Model for Gravity -- What mechanism distorts space in the real case?

[Ibix]

Then pair production can't happen instentaniously.

GR is not a quantum theory so should not be expected to make claims about quantum processes. And I don't think pair production necessarily violates conservation of energy anyway.

I saw one going out of existence, or at least it stopped shining.

Stopping shining does not mean its mass vanished. It is the latter that can't happen.

 

[malawi_glenn]

And I don't think pair production necessarily violates conservation of energy anyway.

Any evidence of pair production from "nothing" in general?

 

[Vanadium 50]

Then pair production can't happen instentaniously.

You are quicky moving out of the realm of asking questions, and into the realm of pushing a personal theory, a theory that will inspire people to describe with adjectives.

Pair production does not mean pairs appear out of nowhere. It means particles are produced by the interaction of other particles, like a photon and a nucleus.

If you didn't know this, you should have looked it up before posting. If you did know this and posted it anyway, well, people are going to use more adjectives then.

 

[PeterDonis]

For this to be the mechanism for explaining how new mass distorts space, one has to substitute for the stress-energy tensor a step function (Cu(x)).

You are misunderstanding what a GR spacetime model is. It is a model of spacetime. It already includes all "time variation" of everything in a self-consistent way. It is a global description of an entire history of a physical system (such as the universe). It is not a "snapshot" at an instant of time that then has to be evolved in time.

Note that you cannot just put a "new mass" into such a model; it won't be consistent. Mass cannot just appear out of nowhere. It has to be conserved. So if the only way for you to find a "mechanism" is to magically make a mass appear out of nowhere and then see what happens, you will never find any such mechanism in GR. Sorry.

If you insist on some kind of "time evolution" model in the context of GR, you would want to look at the ADM formalism, which @Dale mentioned in an earlier post. This is a way of generating a full spacetime model (the kind described above) by starting with conditions on a particular spacelike hypersurface ("space" at an instant of "time"), and then evolving things in time. But any result you obtain this way can also be obtained the "global" way, with a full spacetime model as described above. And any result you obtain this way still has to satisfy the conservation law I described above. The spacelike hypersurface on which you define your starting conditions has to be evolved backwards in time as well as forwards, in order to obtain a complete self-consistent solution.

Whether the ADM formalism would satisfy your definition of a "mechanism" is a matter of your personal preferences, not physics.

 

[Dale]

Then pair production can't happen instentaniously.

The stress energy for the pair production must already be present before the pair is produced.

 

[Nugatory]

Then pair production can't happen instantaneously.

No one has ever said that it does (except some pop-sci presentations that oversimplify to the point of misleading). As far as QM is concerned, at time $T$ we prepare a state that includes everything required for pair production (a sufficiently energetic photon and a convenient massive nucleus) and at some later time $T+\Delta T$ we observe that we have an electron-positron pair and that the momentum of the nucleus has changed. What happened between $T$ and $T+\Delta T$? Quantum mechanics won't tell us; that question cannot even be posed within the mathematical formalism of the theory.

Pair production conserves energy and momentum so the transition between the initial and final states does not have to violate any of the invariants of general relativity. This is a completely different situation than the "gravitating mass appears from nowhere" situation that you brought up earlier.

 

[Nugatory]

And I don't think pair production necessarily violates conservation of energy anyway.

It doesn't - full stop.
[Edited to unbotch the quote - sorry@ Ibix, the earlier unedited quote misrepresented what you said - my sloppy mousing]

 

[talanum52]

And I don't think pair production necessarily violates conservation of energy anyway.

Think about it: you have nothing and then you have mass-energy (and there is no negative mass). - Ignore this: you have initially some energy. Problem is: how did energy ultimately start to exist?

 

[Dale]

Think about it: you have nothing and then you have mass-energy

This is incorrect, as has already been explained to you by multiple people here. Energy and momentum are conserved with all of the stress energy of the pair necessarily being present before pair production.

Please do not repeat this false claim again.

 

[Ibix]

Think about it: you have nothing and then you have mass-energy (and there is no negative mass). - Ignore this: you have initially some energy. Problem is: how did energy ultimately start to exist?

If you mean "relativity doesn't describe the origin of the universe" then sure, that's well known. If you mean "pair production produces something out of nothing" then see the post above yours.

 

[malawi_glenn]

When did we measure the creation of say a pair of electron and positron out of "pure energy"?
(note that a photon can not convert it self to a pair of $e^-$ and $e^+$ alone, there needs to be a third particle, usually a proton, involved in order for both energy and linear momentum to be conserved).

 

[jbriggs444]

When did we measure the creation of say a pair of electron and positron out of "pure energy"?
(note that a photon can not convert it self to a pair of $e^-$ and $e^+$ alone, there needs to be a third particle, usually a proton, involved in order for both energy and linear momentum to be conserved).

It is my understanding, perhaps flawed, that photon-photon interactions are possible without an intermediary.

https://en.wikipedia.org/wiki/Two-photon_physics

Energy and momentum conservation are not a problem for this. If you can run an annihilation forward while conserving energy and momentum then the time reversal must conserve them as well.

 

[malawi_glenn]

Energy and momentum conservation are not a problem for this.

No its not. But $\gamma \to e^+ + e^-$ is.

 

[jbriggs444]

No its not. But $\gamma \to e^+ + e^-$ is.

But we are talking about $\gamma + \gamma \to e^+ + e^-$ here. What is the problem with that?

 

[Nugatory]

Whatever process we consider, it conserves mass-energy, does not imply any discontinuity in the stress-energy or Einstein tensors, and therefore does not conflict with GR - at least not the way @talanum52 is mistakenly suggesting.

