The Mystery of Superluminal Recession Velocities in Cosmology

[marcus]

recessionary inertia, or recessionary momentum

That's right, I don't know a better way to put it.
recessionary momentum, if you can define it, would be critical to your
topic of superluminary recession speed. Yes?
So it is highly pertinent. Have a go at defining what you mean by it.

My feeling is some honest unadversarial feedback may help you, and that is
what I am trying to provide. Have to go, but will be back later.

 

[jonmtkisco]

Hi Marcus,

You'll be more helpful to people if you do learn "a better way to put it." Let me help you do that: Stop using condescending terminology like telling people they are "confused." If you can't resist the temptation to condescend, you will get adversarial responses.

I can't tell if your question about recessionary momentum is sincere or not.

Since velocity and invariant mass are the two elements of momentum, obviously the measurement of momentum is observer-dependent. In relativity there is no such thing as absolute momentum because there is no such thing as an absolute measure of velocity.

In the context of my post, I was alluding to the conservation of recessionary momentum that would be measured by an observer in anyone galaxy, based on observed recession velocity. If that observer can take measurements at Gy intervals, she will find that recessionary momentum (relative to her) is conserved, after accounting for the deceleration of cosmic gravity and the acceleration of dark energy during each interval. Observers on other galaxies will agree with that conservation of momentum, although the specific recession momentum they calculate relative to themselves may be a different number.

Recessionary momentum is conserved because (except for the ambuiguity regarding dark energy) the expansion of the universe is believed to be an adiabatic process which complies with the laws of thermodynamics.

Jon

 

[Haelfix]

So the next step is to actually write down a general mathematical formula for this 'recessionary momentum' that you think is generically invariant.

Alternatively you could simply pick up a textbook on GR and look up all the invariants of a system. The classification of (semi) Riemanian manifolds that satisfy Einsteins field equations was done long ago, and everything that you can think of that actually is a bonafide invariant, has been written down.

 

[jonmtkisco]

Hi Haelfix,

The FLRW metric is the definitive equation for calculating the conservation of recessionary momentum. One of the Friedmann equations is called the "Energy Conservation" equation.

Jon

 

[yuiop]

Hi Marcus,

On a number of occasions you have stated that space is not expanding but rather the distance between galaxies is increasing. This seems a vague statement and avoids the issues. Could you make it clear exactly what you mean by "the distance between galaxies is increasing". I will give a simple example that I hope makes the issues clear. If you drive from your home to the local shops in your car it could be said that the distance between your home and the car is increasing over time. There are two explantions for what is happening:

1) Your car really is moving relative to your home. This is probably what we would commonly refer to as velocity. In this example your home or your car is moving relative to space and at least one of them is subject to Special Relativity effects such as length contraction and time dilation. You car is also limited to moving at less than c relative to your home.

2) The distance between your car and your home is increasing due to the expansion of the space between your home and your car and they are both at rest with respect to space and are not subject to length contraction or time dilation and are not limited to a mutual recessional relative velocity of the speed of light.

Which explanation is what you mean by the distance between galaxies is increasing?

 

[Wallace]

I can't answer for marcus, but physically option 1) is the correct answer, with caveats. This motion must be described in General Relativity (i.e. including gravity) and when considering the motion one must be careful to consider what the observables in the system are, i.e. you can't make an measurement of the velocity of a distant galaxy, you can only see its redshift which is not the same as a measure of velocity due to the effects of gravity.

Option 2) is an easier way of conceptualising the recession of galaxies, since it hides a lot of the details within the metaphor of 'expanding space'. It is entirely uncontroversial however to simply state that 'the expansion of space' is not a physical theory, it is not a causative process that makes anything happen. If you like, it is the result of the recession of galaxies, rather than the other way around.

 

[marcus]

..Which explanation is what you mean by the distance between galaxies is increasing?

off topic here, Kev. Let's start a separate thread about what is meant by distances increasing. Sounds like Haelfix and Jon are having a constructive talk and I don't want to distract from it by crosstalk.

