Causal mechanism for gravity

[James R]

Photons have momentum, and that goes in the stress-energy pot for curving spacetime. So, why do photons already travelling at c, not become black holes?

Roughly speaking, it's because the energy-momentum tensor associated with them isn't big enough to create a black hole. Put another way, there isn't enough energy in a small enough space (the energy density isn't high enough).

 

[James R]

Baez made no mention of frames of reference.

If you have issues with Baez's explanation, you could take them up with him, you know.

We can "create" as much energy as we want, without limit, in an area as compact as we want, by accelerating a mass in our thought experiment.

Energy has to come from somewhere to accelerate a mass. You can't create energy out of nothing (in a fixed reference frame).

If black holes were created by mass alone this would be a non-issue.

But they aren't.

Also, the frames-of-reference explanation is "simply" a logical contradiction, not an explanation of why general relativity doesn't predict a black hole in those circumstances.

That word "relativity". What do you think it means? Relativity is all about frames of reference. In GR, gravity is an effect that is perceived as a result of being in an accelerated frame of reference; there is no gravitational "force" in GR.

You say there's a contradiction in the logic, somewhere, but you don't say where. What are you talking about?

 

[James R]

Derek.H.:

If we launch two ships in opposite directions from a point in space which is unmoving , relative to the CMB , and have them accelerate to the same velocity , relative to that point , they should reflect the same amount of time-contraction. If they don't , that shows that the "substrate" is not static , but is moving .

It is true that if you did this experiment you would see the "same amount of time contraction" (or time dilation, more accurately). But that wouldn't tell you anything special about the CMB because you could speed yourself up to 1000 km/hr (or whatever you like) relative to the CMB, launch your two spaceships from that state of motion, and observe exactly the same result.

Likewise , if two ships so equipped pass each other in the deep , then comparing their clock-rates will also reveal which one is passing through the substrate at a higher rate of speed.

That doesn't work, because their "clock rates" will depend on who is observing them. If the observer is on spaceship A, he will measure spaceship B's clock as running slower than his, but if he is on spaceship B, he will measure spaceship A's clock as running slower than his.

This would correspond to a higher relativistic-mass , compared to the slower ship . Should the faster ship approach lightspeed , it should generate such a virtual-mass , as to BE a black-hole .

By talking about a "slower ship" and a "faster ship" you're assuming a particular frame of reference. In fact, you specified the frame of the CMB at the start. But talking about something forming a black hole just because it moves fast brings us back to the original question. As has already been explained, black holes don't form just because mass moves fast.

Keep in mind , no particle ever created has gone fast enough to manifest this much "total-energy".

Particles have been clocked at well over 99.999999% of the speed of light.

 

[Derek.H.]

Roughly speaking, it's because the energy-momentum tensor associated with them isn't big enough to create a black hole. Put another way, there isn't enough energy in a small enough space (the energy density isn't high enough).

But it could be , if we assume some super future physics tech .
So...the question stands !
D.

 

[James R]

But it could be , if we assume some super future physics tech .

Or if we assume that magical fairies can make it happen!

 

[Derek.H.]

Or if we assume that magical fairies can make it happen!

Okay , it may be unrealistic , but it's the thought experiment that counts.
The point of the "Ships" example was to point out that moving the entire system one way or another , changes the relativistic time/mass measurements significantly , with only ONE vector (velocity/direction) yielding perfectly symmetrical amounts of distortion , regardless of the direction of ships . This vector is that of the space matrix-fabric , and will vary from location to location , everywhere in the extant universe .
*It is herein postulated that space itself flows in great currents throughout the heavens , creating astronomical oddities such as the "Great-Attractor" , and the "Quasar-Enigma" .
*As was said in "Total-Rekall" :
"...they're all connected !!" .
D.H.

 

[James R]

The point of the "Ships" example was to point out that moving the entire system one way or another , changes the relativistic time/mass measurements significantly , with only ONE vector (velocity/direction) yielding perfectly symmetrical amounts of distortion , regardless of the direction of ships .

I just explained to you why you're wrong about that. Maybe go back and read it.

 

[paddoboy]

*It is herein postulated that space itself flows in great currents throughout the heavens , creating astronomical oddities such as the "Great-Attractor" , and the "Quasar-Enigma" .
*As was said in "Total-Rekall" :
"...they're all connected !!" .
D.H.

The universe/space/time is expanding over large scales.
Over smaller planetary/stellar/galactic and galactic wall systems, the gravitational effects see such expansion overcome.
There will be a time in the far distant future, when once M31 and the MW, along with the galaxies that make up the wall, all merge into one, that the far distant galaxies will have moved beyond our observable horizon. Which in fact will mean that cosmologists [if any still exist] in that far distant future, will have no observational evidence for the expanding universe.

 

[foghorn]

Roughly speaking, it's because the energy-momentum tensor associated with them isn't big enough to create a black hole. Put another way, there isn't enough energy in a small enough space (the energy density isn't high enough).

That's the way I sort of understand it as well. The mass/energy density in a small enough area ( Schwarzschild radius) doesn't appear.
Ignoring what I just said, the other ''drawback'' to a very small mass ''black hole'', would be how long it existed due to Hawking Radiation.

 

[RJBeery]

Roughly speaking, it's because the energy-momentum tensor associated with them isn't big enough to create a black hole. Put another way, there isn't enough energy in a small enough space (the energy density isn't high enough).

Energy has to come from somewhere to accelerate a mass. You can't create energy out of nothing (in a fixed reference frame).

From these quotes, it looks like you believe that, under the correct conditions, a black hole would be created from stress-momentum energy (mass + kinetic) in the same way that a black hole can be created from stress-angular momentum energy (mass + rotational energy). Do you believe that?

