Angular motion in special relativity?

[Endercreeper01]

You know how in Special Relativity then there are things that happen to objects as they approach the speed of light? What would the effects be like when something has angular motion? For example, when something has a velocity close to the speed of light, c, then it's length contracts in the direction of motion. The length l'=l/γ (where γ=(1-v^2/c^2)^(-1/2)). I think it would just be how much it decreases in radius, but is that correct? And also with length contraction, you use the velocity of it relative to something else. The relative velocity that 1 object is relative to another v'=(v1+v2)/(1+(v1v2/c^2)), But what are relative velocities like with angular motion?

[swansont]

Rotational motion is an acceleration, and you have to be careful using SR in an accelerated frame. It was this idea that led Einstein to develop GR and the idea of warped spacetime, because you can't describe the situation with Euclidean space.

[Strange]

This is the "Ehrenfest Paradox" - note that, like all so-called paradoxes in physics, it only appears to be a paradox. A full analysis is pretty complicated and requires taking the properties of real materials into account as well as general relativity.

http://en.wikipedia.org/wiki/Ehrenfest_paradox

[Endercreeper01]

This is the "Ehrenfest Paradox" - note that, like all so-called paradoxes in physics, it only appears to be a paradox. A full analysis is pretty complicated and requires taking the properties of real materials into account as well as general relativity.

http://en.wikipedia.org/wiki/Ehrenfest_paradox

If the circumference contracts, shouldn't that mean the radius should also? Because then if the circumference shrinks, the radius has to.

[Strange]

If the circumference contracts, shouldn't that mean the radius should also? Because then if the circumference shrinks, the radius has to.

 

Quite the reverse. As that Wikipedia page says, "For physically reasonable materials, during the spin-up phase a real disk expands radially due to centrifugal forces."

 

But note that the relationship between the radius and the circumference will no longer be the Euclidean 2π (due to the curvature of spacetime that swansont mentioned).

Edited August 7, 2013 by Strange

[Endercreeper01]

 

Quite the reverse. As that Wikipedia page says, "For physically reasonable materials, during the spin-up phase a real disk expands radially due to centrifugal forces."

 

But note that the relationship between the radius and the circumference will no longer be the Euclidean 2π (due to the curvature of spacetime that swansont mentioned).

when you have a part of a disk with an angle θ that it makes (with a full disk θ=2π), then it would be how much the arc length s would change because the direction is rotational and since the radius would stay the same and s=θr then it also means θ would be changed so there would be θ'=θγ. With a full disk, then it is just like with the partial disk. In this case, them θ=2π, so then mabey it is just that it would become a partial disk and it would be 2π changing instead of r so then that would make it a part of a disk. Is this correct?

[Strange]

I don't fully understand what you are saying however, yes, the circumference (as measured by an observer on the disk) is 2πrγ.

 

I'm not sure what you mean by "become a partial disk". The disk is still a complete disk, but the geometry is no longer Euclidean.

[Endercreeper01]

I don't fully understand what you are saying however, yes, the circumference (as measured by an observer on the disk) is 2πrγ.

 

I'm not sure what you mean by "become a partial disk". The disk is still a complete disk, but the geometry is no longer Euclidean.

i mean that because the circumference changes and the radius does not, this means that the angle θ changes. With a full disk, θ=2π, so the circumfrence, which is the same as the arc length of a full circle, is 2πrγ, but then if r does not change, then θ changes. For a full disk, when v=0, then θ=2π, but when v does not equal 0, then θ=2πγ. This means that part of it gets cut off and the angle it makes is 2πγ.

But we are also forgetting that it depends on relative velocities. What are relative velocities like with angular motion?

[Toffo]

When viewed from the Sun, the Earth looks kind of narrow, because of the orbital motion.

 

Some sunrays miss the Earth, because of the narrowness.

 

Everybody agrees that motion causes the Sun facing side of the Earth to receive less sunlight.

 

And everybody agrees that the Earth moves around the Sun, while the Sun does not move around the Earth.

[Strange]

When viewed from the Sun, the Earth looks kind of narrow, because of the orbital motion.

 

Really?

 

Everybody agrees that motion causes the Sun facing side of the Earth to receive less sunlight.

 

 

Do they?

[Toffo]

 

Really?

 

 

Do they?

Yeah it works roughly as I said.

 

 

 

A static piece of paper in front of a light source blocks 10% of the light.

 

Then we move the same piece of paper around at speed 0.86 c. Now the paper blocks 5 % of the light.

 

Do you disagree?

[Strange]

A static piece of paper in front of a light source blocks 10% of the light.

 

Then we move the same piece of paper around at speed 0.86 c. Now the paper blocks 5 % of the light.

 

Do you disagree?

