Must (Ve) expansion of the universe be C?

[Matterwave]

How do you define "average recession speed"? This is not a meaningful quantity as far as I am aware.

 

[bobie]

- they say that it has fluctuated and now indeed it is accelerating. That implies that you are aware of different rates at different times. Make an average and tell me what it is.
- my assumption was: if T₀ =13.8 Gy and there are objects at >14.4 , 25, 40 Gly, that implies that the average expansion rate is > C

The key factor in the issue is T₀ : why is it 1/H₀?

The surface of a balloon is expanding at the rate 1cm+1/10mm/s, if you repeat observation you may establish if and how much/often the rate changes, you may conclude that a point at distance 10m is recessing at 1m/s , now,- for how long has it been expanding?

What information do you need to answer that question? when you can say T₀ 100s?

 

[mfb]

There is no such thing as an "average recession speed". The whole concept of a "recession speed" is pointless if you don't say "for this object".

For a given object, you can indeed calculate an average recession speed - this will depend on the distance of the object, so it is not a single unique number. There are objects where such a calculated recession speed is a multiple of the speed of light, yes.

The key factor in the issue is T₀ : why is it 1/H₀?

It has been mentioned multiple times that it is not.


Maybe a step-wise example is easier to understand. The actual physics happens with a continuous universe, of course:

Measure the distance of nearby objects (let's say 10 million light years) by their brightness (see cosmic distance ladder for details). Measure their redshift to determine the speed of expansion of space between those objects and us. The speed divided by the distance is the recent expansion rate, averaged between "now" and "10 million years ago". Expansion does not change so significantly within 10 million years, so let's call this "the expansion speed in the last 10 million years".
Measure the redshift of objects 20 million light years away. You know how space expanded in the last 10 million years, you can calculate backwards how the object receded 10 million years ago and how far away it was. In this way, you can calculate the expansion rate we had 10 to 20 million years ago.
Continue this with more and more distant objects and you get the complete history of expansion.

 

[George Jones]

Bobie, since you keep quoting me, I feel that I should expand on my comments about cosmological modeling, but I don't know if I have the stamina. There is, however, one thing that I do want to say.

Bobie, you do realize, don't you, that we routinely observe speeds greater than c in special relativity, e.g., in the Large Hadron Collider. (mfb and Matterwave: humour me, I haven't lost my marbles.)

 

[Matterwave]

Bobie, you do realize, don't you, that we routinely observe speeds greater than c in special relativity, e.g., in the Large Hadron Collider. (mfb and Matterwave: humour me, I haven't lost my marbles.)

Sorry, but I can't agree with you there if you mean an actual speed. Actual speeds in the lab are always limited by c because we are measuring actual speeds here (these are local measurements), not apparent recessional velocities like in cosmology.

The only thing I can think of that you might be talking about would be "closing speed" between two beams of particles moving at ~c. The distance between two beams moving towards each other, each at speed ~c, as measured in a third frame of reference, would close at a rate ~2c. But a closing speed is not a real speed (just as a recessional velocity is not a real velocity). A closing (or separation) speed is limited by 2c instead of c.

 

[bobie]

, I feel that I should expand on my comments about cosmological modeling, but I don't know if I have the stamina.

Hi George, you don't have to go to great lengths, I actually wanted to ask this in the other thread:
I suppose that the evaluation of distance is arbitrary only to a certain extent. Suppose FLWR does not exist, to what extent is it possible to stretch the distance? Can you imagine a model in which actual distances are multiplied by a factor of 100?
One more thing, when you mention distance, do you mean proper distance? I mean: do you find first D_now and from that, dividing by S, D_then, or vice versa?
Thank you, George your contribution is invaluable!

As to C, I have read everywhere that actual velocity of an object cannot exceed it, only relative velocity can, but I am not questioning that here, that would be dangerous and detour OP.
I accepted the fact that the edge of observable universe, in your model, is at 3.15C V_e, probably tou take it as actual, I as relative.
My question here is if it is compatible with your model to rescale it by 1/2 - 1/3. What consequences would that have on other parameters, what principles would exclude that.
A very simple question, I thought

 

[bobie]

For a given object, you can indeed calculate an average recession speed
Measure the distance of nearby objects (let's say 10 million light years)...The speed divided by the distance is the recent expansion rate, averaged between "now" and "10 million years ago". Expansion does not change so significantly within 10 million years, so let's call this "the expansion speed in the last 10 million years".
Measure the redshift of objects 20 million light years away.
Continue this with more and more distant objects and you get the complete history of expansion.

