Superluminal Recession & Cosmological Redshift

[jonmtkisco]

I'm taking the liberty of revising and restating this topic which started in a separate thread. Comments are welcome.

A lively debate is underway today by mainstream cosmologists as to whether the expansion of the universe implies that empty space between galaxies is also expanding. When faced directly with the question, most cosmologists will say that galaxies are moving apart because they were previously moving apart, but decline to state flatly that space itself expands. And yet it has been customary for textbooks and technical literature to explain both superluminal recession and cosmological redshift only as the result of space itself expanding. What seems clear is that the observational predictions of GR must be precisely identical regardless of whether space itself expands. Therefore, at a minimum we need a comprehensive theoretical description of both superluminal recession and cosmological redshift that does not resort to the concept of expanding space. Here are some thoughts on that subject.

Accurate application of Special Relativity depends on having a global inertial reference frame, which may be arbitrarily selected, but which cannot be accelerating, and by the same token cannot include significant gravitational objects. On the other hand, our universe appears to be homogeneously filled with gravitating matter. This means that instead of one global reference frame, we have an infinite series of tightly packed local reference frames.

Superluminal Recession

In our gravitation-filled universe, the rule of SR that no object can exceed the speed of light, c, relative to any other object, simply doesn’t apply. Objects at rest in any two local reference frames which are in motion relative to each other may have a relative velocity exceeding c. This is true even if the two frames are immediately adjacent to each other.

One might be tempted to call this is a "license to steal", in the sense that the SR speed limit of c doesn't seem to apply hardly anywhere in our universe. But the reality isn't that dire. The degree by which the velocity of an object in a local frame can exceed c relative to any other local frame is dictated entirely by General Relativity’s applicable metric of gravity. If the gravitational density is low, the degree of "violation of the speed limit" in nearby frames is infinitesimal. If the gravitational density is high, this speed limit can be "violated" to a larger degree. Even a low gravitational density enables large violations of the speed limit if the objects are extremely distant from each other, currently in the range of z=1.6.

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 beachball. The FLRW metric (to the extent its equation of state doesn't require modification on account of the then-dominant quark-gluon plasma) calculates that matter particles located just millimeters away from each other were receding from each other at velocities many times faster than c. This demonstrates that a tiny distance between distinct local frames is no inhibitor to observing a massive "violation" of the SR speed limit. All that’s needed is truly astounding gravitational density -- which is what theory calculates for our very early universe.

Note that any pair of particles which are observed to have a given relative recession velocity now haven’t gained relative velocity over time as their mutual distance increased. On the contrary, their relative recession velocity was enormously higher in the very early universe. In early times, the self-gravity of the universe hugely decelerated every galaxy pair's mutual recession rate; in late times, dark energy has reaccelerated them but to a much lesser degree. Absent the competing effects of those two accelerations, each pair of particles would retain the same relative recessionary momentum they had in the very early universe.

One must confront the question whether superluminal recession is a “physically real” phenomenon or just an observational artifact. If it is physically real, then it will continue regardless of how low the cosmic gravity density declines in the far future. Consider a model universe with dark energy [edit: Lambda=0 doesn't work well here]. As time passes, the gravitational density declines, and in the limit will approach zero (except for the gravity of the dark energy itself, which is more than offset by its antigravity negative pressure effect). By then superluminally receding particles (which are, say, at z=3 today) will be many times further apart. Yet this clearly begs the question, when gravitational density drops to zero in a given large but finite region, as it eventually must, how can superluminal relative recession velocities remain possible from one end of that region to the other, regardless of how widely separated the two particles are? Within its bounds, that region has in fact become converted to a true SR-compliant global frame. This logic suggests the theoretical possibility that superluminal recession is not physically real and might be an observational artifact.

If superluminal recession is merely an observational artifact, then the explanation must lie in the cosmological redshift that occurs as photons emitted by the receding particle (or galaxy) transition from each local gravitational frame to the next such frame along their path (keeping in mind that local frames are confined to an infinitesimal point and lack discrete boundaries.)

Cosmological Redshift

In order to explain cosmological redshift without resorting to the expansion of space itself, the only tools left in our kitbag are SR relativistic Doppler Effect and gravitational redshift. Since neither of these effects can do the job alone, the solution seems to lie in combining them properly.