 

 

Let's just say I don't necessarily agree. It is an interesting problem and I would need to see more detail. For example, if you are talking about orbiting at 0.86c then, as noted above, you cannot simply use length contraction from special relativity.

[Endercreeper01]

 

 

Let's just say I don't necessarily agree. It is an interesting problem and I would need to see more detail. For example, if you are talking about orbiting at 0.86c then, as noted above, you cannot simply use length contraction from special relativity.

actually, this is correct because when you have something orbiting something else with a velocity v, then it is just like with regular length contraction. The length l'=lγ, so if first it blocked 10% and then v=.86c, then γ=1/2, so it is 1/2 the original length and so only 5% is blocked. But the thing with this is that it depends on the relative velocity and so it is relative. Relative to the piece of paper, then the light source is shrinking by that amount, so it blocks 1/2 of the light it did before. To a stationary observer and the light source, then the paper is shrinking and blocking only 5% of the light.

[Toffo]

actually, this is correct because when you have something orbiting something else with a velocity v, then it is just like with regular length contraction. The length l'=lγ, so if first it blocked 10% and then v=.86c, then γ=1/2, so it is 1/2 the original length and so only 5% is blocked.

 

 

Yes. Exactly. And to the quoted text below I say: No. It can not be that way. All observers must agree about the percentage. (Maybe some day I'll learn to use this quote system correctly )

 

But the thing with this is that it depends on the relative velocity and so it is relative. Relative to the piece of paper, then the light source is shrinking by that amount, so it blocks 1/2 of the light it did before. To a stationary observer and the light source, then the paper is shrinking and blocking only 5% of the light.

 

[Endercreeper01]

No. It can not be that way. All observers must agree about the percentage.

No, special relativity is called relative for a reason. In special relativity, then space and time are relative and not absolute, so then not everyone has to agree on the pecentage

[swansont]

No, special relativity is called relative for a reason. In special relativity, then space and time are relative and not absolute, so then not everyone has to agree on the pecentage

Everyone must agree on a result, or that an event occurred, so this depends on what you are measuring. Say, a signal light would go on if a sunlight meter dropped below a certain threshold. You can't have the signal going off in one frame but not in another. The moving earth would length contract (and other effects) but their clocks would also run slow. To an external observer they get less light, but in less time.

[Endercreeper01]

Everyone must agree on a result, or that an event occurred, so this depends on what you are measuring. Say, a signal light would go on if a sunlight meter dropped below a certain threshold. You can't have the signal going off in one frame but not in another. The moving earth would length contract (and other effects) but their clocks would also run slow. To an external observer they get less light, but in less ti

Then it would just be that it blocked 1/2 of the light before, if everyone agreed because to an outside observer, the paper shrinks and to the paper, the light source shrinks by 1/2

[Toffo]

Then it would just be that it blocked 1/2 of the light before, if everyone agreed because to an outside observer, the paper shrinks and to the paper, the light source shrinks by 1/2

 

More important is that to the paper the apparently moving light source apparently sprinkles the the light all around. (but not really)

 

A light source that really moves around, really sprinkles the light all around, which increases the entropy of the light. All observers agree about entropy.

[Endercreeper01]

A light source that really moves around, really sprinkles the light all around, which increases the entropy of the light. All observers agree about entropy.

Yes, but they don't agree on how much the light is blocked.

[Toffo]

Yes, but they don't agree on how much the light is blocked.

Yes they do. If a photon collides with the blocking object, it collides according to everyone.

 

Collisions are absolute.

[Endercreeper01]

Yes they do. If a photon collides with the blocking object, it collides according to everyone.

 

Collisions are absolute.

Yes, but then the object shrinks relative to an outside observer by a factor of gamma and so less light relative to them

[Toffo]

Yes, but then the object shrinks relative to an outside observer by a factor of gamma and so less light relative to them

 

 

A red-hot cube moves left and right. (The cube is cube-shaped when at rest)

 

The motion causes the brightness of the cube surface to decrease. (Time dilation of radiation process)

 

The brightness of the surfaces of the sides of the cube that shrink stay constant though. That's because each square inch will contain an increased number of of atoms, which radiate at decreased rate.

 

Do you guys agree?

[Endercreeper01]

Yes they do. If a photon collides with the blocking object, it collides according to everyone.

 

Collisions are absolute.

But the size of the object changes relative to different observers

[Toffo]

But the size of the object changes relative to different observers

 

 

 

This is a hoop at rest: O

This the same hoop spinning: o

 

The smaller hoop has smaller area, therefore it emits and absorbs less radiation.

 

Is the spin relative or is it absolute? Answer: Absolute.

[Endercreeper01]

 

 

 

This is a hoop at rest: O

This the same hoop spinning: o

 

The smaller hoop has smaller area, therefore it emits and absorbs less radiation.

 

Is the spin relative or is it absolute? Answer: Absolute.

Spin is relative just like velocity is relative