 

[yuiop]

I can't answer for marcus, but physically option 1) is the correct answer, with caveats. This motion must be described in General Relativity (i.e. including gravity) and when considering the motion one must be careful to consider what the observables in the system are, i.e. you can't make an measurement of the velocity of a distant galaxy, you can only see its redshift which is not the same as a measure of velocity due to the effects of gravity.

Option 2) is an easier way of conceptualising the recession of galaxies, since it hides a lot of the details within the metaphor of 'expanding space'. It is entirely uncontroversial however to simply state that 'the expansion of space' is not a physical theory, it is not a causative process that makes anything happen. If you like, it is the result of the recession of galaxies, rather than the other way around.

Hi Wallace,
You bring up a very interesting point when you said "If you like, it is the result of the recession of galaxies, rather than the other way around." The recessional velocity of galaxies does seem to alter the geometry of space. If we took a snapshot of a hypothetical universe without a cosmological constant we would guess that it would have a closed geometry and would collapse, if we did not information about the velocities of the galaxies, whatever the mass density of the universe was as long as it is not zero. We often read that if Omega(total) is less than one then the universe has an open geometry and if it is greater than one the the universe has a closed geometry. This only makes sense when we take recessonal velocities (or the Hubble constant) into account and the geometry is largely determined by the velocities in a way that differs from a simple application of a static Schwarzschild metric. This becomes very relevant when people ask questions like wouldn't the mass and volume of the universe suggest we may be in a black hole. The recessional velocities suggest that the simple R<2GM/c^2 definition of a black hole is not suffient in this case.

 

[jonmtkisco]

Hi Kev,
You make an excellent observation that recession velocity seems to alter the geometry of space.

It makes me wonder what exactly the physical interpretation is for the fact that a given mass in a given large volume will have no spatial curvature if its constituent particles are moving away from each other at the escape velocity of their combined mass, but it will have substantial positive curvature if the same galaxies are at proper rest with each other. How can varying the motion of mass cause this physical effect?

The answer must lie within the definitive FRW metric. Something like, the kinetic energy embodied in the motion itself has the power to prevent geometric curvature that would otherwise occur.

Jon

 

[marcus]

Jon, Haelfix is being very helpful. Please proceed saying what recessionary momentum is.

So the next step is to actually write down a general mathematical formula for this 'recessionary momentum' that you think is generically invariant.

Alternatively you could simply pick up a textbook on GR and look up all the invariants of a system. The classification of (semi) Riemanian manifolds that satisfy Einsteins field equations was done long ago, and everything that you can think of that actually is a bonafide invariant, has been written down.

Hi Haelfix,

The FLRW metric is the definitive equation for calculating the conservation of recessionary momentum. One of the Friedmann equations is called the "Energy Conservation" equation.

Jon

Sounds like you have an idea of how recessionary momentum might be defined! Please proceed. Write down some definition for it that makes it a calculable physical quantity.
I personally would be delighted if you can come up with something. (When I ask for someone to define a quantity I don't necessarily mean that rhetorically. I urge you kindly to try. Either way we all learn something---gain some way. Not a zero sum )

...The answer must lie within the definitive FRW metric...

Glad you showing such high regard for the FRW metric lately! Key to the standard superluminary recession picture. Based on a more normal mainstream set of coordinates. Distances as seen by observers at rest with respect to the CMB, or with respect to the flow.

 

[jonmtkisco]

Hi Marcus,
As I understand it, the energy conservation equation for FRW is:

\dot{\rho} = -3H \left(\rho + \frac{p}{c^2} \right)

I suggest that as a good starting point for calculating the answer you seek. This equation speaks to the totality of the matter contained in a large domain such as our observable universe. It seems to me that if energy conservation works for the totality of matter in a given domain, it demonstrates that energy is conserved for the individual matter constituents comprising that totality, as long as homogeneity is preserved at the local level (which is what my scenario assumed).

Jon

 

[marcus]

Jon, you have taken a first step. What you originally said was

galaxies are moving apart because they were previously moving apart. I.e., they have recessionary inertia. Inertia does not change by itself as a function of time, only by the application of "external" forces.
...