 

[James R]

From these quotes, it looks like you believe that, under the correct conditions, a black hole would be created from stress-momentum energy (mass + kinetic) in the same way that a black hole can be created from stress-angular momentum energy (mass + rotational energy). Do you believe that?

If you're asking me whether I believe that black holes can form when there's enough mass in a small enough space, the answer is yes. You can use the energy-momentum tensor to describe the arrangement and show, for instance, that the Schwarzschild solution is a valid solution of the Einstein equations.

 

[exchemist]

If you're asking me whether I believe that black holes can form when there's enough mass in a small enough space, the answer is yes. You can use the energy-momentum tensor to describe the arrangement and show, for instance, that the Schwarzschild solution is a valid solution of the Einstein equations.

I suspect the issue is not the mass term but the kinetic energy term. From the simple logic of the arguments put forward earlier, it seems to me that k.e., being frame-dependent, cannot contribute to whatever is needed to form a black hole. But I freely admit I have no idea at all how this is handled in the maths of GR.

 

[foghorn]

I suspect the issue is not the mass term but the kinetic energy term. From the simple logic of the arguments put forward earlier, it seems to me that k.e., being frame-dependent, cannot contribute to whatever is needed to form a black hole. But I freely admit I have no idea at all how this is handled in the maths of GR.

Yes, I must admit I'm abit puzzled by kinetic energy being a relative quantity. If something is not a black hole in one frame, it can't be a black hole in any frame.

 

[exchemist]

Yes, I must admit I'm abit puzzled by kinetic energy being a relative quantity. If something is not a black hole in one frame, it can't be a black hole in any frame.

Quite. GR must reach that conclusion in its maths too, it seems to me.

It rather looks to me as if RJB's question really amounts to asking how that comes out of the maths - but without doing the maths. I'm not sure anyone here will be able to help with that.

 

[RJBeery]

If you're asking me whether I believe that black holes can form when there's enough mass in a small enough space, the answer is yes. You can use the energy-momentum tensor to describe the arrangement and show, for instance, that the Schwarzschild solution is a valid solution of the Einstein equations.

That's the logical contradiction -- momentum is a relative term, but supposed black holes are an absolute feature. We cannot rely on some energy-momentum threshold to be crossed when that energy-momentum value changes with each observer.

 

[James R]

Forget GR for a moment. Energy isn't conserved in any accelerating frame of reference.

Jump in your car and accelerate down the road. From your reference frame sitting in the driver's seat, all of the houses you're driving past are somehow gaining kinetic energy from nowhere.

Look out! You're driving straight towards a brick wall. If you collide with it in your stationary car (the car is stationary in the driver's frame of reference), the wall's kinetic energy will cause all sorts of damage to your car, even though the wall didn't get that energy from any obvious source.

 

[James R]

That's the logical contradiction -- momentum is a relative term, but supposed black holes are an absolute feature. We cannot rely on some energy-momentum threshold to be crossed when that energy-momentum value changes with each observer.

Sure we can, as long as when we change frames some of the terms in the energy-momentum tensor increase while others decrease, in some appropriate way.

 

[foghorn]

Quite. GR must reach that conclusion in its maths too, it seems to me.

It rather looks to me as if RJB's question really amounts to asking how that comes out of the maths - but without doing the maths. I'm not sure anyone here will be able to help with that.

Alas, I think those chaps have moved on. Did you notice RJB's post with a link to this Baez page:
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html

If you go too fast, do you become a black hole?
When an object approaches the speed of light, its mass increases without limit, and its length contracts towards zero. Thus its density increases without limit. Sometimes people think that this implies it should form a black hole; and yet, they reason, since its mass and volume haven't changed in its rest frame, it should not form a black hole in that frame—and therefore not in any other frame either. So does a black hole form or not?

The answer is that a black hole does not form. The idea that "if enough mass is squeezed into a sufficiently small space it will form a black hole" is rather vague. Crudely speaking, we might say that if an amount of mass, M, is contained within a sphere of radius 2GM/c2 (the Schwarzschild radius), then it must be a black hole. But this is based on a particular static solution to the Einstein field equations of general relativity, and ignores momentum and angular momentum as well as the dynamics of spacetime itself. In general relativity, gravity does not only couple to mass as it does in the newtonian theory of gravity. Gravity also couples to momentum and momentum flow; the gravitational field is even coupled to itself. It is actually quite difficult to determine the correct conditions for a black hole to form. Hawking and Penrose proved a number of useful singularity theorems about the formation of black holes. But even these theorems do assume certain conditions which we cannot be sure are true "out there".

 

[RJBeery]

Sure we can, as long as when we change frames some of the terms in the energy-momentum tensor increase while others decrease, in some appropriate way.

If the conditions for a black hole are related to energy density, then the (apparent) volume of an object would have to decrease as its (apparent) momentum has decreased, due to a change in observer, in order to do what you're suggesting. Do you believe this is what occurs in general relativity?

 

[exchemist]

Alas, I think those chaps have moved on. Did you notice RJB's post with a link to this Baez page:
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html

Yes. In fact I found where Baez got it from - someone called Gibbs, here: http://sasuke.econ.hc.keio.ac.jp/~ken/physics-faq/black_fast.html

There's some extra text in this version which helps:

"In fact objects do not have any increased tendency to form black holes due to their extra energy of motion. In a frame of reference stationary with respect to the object, it has only rest mass energy and will not form a black hole unless it's rest mass is sufficient. If it is not a black hole in one reference frame then it is not a black hole in any reference frame."

However, like the version RJB quoted, it doesn't go into the derivation of the conditions for black hole formation in enough detail to show exactly why kinetic energy does not contribute, presumably due to the hairiness of the relevant maths.