Superluminal Recession & Cosmological Redshift

[marcus]

Hi Marcus,
I guess what I wrote was subject to misinterpretation. I wasn't saying that the calculator is difficult to use. It is very easy to use.
...

Whew! Glad to hear that, Jon. confirms my impression that people do find it easy to use.

More to the point (since that turned out to be a non-issue) I wanted to say I'm glad you are playing around with the Morgan calculator. Some of the spreadsheet programs are more sophisticated for sure, but then as I understand it you have to download something. What I like about Morgan is it is immediately accessible with one click to anybody. So if you come up with an example to show something (as you for instance might) you can immediately share the example with any interested person at the forum.

Makes it easy for people to learn about recession speeds in the standard cosmology (Friedmann equation) picture with the usual parameters (i.e. 0.27, 0.73, 71 or so)

 

[jonmtkisco]

If the cosmic clock ran slower in the past than it does now (as measured by an "external observer", we can do a very rough calculation to constrain how much slower it must have run then.

According to the standard model, the CMB photons were emitted from the surface of last scattering at about z=1089 about 13.66Gy ago, when that surface was only about 42.2MLy from us (according to the Morgan calculator). So if "space itself" is not expanding, then the CMB photons have traveled a measly 42.2MLy in an enormous elapsed time of 13.66Gy; their average speed in transit has been 1/1089 the speed of light (c). Therefore, assuming that c is constant (according to the local clock,) during their transit period the cosmic clock on average has run at 1/1089 the current clock rate. If the change in clock rate over time has been linear, the clock at the surface of last scattering ran at 1/2178 the current clock rate.

My sense however is that the clock rate would have increased very rapidly at first, and much more slowly later on. In that case, the clock at the surface of last scattering was a great deal slower than the figure given above.

Unfortunately, there is a very basic problem in the math that goes along with this approach. As time moves forward and the universe gets larger and larger, photons are emitted from distances further and further away from us (as the universe expands). Yet they reach us at exactly the same time as photons which were emitted earlier at a lesser distance from us. A changing cosmic clock must cause all photons to have the same speed at the same time, regardless of distance from us. Therefore it is impossible for photons emitted earlier at a lesser distance to arrive at the same time as photons emitted later at a greater distance. The clock may be slower, but time never moves backwards.

So either there is something wrong with the model built into the Morgan calculator, or superluminal recession cannot possibly be explained by a variance in the cosmic clock.

Here's one brief example: The Morgan calculator says that at z=63, the distance of the object at the time of emission was .63GLy. Then 60 million years later, at z=31, the distance of the object at time of emission was 1.2GLy. Yet both sets of photons arrived here simultaneously. Not possible.

Jon

 

[zankaon]

Perhaps one simplistic model, might be to think of a manifold (i.e. continuum) being stretched uniformly for a given stage of universe (i.e. for given value of Hubble parameter). Then concomitantly (i.e. for given value of Hubble parameter), one also has local depressions forming (i.e. indentations i.e. curvature), representing local gravitational aggregation.

So it might seem that a given value of Hubble parameter, denoting a given stage of universe's evolution, can serve as a cosmic (universal) time. This is quite different from GRT (Gen. Rel.) description. Again emphasizing the differences between the two descriptions; but yet descriptive of the same manifold.

 

[jonmtkisco]

Hi zankaon,

So it might seem that a given value of Hubble parameter, denoting a given stage of universe's evolution, can serve as a cosmic (universal) time. This is quite different from GRT (Gen. Rel.) description.

I don't see how the model you describe is different from the standard cosmological model. The standard model assumes that a uniform cosmic time applies wherever the Hubble flow is homogeneous, which does not include the areas you describe as gravitational indentations. Mostly in late times, clocks in those areas are believed to run slower (to some degree) than the cosmic time.

Jon

 

[jonmtkisco]

So either there is something wrong with the model built into the Morgan calculator, or superluminal recession cannot possibly be explained by a variance in the cosmic clock.

