B What Is the Gravitational Memory Effect?

[tionis]

https://arxiv.org/abs/1502.06120][/PLAIN]

https://arxiv.org/abs/1502.06120][/PLAIN]

The passage of gravitational radiation past a pair of nearby inertial detectors produces oscillations in their relative positions. After the waves have passed, and spacetime locally reverts to the vacuum, the detectors in general do not return to their initial relative positions. The resulting displacement, discovered in 1974 [1-11], is known as the gravitational memory effect.

Would someone please explain what this quote is saying? What does it mean when they say that spacetime locally reverts to the vacuum? Wasn't the passing gravitational wave made of spacetime vacuum to begin with? And what about the detectors not returning to their original relative position? Is that something they can measure and how do they do it? Thanks.

 

[PeterDonis]

What does it mean when they say that spacetime locally reverts to the vacuum?

The paper's terminology is somewhat misleading, at least for non-experts (but this is certainly an expert-level paper and is not going to be understandable without a lot of background in the subject). By "vacuum" they really mean "flat", or more precisely "flat to a good enough approximation for purposes of discussion in this paper".

Wasn't the passing gravitational wave made of spacetime vacuum to begin with?

Yes, but spacetime within the passing GW is not flat.

what about the detectors not returning to their original relative position? Is that something they can measure and how do they do it?

Basically you assume that there are objects "fixed at infinity" that you can use to determine the positions of the detectors. However, once again, this is an expert-level paper and the measurement process they are envisioning is quite abstract; it won't necessarily correspond to any simple intuitive process.

 

[tionis]

Your explanation is good. I have another question: if you remove all matter and energy from the universe, in essence leaving just spacetime. Would spacetime gravitate?

 

[PeterDonis]

if you remove all matter and energy from the universe, in essence leaving just spacetime. Would spacetime gravitate?

It depends on what you mean by "gravitate". Spacetime can be curved in the absence of matter and energy, because there are solutions of the Einstein Field Equation with zero stress-energy tensor (zero matter and energy) other than flat Minkowski spacetime (for example, Schwarzschild spacetime describing a black hole). So if "gravitate" means "curved spacetime", then spacetime could gravitate in the absence of matter and energy. Whether it would is an unanswerable question, since we can't remove all matter and energy from the actual universe.

 

[tionis]

It depends on what you mean by "gravitate". Spacetime can be curved in the absence of matter and energy, because there are solutions of the Einstein Field Equation with zero stress-energy tensor (zero matter and energy) for example, Schwarzschild spacetime describing a black hole).

But the Schwarzschild spacetime requires a mass to undergo collapse right? Are there any examples were spacetime collapses on its own to a black hole without no mass-energy present?

 

[PeterDonis]

the Schwarzschild spacetime requires a mass to undergo collapse right?

No. We are talking about idealized solutions here, and the idealized version of Schwarzschild spacetime is vacuum everywhere. Granted, this does not describe any actual black holes in our actual universe, since those will all have formed by gravitational collapse of some massive object. But it's a perfectly valid idealized solution.

Are there any examples were spacetime collapses on its own to a black hole without no mass-energy present?

No, but that's not what you asked. The idealized Schwarzschild spacetime has a black hole that exists forever, and it has "gravity" in it.

 

[tionis]

No. We are talking about idealized solutions here, and the idealized version of Schwarzschild spacetime is vacuum everywhere.

Wait, the solution that Karl Schwarzschild wrote down in the trenches was an empty spacetime solution with no mass? I thought it was from a collapsed spherical object. So in fact there are mass-free solutions for black holes. This is new to me.

 

[PeterDonis]

the solution that Karl Schwarzschild wrote down in the trenches was an empty spacetime solution with no mass?

Schwarzschild discovered more than one solution. The one I'm talking about is the vacuum solution; the other one, the "collapsed spherical object" one, is for the interior of a spherically symmetric object (and not a black hole, an ordinary object like a planet or star).

So in fact there are mass-free solutions for black holes.

No, there are stress-energy free solutions. The black hole still has mass; that's what the $M$ is in the metric. "Mass" is not the same thing as "stress-energy"; the latter is what "matter and energy" really means in GR.

 

[tionis]

No, there are stress-energy free solutions. The black hole still has mass; that's what the $M$ is in the metric. "Mass" is not the same thing as "stress-energy"; the latter is what "matter and energy" really means in GR.

Why there aren't mass-free solutions in GR, Peter? If the spacetime vacuum gravitates into an sphere, couldn't we interpret the resulting object as having gravitational mass/energy without an actual mass having to collapse?

 

[PeterDonis]

Why there aren't mass-free solutions in GR, Peter?