A.B. Whiting may have been on the right track when he derived the gravitational component of cosmological redshift in a universe with static gravitational density by calculating the difference between the matter density now and zero matter density. As he says, just multiplying the SR Doppler redshift and the gravitational redshift together calculates the correct instantaneous cosmological redshift for a flat FLRW universe with static 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 (with matter density varying from that at emission to zero now.) Something like this:

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

I want to emphasize that, unlike my earlier attempt at a solution, I do not think a separate element should be included to account for clock rate differentials. 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.

Conclusion

Hopefully these thoughts are broadly consistent with the eventual solution I think must inevitably be derived to provide an comprehensive alternative explanation of superluminal recession and cosmological redshift without resorting to the concept that space itself is expanding.

Jon

[marcus]

On the other hand, our universe appears to be homogeneously filled with gravitating matter. This means that instead of one global reference frame, we have an infinite series of tightly packed local reference frames.

It was a constructive step to rearticulate your position and start a new thread. You are right that there is no one global Lorentz frame. The universe can't be put into a fixed SR context.

However you attribute this to the presence of gravitating matter. You say you are considering the case of Lambda > 0. The de Sitter universe doesn't naturally fit in a global Lorentz framework and yet it has no matter. So that might be something for you to think about.


One must confront the question whether superluminal recession is a “physically real” phenomenon or just an observational artifact. If it is physically real, then it will continue regardless of how low the cosmic gravity density declines in the far future. Consider a model universe with dark energy [edit: Lambda=0 doesn't work well here]. As time passes, the gravitational density declines, and in the limit will approach zero. By then superluminally receding particles (which are, say, at z=3 today) will be many times further apart. Yet this clearly begs the question, when gravitational density drops to zero in a given large but finite region, as it eventually must, how can superluminal relative recession velocities remain possible from one end of that region to the other, regardless of how widely separated the two particles are? Within its bounds, that region has in fact become converted to a true SR-compliant global frame. This logic suggests the theoretical possibility that superluminal recession is not physically real and might be an observational artifact.

As matter thins out, our universe is expected to approximate a deSitter universe more and more closely. That doesn't fit an SR frame. It has just as much superluminal expansion as we do now. You haven't shown that the region becomes converted to a true SR-compliant global frame.

You want Hubble Law to cease as matter thins out, I guess, or for the parameter to go to zero. I gather it is expected that in the late time universe the Hubble Law parameter will approach something like 60 km/s per Mpc. Percentage increase of large distances will level out from the present roughly 1/140 percent per million years to about 1/160 of a percent per million years. You'd need to show your claim mathematically. Maybe one of the others can give you some advice as to how to proceed with that.

You haven't yet shown that superluminal recession is an observational artifact. So the rest seems moot:

If superluminal recession is merely an observational artifact, then the explanation must lie in the cosmological redshift that occurs as photons emitted by the receding particle (or galaxy) transition from each local gravitational frame to the next such frame along their path (keeping in mind that local frames are confined to an infinitesimal point and lack discrete boundaries.)

We have no evidence it is an artifact, but it is good you are asking how the cosmological redshift comes about---what the mechanism is. It is possible to think of a lightwave as making transitions from one local frame to another. Some people think like that. But in my opinion it isn't very physical. Local frames are a human construction. They are something we imagine, not something physical. I prefer to think of the redshift happening in a slightly different way---Maxwell's equation (the usual electromagnetic wave equation) operating is a context where distances increase slightly as the wave undulates thru. But it is just a question of taste really. Wave propagation a la Maxwell is a geometrical phenomenon. I think of the geometry of the E and B fields in a space where distances gradually increase. I just don't like to objectify a big bunch of local frames as if they were a real thing---they are something humans use to approximate and compute with.


Hopefully these thoughts are broadly consistent with the eventual solution I think must inevitably be derived to provide an comprehensive alternative explanation of superluminal recession and cosmological redshift without resorting to the concept that space itself is expanding.