Here's one brief example: The Morgan calculator says that at z=63, the distance of the object at the time of emission was .63GLy. Then 60 million years later, at z=31, the distance of the object at time of emission was 1.2GLy. Yet both sets of photons arrived here simultaneously. Not possible.
Jon

On further thought, I believe the problem is that the Morgan calculator implements the standard FLRW interpretation of "space itself expanding" (which I'll refer to as the "expanding-space model") in a way which is incompatible with calculating parameters based on historical clock variance (which I'll refer to as the "clock-variance model.") That shouldn't be surprising. The expanding-space algorithm assumes that high-z photons have been sort of swimming upstream, into a visceral welling-up of intervening empty vacuum, for a very long time, in fact since a time when the presently observable universe was very much smaller than today.

If one starts with the assumption that newly-existing space does NOT viscerally well up between the photons' emission sources and their eventual target, slowing the photons' approach, then one must assume that all of the photons emitted at very early times from locations inside the bounds of our "presently observable universe" (e.g. CMB photons emitted at a distance of 42.2MLy from us) have passed us by long ago, and are no longer observable by us. We can be certain of this because, as I mentioned, photons emitted more recently and from much greater initial distances have already passed us by. At any given point in time, all photons must travel at the same speed.

This suggests an interpretation that the CMB photons we presently observe were emitted from a surface of last scattering which is more recent and much more distant than is predicted by the expanding-space model. In fact, it seems highly probable to me that they would have been emitted from an initial distance far beyond the present Particle Horizon calculated by the expanding-space model.

Clearly one mandatory requirement of the clock-variance model is that the higher the z-value of a photon, the greater the initial distance at which it was emitted. The is the opposite of the expanding-space model.

Jon

 

[yuiop]

On further thought, I believe the problem is that the Morgan calculator implements the standard FLRW interpretation of "space itself expanding" (which I'll refer to as the "expanding-space model") in a way which is incompatible with calculating parameters based on historical clock variance (which I'll refer to as the "clock-variance model.") That shouldn't be surprising. The expanding-space algorithm assumes that high-z photons have been sort of swimming upstream, into a visceral welling-up of intervening empty vacuum, for a very long time, in fact since a time when the presently observable universe was very much smaller than today.

If one starts with the assumption that newly-existing space does NOT viscerally well up between the photons' emission sources and their eventual target, slowing the photons' approach, then one must assume that all of the photons emitted at very early times from locations inside the bounds of our "presently observable universe" (e.g. CMB photons emitted at a distance of 42.2MLy from us) have passed us by long ago, and are no longer observable by us. We can be certain of this because, as I mentioned, photons emitted more recently and from much greater initial distances have already passed us by. At any given point in time, all photons must travel at the same speed.

This suggests an interpretation that the CMB photons we presently observe were emitted from a surface of last scattering which is more recent and much more distant than is predicted by the expanding-space model. In fact, it seems highly probable to me that they would have been emitted from an initial distance far beyond the present Particle Horizon calculated by the expanding-space model.

Clearly one mandatory requirement of the clock-variance model is that the higher the z-value of a photon, the greater the initial distance at which it was emitted. The is the opposite of the expanding-space model.

Jon

Hi Jon,

I just to clear up some definitions here (for my benefit so that I know we are talking about the same thing ;)

In the "space itself expanding" model there is no time dilation because galaxies are stationary with the "local space". That is pretty much the standard interpretaion in non mathematical descriptions of cosmology.

One alternative to the "space itself expanding" interpretation is galaxies moving through static space and that requires time dilation which I will call the SR model. In the SR model the radiation we see now as the CMB comes from a priordial "gas" moving at about 0.99c relative to us so the radiation was not emitted 300,000 years after the big bang but much later due to time dilation. One difficulty with the Sr interpretation is even the significant time dilation of the surface of last scattering is not enough to account for the significant delay in the light getting to us as well as getting the angular distance of fluctions in the CMB and the redshift/ luminosity predictions to the SR model to match up with actual observations. One possible fix to those problems may be to assume significant rapid inflation before the the time of last scattering which effectively gives the surface a head start. I hope someday, a better mathematician than me will try and work out the correlation of a SR+Initial Inflation model with observations. My hunch is that such a model will not require a cosmological constant and accelerating expansion. Such a model assumes static spacetime that is neither expanding or accelerating and that the speed of light and time itself is constant from the big bang until now if we ignore local gravitational variations and peculiar motions.