And people... this is a digression. Back on track, please?

 

[gmax137]

When I hear a call for the "mechanism" I think of the angels flapping their wings to keep the planets in their orbits. Physics has been done with such "mechanisms" for longer than any of us can remember.

 

[Vanadium 50]

I think of the angels flapping their wings to keep the planets in their orbits.

In modern times, this has become an animation or angels flapping their wings to keep the planets in orbit.

 

[mitchell porter]

Just what mechanism distorts space in the real case? General Relativity doesn't provide a mechanism.

In your opinion, do Newton's theory of gravity or Maxwell's theory of electromagnetism provide mechanisms for the physics they describe? Because General Relativity isn't that different.

 

[pervect]

The general relativity equation just shows an equalness between curved spacetime and the stress energy tensor, not a mechanism how the curvature arises when mass moves into a new position or new mass gets produced. It does not describe this process.

The "moving mass" changes the stress energy tensor, and the stress energy tensor can be more or less thought of as the "source of the gravitational field", i.e the source of curvature".

So, it does, IMO, answer the question. One major difficulty is in explaining what the stress energy tensor is, and why we need it. At least equally daunting - actually, probably more daunting - is a general explanation of what we mean by curvature, but I will just mention it as a problem and not talk about it in this post. IF we understand at least the right-hand side of Einstein's field equations (the stress-energy tensor), we'll be a step ahead of understanding neither side. Which at least alleviates the issue of GR being "the thing on the left side that you don't know what it is is equal to the thing on the right side that you don't know what it is, either". With enough work, we can understand first one side, and with more work, we can (potentially) understand both!

In the end, you still can't really answer "why" the stress energy tensor causes curvature, as in general why questions have no fixed endpoint. You can always ask "why" about any explanation. You can point out that the representation of curvature is always equal to the representation of the stress-energy tensor, and with enough background you can use this to perform actual calcuations, to compare with measurements, which is the ultimate goal of any theory.

The probably too-technical explanation of why we use the stress energy tensor is that it's covariant in special relativity. This basically means that we can specify how it transforms when we change coordinates. This is important and useful - but it requires a shared understanding of the concept of covariance and it's importance. That's something I started to talk about, but I gave up because it was becoming too long and muddled. It starts with the idea that coordinates are just labels, which also seems to not generally be appreciated by the larger audience.

So, lets step back away from covariance. The stress energy tensor incorporates both the effects of what we traditionally think of mass, and other things that are not usually thought of as having mass, such as radiation (important in cosmology), and fields in general. This is hardly a complete description, but it provides at least an overview of why we use the stress-energy tensor as the source of gravity in general relativity, and not "mass". We used to use "mass" in Newton's theory of gravity, but when we move beyond Newton, the concept of mass turns out to be basically inadequate. I will point out that even before general relativity, the "mass" of electromagnetic fields became a problem, in such notions as the "electromagnetic mass" problem. Wiki has a short description of this issue, see https://en.wikipedia.org/wiki/Electromagnetic_mass. Max Jammer has a couple of semi-popular books on the concept of Mass in classical and modern physics, of which I've read the one on classical physics (though I don't have it handy). One gets into general unpleasantness, with the mass of a truly classical point charge due to it's field becoming infinite :(. This is just a short overview - as I've said, people have literally written books about the issue.

The logical endpoint of the process of extending the concept of mass turns out to be (with our current understanding) to replace the whole idea of mass with the stress energy tensor, and things work well enough with this approach where we can calculate things.

I'm not sure if I've totally succeeded in my basic goal, which is to motivate the idea of the stress energy tensor. It's a hard problem - in the end , most texts that I've seen introduce it, without much attempt to motivate it, and leave the student to - perhaps - figure it out on their own.

This is a bit of an afterthought - but if the idea of point particles with point masses is just too deeply ingrained to avoid, one can model a swarm of point like particles bouncing around and interacting only when they directly "touch" as having a stress energy tensor. Less discussed (at least clasically) is the idea of how such a swarm of point particles can be used to represent a field, with possible complications such as the point particles having negative masses to generate attractive forces. But it may be helpful in motaivation, at least, to realize that such a swarm of particles CAN be represented by a stress-energy tensor, with any piece of the swarm having an energy density (energy / unit volume), a momentum density, and a pressure. It's not perfect (for instance, it doesn't help much with the problem of the infinite electromagnetic mass of a point charge I alluded to earlier), but it might be a helpful step up to understanding the stress energy tensor. Realizing that a swarm of particles has such a stress energy tensor, one is then just left with the challenge of thinking of an extended object as being able to be represented by such a swarm of idealized point-like particles - with only contact interacations, no interactions "at range".

Next up for a serious treatment would go back to the issue of how this entity that we've come up with (the stress energy tensor) transforms, so that we can work in different frames of reference (say, a stationary frame, and a moving frame, for example). This is complicated somewhat by the details of special relativity, in which things transform differently than they did before.

I'm not going to attempt this - but I wanted to mention it, as one of the goals of the whole "covariance" problem I mentioned earlier is to represent physics in such a way that we can use multiple coordinate systems interchangeably, and have all the results be self consistent. This basically consists of mathematical entities that we can use to represent a system in some frame or coordiante system A with transformations back and forth to coordinate system B. The idea of covariance is to insure that a solution in A (which is assumed to exist and be unique for the time being) is also a solution in B, and vica versa. This way we are just able to talk about the solution to a physical problem without having to specify the minutae such as having to specify a specific coordinate system. We simply talk about "the" solution, and it is understood that with the aid of the principle of covariance, we know how to transform "the solution" into whatever coordinates or frame we desire.