Personally I dont say "space expands", the reason is I don't like to objectify space, make it seem to people like a substance or a real thing.
I also refrain from saying "space does not expand". that would be an even more counterproductive thing to say. The Einstein equation is about DISTANCES namely it is a differential equation governing the evolution of the metric. So one can clearly say that distances expand, in our universe. It is basically what General Relativity is about.

I don't see the point of your alternative explanation, Jon. I understand superluminal recession and cosmological redshift easily simply in the context of systematically increasing distances (according to the Einstein equation). I don't resort to saying space itself is expanding---that phrase strikes me as something of a strawman or a red herring, somehow. Something fishy. Given the choice I suspect I'd prefer people would just think of space as expanding rather than imagine that they have to make up alternative explanations such as the present one.

At any rate, an interesting attempt. And I think it was time to revise and restate your ideas in a new thread.

[jonmtkisco]

Hi Marcus,

I offer faint thanks for your faint praise.

I did not claim to prove that superluminal recession is just an observational artifact, I said the logic of the scenario suggests the possibility.

It doesn't help achieve my scenario if the Hubble velocity peters way out. I need recession velocities to remain superluminal across a spatial interval small enough to have a legitimate possibility of containing vanishingly close to zero particles (and therefore effectively zero gravity) at some far future date.

I'd prefer to use the example of a matter-only Einstein-de Sitter universe with Lambda=0. Then an unadulterated SR global frame could exist within some finite subdomain. However, that equation may not close, because the further the particles are apart, the more they've already been slowed by gravity, and there may be no superluminal particles left at the opposite borders of any region small enough to be reasonably devoid of gravity.

A common scenario describes that in the far future, the great majority of ponderous matter will consolidate into widely scattered supermassive black holes. If that occurred at late times in an Einstein-de Sitter universe (Lambda=0), it would increase the opportunity for a pair of BH's to be receding from each other superluminally for a limited time, with vanishingly little matter density remaining interposed between them. If that scenario worked out, it would strengthen the argument that superluminal recession might not be physically real.

In the de Sitter model, of course the exponentially accelerating recession velocity itself does not disqualify it from being a pure SR global frame. Instead it's just the gravity of Lambda, and maybe also the negative pressure of Lambda. So I'll probably give up on trying to use any scenario with Lambda.

Of course it's quite possible that superluminal recession is a physically real phenomenon, at least judged by some standard of reality. We also should consider the possibility that any rulers we use to measure recession velocity may have experienced Lorentz contraction.

Others are welcome to help think about how best to explain superluminal recession and cosmological redshift without resorting to the notion of expanding space. I hope none of us considers this subject to be unworthy of brainstorming.

Jon

[jonmtkisco]

Thinking more about whether superluminal recession might or might not be a physically real phenomenon...

Consider the scenario of a very underdense, matter-only universe (Lambda=0) with the negative spatial curvature specified by the FLRW metric. At any given radius from an observer at the center of her observable universe, galaxies recede faster than the escape velocity of the mass/energy contained within that radius. Compared to a flat universe, recession velocities are relatively high compared to the contemporaneous matter density. At some point in the late history of this universe, it seems likely that two galaxies (or particles) will have superluminal relative recession velocity, with vanishingly little matter (and therefore gravity) in the region between them. That region then qualifies as an SR global frame, so here we might expect to achieve a violation of the SR speed limit of c.

It seems to me that one of two possible conclusions applies here.

1. Superluminal recession is actually an observation artifact rather than physically real, or

2. Mother Nature doesn't like negative spatial curvature, and won't let this situation occur.

I said in the first post that GR's applicable metric dictates by how much a local frame may violate the speed limit of c compared to another local frame depending on the cosmic gravitational density and distance between them. I see nothing in GR itself which directly controls this; it is the FLRW metric which controls it, but it is not an absolute control.

If you want to have flat spatial curvature in an FLRW universe, you can exceed the speed limit by only so much, as a function of gravitational density and distance. Exceed it by more than that, and the FLRW metric forces you into negative curvature. But with enough spatial curvature, apparently it is possible to exceed the speed limit by an arbitrary amount within an arbitrarily small distance, with an arbitrarily low gravitational density.