Your "clock-variance model" seems to based on the interpretaion that galaxies are essentially stationary and that the appaernet motion and redshift is due to clocks speeding up as the universe ages. In this model the speed of light is constant from the time of the big bang but the increasing clock rates make radar distances appear to be getting longer over time. Such a model requires local rulers and physical objects such as the Earth to be shrinking over time so that the speed of light appears constant over time locally. In this model some galaxy that was 13 billion light years away now was 13 billion light years away at the time of last scattering just after the big bang and it only theclock variance that causes us to percieve the galaxies as receding. Is that a correct interpretation of what you describe as the "clock-variance model"?

 

[Garth]

Note:

If by the "Clock Variance" model it is really intended to mean the speeding up of atomic clocks and the shrinking of rulers made of atoms with cosmological time, as would happen with a variable mass theory in which fundamental particle masses increase with time, then that would entirely equivalent to an BB expanding universe model.

It would be simply a matter of how you define a second, that is, what physical process you use in your clock.

For example:

Sample two photons, one emitted by a caesium atom the other sampled from the CMB radiation.

The first, an "atomic" second, is defined as the duration of exactly 9.19263177x10⁹ periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

The second, a "photonic" second, is defined as the duration of exactly 1.604x10¹¹ periods of the radiation corresponding to the peak of the CMB black body spectrum.

Both systems of time measurement are physically significant and agree with each other in the present era, although they will diverge from each other at other times.

In the photonic universe model the expanding universe with fixed rulers has been replaced by a static universe with shrinking rulers - the BB singularity in one is a zero volume universe full of finite sized particles, in the other it is a fixed volume universe full of infinite sized (because their masses are zero at this event) particles. Both 'singularities' are equally crowded!

It is simply a matter of how you define your measurements.

Garth

 

[jonmtkisco]

Hi Kev and Garth,

Thanks for thinking about this. Let me try to clarify.

With the clock-variance model, I'm trying to stick as close as possible to the standard model, but to describe it without resort to the concept that empty space itself is expanding or being newly created. There has been much technical literature lately debating what it means for the universe to be expanding, and I'm just trying to dissect the physical meaning of that one step at a time, using the least exotic physics available. By "least exotic", I mean reliance on physical effects which have been demonstrated in a laboratory or which are uniquely compelled by unambiguous cosmological observations. I consider all of SR to be in the "least exotic" category, along with pretty much all aspects of spatially flat GR that don't rely on the concept of space itself expanding. However, I've been surprised to find out how deeply the expanding space concept is embedded into standard GR interpretations.

A global SR frame could be a conceptual starting point for the non-expanding space model. However, we know that a global SR frame is theoretically impossible in a universe immersed in a homogeneous gravity field. I prefer to describe the model as a non-expanding collection of tightly packed infintesimal local GR frames. In this model, galaxies and other matter are described as really, actually moving (i.e. the Hubble flow) in pre-existing space, and not causing new space to come into existence as a result of their movement. In the absence of space itself expanding, I'm trying to articulate exactly which rules of physics, and which physical phenomena, can best play the role of physical agent for cosmological redshift and for enforcing the speed limit c, (if in fact there even is such a speed limit across GR frames.) The causational factors I've focused in on are proper distance, proper recession velocity, gravitational density, and potential clock variances from a timelike and/or spacelike perspective.

I'm thinking about clock variance from a straightforward SR perspective. In other words, when time is dilated for the traveling twin in the twins paradox, the traveling twin ages more slowly, but does not experience any local physical effect such as the orbits of her bodily electrons shrinking. In SR, of course, from the perspective of a local observer, local time seems to pass in the normal way, and no local rulers or laws of physics are changed in the local frame. At very close to c, the non-travelling twin in a different inertial frame may observe the traveling twin to undergo a Lorentz contraction in the direction of motion, but that does not mean that the non-travelling twin observes the traveling twin's rulers to be uniformly shrunk without regard to orientation. As you know, one of the interesting aspects of SR is that both twins observe the other twin's clock to be running faster than their own, so long as the movement continues in a single direction. We can also think about gravitational time dilation from a straightforward GR perspective. As far as I know, no one has ever claimed that a gravitationally blueshifted photon source is physically expanded or that a gravitationally redshifted photon source is physically shrunk, as measured by a distant observer.

Garth, I'm definitely not getting into the kind of scenario you describe.