We have agreed, I think, that is about recessionary momentum. Now the question is, can a galaxy actually HAVE recessionary momentum---as you say it does.
Either the idea is bogus (purely verbal) or it is quantitative and you can actually say what the quantity of a galaxy's recessionary momentum is.

Haelfix had a constructive suggestion. He might help you some more:

So the next step is to actually write down a general mathematical formula for this 'recessionary momentum' that you think is generically invariant.

Alternatively you could simply pick up a textbook on GR and look up all the invariants of a system. The classification of (semi) Riemanian manifolds that satisfy Einsteins field equations was done long ago, and everything that you can think of that actually is a bonafide invariant, has been written down.

You have written down Friedmann equation. That's good! In cosmology almost everything comes out of a couple of Friedman equations. In a universe constructed according to the Friedmann model, the coordinate system that I like to use (observers at rest with respect to CMB, or with respect to the flow) is the natural system----and superluminary recession speeds are very much in style. So you can bet I'm happy to see Friedmann.

But how do you show your concept is not unphysical? How do you get from Friedmann model to a formula where you can say what a galaxy's recessionary momentum is?

Say the galaxy mass is 1000 kilograms and the recession speed from us is 1000 kilometers a second. What is the recessionary momentum? Or say the speed is 1 million kilometers a second. What is the recessionary momentum? what concerns me is the thought that you can't define the concept in such a way that it is calculable---so that it is just not a physical quantity. Do you see my point? Please give it a try.

 

[jonmtkisco]

Hi Marcus,

For some reason we're talking past each other here. There is no reason for me to write down the formula for conservation of momentum because that's what the Friedmann equations are. I'm not inventing any new idea at all on this subject. The underlying motivation behind Friedmann's equations was to model a universe that conserves momentum in accordance with GR and the First Law of Thermodynamics. The competing accelerations of gravity and Lambda are built into the equations, along with energy conservation.

I'll get you started with a simple approach to the math: Every homogeneous subset of a flat FLRW universe recedes at exactly the escape velocity of its mass/energy. That's true even when Lambda is included in the mix, but you have to add the mass/energy of Lambda to the galaxy's mass. Think of your 1000 KG mass as existing in a "cell" containing its proportionate share of our observable universe's volume. Imagine the full observable universe to be filled homogeneously with identical such cells. Then the recession velocity of each such galaxy away from the center of its cell will be equal to the escape velocity of that galaxy and its cell's Lambda combined.

You haven't helped so far with this effort, so I'll leave it to you to work out the rest of the math, which apparently is of more interest to you than to me.

Jon

 

[Wallace]

I've tried to convince Jon in the past that the recession of galaxies is loosely analogous to them having a kind of momentum, i.e. they move away now because they did so a moment ago. Clearly however, this merely a very simple analogy. Momentum, being a 3D Newtonian concept is most certainly not conserved in an expanding Universe, and is unmeasurable for a distant galaxy in any case.

You certainly couldn't calculated anything useful starting from this idea. Like all analogies, you shouldn't push it to far. In the case of this analogy, you really can't push it anywhere useful in terms of actually calculating anything. The dynamics of an FRW universe should be calculated with the FRW metric. It is the simplest and easiest way to do it. There are many different ways of trying to conceptualise the expanding Universe, but these should not be confused as alternative theories or different physical realities. Everyone agrees that there is one way to do the calculations, and that is to use the FRW metric.

 

[jonmtkisco]

Hi Wallace,

Momentum, being a 3D Newtonian concept is most certainly not conserved in an expanding Universe, and is unmeasurable for a distant galaxy in any case.

Do you agree that the reason why a tiny massive test particle's recession momentum isn't conserved in a flat universe is because of the effects of gravity and Lambda? There isn't anything else I can see to affect momentum (other than spatial curvature in a nonflat universe). As you say, these factors are captured in the FRW metric.

Could one estimate the "internal" recessionary momentum of a standalone two galaxy system, by calculating the mutual recession velocity (using cosmological redshift, luminosity distance, etc.) and multiplying it by the estimated combined mass of the two galaxies?