Maybe one could rationalize that clocks run slower in negatively curved regions than in flat regions, so the recession speeds are actually lower than they seem. But, other factors being equal, calculated recession speeds in the FLRW metric increase when the curvature goes negative, they don't decrease or top out. In fact if they decreased so as to offset a possible clock difference, it might never be possible for the metric to calculate the existence of negative curvature. Which is a problem that the metric clearly doesn't suffer from.

I suppose one valid question is, if the very large but finite region between the two galaxies (or particles) is devoid of matter and gravity, how can that region have negative spatial curvature? Something about this situation seems circular. Yet isn't there still a violation of the SR speed limit even if that finite region is inferred to have become spatially flat?

Jon

[Chaos' lil bro Order]

I'm taking the liberty of revising and restating this topic which started in a separate thread. Comments are welcome.

A lively debate is underway today by mainstream cosmologists as to whether the expansion of the universe implies that empty space between galaxies is also expanding. When faced directly with the question, most cosmologists will say that galaxies are moving apart because they were previously moving apart, but decline to state flatly that space itself expands. And yet it has been customary for textbooks and technical literature to explain both superluminal recession and cosmological redshift only as the result of space itself expanding. What seems clear is that the observational predictions of GR must be precisely identical regardless of whether space itself expands. Therefore, at a minimum we need a comprehensive theoretical description of both superluminal recession and cosmological redshift that does not resort to the concept of expanding space. Here are some thoughts on that subject.

Accurate application of Special Relativity depends on having a global inertial reference frame, which may be arbitrarily selected, but which cannot be accelerating, and by the same token cannot include significant gravitational objects. On the other hand, our universe appears to be homogeneously filled with gravitating matter. This means that instead of one global reference frame, we have an infinite series of tightly packed local reference frames.

Superluminal Recession

In our gravitation-filled universe, the rule of SR that no object can exceed the speed of light, c, relative to any other object, simply doesn’t apply. Objects at rest in any two local reference frames which are in motion relative to each other may have a relative velocity exceeding c. This is true even if the two frames are immediately adjacent to each other.

One might be tempted to call this is a "license to steal", in the sense that the SR speed limit of c doesn't seem to apply hardly anywhere in our universe. But the reality isn't that dire. The degree by which the velocity of an object in a local frame can exceed c relative to any other local frame is dictated entirely by General Relativity’s applicable metric of gravity. If the gravitational density is low, the degree of "violation of the speed limit" in nearby frames is infinitesimal. If the gravitational density is high, this speed limit can be "violated" to a larger degree. Even a low gravitational density enables large violations of the speed limit if the objects are extremely distant from each other, currently in the range of z=1.6.

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 beachball. The FLRW metric (to the extent its equation of state doesn't require modification on account of the then-dominant quark-gluon plasma) calculates that matter particles located just millimeters away from each other were receding from each other at velocities many times faster than c. This demonstrates that a tiny distance between distinct local frames is no inhibitor to observing a massive "violation" of the SR speed limit. All that’s needed is truly astounding gravitational density -- which is what theory calculates for our very early universe.

Note that any pair of particles which are observed to have a given relative recession velocity now haven’t gained relative velocity over time as their mutual distance increased. On the contrary, their relative recession velocity was enormously higher in the very early universe. In early times, the self-gravity of the universe hugely decelerated every galaxy pair's mutual recession rate; in late times, dark energy has reaccelerated them but to a much lesser degree. Absent the competing effects of those two accelerations, each pair of particles would retain the same relative recessionary momentum they had in the very early universe.

One must confront the question whether superluminal recession is a “physically real” phenomenon or just an observational artifact. If it is physically real, then it will continue regardless of how low the cosmic gravity density declines in the far future. Consider a model universe with dark energy [edit: Lambda=0 doesn't work well here]. As time passes, the gravitational density declines, and in the limit will approach zero (except for the gravity of the dark energy itself, which is more than offset by its antigravity negative pressure effect). By then superluminally receding particles (which are, say, at z=3 today) will be many times further apart. Yet this clearly begs the question, when gravitational density drops to zero in a given large but finite region, as it eventually must, how can superluminal relative recession velocities remain possible from one end of that region to the other, regardless of how widely separated the two particles are? Within its bounds, that region has in fact become converted to a true SR-compliant global frame. This logic suggests the theoretical possibility that superluminal recession is not physically real and might be an observational artifact.

