The Mystery of Superluminal Recession Velocities in Cosmology

[marcus]

...
Keep in mind that galaxies which have any given Hubble recession rate from us now, had approximately the same recession relative to us in the very early universe. In early times, the self-gravity of the universe decelerated every galaxy pair's mutual recession rate; in late times, dark energy has reaccelerated them. But absent those two mostly mutually-offsetting accelerations, generally speaking relative to us, every galaxy would retain the same recession velocity now that it had in the very early universe...

What you said seems clearly wrong. It is wrong for z = 7 in as much as 3 is different from 2 (3c is not approximately the same as 2c) and it is wrong for z = 1089 inasmuch as 57 is different from 3.
And it will get more extremely wrong the farther back in time we go. I can see this intuitively without using a calculator. I suggested that you use the calculator as a way of getting some experience---I still think it would do you good.

The reason what you say is wrong and gets more wrong as you go back in time is that your argument has a flaw. When you say "those two mostly mutually-offsetting accelerations" you are talking about gravity versus dark energy and they are NOT mutually offsetting in the early universe. The farther back in the early universe you go, the more dominant is the effect of gravity.

So the influences of dark energy and gravity are not at all mutually offsetting if you go back a ways. If you think going back further will make it better then you must have it backwards. You will just get wrong by more factors of ten---more orders of magnitude.

at z=7 it is 2 versus 3 which is at least the same order of magnitude
at z= 1100 it is off by an order of magnitude as 57 is different from 3
at z = 1000000 it is going to be off by even more orders of magnitude and so on.

Perhaps I'll just stop trying to explain this. You may find someone else to discuss it with.
Maybe you and I can discuss some other of you recent statements.

 

[Wallace]

I haven't followed the details of this discussion, but I strongly suspect the problem lies in distances. You must be careful about co-moving and proper distances. If you want to know the change in recession speed of a particular galaxy then you need to keep the co-moving distance that you are enquiring about the recession speed of the same. This of course means its physical distance changes, and to find how it had changed requires an integral over the times you are talking about.

What I strongly suspect Jon is doing is taking a constant physical distance, rather than a constant co-moving distance. Remember that the Hubble constant at any epoch is defined as the rate of change of physical (or proper) distance, since the rate of change of co-moving distance is zero for objects in the Hubble flow.

If you use a calculator like Ned Wrights it will use co-moving co-ordianates correctly and do the require extra integral. I suspect that Jon is not doing this.

You are both answering a question correctly, but I think marcus is correctly answering the question under discussion.

 

[marcus]

Thanks Wallace.
I was going to ask Jon about a different statement at this point and let that one rest.

Like this statement, Jon

(i) the Hubble radius is in fact well known to be not very different from the calculated present scale factor of the universe (some people refer to this as one of those "cosmic coincidences"),..

Lets discuss this. There are various conventions about the scale factor. Some people normalize it so that the present value of the scale factor is ONE.

Somehow I don't think it is well-known that the scale factor is currently about equal to the Hubble radius, so maybe you could explain.

In the conventions you use, what is the present value of the scale factor?
=============

I think it IS a cosmic coincidence that the present Hubble radius is nearly equal to c times the present age of the universe (in the sense of how long expansion has been going on). But that is not what you said here. So a little clarification would help.

 

[jonmtkisco]

Hi Wallace and Marcus,
Honestly this is not my discussion, I don't really understand what point Marcus is getting at.

I made a simple statement -- I meant only that the PROPER recession VELOCITY between any "average" pair of galaxies is roughly the same now as it was in the very early universe. It was decelerated for the first 7 Gy or so by gravity, and subsequently has been reaccelerated by dark energy. This is very broadly consistent with the fact that the increase in the Hubble Radius to date roughly approximates the increase in the actual scale factor. My original statement made NO assertion about proper or comoving DISTANCES between galaxies, or even about the overall Hubble factor.

Marcus then challenged me to use a web calculator to test my statement. Now he appears to have gotten tired of arguing about his challenge, which is probably for the best.

If Marcus has answered some question correctly, it is a question he himself posed. I do not believe it has anything to do with the validity of my original statement, which remains true.

Jon

 

[jonmtkisco]

Hi Marcus,

Somehow I don't think it is well-known that the scale factor is currently about equal to the Hubble radius, so maybe you could explain.

From the Wikipedia entry on "Hubble Volume" (emphasis added):

The distance c / H₀ is known as the "Hubble length". It is equal to 13.8 billion light years in the standard cosmological model, similar to but somewhat larger than c times the age of the universe. This is because 1 / H₀ gives the age of the universe by a backward extrapolation which assumes that the recession speed of each galaxy has been constant since the big bang. In fact, recession speeds initially decelerate due to gravity, and are now accelerating due to dark energy, so that 1 / H₀ is only an approximation to the true age. The surprising accuracy of this approximation formed the basis for an April fool paper posted on arXiv.

Jon

 

[marcus]

I don't really understand what point Marcus is getting at...

I made a simple statement -- I meant only that the PROPER recession VELOCITY between any "average" pair of galaxies is roughly the same now as it was in the very early universe.