Hi mfb, please let me know if you agree that your argument on expansion was circular. (see post #31)

I am not sure I understood what you are saying here, are you saying that when you find the average rate for an object 10Mly far away that value is valid only for that given object and not for all objects in U at that time?

 

[bobie]

It has been mentioned multiple times that it is not.
.

wiki says it is 1/H₀ by a small factor F, (a fractional contribution 1...), you mean: I should have written T₀= ≈1/H₀?

The age t0 is then given by an expression of the form
[tex]t_0 = \frac{1}{H_0} F(\Omega_r,\Omega_m,\Omega_\Lambda,\dots) [/tex]

In what way this expansion is related to the age of U , in any model?

 

[Matterwave]

Hi George, you don't have to go to great lengths, I actually wanted to ask that in the other thread:
I suppose that the evaluation of distance is arbitrary only to a certain extent.
Suppose FLWR does not exist, to what extent is it possible to stretch the absolute distance?
Can you imagine a model in which actual distances are multiplied by a factor of 100?
One more thing, when you mention distance, do you mean proper distance? I mean do you find first D_now and from that, dividing by S, D_then, or vice vera?

There's no such thing as "absolute distance" when it comes to cosmology, I'm afraid. We can't actually go out there with a ruler and measure distances like that.

But what we DO have are a large number of ways to determine the distance to an object, irrespective of the FLRW metric. I don't know why you keep disregarding these distance ladders. I have mentioned them several times, and others have given you information on these ways of finding the distance, but you disregard all those points and then impose your own arbitrary comments on distances in cosmology.

Several ways of measuring distances to far away objects:
1) Using a luminosity vs distance relationship (things farther away look dimmer). This is called the "luminosity distance". I have mentioned specifically, in my previous post, several different ways of doing this. In a static, non-expanding, flat, universe, the luminosity distance would be equal to the proper distance.
2) Using an angular size vs distance relationship (things farther away look smaller). This leads to a measurement of the angular distance. Again, in a static, non-expanding, flat, universe, the angular distance would be equal to the proper distance.

The proper distance itself cannot be measured. The proper distance depends on the model for the expansion of the universe.

But all of these considerations are already taken into account by cosmologists. I do not expect cosmologists to be so incapable as to neglect these effects.

As to C, I have read everywhere that actual velocity of an object cannot exceed it, only relative velocity can.

What is "actual velocity" if not a relative velocity? Relative velocities ARE the actual velocities. They cannot exceed c.

 

[Matterwave]

wiki says it differs by a small factor, is it wrong?
T₀= ≈1/H₀

mfb (as well as I) said that 1/H0 is NOT T0. Your point is not a refutation of his point, but supporting his point!

 

[bobie]

mfb (as well as I) said that 1/H0 is NOT T0. Your point is not a refutation of his point, but supporting his point!

I did not refute nor support. I quoted what I read, I only changed ≈ to = , I said many times T₀= 1/ H₀ (omitting F). Is it a big problem? does it make any difference? are you splitting hairs? I was just referring to the fact that age of U is linked/related to/ based on the expansion rate, (not to its exact value). Does that change the substance? I asked why is it related to H₀, what is the nature and necessity of this relation. And I gave you the example of the balloon , so that you might realize it is not a necessity (post #28 and #37)

As to distance, I already corrected the slip 'absolute' I meant 'proper', distance is just distance.
what do you mean in your post #44 by 'distance'?

But what we DO have are a large number of ways to determine the distance to an object,
Several ways of measuring distances to far away objects:
.

Please, when you reply. alwas check what my posts look like, because I always edit them soon after I posted ( I write in a rush and make a lot of mistakes).

 

[Matterwave]

As to distance I already corrected the slip 'absolute' I meant 'proper', distance is just distance.
what do you mean in your post #44 by 'distance'?

I gave you what I meant right in the body of the post...I even gave you their proper names... If you want their formal definitions, then fine. The luminosity distance is defined as the distance ##d_L## such that the flux from a given astronomical object ##\Phi## with luminosity ##L## is equal to:

$$\Phi=\frac{L}{4\pi d_L^2}$$

The angular distance is the distance ##d_A## such that an object of proper length ##l## aligned perpendicular to the line of sight subtends an angle ##\delta\theta<<1## on our sky given by:

$$\delta\theta=\frac{l}{d_A}$$

 

[bobie]

This issue is interesting but not relevant, I want to stick to the OP. You acknowledge that evaluating 'proper' distance, the present issue, is arbitrary, that's OK.
I must limit the number of posts, since, when the thread becomes unwieldy, they close it and I'd like to get an answer.