If superluminal recession is merely an observational artifact, then the explanation must lie in the cosmological redshift that occurs as photons emitted by the receding particle (or galaxy) transition from each local gravitational frame to the next such frame along their path (keeping in mind that local frames are confined to an infinitesimal point and lack discrete boundaries.)

Cosmological Redshift

In order to explain cosmological redshift without resorting to the expansion of space itself, the only tools left in our kitbag are SR relativistic Doppler Effect and gravitational redshift. Since neither of these effects can do the job alone, the solution seems to lie in combining them properly.

A.B. Whiting may have been on the right track when he derived the gravitational component of cosmological redshift in a universe with static gravitational density by calculating the difference between the matter density now and zero matter density. As he says, just multiplying the SR Doppler redshift and the gravitational redshift together calculates the correct instantaneous cosmological redshift for a flat FLRW universe with static 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 (with matter density varying from that at emission to zero now.) Something like this:

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

I want to emphasize that, unlike my earlier attempt at a solution, I do not think a separate element should be included to account for clock rate differentials. 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.

Conclusion

Hopefully these thoughts are broadly consistent with the eventual solution I think must inevitably be derived to provide an comprehensive alternative explanation of superluminal recession and cosmological redshift without resorting to the concept that space itself is expanding.

Jon

Great post Jon, it was a pleasure to read.

There are some very interesting ideas I've never heard in there before. In particular, if I am understanding one of your points correctly, you have described a possible 'solution' to the cause of dark energy accelerating properties with respect to the Universe's expansion. Which I'm interpretting as a scenario where a Big Bang event occurs and because the Universe's density is so great at this epoch, say the first 1s, that gravitational effects dampen the Universe's acceration as a form of 'gravity braking', and that as time progressed thereafter, the gravitational effects lessened with the thinning of the Universe's overall density. So in effect, the Universe that we think of as accelerating may be rather like a car driver easing his foot off the brakes whilst holding his other foot at a constant 100km/h. Maybe the Big Bang for lack of a better term, exploded with a force that remained constant.

Could dark energy be explained as the thinning of gravitational braking? We know the gravitational force was the first of the 4 forces in the Universes, so the gravitational braking would be especially high when there was no EM force to provide counter pressure, as in neutron stars and such. The Inflationary period could possibly be explained as the period between the gravitational force and EM force? I think of the EM force as a passenger in the car leaning over the driver's lap and lifting up his foot off the break slightly. Of course these analogies only get you so far and you must back up any claims with mathematic proofs.

I don't know, but it was a interesting post to read. Cheers.

[Janus]

Great post Jon, it was a pleasure to read.

There are some very interesting ideas I've never heard in there before. In particular, if I am understanding one of your points correctly, you have described a possible 'solution' to the cause of dark energy accelerating properties with respect to the Universe's expansion. Which I'm interpretting as a scenario where a Big Bang event occurs and because the Universe's density is so great at this epoch, say the first 1s, that gravitational effects dampen the Universe's acceration as a form of 'gravity braking', and that as time progressed thereafter, the gravitational effects lessened with the thinning of the Universe's overall density. So in effect, the Universe that we think of as accelerating may be rather like a car driver easing his foot off the brakes whilst holding his other foot at a constant 100km/h. Maybe the Big Bang for lack of a better term, exploded with a force that remained constant.



In your car analogy, the foot on the gas Is dark energy. An analogy that fits a universe without acceleration of the expansion would be closer to this:
Start with a car initially moving 100kph, coasting and with your foot on the brake. Then ease up on the brake as time goes on. The car continues to slow as time goes on, but the rate at which it slows decreases.

This analogy matches what we would expect to see in a universe without dark energy. The decreased effect of gravity is something fully expected. In fact, this is what was bieng investigated in the study that first indicated the acceleration. They were, in essence, trying to determine how fast the universe was "letting up on the brake". What they found was that the universe apparently also had its "foot on the gas".

