The Mystery of Superluminal Recession Velocities in Cosmology

[jonmtkisco]

Hi Wallace,

I don't quite follow this? How can the recession velocity 'at time of reception' of the distant galaxy be a factor? Once the photon leaves the emitting galaxy it doesn't know or care about what that galaxy does.

Apparently the explanation of this point wasn't clear in my post. I said:

The equations divide by two in order to exclude the gravitational decrease in the emitter's proper recession velocity occurring place after the photon is emitted.

The reason for the attached diagram was to show that the equation must take account of the receiver's recessionary movement (away from the emission point) after the time of emission, but must NOT take account of the emitter's recessionary movement (away from the emission point) after that time. We are in agreement that what happens to the emitter after emission isn't relevant. A subtlety is required in order for the equation to accomplish this result from the data available, which after all does not distinguish between the recession of one party and the recession of the other party, since their recession is relative as between each other only. That's why I attribute 1/2 of the total post-emission recessionary movement to each party, rather than attribute the entire recessionary movement arbitrarily to just one of the parties.

Jon

 

[MeJennifer]

I want to try out a simpler way to think about gravitational redshift. The standard explanation makes it sound as if gravity acts directly on the energy of a photon, either decreasing the energy (redshift) if it is "climbing out of a gravity well," or increasing the energy (blueshift) if its "falling into a gravity well." To me, it seems easier if one does NOT think of gravity acting on the energy level. Instead, the only effect of gravity is to cause time dilation or contraction.

Thus, if a photon travels from the surface of a massive planet to an observer at a distant point in empty space, the local clock on the planet runs slower relative to the space clock. The observer's faster pace of life (faster clock) causes him to perceive the photon as having a lower frequency (fewer oscillations per clock tick) than would be calculated using the planet clock. The photon has not "changed" at all, it is just perceived differently depending on which clock is used to measure its frequency. This description is consistent with the concept that gravitational redshift does not "occur enroute", instead it "occurs as a single discrete event" at whatever point its frequency is measured. It also is consistent with the fact that in a matter-only universe the Integrated Sachs-Wolfe effect does not affect the redshift of photon which passes through a succession of overdense and underdense regions along its path. The gravitational redshift is calculated solely by the relative clock differential at the two end points. E.g., by comparing the clock at the observer with the clock at the emitter using the SR time dilation equation.

That is the correct description. Curved spacetime does not influence the frequency of a photon, and neither does it stretches its wavelength as these would be in clear contradiction to the equivalence principle.

The reception of a "red shifted" photon is really a unaltered photon observed by a relatively blue shifted
receiver.

See for instance: http://xxx.lanl.gov/abs/physics/9907017

 

[jonmtkisco]

Hi Kev,

I think the Davis & lineweaver diagram is correct without the switch (No typo). The (0,0) model has no gravity and no antigravity while the (1,0) model has significant gravity due to normal matter and no antigravity. The reason the velocity for a given redshift is lower in the (1,0) model is due to the slow down of the recessional velocity by gravity which eventually leads to a collapse of the universe. The greater redshift in the (1,0) model relative to the (0,0) model for a given recessional velocity is due to gravitational redshift which is present in the former but not in the latter.

I hear ya', but I still think it's a typo. In proper distance coordinates, cosmological redshift in a (0,0) universe should be close to SR Doppler redshift alone. Actually it seems like it should identical to SR Doppler redshift alone, I'm not sure why it's even a separate line. Maybe some sort of coordinate confusion.

Conversely, the higher Omega_m is (with Lambda=0), the more the proper velocity of the observer away from the original emission point slows down during the travel of the photon; therefore the less redshift he will observe as a function of whatever the proper recession velocity was at emission time.

The issue here is not what the "true recession velocity" is; rather we are looking for the relationship between the "true recession velocity" and the "observed recession velocity." So for this specific purpose it doesn't matter whether the overall recession velocity of the universe is relatively high or low. By the way a (1,0) universe will not ever collapse, instead its expansion rate will decrease asymptotically toward zero.

In other words you can calculate the increase in wavelength using either concept/model and get the same results but it is important to realize they are essentially the same thing and not to apply the both concepts at the same time and double count. Mathematically they are the same, just the interpretation of "what is really happening" is different.

Agreed. Double counting must be avoided. The reason I prefer the "clock differential" model of gravitational redshift is because I think it makes it easier to treat the Doppler and gravitational components of redshift in a consistent way.

