Rotation and gravitational potential in relativity.

[koti]

A ball (frame1) with a rest mass of 1kg moving at some significant fraction of c, accelerating further at 1m/s without friction relative to a frame2. It's relativistic mass (or energy) would be some value which is larger than that of a stationary steel ball relative to frame2... its rest mass would be still 1kg regardless of relative motion and/or acceleration so its gravitational potential would be also the same regardless of relative motion and/or acceleration.

What happens to the gravitational potential of the ball if we add rotation to it? Does the gravitational potential change? And if yes, should the rest mass change? (That would seem odd)

[swansont]

3 hours ago, koti said:

 What happens to the gravitational potential of the ball if we add rotation to it? Does the gravitational potential change? And if yes, should the rest mass change? (That would seem odd)

Rotation changes the mass. A spinning sphere is more massive than a stationary one. It's only the linear motion, center-of-mass KE that does not get incorporated. That is accounted for separately in the relativistic equation E² = p²c² + m²c⁴

Put another way, spin doesn't go away when you transform into or out of the rest frame. It is not relative.

 

[koti]

12 minutes ago, swansont said:

Rotation changes the mass. A spinning sphere is more massive than a stationary one. It's only the linear motion, center-of-mass KE that does not get incorporated. That is accounted for separately in the relativistic equation E² = p²c² + m²c⁴

Put another way, spin doesn't go away when you transform into or out of the rest frame. It is not relative.

 

So the ball spin would add up to the overall mass/energy of the system, that is clear. Will the ball’s gravitational potencial be increasing as well? I guess what I mean is will relativistic mass or rest mass change? I know its not a good idea to use these terms but Im too dull to phrase it better.

[J.C.MacSwell]

3 hours ago, koti said:

So the ball spin would add up to the overall mass/energy of the system, that is clear. Will the ball’s gravitational potencial be increasing as well? I guess what I mean is will relativistic mass or rest mass change? I know its not a good idea to use these terms but Im too dull to phrase it better.

The gravitational potential will increase due to the spin, as will the rest mass of the ball/system.

The rest mass and relativistic mass will increase due to the sum of the increased relativistic masses of it's parts. In it's rest frame the rest mass and relativistic mass is the same thing though.

[swansont]

7 hours ago, koti said:

So the ball spin would add up to the overall mass/energy of the system, that is clear. Will the ball’s gravitational potencial be increasing as well? I guess what I mean is will relativistic mass or rest mass change? I know its not a good idea to use these terms but Im too dull to phrase it better.

There is no distinction in this case. Rotation is internal to the system.

[koti]

4 hours ago, J.C.MacSwell said:

The gravitational potential will increase due to the spin, as will the rest mass of the ball/system.

The rest mass and relativistic mass will increase due to the sum of the increased relativistic masses of it's parts. In it's rest frame the rest mass and relativistic mass is the same thing though.

This is clear, thank you. 

14 minutes ago, swansont said:

There is no distinction in this case. Rotation is internal to the system.

This is the core of my question, I wish I phrased my initial post better. Why is there no distinction in this case? The rest mass doesn’t change for the ball whatever its velocity but when its start spinning, its gravitational potential starts increasing. Why is gravitational potential „distinguishing” between ball velocity and spin?

[swansont]

32 minutes ago, koti said:

This is the core of my question, I wish I phrased my initial post better. Why is there no distinction in this case? The rest mass doesn’t change for the ball whatever its velocity but when its start spinning, its gravitational potential starts increasing. Why is gravitational potential „distinguishing” between ball velocity and spin?

Translational motion can't affect the physics. One of the postulates of relativity. You can't transform into a frame where the ball isn't spinning, but you can transform into a frame where it's at rest. So you have a term that accounts for the energy of the relative motion. E^2 = p^2c^2 + m^2c^4

[koti]

On 16.03.2018 at 9:54 PM, swansont said:

Translational motion can't affect the physics. One of the postulates of relativity. You can't transform into a frame where the ball isn't spinning, but you can transform into a frame where it's at rest. So you have a term that accounts for the energy of the relative motion. E^2 = p^2c^2 + m^2c^4

So if we draw an arrow on the ball and it will be showing the same direction while the ball is given a motion, the physics do not change while if the arrow starts to show different direction/s then consequences. Do I have that right? 