So while your analogy does fit the presently understood situation, it doesn't "explain" dark energy, because it doesn't explain were the "foot on the gas" comes from.

[marcus]

Great post Jon, it was a pleasure to read.
...

I find myself enjoying these posts too, as an example of able courtroom argument. Concerns about the physical content or lack thereof, though. Maybe, Chaos' lil, since you read the first post you can tell me how you take the following.

I'd like to hear an independent check from someone else besides the author. So here it is. This is the main point---the rest depends on this.

As far as I can see, physically speaking the reasoning here is vacuous (although as a courtroom argument or legal brief it is very nicely argued!) If you disagree, Chaos-lil, please explain--I'd like to hear your take.

BTW I have highlighted in red a key statement which seems in error. When density thins out in some finite piece of the universe it does not necessarily give rise to an SR-compliant region of spacetime.

==quote with blue comment==
If the gravitational density is low, the degree of "violation of the speed limit" in nearby frames is infinitesimal. If the gravitational density is high, this speed limit can be "violated" to a larger degree.

associates FTL recession with the circumstance of high density

Consider our very early observable universe, ... The FLRW metric ... calculates that matter particles located just millimeters away from each other were receding from each other at velocities many times faster than c. This demonstrates that a tiny distance between distinct local frames is no inhibitor to observing a massive "violation" of the SR speed limit. All that’s needed is truly astounding gravitational density -- which is what theory calculates for our very early universe. ...

not true high gravitational density is NOT all that is needed, nor is it sufficient. it just happens that in this example there is a circumstantial association between FTL recession and high density

One must confront the question whether superluminal recession is a “physically real” phenomenon or just an observational artifact. ... when gravitational density drops to zero in a given large but finite region, as it eventually must, how can superluminal relative recession velocities remain possible from one end of that region to the other, regardless of how widely separated the two particles are? Within its bounds, that region has in fact become converted to a true SR-compliant global frame. This logic suggests the theoretical possibility that superluminal recession is not physically real and might be an observational artifact.

Look at the boundary conditions of the region. Just because a region is nearly empty does not mean it is flat.
You can't fit an SR-compliant frame to a region just because it has low density----if the boundary has nontrivial geometry this will affect the geometry of the region.


If superluminal recession is merely an observational artifact, then ...

==endquote==

Everything that follows is based on the assumption IF superlight recession is merely an observational artifact. But that seems moot (empty of meaning) because the initial assumption has no basis. Or at least no basis is provided here.

Your thoughts?

[jonmtkisco]

Hi Chaos,

I agree completely with Janus' response to your post.

Think of receding galaxies as being Newtonian cannonballs fired from the surface of the moon (no atmospheric friction). If a cannonball is fired exactly at its Newtonian escape velocity, its speed away from the moon will become slower and slower over time, asymptotically approaching zero when the distance reaches infinity. As a function of increasing distance, the declining force of gravity and the declining velocity exactly balance each other.

Jon

[jonmtkisco]

Hi Marcus,

I appreciate your substantive critiques as well, even if they are negative in tone and devoid of any contribution on your part about how to explain superluminal recession and cosmological redshift without resorting to the notion of expanding space.

not true high gravitational density is NOT all that is needed, nor is it sufficient. it just happens that in this example there is a circumstantial association between FTL recession and high density
This comment is cryptic so I don't understand why you say my point is wrong. In a flat matter-only expanding universe (Lambda=0), the FLRW metric does not permit superluminal recession velocity to exist without either a lot of gravitational density or a combination of lesser density and very large distances. It's dictated by the GR metric, so how can it be merely a circumstantial association? This is exactly the point I'm trying to make.

If you're referring simply to the fact that something causing geometric expansion rates (like inflation) is needed to impart the original superluminal recession velocities to the particles, I agree with that. Other than in a de Sitter-like universe with a dominant cosmological constant, some force is need to impart an initial velocity to the particles, and it needs to impart relative velocities that are superluminal from the start. But those superluminal initial velocities are not merely curious optional features of a (nearly or entirely) flat universe with the gravitational density and Hubble rate we have; the FLRW metric makes them mandatory for us.

Look at the boundary conditions of the region. Just because a region is nearly empty does not mean it is flat.