I know you don't. My point was also about what you call proper recession velocities. The rate at which the physical distance between two galaxies or bunches of matter is increasing.

You made a simple statement, based on what appears to be a confusion. Your statement was that the recession speed very early should be about the same as it is now.

This statement is way off the mark---if you go back far enough you will see it is off by many orders of magnitude.

===============

I also did not mention comoving distance. I am talking about physical distance as would be measured by a chain of observers using radar ranging between neighbors. I didn't invoke any other distance scale because I was talking about the physical or proper distance between two concrete bunches of matter.

================

Your argument is that there has been deceleration for about 7 billion years followed by acceleration for about 7 billion years, so that should cancel. But this is wrong because the rates of acceleration and deceleration differ wildly.

Take the example of the CMB, emitted at time roughly 400,000, that is less than a million years. Consider two patches of matter, one that became US and one that emitted some CMB that we are now seeing.
The two batches of matter have experienced decelerated expansion for 7 billion years (roughly) and then accelerated expansion for about the same length of time.

You argued that the effects offset each other and that the recession speeds should be approximately the same now as then. However in reality the deceleration was much more severe, so that the real physical recession speed then was about 57c and that now is about 3c.

You seem to think I am arguing with you, Jon. I am not arguing. I am trying to explain something to you.

 

[marcus]

Hi Marcus,
From the Wikipedia entry on "Hubble Volume" (emphasis added):

Jon, the Wikipedia entry you quoted confirms just what I said. It does not support your statement however. I believe your statement was wrong. The fact that you cited that passage from Wikipedia suggests to me that you may be confusing two things----the current scale factor and the distance one gets by multiplying c times the age of the universe. If you are equating those two things then I would like to help you get unconfused about that.

Here is your post, with what I said in bold:
========quote=======

Hi Marcus,

Somehow I don't think it is well-known that the scale factor is currently about equal to the Hubble radius, so maybe you could explain.

From the Wikipedia entry on "Hubble Volume" (emphasis added):

The distance c / H0 is known as the "Hubble length". It is equal to 13.8 billion light years in the standard cosmological model, similar to but somewhat larger than c times the age of the universe. This is because 1 / H0 gives the age of the universe by a backward extrapolation which assumes that the recession speed of each galaxy has been constant since the big bang. In fact, recession speeds initially decelerate due to gravity, and are now accelerating due to dark energy, so that 1 / H0 is only an approximation to the true age. The surprising accuracy of this approximation formed the basis for an April fool paper posted on arXiv.
===endquote===

The Wikipedia quote confirms exactly what I said earlier. So I am still asking you to explain what YOU said . On what basis do you equate the current scale factor with the age of the universe multiplied by c?

Here is the statement of yours which needs explanation

Hi Marcus,

No it's not really my own deduction. It's a combination of two data points: (i) the Hubble radius is in fact well known to be not very different from the calculated present scale factor of the universe (some people refer to this as one of those "cosmic coincidences"),

Again, I am not interested in arguing. You seem confused about some very basic stuff and I would like to help you get clear about it. So I suggest for your own benefit that you try to justify what you said carefully. How do you define the present scale factor? Why is it approximately the same as the age of the universe multiplied by c? (Which we say is by cosmic coincidence similar to the Hubble radius.)

 

[jonmtkisco]

I'll respond to this post later.

 

[jonmtkisco]

OK, I got that one wrong. I agree that the relative velocity between pairs of galaxies has slowed down a lot over time.

All of this is a tangent from the point of my post #100, which is an attempt to provide a bottoms-up solution for cosmological redshift.

Jon

 

[marcus]

Jon, in my previous two posts #108 amd #112. I was asking you about a different matter. I was asking you to clarify what you said in your post #103.
It is as least as potentially serious as the business of whether recession speeds stay about the same or decrease (I gather you are all right about that one now.)
Here is your post #103, there are actually two statements I wish you'd clarify.

... (i) the Hubble radius is in fact well known to be not very different from the calculated present scale factor of the universe (some people refer to this as one of those "cosmic coincidences"), and

(ii) ... 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.
...

My main question was about what you call the present value of the scale factor? Please read my previous posts #108, 112 where I asked you about your statement (i). Puzzled by it. could use some explanation.

Also in statement (ii) exactly is recessionary inertia? You make a general statement about inertia which I guess covers ordinary inertia so maybe recessionary inertia is just the common ordinary inertia?

I'm not bothered by the statement that galaxies are moving apart in part because they were previously, in a differential equation model the past can be part of the explanation. Inertia in the conventional sense need not play a role: a distance can be increasing in part simply because it was increasing in the past--- and any change in the rate is something the equation will calculate for us. At least that is one way to look at it---though not one I would necessarily prefer. But it is another thing to introduce the idea of recessionary inertia. If it has physical reality, then you should define it for us so we can see how one would calculate the quantity.

 

[jonmtkisco]

Sorry Marcus, my train of thought really ended at post #100 and the first two paragraphs of #101. I will not defend anything I said after that, which was all in response to late night challenges. It's not a good idea to respond late at night.

Jon

PS, the current scale factor is 3X the Hubble length. Yup.

 

[marcus]

the current scale factor is 3X the Hubble length. Yup.