Jon

 

[yuiop]

I've tried to convince Jon in the past that the recession of galaxies is loosely analogous to them having a kind of momentum, i.e. they move away now because they did so a moment ago. Clearly however, this merely a very simple analogy. Momentum, being a 3D Newtonian concept is most certainly not conserved in an expanding Universe, and is unmeasurable for a distant galaxy in any case.

You certainly couldn't calculated anything useful starting from this idea. Like all analogies, you shouldn't push it to far. In the case of this analogy, you really can't push it anywhere useful in terms of actually calculating anything. The dynamics of an FRW universe should be calculated with the FRW metric. It is the simplest and easiest way to do it. There are many different ways of trying to conceptualise the expanding Universe, but these should not be confused as alternative theories or different physical realities. Everyone agrees that there is one way to do the calculations, and that is to use the FRW metric.

It is very nice that we have the FRW metric to plug numbers into but Friedmann, Robertson, Walker and Lemaitre did not have that luxury. I assume they must have had a physical concept in mind when they came up with the metric although it is possible that they derived it in an entirely abstract mathematical way from other abstract equations.

I am wondering why you consider momentum of a distant galaxy to be unmeasurable. Is it because the velocity of the galaxy depends on who is measuring it? If that is the case it should be noted that in Special Relativity, velocity is not an observer independent quantity but we can still do calculations by just taking velocity relative to the particular observer under consideration. Maybe the problem is that it is difficult to be certain of the mass of the galaxy and that is a big problem because galaxies come in a wide range of sizes. However we make certain estimates of the mass of galaxies from rotation velocities and indeed that is what first led us to conclude that dark matter must be a significant component of galaxy masses. The third difficulty is that we have to have a clear image of whether the galaxies are comoving with expanding space or moving relative to space in which case the relatavistic mass due to Special Relativity has to factored into the momentum equation. I don't see that any of these problems are insurmountable at least in principle if you have a clear physical picture of what is going on. The crux of these threads is try to and get to a clear physical picture. I assume the greats such as Friedmann, Lemaitre, Robertson and Walker actually had one. From the last few posts it seems Friedmann did think something useful could be calculated from momentum and one of those things is the FRW metric.

 

[jonmtkisco]

I think the easiest way to think about this is in terms of recession velocity rather than momentum. For practical purposes, we can assume that the change in any galaxy's mass over time is insignificant, so change in momentum is just a factor of change in recession velocity, with mass being a constant multiplier.

Having said that, it seems perfectly obvious that a galaxy's recession velocity (away from us) would remain constant over time, but for the competing accelerations of gravity and dark energy. There is no rationale why its recession velocity would change arbitrarily. The FLRW metric assumes recession velocity does not change without a reason.

Jon

 

[marcus]

I think the easiest way to think about this is in terms of recession velocity rather than momentum. For practical purposes, we can assume that the change in any galaxy's mass over time is insignificant, so change in momentum is just a factor of change in recession velocity, with mass being a constant multiplier.

the only way this can be true is if you take the recession momentum to be equal to the recession velocity multiplied by the mass, which you take to be constant. I see what you are doing: you have a way of defining the recessionary momentum. Mass times velocity, the Newtonian idea. This is progress of a sort---towards getting clear about the quantities.

this is what I asked from you earlier. I am trying to help you get clear about what you are saying---how the quantities would be defined. far from adversarial it is the kind of help you seem to need.

OK, so you are thinking of what's called the Newtonian momentum, mass times velocity.

so what I am wondering is this. what is the momentum of a galaxy with a mass of 1000 kilograms which has a recession speed of 3 c? Or for round numbers say one million kilometers a second.
(just for simple numbers I have taken a ridiculously small galaxy mass---a hundred billion solar masses would be more realistic but for convenience let's say 1000 kilo )

Using your formula, it would be a trillion metric units---a trillion kilogram meter per second.
Do you agree?

Do you know any physical law that applies here? Is there a conservation law, or a law relating force to the rate of change of recessionary momentum?

I'm asking because you have defined a completely new kind of momentum---the Newtonian momentum somehow associated with a speed faster than light! And I never heard of any physical law that applies here.

What physical law have you found that applies? Haelfix had a really helpful suggestion, he said look for invariants---quantities defined in the GR context which don't depend on the choice of coordinates. I didn't see any followup. You mentioned the Friedmann equation but that doesn't say anything about this sort of momentum-ish quantity.