You can't fit an SR-compliant frame to a region just because it has low density----if the boundary has nontrivial geometry this will affect the geometry of the region.

That's a valid qualification but I think it's not a fatal one. Yes if there's a significant amount of matter hovering near the boundary of the region, it will gravitate into the region, adulterating the region's SR purity. One can address that by referring to two extremely tiny test particles (instead of galaxies or black holes) which are receding from each other at superluminal velocities, and ensuring that the vanishingly empty region extends well beyond the test particles, not just directly between them.

Jon

[jonmtkisco]

Here is a rejiggering of the cosmological redshift equation I suggested, which is simpler and I think is more mathematically accurate:

\frac{\lambda_{r}}{\lambda_{e}} = \int\begin{array}{cc} t_{r}\\t_{e} \end{array} \left( SR \ Doppler \ redshift \left[v_{rec \left( t \right) } \right] \right)\left( gravitational \ redshift \left[ \rho_{t} , 0 \right]\right) dt

where: \lambda is wavelength, v_{rec \left( t \right) } is recession velocity at each time interval, \rho_{t} is density at each interval, and gravitational redshift is calculated as between current density and 0 density at each interval.

Jon

[jonmtkisco]

It strikes me that at any given Hubble rate, the less gravity density there is, the easier it is to sustain a higher proportion of the receding galaxies at superluminal recession velocities over a long period of time, and vice versa.

Doesn't it seem like it should be the opposite: At any given Hubble Rate, the less gravity density there is, the less likely superluminal recession would be, and in the limit of vanishingly small gravity (an SR global frame) there would be no superluminal recession at all?

Edit: Well maybe the problem is that this concept of duration is too superficial. Other things being equal, a very underdense universe will arrive at our (current) density and Hubble rate after much less elapsed time than an overdense universe would. But even so, once the parameters reach those values, a very high percentage of the galaxies will thereafter remain at superluminal velocities for all eternity. Whereas in a very overweight universe, even after our parameter values are reached, the recession velocities of many more galaxies will thereafter progressively drop to below c. Hmmmm.

Jon

[marcus]

Jon, let's focus on the core of your argument and make sure I understand just what it is you are saying. As I see it you consider two cases. The first one (post #1) has Lambda > 0 and the second case (post #4) has Lambda = 0 and Omega < 1. I will quote and then try to paraphrase you as clearly as I can..

In both cases you want to argue that FTL recession doesnt really happen---is illusory. The way you argue this is by constructing an apparent contradiction.

Here's the first case (post #1)


One must confront the question whether superluminal recession is a “physically real” phenomenon or just an observational artifact. If it is physically real, then it will continue regardless of how low the cosmic gravity density declines in the far future. Consider a model universe with dark energy [edit: Lambda=0 doesn't work well here]. As time passes, the gravitational density declines, and in the limit will approach zero (except for the gravity of the dark energy itself, which is more than offset by its antigravity negative pressure effect). By then superluminally receding particles (which are, say, at z=3 today) will be many times further apart. Yet this clearly begs the question, when gravitational density drops to zero in a given large but finite region, as it eventually must, how can superluminal relative recession velocities remain possible from one end of that region to the other, regardless of how widely separated the two particles are? Within its bounds, that region has in fact become converted to a true SR-compliant global frame. This logic suggests the theoretical possibility that superluminal recession is not physically real and might be an observational artifact...

First as a technical point, in the Friedmann model the density never drops to exactly zero. Nor is that realistic, there is always some matter in between galaxies. So we had better say the density of matter approaches zero. That is not a criticism of you, just clarification.

Now the argument goes as follows: consider a large but finite region of space S.
and a time-interval I in the late universe
and construct a big finite chunk of spacetime SxI (Friedmann model coordinates help here)

You say: if the interval I is chosen late enough, S will be nearly empty of matter.

Therefore we can approximtely fit the block of spacetime SxI with an SR-compliant frame!

Ahah! you say. Two galaxies with this nearly empty block can't be receding FTL from each other.

Then, in a separate argument, you may hope to show that if FTL is illusory in the late universe it could be dubious in the present as well. I'm not sure how that would go.

