or not. What is not open to debate is that we see no evidence of universe rotation-- to some, that's because it doesn't rotate, to others, it is an indication of the correctness of Mach's principle.

What would be the evidence? Wouldnt there be some peculiarities ( although possibly difficult to measure OR at scales too large for us to comprehend )? Like in the 2 d rotation of the record player ... if I was in a middle song on the record .... would things spin slightly differently if I went to the end of the record than if I went to the center of the record?

To make matters worse ... to get to distant reaches of our "expanding" universe we would need to build in these changes into the observed redshift. So we may need to detect slight variations at very far distances which also have extreme redshifts.

[HenrikOlsen]

The main idea, as I understand it, is that it's impossible to determine if there is global rotation without being able to observe everything, so the question of whether there is net global rotation is scientifically meaningless because it's impossible to answer.

Local rotation of a frame on the other hand is measurable without referring to observations of objects in other frames.

[Andrew D]

That was the point sort of ... Wouldnt the coordinates be based on the stars and galaxies that would be rotating?

You could do that if you wanted, but the stars and galaxies wouldn't be 'rotating', they would be revolving around the axis of rotation. The point though, is that it's trivial: you don't learn anything, you just add a lot of complication to your model without gaining any benefits.

[Ken G]

What would be the evidence? Wouldnt there be some peculiarities ( although possibly difficult to measure OR at scales too large for us to comprehend )?

It would leave a signature on the CMB-- but I can't tell you exactly what without researching it. It's all part of making cosmological models.

[tommac]

It would leave a signature on the CMB-- but I can't tell you exactly what without researching it. It's all part of making cosmological models.

Cool! This discussion definitely helped me out.

[tommac]

Wouldnt it follow that our universe should be revolving and rotating? It seems natural that it would since everything else that we can observe does. Atoms, moons, planets, stars, galaxies, galaxy clusters ...

I have no evidence of it ... nor am I suggesting it on any basis ... but it seems like it would be natural for our universe to either be rotating or revolving around something. I was just curious if there was any mainstream evidence for or against it doing so.

[Strange]

Wouldnt it follow that our universe should be revolving and rotating? It seems natural that it would since everything else that we can observe does. Atoms, moons, planets, stars, galaxies, galaxy clusters ...

Not everything we can observe rotates. Atoms don't, in general. I don't know about galaxy clusters, but I doubt there is a universal rule that they rotate; I imagine the dynamics are much more complex. My TV doesn't. My coffee does after I stir it, but it soon stops. Etc.

[WayneFrancis]

Wouldnt it follow that our universe should be revolving and rotating? It seems natural that it would since everything else that we can observe does. Atoms, moons, planets, stars, galaxies, galaxy clusters ...

I have no evidence of it ... nor am I suggesting it on any basis ... but it seems like it would be natural for our universe to either be rotating or revolving around something. I was just curious if there was any mainstream evidence for or against it doing so.

Someone ask tommac what he means by atoms revolving please. Also point out that moons, planets, stars and galaxies revolve around/with other objects. What does tommac think the universe can be revolving with?

Also point out to tommac all of those objects rotate due to conservation of angular momentum as matter condenses and that there is no sign that the universe is trying to condense down to any point.

[tommac]

Not everything we can observe rotates. Atoms don't, in general. I don't know about galaxy clusters, but I doubt there is a universal rule that they rotate; I imagine the dynamics are much more complex. My TV doesn't. My coffee does after I stir it, but it soon stops. Etc.

Fair enough ....

Galaxy clusters dont rotate or revolve around their center of mass? If not what stops them, the expansion of the universe?

[Strange]

Fair enough ....

Galaxy clusters dont rotate or revolve around their center of mass? If not what stops them, the expansion of the universe?

I just mean that they are in complex orbits around mutual centers of mass. The notion of a cluster rotating implies some fixed rigid structure.

[tommac]

I just mean that they are in complex orbits around mutual centers of mass. The notion of a cluster rotating implies some fixed rigid structure.

OK ... but we can agree that they are rotating around something ( even if it is not a fixed rigid structure )

[Strange]

OK ... but we can agree that they are rotating around something ( even if it is not a fixed rigid structure )

Orbiting, maybe. But that is not the same as rotating. But so what. The point is, not everything in the universe is revolving, rotating or orbiting.

[Andrew D]

... not everything in the universe is revolving, rotating or orbiting.

Are you sure? Examples?

[Agemegos]

The reason I am asking all of this is our Universe was rotating what would we expect to see in 3d?

A centrifugal force and a Coriolis force.

[Agemegos]

I guess what I am trying to figure out is if one can tell the difference if an observer is moving towards everything else or if everything else is moving towards the observer.

Relativity is based on the postulate that there is no way to tell, and that therefore there is no difference.

Lets say everything is moving at us at near the speed of light from one direction, then wouldnt SR limit my movement towards them to prevent the relative speed between the two of us to be greater than the speed of light?

No. Instead it would fool with your clocks, your measurement systems &c. in such a way that their approach speed was still less than c. Remember that you aren't moving in your own frame of reference.

So imagine that you have established a frame of reference that is stationary with respect to yourself (call it O). In this frame of reference, there is an alien ship to your north moving southwards at, say, 60% of c. Now you accelerate northwards at one gee (according to O) for 212 days (according to O). In the frame of reference O you are now moving northwards at 60% of c. According to O you and the alien ship are now closing on one another at 120% of c, but that's okay because both of you are moving slower than c.

But you disagree with O. According to you your acceleration was not a steady 1 gee, the elapsed time was not 212 days, and the alien ship is closing on you at only 88% of c. If you establish your new frame of reference O' you will discover that the reason for the discrepancy is that O is set up wrongly. Its distances are all too short in the north-south direction, its clocks are all running slow, and its clocks are systematically set wrong. It is because of these errors that it says that the alien ship is moving at 60% of c.

[tommac]

Thank you!

Relativity is based on the postulate that there is no way to tell, and that therefore there is no difference.



No. Instead it would fool with your clocks, your measurement systems &c. in such a way that their approach speed was still less than c. Remember that you aren't moving in your own frame of reference.

So imagine that you have established a frame of reference that is stationary with respect to yourself (call it O). In this frame of reference, there is an alien ship to your north moving southwards at, say, 60% of c. Now you accelerate northwards at one gee (according to O) for 212 days (according to O). In the frame of reference O you are now moving northwards at 60% of c. According to O you and the alien ship are now closing on one another at 120% of c, but that's okay because both of you are moving slower than c.

But you disagree with O. According to you your acceleration was not a steady 1 gee, the elapsed time was not 212 days, and the alien ship is closing on you at only 88% of c. If you establish your new frame of reference O' you will discover that the reason for the discrepancy is that O is set up wrongly. Its distances are all too short in the north-south direction, its clocks are all running slow, and its clocks are systematically set wrong. It is because of these errors that it says that the alien ship is moving at 60% of c.

[grapes]

Not everything we can observe rotates. Atoms don't, in general. I don't know about galaxy clusters, but I doubt there is a universal rule that they rotate; I imagine the dynamics are much more complex. My TV doesn't.

If your TV is fixed to the earth, wouldn't it rotate as often as the earth rotates?

[Strange]

If your TV is fixed to the earth, wouldn't it rotate as often as the earth rotates?

Relatively speaking, maybe.