I am trying to apply my very modest math skills to calculate how much clock variance might play a role due to both gravitational and SR Doppler time dilation. So far I've tentatively calculated that the combination of these two time dilations creates a clock differential at z=1 where our clock runs about .65 as fast as the clock was running at the emitter at emission time. By itself, this isn't quite enough time dilation to achieve the .5 cosmological redshift the standard model does, but I'm still thinking through the calculations. I'm not starting with a rigid assumption that "actual" recession velocities range exactly up to c, or for that matter that they can't be superluminal.

One must be very careful about selecting distance and recession velocity parameters that are not tainted by the expanding-space concept. As I said, that's why the Morgan calculator is of limited value for this purpose. One must also consider whether a redshifted photon experiences significant post-emission blueshift because its energy is accelerated by the cosmic gravitational field it passes through (like the rocketeer in the Radar Ranging paper). Unfortunately there are a lot of simultaneously moving parts. We need to find ways to simplify the analysis.

Jon

 

[jonmtkisco]

I want to take a step back from the idea of cosmic clock variance in order to reassess the basic mechanics of cosmological redshift and superluminal expansion. I said in an earlier post that if "space itself" is not expanding, then high-z (high redshift) photons must originate from a greater distance than low-z photons which arrive here at the same time. I now think that statement was misleading. This is a subject where confusion comes easily and there always seems to be another surprise around the next corner.

The key point I neglected is that high-z photons were omitted from objects whose initial recession velocities (away from the Observer) were much higher than the objects from which low-z photons were emitted.

In a flat, constantly decelerating Lambda=0 Einstein-de Sitter universe (whose present age with H₀=71 is 9.18Gy), the Morgan Calculator says the surface of last scattering was receding from us at 63.7c when the CMB photons were emitted. In the local frame of emission, the newly emitted CMB photons began moving away from the scattering surface at 1c, so the CMB photons pointed in our direction were still receding away from us (the Observer) then at a net 62.7c. Over the ensuing elapsed time of about 9.18Gy, these CMB photons slowly eroded that recession speed until eventually they stopped receding and then slowly started to overtake our galaxy (which has been receding from their perspective) until they finally reached us just today.

I interpret that the CMB photons were able to overtake our receding galaxy for two reasons: (1) Our galaxy's recession rate away from the approaching CMB photons decelerated continuously between the emission time and the present, due to the effect of the cosmic gravitation field, and (b) the photons actually accelerated their own speed towards us during the early part of their travel (!)

How is it possible for a photon to accelerate in empty vacuum if it's already traveling at c? Simple: by passing through a large series of separate local frames. As time elapsed, each CMB photon passed by particles moving in the Hubble flow that were receding from the CMB photon's coordinate emission point at ever-faster velocities. Hubble velocity is proportional to distance. As the photon entered the local frame of each such particle (or galaxy), it was required to have a speed equal to c relative to that particle or galaxy. So the photon had to increase its velocity relative to (away from) its emission point. At some point in time, the galaxies being passed by the photon no longer had ever-faster recession speeds; they would have, but they had been decelerated by the cumulative effect of the cosmic gravity field over the ever longer elapsed time since the photon's emission. Then the photon began to decelerate its velocity away from its emission point, as necessary so as to pass by each remaining local galaxy at just c.

This change in the CMB photon's velocity relative to the emission point is demonstrated by dividing the total travel distance the photon covered, 13.3GLy, by the total elapsed travel time, about 9.18Gy: The average velocity of the photon away from its emission point is 1.45c. (Total travel distance is calculated as (D_then + D_now)/2. Its peak velocity away from its emission point must have been far greater than that figure, but I haven't worked out how to calculate that. By comparison, a photon emitted from a galaxy at z=1 has an average velocity of 1.02c away from its emission point.

So there we have it, apparently it is an everyday occurrence for photons to change speeds and to significantly exceed c relative to their emission point. This does not violate SR, because the photon's speed is always exactly c in any local frame in which it is measured. And from my analysis, GR doesn't forbid the behavior, it requires it.

Jon

 

[jonmtkisco]

A slight correction. On further reflection, I do not think the CMB photon ever decelerates relative to its emission point. Instead, I think it continues accelerating away from the emission point over the entire elapsed time of travel, but at an ever slowing rate of acceleration. The photon reaches its highest velocity away from the emission point at the time it reaches us, the Observer. At that time, the relative velocity has peaked at 32.8c, which is calculated as (V_then + V_now)/2. This is obviously much greater than the same photon's average velocity between emission and observation, which as I said is 1.45c.

Jon