There is no SR time dilation component in comoving coordinates.

Comoving coordinates sometimes obscure the simplicity or subtlety of what gravity is doing. That's why my discussion is all in proper distance coordinates.

Jon

 

[yuiop]

Hi Kev,

I hear ya', but I still think it's a typo. In proper distance coordinates, cosmological redshift in a (0,0) universe should be close to SR Doppler redshift alone. Actually it seems like it should identical to SR Doppler redshift alone, I'm not sure why it's even a separate line. Maybe some sort of coordinate confusion.

SR distance coordinates are proper distance coordinates. The Davis & lineweaver diagram shows the (0,0) velocity using the FRW metric which uses comoving coordinates which is the accepted way of doing cosmology. As I was trying to show in post #85, there is a fictitious acceleration or curvature even when there is no mass or cosmological constant in the FRW metric using comoving coordinates. The acceleration of the universe that is described as the "discovery of the century" may turn out to be the "blunder of the century" (again) because it is a fictitious force introduced to cancel out the fictitious gravitational effect of the FRW metric. It is a bit like centrifugal force. This is a fictitious force which in Newtonian physics was canceled by the force of gravity of a free falling body. Einstien showed that physics based on two fictitious forces cancelling each other out is not good physics and his breakthrough in GR is that there is no force of gravity acting on free falling bodies.

...
By the way a (1,0) universe will not ever collapse, instead its expansion rate will decrease asymptotically toward zero.

I accept that correction but it should be recognized that there is an implicit assumption of recessional velocity in that statement. Without galaxies having outward escape velocity even a (1,0) universe would collpase.

...
Comoving coordinates sometimes obscure the simplicity or subtlety of what gravity is doing. That's why my discussion is all in proper distance coordinates.

Jon

I agree, but you should bear in mind that all conventional texts on cosmology work in co-moving coordinates.

 

[Wallace]

The reason for the attached diagram was to show that the equation must take account of the receiver's recessionary movement (away from the emission point) after the time of emission, but must NOT take account of the emitter's recessionary movement (away from the emission point) after that time. We are in agreement that what happens to the emitter after emission isn't relevant. A subtlety is required in order for the equation to accomplish this result from the data available, which after all does not distinguish between the recession of one party and the recession of the other party, since their recession is relative as between each other only. That's why I attribute 1/2 of the total post-emission recessionary movement to each party, rather than attribute the entire recessionary movement arbitrarily to just one of the parties.

Jon

(emph mine)

The data doesn't tell us anything about the recession velocity. Only the redshift. I still have no idea how you could use what you describe to calculated the expected redshift, given some other observable in some model.

 

[jonmtkisco]

Hi Wallace,
If you start with a known Hubble rate and proper distance, I was suggesting you could calculate a predicted cosmological redshift. First you calculate the relative proper velocity between (1) the inertial frame of the receiver at reception time, and (2) the inertial frame of the emitter at emission time. Then you just use this calculated velocity to calculate the SR relativistic Doppler shift. I think that should give the correct answer for the cosmological redshift.

My thought was that this calculated velocity already includes gravity's effect in reducing the relative recession velocity during the photon's travel, so you don't need to calculate any separate component for gravitational redshift.

Jon

 

[Wallace]

But does it work?

 

[jonmtkisco]

Hi Wallace,

First, I must clarify that in my simplified description for a "bottoms-up" method to calculate cosmological redshift, I omitted the step which corrects for change in time dilation. The complete set of steps is:

1. Calculate the relative proper velocity between the inertial frames of (i) the receiver at reception time and (ii) the emitter at emission time. In a flat universe, the higher the average background matter density during the travel period, the more this calculated velocity will be reduced, as compared to the relative velocity between the emitter and receiver at the time of emission.

2. Calculate the Doppler redshift using the SR relativistic Doppler redshift equation. The greater the relative recession velocity between the receiver is from the emitter, the more the predicted redshift will be increased by the relativistic correction to the Classical Doppler formula.

3. Calculate the difference in gravitational time dilation beween the inertial frames of (i) the receiver at reception time and (ii) the emitter at emission time. E.g., for an emitter currently at z=1, the scale factor (a) was half of today's value, and therefore the gravitational density was r³ or 8 times greater. Apply the time dilation change as a correction to the relativistic Doppler redshift calculation. The greater the difference in time dilation, the more the total predicted cosmological redshift will be reduced by this correction.