In many treatments, the current scale factor is set exactly to 1. Can you give a reference like some online textbook where the current value is 3X Hubble length?
You may be confusing the scale factor with the particle horizon, which is approximately 3X the Hubble length. But that is not a coincidence.
You said before

(i) the Hubble radius is in fact well known to be not very different from the calculated present scale factor of the universe (some people refer to this as one of those "cosmic coincidences")

What I want to know is what you mean by the current scale factor.

===============
I see you are turning in. Have a good rest! Here is something you might consider in the morning when you are fresh.

(ii) ... 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.

Jon, about your statement (ii) above, could you be confusing inertia with momentum?
It is about momentum that one would most often say that it does not change except by application of an external force.
But you are saying this about inertia.
What quantity do you actually have in mind and how would one actually calculate it?

For example, suppose what you really meant is the Newtonian momentum, which is the mass of an object times its velocity.
Then if the object is a galaxy and the recession speed is 7c, then the magnitude of the quantity would be the mass times 7c.
I don't need a long formula in LaTex just a clear idea of how one would determine it. Because otherwise what we're
talking about would not be physically well-defined.

 

[jonmtkisco]

Hi Marcus,

These both are examples of insincere nitpicking instead of helping analyze the substantive matters I'm trying to focus on. I'm confident that the meaning of what I said came across just fine without this kind of improvement.

Yes when I say inertia I'm speaking colloquially about momentum. I'm not confused about what momentum is. In informal discussions regarding topics where it doesn't make any substantive difference, people often use the terms interchangeably, even if that isn't the King's English.

Of course the scale factor (a) today typically is stated as 1 (although that's a completely arbitrary number used to simplify calculations). I am not confused about that. I should have used the term "radius" in order to please the teacher. As you know perfectly well, the radius of our observable universe is typically stated to be approximately 46 GLy or 4.35E+26 meters; roughly 3x the Hubble length just as I said.

Precise terminology is important when it's important, and it's not when it's not. When you have a substantive point to contribute, I very much appreciate it, even if I don't immediately recognize my error. If you think a terminology clarification is important, offer it and then let it go. Please try not to distract from the underlying point of my post; whether intended or not, it ends up hijacking my post.

And PLEASE, no more lectures about my flaws as an informal amateur technical author.

Jon

 

[marcus]

Jon, you sound adversarial. Please don't take my concerns amiss. There is a danger when you equate the FRW scale factor with the particle horizon (radius of observable universe) that you will confuse newcomers.

You sounded extremely confused because you said that Hubble radius = scale factor was known as the COSMIC COINCIDENCE. That isn't true. Now you say what you meant was Hubble radius = Particle horizon.

Again that isn't true. And again you say Particle horizon is about 3XHubble radius.

So we are left with Hubble radius = 3 x Hubble radius, which isn't true and it is not what people call the cosmic coincidence.
============

You insist you are not confused about these things but the evidence is that you were very confused at the time you posted about them.

I am glad you are not confused now. What I hope is that you will not adopt an adversarial attitude and accept my offer to help you get clear about some basic cosmology concepts.

Please realize that in a physics forum it makes things very inefficient for those trying to explain stuff when newcomers equate momentum with inertia. It is important to have some minimum of consistency.

We still have the issue, which you have not addressed, of what you mean by recessionary inertia. If what you meant is recessionary momentum, then what is that?

Does a galaxy, for example, have recessionary momentum? If so, and if I know the mass of the galaxy, how do I define the momentum?

Believe me it is a serious physics issue. If the quantity is well-defined and plays a role in cosmology we should certainly know about it.

Let's not be argumentative, let's work this out. Either the concept is bogus or it is physically well-defined. Maybe it's well-defined! Give it a try and see if you can say how to calculate the quantity for a given galaxy of known mass.

Hi Marcus,

These both are examples of insincere nitpicking instead of helping analyze the substantive matters I'm trying to focus on. I'm confident that the meaning of what I said came across just fine without this kind of improvement.

Yes when I say inertia I'm speaking colloquially about momentum. I'm not confused about what momentum is. In informal discussions regarding topics where it doesn't make any substantive difference, people often use the terms interchangeably, even if that isn't the King's English.

Of course the scale factor (a) today typically is stated as 1 (although that's a completely arbitrary number used to simplify calculations). I am not confused about that. I should have used the term "radius" in order to please the teacher. As you know perfectly well, the radius of our observable universe is typically stated to be approximately 46 GLy or 4.35E+26 meters; roughly 3x the Hubble length just as I said.

Precise terminology is important when it's important, and it's not when it's not. When you have a substantive point to contribute, I very much appreciate it, even if I don't immediately recognize my error. If you think a terminology clarification is important, offer it and then let it go. Please try not to distract from the underlying point of my post; whether intended or not, it ends up hijacking my post.

And PLEASE, no more lectures about my flaws as an informal amateur technical author.

Jon

 

[jonmtkisco]

Hi Marcus,

Jon, you sound adversarial.

... you will confuse newcomers...

You sounded extremely confused...

the evidence is that you were very confused...

Let's not be argumentative...

Jon

 

[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