Edit: If what I wrote is correct which it looks like it is, I guess I should have posted in classical physics instead of relativity. 

Edited March 17, 2018 by koti

[Bender]

Does the linear motion not change its gravitational potential? I would think the gravitational potential is just different in different reference frames, like the kinetic energy is different. 

[koti]

25 minutes ago, Bender said:

Does the linear motion not change its gravitational potential? I would think the gravitational potential is just different in different reference frames, like the kinetic energy is different. 

I think its like I wrote in my previous post, that if we draw an arrow on the ball and put the ball in any motion that does not change the direction of that painted arrow - the gravitational potential for that frame stays at the value of its rest mass (stays the same) If we put the ball in a motion that would change the direction of the arrow drawn on the ball - its gravitational potential will change.

If not I have to go back to my mental drawing board. 

[swansont]

1 hour ago, koti said:

So if we draw an arrow on the ball and it will be showing the same direction while the ball is given a motion, the physics do not change while if the arrow starts to show different direction/s then consequences. Do I have that right? 

Edit: If what I wrote is correct which it looks like it is, I guess I should have posted in classical physics instead of relativity. 

If I'm understanding you correctly, right. Rotating frames are not inertial.

[koti]

10 minutes ago, swansont said:

If I'm understanding you correctly, right. Rotating frames are not inertial.

Yes, my description is crude but I get it now. Your statement that „Translational motion cannot affect the physics” ticked me to understand.

I have a „why” at the tip of my tongue but I’m beginig to realize that it would be a null question.

Edited March 17, 2018 by koti

[Bender]

7 hours ago, koti said:

I think its like I wrote in my previous post, that if we draw an arrow on the ball and put the ball in any motion that does not change the direction of that painted arrow - the gravitational potential for that frame stays at the value of its rest mass (stays the same) If we put the ball in a motion that would change the direction of the arrow drawn on the ball - its gravitational potential will change.

If not I have to go back to my mental drawing board. 

The way I understand you, it is not just about inertial or non-inertial frames. You seem to be suggesting there is a difference when observing in the same reference frame.

Are you suggesting that two objects with the same kinetic energy, but one is only rotating and the other is only translating, would have a different gravitational pull on their surroundings (sufficiently far away not to be influenced by local effects)?

Or, put differently: do you mean that gravity does not affect relativistic mass (or at least the difference between rest mass and relativistic mass)?

[koti]

3 hours ago, Bender said:

The way I understand you, it is not just about inertial or non-inertial frames. You seem to be suggesting there is a difference when observing in the same reference frame.

Are you suggesting that two objects with the same kinetic energy, but one is only rotating and the other is only translating, would have a different gravitational pull on their surroundings (sufficiently far away not to be influenced by local effects)?

Or, put differently: do you mean that gravity does not affect relativistic mass (or at least the difference between rest mass and relativistic mass)?

Gravity never affects any mass, its the other way around - mass/energy causes spacetime curvature and we perceive that as gravity. 

The answer seems to be yes - an object rotating would have a higher gravitational potential than a non rotating object for all the reference frames, the effect is miniscule though. I found a video of Sean Carrol nicely explaining my question, start watching from 6:45: 

Which brings me to another realated question...what rest mass an object would have to have for it to start spinning (limited by c obviously) to reach a black hole colapse? Is that even possible? 

Edited March 18, 2018 by koti

[Bender]

I'll watch the video later, but one remark now: consider two masses spinning around each other connected with a rope. Their kinetic energy now would have gravitational effects.

When you cut the rope, this effect would suddenly drop, because now most of the kinetic energy is mostly translational.

That doesn't sound right to me.

[koti]

19 minutes ago, Bender said:

I'll watch the video later, but one remark now: consider two masses spinning around each other connected with a rope. Their kinetic energy now would have gravitational effects.

When you cut the rope, this effect would suddenly drop, because now most of the kinetic energy is mostly translational.

That doesn't sound right to me.

I'm not entirely sure as to your masses with rope example, it complicates things further due to rope elascticity for ex.  Unless I'm missing something, I think that a rotating mass creates more gravity for all the reference frames as opposed to a non rotating mass.