But does it work?

I don't know. I may need some help getting the math straight.

When you ask "does it work", I think you mean, does it calculate the same answer as the cosmological redshift equation, which simply compares the scale factor (a) at the time of reception and emission. It's not immediately apparent that it does, because my method applies two relativistic corrections, and the cosmological redshift equation applies none. But the two relativistic corrections I use affect the calculation in opposite directions, so at least to some extent they tend toward cancelling each other out.

I note that the cosmological redshift equation takes gravity into account, since the gravitational slowing of the increase in (a) over time directly affects the calculated redshift. The gravitational reduction in recession velocity over time is directly proportional to distance, which allows Hubble's law (net recession velocity is proportional to distance) to remain exactly true at the time of emission, reception, and at every time in between. The cosmological redshift equation simply excludes ALL SR relativistic effects: both the relativistic components of the Doppler effect and gravitational time dilation. In this sense the nature of the cosmological redshift equation is entirely Newtonian.

As far as I can see, there are only three possible ways that the cosmological redshift equation can ignore relativistic effects and still be correct: (1) if space itself really is expanding and actually causes wavelength to stretch with the scale factor; (2) if Special Relativistic effects inherently become reduced (asymptotically toward zero) over very large cosmological travel distances, or (3) if the relativistic effects (and the "divide by two" component) of my method all exactly cancel each other out.

I am not inclined to accept #1 above, and #2 is a radical idea that has no apparent explanation. So I hope #3 turns out to be true.

Jon

 

[yuiop]

When you ask "does it work", I think you mean, does it calculate the same answer as the cosmological redshift equation, which simply compares the scale factor (a) at the time of reception and emission. It's not immediately apparent that it does, because my method applies two relativistic corrections, and the cosmological redshift equation applies none. But the two relativistic corrections I use affect the calculation in opposite directions, so at least to some extent they tend toward cancelling each other out.

A simple first test of your equations is to do some numerical calculations and compare them with the results from these cosmology calculators: http://nedwww.ipac.caltech.edu/help/cosmology_calc.html

That will at least tell you if you are in the right ball park.

 

[jonmtkisco]

I do not think that the method I described for a "bottoms-up" calculation of predicted cosmological redshift is consistent with the FLRW metric, so it must be incorrect. In particular, the change in matter density as a function of time does not cause any clock rate differential in the homogeneous FLRW metric. In normalized units, the FLRW metric can be simply written as:

ds² = -dt² + a²(t)(dx² + dy² + dz²)

The cosmic clock (t) is invariant for purely comoving observers as a function of the declining matter density. The cosmic clock is just the timelike spacetime distance orthogonal to a hypersurface of constant comoving physical distance, so:

ds² = -dt².

So in the same way that the declining cosmic matter density does not create any gravitational redshift, it also does not create any clock differential between the emitter and receiver.

A.B. Whiting seems to have been on the right track when he derived the gravitational component of cosmological redshift by calculating the difference between the matter density now and zero matter density. I think the remaining step needed to extend his analysis into a general equation for cosmological redshift is to perform an integration of the SR Doppler redshift at each point between the emitter and receiver, multiplied by an integration of the gravitational redshift at each point between the emitter and receiver (calculated using the matter density now and a matter density of zero):

\frac{\lambda_{r}}{\lambda_{e}} = \int\begin{array}{cc} v^{e}\\v_{r} \end{array} SR \ Doppler \ redshift \\\ \int\begin{array}{cc} \rho^{r} \\ \rho_{0} \end{array} gravitational \ redshift

As Whiting says, just multiplying the SR Doppler redshift and the gravitational redshift calculates the correct instantaneous cosmological redshift for a flat FLRW universe with static density.

Something along these lines is needed so that we can obviate the need for the tradititional explanation that the "expansion of space" physically stretches the wavelength of transiting photons. As regards observational predictions of GR, a model universe where space does not expand must be identical to those of a universe with expanding space. Then we can attribute cosmological redshift simply to the difference between an SR universe (i) without gravity and therefore with a single global reference frame, and (ii) with gravity, and therefore with an infinitude of different local reference frames.