There are. Flat Minkowski spacetime has zero mass.

If the spacetime vacuum gravitates into an sphere

It doesn't. The black hole in this idealized solution is eternal; it's always there, infinitely in the past, and infinitely in the future. Nothing "gravitates into a sphere"; the hole's horizon is eternally a sphere.

couldn't we interpret the resulting object as having gravitational mass/energy without an actual mass having to collapse?

I'm not sure what you mean by "gravitational mass/energy"; but I've already said the idealized black hole solution has nonzero mass, and as above, that's without anything having to "collapse". It just has zero stress-energy.

 

[tionis]

There are. Flat Minkowski spacetime has zero mass.

OK, is there any way for this flat spacetime to become a black hole?

It doesn't. The black hole in this idealized solution is eternal; it's always there, infinitely in the past, and infinitely in the future. Nothing "gravitates into a sphere"; the hole's horizon is eternally a sphere.

I really don't understand this. When you say eternal, do you mean since the big bang?

I'm not sure what you mean by "gravitational mass/energy"; but I've already said the idealized black hole solution has nonzero mass, and as above, that's without anything having to "collapse". It just has zero stress-energy.

What I mean is that for example, you take a flat spacetime like the Minkowski one, which doesn't have any mass, and try to find a solution where by some unknown geometric effect or whatever, that flat spacetime turns into a black hole. Now, since this spacetime is mass-free, but the spacetime itself has gravitational energy, we can interpret this collapsed spacetime as having and behaving as if it has mass as per the energy-mass equivalency.

 

[PeterDonis]

is there any way for this flat spacetime to become a black hole?

No. But it also does not describe anything in our actual universe, since our actual universe has matter and energy present and the spacetime that describes it is not flat.

When you say eternal, do you mean since the big bang?

Once again, we are talking about an idealized model, not something that occurs anywhere in our actual universe. In the idealized model, there is no big bang; the black hole exists forever and it is all that exists.

What I mean is that for example, you take a flat spacetime like the Minkowski one, which doesn't have any mass, and try to find a solution where by some unknown geometric effect or whatever, that flat spacetime turns into a black hole.

There is no such solution.

since this spacetime is mass-free, but the spacetime itself has gravitational energy

Flat Minkowski spacetime doesn't have any "gravitational energy". It doesn't have any energy, period. It has zero mass.

 

[tionis]

Flat Minkowski spacetime doesn't have any "gravitational energy". It doesn't have any energy, period. It has zero mass.

I'm confused, Peter. Flat Minkowski is spacetime, and spacetime is gravity, and gravity gravitates.

 

[PeterDonis]

spacetime is gravity

No, it isn't. Curved spacetime indicates the presence of "gravity" (for a suitable interpretation of "gravity"). Flat spacetime does not.

gravity gravitates

This depends on how you interpret "gravity" and "gravitates". PF Insights has a series of three articles on this, written by yours truly:

https://www.physicsforums.com/insights/does-gravity-gravitate/

 

[tionis]

No, it isn't. Curved spacetime indicates the presence of "gravity" (for a suitable interpretation of "gravity"). Flat spacetime does not.

I strongly disagree with this and I know I shouldn't because you are an authority on relativity, but what you are saying is that something other than spacetime is the source of gravity? So there is no gravity in flat spacetime?

This depends on how you interpret "gravity" and "gravitates". PF Insights has a series of three articles on this, written by yours truly:

https://www.physicsforums.com/insights/does-gravity-gravitate/

I will take a look.

 

[PeterDonis]

I strongly disagree with this

You really need to spend some time studying GR. I suggest Sean Carroll's online lecture notes:

https://arxiv.org/abs/gr-qc/9712019

I know I shouldn't because you are an authority on relativity

Whether I am an "authority" or not is beside the point. You should not disagree (or agree) with a theory that you do not yet understand. You should understand it first.

what you are saying is that something other than spacetime is the source of gravity?

Of course. The source of gravity, i.e., what appears as the source on the RHS of the Einstein Field Equation, is the stress-energy tensor.

So there is no gravity in flat spacetime?

Again, it depends on what you mean by "gravity"; that term is too vague to answer your question. To understand what is really absent in flat spacetime, you need to understand what spacetime curvature means, physically. A quick answer is "tidal gravity" (as distinguished from just "gravity", which, as noted, is too vague); a somewhat more technical answer is "geodesic deviation". But those still leave plenty of room for more understanding. Try working through Carroll's lecture notes.

 

[PeterDonis]

Since the actual question asked in the OP has been answered, this thread is closed. @tionis, after you have spent some time learning about GR, hopefully you will be able to formulate more specific questions.