Edited March 18, 2018 by koti

[swansont]

3 hours ago, koti said:

Which brings me to another realated question...what rest mass an object would have to have for it to start spinning (limited by c obviously) to reach a black hole colapse? Is that even possible? 

Angular momentum is a conserved quantity, so a mass will not spontaneously start spinning. It will not be cause by mass.

To see what the mass requirement is for a spinning mass, you would need to calculate the energy density a BH must have, and compare that to the mass energy and rotational energy. (of course, this being GR, it may be trickier than that)

But a spinning mass will bulge at the equator, so the density might actually be less, and it might then be harder for it to collapse.

[koti]

41 minutes ago, swansont said:

Angular momentum is a conserved quantity, so a mass will not spontaneously start spinning. It will not be cause by mass.

To see what the mass requirement is for a spinning mass, you would need to calculate the energy density a BH must have, and compare that to the mass energy and rotational energy. (of course, this being GR, it may be trickier than that)

But a spinning mass will bulge at the equator, so the density might actually be less, and it might then be harder for it to collapse.

But a hypothetical, non elastic body of certain mass could rotate into a colapse? Obviously the rotational energy has to be provided from the outside. 

[Bender]

Perhaps for a neutron star which is near the critical mass to become a black hole, the additional increased rotational energy might be what pulls it over the edge?

[Bender]

8 hours ago, koti said:

The answer seems to be yes - an object rotating would have a higher gravitational potential than a non rotating object for all the reference frames, the effect is miniscule though. I found a video of Sean Carrol nicely explaining my question, start watching from 6:45: 

 

Ok, I watched it, and while it is an interesting video, he just posits it without really explaining.

He even seems to contradict himself. He implies that inertial mass does change depending on the speed, while gravitational mass doesn't. But he also said both are the same.

I think the effect of gravity does change in different inertial reference frames, because time flows at different rates and, as a result, acceleration is different.

Moreover, suppose nuclear or chemical energy gets converted to kinetic energy: how can the system suddenly loose some of its gravitational effect on  spacetime? 

[koti]

23 minutes ago, Bender said:

 He implies that inertial mass does change depending on the speed, while gravitational rest mass doesn't. But he also said both are the same.

 

Because its true - relativistic mass does change depending on speed and rest mass doesn't. He says they are the same in the sense that modern physics treat both rest mass and relativistic mass as energy.

Quote

I think the effect of gravity does change in different inertial reference frames, because time flows at different rates and, as a result, acceleration is different.

I don't think so. For example the gravitational potential increase (why I started this thread) due to rotation seems to change for all the frames. Relativistic time dilation and length contraction are frame dependent phenomena. 

But we need @swansont or @Janus to chip in to be sure. 

[J.C.MacSwell]

1 hour ago, Bender said:

 

Moreover, suppose nuclear or chemical energy gets converted to kinetic energy: how can the system suddenly loose some of its gravitational effect on  spacetime? 

Unless the energy leaves the system, or gets repositioned within the system, there should be no change. (Or is that your point?)

[Bender]

3 minutes ago, J.C.MacSwell said:

Unless the energy leaves the system, or gets repositioned within the system, there should be no change. (Or is that your point?)

That is indeed my point.

42 minutes ago, koti said:

Because its true - relativistic mass does change depending on speed and rest mass doesn't. He says they are the same in the sense that modern physics treat both rest mass and relativistic mass as energy.

If both are the same, how can one have an effect on spacetime, while the other (suposedly) doesn't? 

[koti]

22 minutes ago, Bender said:

If both are the same, how can one have an effect on spacetime, while the other (suposedly) doesn't? 

They’re not the same, they’re just treated under energy instead of mass to make the math simpler.

Edit: I think.

Edited March 18, 2018 by koti

[swansont]

7 hours ago, Bender said:

Perhaps for a neutron star which is near the critical mass to become a black hole, the additional increased rotational energy might be what pulls it over the edge?

Rotation increases the radius, since these are not ideal rigid spheres. So it is not clear what the result would be.

8 hours ago, koti said:

But a hypothetical, non elastic body of certain mass could rotate into a colapse? Obviously the rotational energy has to be provided from the outside. 

It should. Meanwhile, translation will not. The key here is, as you note, energy is added to the object, and it remains in the same frame of reference. The mass must increase.