Jon

 

[jonmtkisco]

As I mentioned, a matter-filled homogeneous universe is comprised of an infinitude of tightly packed local reference frames. Therefore the rules of Special Relativity simply don't apply when shifting from anyone such local reference frame to another adjacent frame. Objects moving in two such adjacent frames may have a velocity relative to each other that exceeds the speed of light, c.

One might be tempted to describe this as a "license to steal", in the sense that the SR speed limit of c doesn't seem to apply hardly at all in a homogeneously gravitational universe. But the reality isn't that dire. The degree by which the velocity of an object in any local frame can exceed c relative to an immediately adjacent local frame is dictated entirely by the applicable GR metric of gravity. So if the gravitational density is low, the degree of "violation of the speed limit" in adjacent frames is infinitesimal. If the gravitational density is high, this speed limit can be "violated" to a larger degree.

Consider our very early observable universe, a fraction of a second after inflation is theorized to have ended, which could be visualized as being the total size of a grapefruit or beachball. The FLRW metric (to the extent its equation of state doesn't require modification on account of the then-reigning quark-gluon plasma) calculates that matter particles located just a few millimeters away from each other had velocities relative to each other in the range of multiple times the speed of light. So a tiny distance between distinct local frames is no inhibitor to a massive "violation" of the speed limit. You just need a truly astounding gravitational density to enable it -- which indeed is what theory calculates for this very early universe. Of course it isn't actually a "violation" of GR, which governs a gravitation-filled universe. By the same token, a low gravitational density enables large violations of the speed limit if the objects are extremely distant from each other.

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.

Jon

 

[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.
...

Is that your own deduction, Jon? It sounds strange. Try using Morgan's calculator on an example, like a galaxy with redshift 7. The URL for Morgan is in my signature. The terminology is a bit dumbed down and nonstandard, but the calculator is basically like what you get at Ned Wright. Put in 0.27 for matter, 0.73 for Lambda, and 71 for the Hubble parameter---then with that prep, try z=7.I will do that too and we can compare results.
Hmmm. z=7 is not the VERY early universe. The CMB comes from z = 1100 and the universe was already hundreds of thousands of years old then. But you are talking about galaxies, and z = 7 is, I think, fairly early for a galaxy to exist.What I get is that for z = 7 the recession speed then was 3.08 c and the recession speed now is 2.07 c. To me that seems quite a bit different. But maybe to you it seems like it is approximately the same recession speed, as you say.

 

[jonmtkisco]

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"), and (ii) Wallace's frequently repeated explanation that 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.

I'm not sure that z= 7 or 8 is enough to analyze my point. I suggest trying z=1089, at the CMB surface of last scattering. Or better yet, the highest z that can be calculated exactly at the end of the theorized inflation era. A straight integration of the FLRW metric (including the radiation-dominated era) calculates z = 1.3E+26 at about 3E-32 seconds after the big bang. I forget whether Morgan's or Ned Wright's calculator are programmed to handle the radiation-dominated era. Some calculators are not.

Jon

 

[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.

I suggest trying z=1089, at the CMB surface of last scattering. Or better yet, the highest z that can be calculated exactly at the end of the theorized inflation phase.
...

OK here goes. z= 1089
then it is not galaxies, but a bunch of matter that eventually condensed to form our galaxy and a bunch of matter that sent us some of the CMB back at that time.
we will find the recession speed then, and compare it with the recession speed now

my guess is that the recession speed then will be around 57c and the recession speed now will be around 3c. To me those do not seem approximately equal. But according to what you say they should be, and maybe they seem approximately the same to you.

Let's both do it. Good practice for you to use the calculator if you haven't before.
========================

this is pushing the accuracy limits of the Morgan calculator I expect, but we should get at least a rough notion of the magnitudes.
what I get is the recession speed then (at z = 1089 as you suggested) was 56.65c
and the recession speed of the same bunch of matter now is 3.3c

 

[jonmtkisco]

Hi Marcus,

As I mentioned in an edit to my previous post, z=1089 might get close to the right answer, but it may not. Better to try z=E+26. But make sure your calculator takes account of the radiation-dominated period, which substantially affects the metric.

My spreadsheet (which does account for radiation domination) says that at about 3E-33 seconds after the big bang, the Hubble velocity is about 1E+52 km/s/Mpc. A Mpc is about 3E+22 meters. The speed of light, c, is 3E+8 meters/second.

Jon

 

[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