If you wish, let me know
- what you meant about (in post #45)
- if you agree with mfb that the average rate measured for an object over a period of time is valid only for that object,
- how / when you can determine t₀ of the balloon (post #37)
- what happens if we re-scale distances by 1/2 , (the main OP question )

Your ideas are highly appreciated.

 

[Matterwave]

I am of the opinion that your questions have been adequately answered. In fact, your OP was answered as early as post #2 by mfb. You are obviously of the opinion that your questions have not been adequately answered. However, as I have in my toolbox no further alternative methods of answering your questions again, I have nothing further that I can contribute to this thread. Sorry.

 

[mfb]

Hi mfb, please let me know if you agree that your argument on expansion was circular. (see post #31)

It was not circular. It was just not explained in every detail.

I am not sure I understood what you are saying here, are you saying that when you find the average rate for an object 10Mly far away that value is valid only for that given object and not for all objects in U at that time?

It is valid for all objects 10 Mly away (neglecting local motion, those objects all have the same apparent recession speed). But not for objects 20Mly away. Or for the same object 1 billion years ago.

T₀ ≈1/H₀

Yes, this is rough coincidence today, it has no special meaning (again, see previous posts). It was wrong in the past and it will be wrong in the future.
≈ instead of = is a big difference.

 

[bobie]

It is valid for all objects 10 Mly away (neglecting local motion, those objects all have the same apparent recession speed). But not for objects 20Mly away. Or for the same object 1 billion years ago.

I am glad you say that, mfb, because that is exacly what I meant from the beginning and in post #37:

- they say that it has fluctuated and now indeed it is accelerating. That implies that you are aware of different rates at different times. Make an average and tell me what it is.

You take the averages of different epochs, make an overall average and there you have what seemed oscure in post #2: V_e, the average expansion rate of U

Yes, this is rough coincidence today, it has no special meaning (again, see previous posts). It was wrong in the past and it will be wrong in the future.
≈ instead of = is a big difference.

I hope you had read my reply to matterwave.
I am not referring to present or past value of 1/H₀, I am asking about the mere presence of H₀ in the formula, why in determining the age of U you need to refer/consider/ relate to the expansion rate.
If you do, there must be a relation, a reason I am sure, why? I am not aware of the necessity of such a relation as I showed in the balloon example

 

[mfb]

You take the averages of different epochs, make an overall average and there you have what seemed oscure in post #2: V_e, the average expansion rate of U

Then you get "current proper distance"/"age of the universe". What's the relevance of that value?

I am not referring to present or past value of 1/H₀, I am asking about the mere presence of H₀ in the formula, why in determining the age of U you need to refer/consider/ relate to the expansion rate.

Because there is no other way? You start with the current universe and work backwards until the distances become zero.

If you do, there must be a relation, a reason I am sure, why? I am not aware of the necessity of such a relation as I showed in the balloon example

Expansion rates are not arbitrary, they follow the FLRW equations (according to our measurements).

 

[marcus]

...
Expansion rates are not arbitrary, they follow the FLRW equations (according to our measurements).

That's the crux! If a member will not be satisfied with others' verbal interpretation of the Friedman equation (aka FLRW for Friedman Lemaître Robinson Walker) then if they are sincerely interested in learning they must be shown the equation and make an effort to assimilate it. At least I see no other way.

I made a graphic plot of T and 1/H, to illustrate the relation between them.
There is a thumbnail of the graph, and a little bit of explanation of the Friedman equation here:
https://www.physicsforums.com/showthread.php?p=4779726#post4779726
Click on the thumbnail there to enlarge. I'll try to also put the plot in line here:

The curves cross at around year 15 billion, that is a little over one billion years from now, in the future. It is not true that, at present, T = 1/H

To essentially repeat what several others have said: the present value H₀ is a key datum derived from observations and provides an important INPUT to the equation by which one figures out the estimated age T₀. The Friedman equation is what mediates between the two and that relationship is what has to be understood. There is no simple naive EQUALITY like T = 1/H

The Hubble radius (in Gly) is numerically the same as the Hubble time (i.e. 1/H) expressed in Gy. So the red curve gives the Hubble time in Gy as well as the Hubble radius. Either quantity is a reciprocal indicator of expansion RATE, not a measure of SIZE. You can see from the plot that the expansion rate is due to level off while distances continue to grow. The rate is due to level off at around 1/170 % per million years,i.e. the Hubble time 1/H is due to level off around 17 billion years, as the graphic plot indicates.