So the next step is to actually write down a general mathematical formula for this 'recessionary momentum' that you think is generically invariant.

Alternatively you could simply pick up a textbook on GR and look up all the invariants of a system. The classification of (semi) Riemanian manifolds that satisfy Einsteins field equations was done long ago, and everything that you can think of that actually is a bonafide invariant, has been written down.

Hi Haelfix,

The FLRW metric is the definitive equation for calculating the conservation of recessionary momentum. One of the Friedmann equations is called the "Energy Conservation" equation.

Jon

But I'm sure you realize that just because it is called that doesn't mean it has anything to do with this particular recessionary momentum quantity as you have defined it. Wallace had something to say about momentum conservation in GR. I'll see if I can find it. I think he said it wasnt' a conserved quantity.

I've tried to convince Jon in the past that the recession of galaxies is loosely analogous to them having a kind of momentum, i.e. they move away now because they did so a moment ago. Clearly however, this merely a very simple analogy. Momentum, being a 3D Newtonian concept is most certainly not conserved in an expanding Universe, and is unmeasurable for a distant galaxy in any case.

You certainly couldn't calculate anything useful starting from this idea. Like all analogies, you shouldn't push it to far. In the case of this analogy, you really can't push it anywhere useful in terms of actually calculating anything. The dynamics of an FRW universe should be calculated with the FRW metric. It is the simplest and easiest way to do it. There are many different ways of trying to conceptualise the expanding Universe, but these should not be confused as alternative theories or different physical realities. Everyone agrees that there is one way to do the calculations, and that is to use the FRW metric.

To me that suggests, if you go by what Wallace says, that the concept of recessionary inertia or recessionary momentum that you introduced actually doesn't exist as a physical quantity. Not a reliable guide to intuition in other words. But Wallace or any of us could be wrong. Conceivably someone might be able to define it and discover a law that gives it meaning! (I suspect not but) please give it a try, unless you have decided to discard the notion as bogus.

 

[jonmtkisco]

Hi, Marcus

Do you know any physical law that applies here? Is there a conservation law, or a law relating force to the rate of change of recessionary momentum?

I'm asking because you have defined a completely new kind of momentum---the Newtonian momentum somehow associated with a speed faster than light! And I never heard of any physical law that applies here.

To co-opt our ultimate guru Wallace's line, don't blame me either for the fact that cosmology is complex. I didn't invent the Friedmann equations. As I've mentioned repeatedly, they were devised specifically to implement both GR and the First Law of Thermodynamics in an adiabatic system. Yes, the First Law of Thermodynamics is an energy conservation law. The Friedmann equations dictate that in a matter-only Lambda=0 flat universe, the radius of a geometrically flat domain of homogeneous dust will expand at the escape velocity of its invariant mass. Each particle of dust behaves exactly like a Newtonian cannonball: if there were no gravity, its momentum would be conserved; in the presence of gravity, its energy is conserved but not its momentum - its kinetic energy converts to potential energy.

It bothers me - as it apparently bothers you too - that our fundamental cosmic GR metric, FLRW, incorporates such blatantly Newtonian underpinnings. One might expect, and even wish, that FLRW would predict exotic relativistic effects when relative recession velocities approach and cross the threshold between speeds above and below c. But FLRW predicts nothing of the kind -- relative recession velocities decrease smoothly as the threshold is crossed, and energy is conserved using the same simple algorithm as always. Absolutely nothing noteworthy happens in the metric when we cross this bright line.

As I mentioned in an earlier post, the equation for cosmological redshift has the same fundamentally Newtonian aspect. The redshift increases smoothly as one crosses the threshold to superluminal recession velocities. No fuss no muss. Again our FLRW metric at work.

I find the blandness of this aspect of the FLRW metric to be so startling that I've devoted another whole thread to exploring the subject on this forum. I hope that you and others will find it compelling to brainstorm more deeply and proactively about this, in preference to congratulating ourselves for mutely acquiescing in the belief that this unique aspect of GR is too complex to ever be understood intuitively by mortals.

Jon