 

[PeterDonis]

But what we DO have are a large number of ways to determine the distance to an object, irrespective of the FLRW metric.

Not only that, we also have observed *relationships* between the different distance measures; and those relationships can be used to place significant constraints on the possible models that can explain the data. For example, see Ned Wright's cosmology tutorial here:

http://www.astro.ucla.edu/~wright/cosmo_02.htm

 

[julcab12]

For the sake of reference. Here is an animated chart in line with FLRW on curvatures.

http://background.uchicago.edu/~whu/intermediate/clcurvature.html"The animation shows two scenarios: for the yellow curve, ΩΛ is fixed to zero and ΩM gradually decreases, so that ΩK increases and the curvature is increasingly negative. And indeed, the peaks move to the right. For the blue curve, ΩK is fixed to zero (a flat universe) and ΩM gradually decreases (so that ΩΛ increases accordingly). This time, it follows that the peaks move slightly to the left as the amount of dark energy increases."

 

[marcus]

I've been trying to understand how a newcomer could, as may have happened in this case, get confused about the connection between the age of expansion (call it T) and the Hubble time (call it 1/H) or equivalently the distance version of the Hubble time (call it R = c/H). Since we've turned a page I'll bring forward a graph that may help:

...I made a graphic plot of T and 1/H, to illustrate the relation between them.
There is a thumbnail of the graph, and a little bit of explanation of the Friedman equation here:
https://www.physicsforums.com/showthread.php?p=4779726#post4779726
...

The curves cross at around year 15 billion, that is a little over one billion years from now, in the future. It is not true that, at present, T = 1/H...

To repeat for clarity, the Hubble time is just the reciprocal of the growth rate. The Hubble radius R is just equal to the Hubble time multiplied by c. If the time is 14.4 Gy, then the radius is 14.4 Gly (if one is a number of years the other is the same number of lightyears).

Since they are reciprocals, if the Hubble rate increases the Hubble radius must decrease, and viceversa. The Hubble radius R does not grow at the speed of light. If fact you can see that it is beginning to level out around 17 billion lightyears.

I think this is where an intelligent Noobie could get confused. When someone tells you the definition of the Hubble radius, if you don't listen very carefully you can easily get the wrong idea and think that it represents the "size" of the universe in some sense and that it is growing at the speed of light!

The Hubble radius is certainly not in ANY sense the radius of the universe! It is simply a way of keeping track of the rate that actual physical distances between pairs of stationary objects/markers/observers etc are increasing. The Hubble radius does not even have to grow--it can DECREASE while the universe is undergoing expansion, or it can increase but at an entirely independent rate.

The Hubble radius AT ANY GIVEN MOMENT is basically just the SIZE of those physical distances which are increasing to the tune of c, the speed of light, AT THAT MOMENT. It tells you what other distances (between CMB stationary markers as always) are doing, at that moment, because their speed of growth is always in proportion to their size. So Hubble radius embodies the same info as Hubble time 1/H or as Hubble rate H itself.

 

[marcus]

So here's a perfectly reasonable confusion that could happen to someone. they hear the definition:
"The Hubble radius is the SIZE of those actual distances (between stationary markers) which are growing by c at that moment."

And they say to themselves Ahah! I hear the word radius therefore we must be talking about the radius of the universe!

And they say Ahah! it sounds like the Hubble radius must itself be growing at the speed of light!

Therefore the universe has a definite known radius and a definite speed of expansion which is the speed that radius is growing!

Alas it is not so. The universe does not have a definite known radius and a well-defined "speed of expansion". That phrase is meaningless as far as we know. According to the standard model it has a percentage RATE of distance growth, not a speed.

And Hubble radius is not defined as a distance between a designated pair of objects each at CMB rest. It is defined as a critical size or threshold size, valid at a particular moment, dividing the distances growing < c from those growing > c.
that critical distance seems to change over time according to the Friedman equation---which is a model that fits massive amounts of data amazingly well and arises from the GR equation (currently accepted law of gravity and geometry). We can be pretty sure we understand (to good approximation) how H changes with time which amounts to the same thing as knowing how R changes, since it is the reciprocal c/H. In any case it should be clear that the Hubble radius is not itself subject to Hubble law distance expansion. It is not growing at the speed c! Indeed it is showing signs of leveling off and eventually changing very little if at all