But anyway I think we disposed of that argument in post #1. What made it a no-brainer was Lambda > 0. Because there was dark energy, the spacetime block SxI turned out to be approximately congruent to a chunk of deSitter space. deSitter space is a 4D spacetime in which there is no matter at all, and yet FTL expansion goes on forever.

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

So now we have to consider your second case (post #4). this time you make essentially the same argument but with dark energy out of the picture. You put Lambda = 0, and you say underdense which I guess means total Omega < 1.

Again you use the Friedmann model obviously. Again you go for a large finite chunk of spacetime SxI which is nearly empty. Density cant be assumed exactly zero, but as close to zero as you think you need just by going far enough out.

Thinking more about whether superluminal recession might or might not be a physically real phenomenon...

Consider the scenario of a very underdense, matter-only universe (Lambda=0) with the negative spatial curvature specified by the FLRW metric. At any given radius from an observer at the center of her observable universe, galaxies recede faster than the escape velocity of the mass/energy contained within that radius. Compared to a flat universe, recession velocities are relatively high compared to the contemporaneous matter density. At some point in the late history of this universe, it seems likely that two galaxies (or particles) will have superluminal relative recession velocity, with vanishingly little matter (and therefore gravity) in the region between them. That region then qualifies as an SR global frame, so here we might expect to achieve a violation of the SR speed limit of c.
...

If I understand you, you are trying to get a contradiction. The Friedmann model tells you that there are two galaxies, say at opposited sides of this big nearly empty region S, which are receding FTL from each other. BUT you say, this big chunk of spacetime SxI can be approximately fitted with an SR-compliant frame. Ahah! Contradiction!

In courtroom terms, this raises doubts in the jury's mind. Maybe the FTL recession isn't real. Could it be just an illusion---an artifact of how we observe?

Then I guess you could be planning to work back---if FTL is unreal in the late universe maybe it is illusory even now, at the present day. You've given some arguments elsewhere as i recall, along those lines.

Now, is this an accurate sketch of how you are arguing the case?

I'm anxious to get it boiled down to brief, and make sure I understand.

[marcus]

In the second case, the argument also breaks down. It breaks down where you say It seems likely

You take a region S of fixed size. To get a SR frame to approximately fit you need to go far out in the future, so (for example) the density gets very small.

But the Hubble parameter is going down as well, so as the density gets very small you also find that there is no more FTL recession between pairs of objects in the region. So there is no contradiction.

The attempted argument is by contradiction, you are trying to show that while the Friedmann model shows FTL this is inconsistent with fitting an SR frame onto a region in late universe. But the contradiction doesnt emerge because you arent getting FTL from the Friedmann model.

[jonmtkisco]

Sorry to do this again, but my suggested equation for a bottoms-up calculation of cosmological redshift needs to be tweaked again. Hopefully this is the last tweak.

\frac{\lambda_{r}}{\lambda_{e}} = \int\begin{array}{cc} t_{r}\\t_{e} \end{array} \left( SR \ Doppler \ redshift \left[ \frac{ \left( V_{emit} + V_{rec} \right) }{2} \right] \right)\left( gravitational \ redshift \left[ \rho_{t} , 0 \right]\right) dt

where: \lambda is wavelength, V_{emit} is the proper recession velocity between the emitter and receiver at the time of emission, V_{rec} is the proper recession velocity between them at the time of reception, \rho_{t} is density at each interval, and gravitational redshift is calculated as between current density and 0 density at each interval.

The reason for this change is that the SR Doppler redshift value should remain constant at each interval over which the gravitational redshift integral is constantly changing. The SR Doppler Effect component should measure only the final net velocity difference between the emitter at emission time and the receiver at reception time.

Jon

[jonmtkisco]

Hi Marcus,

I think your description of what I said is fairly accurate. I explicitly set aside the idea of using Lambda>0 after the first post in this thread, because Lambda gravitates. All of the subsequent posts have Lambda=0.

You take a region S of fixed size. To get a SR frame to approximately fit you need to go far out in the future, so (for example) the density gets very small.

But the Hubble parameter is going down as well, so as the density gets very small you also find that there is no more FTL recession between pairs of objects in the region.

I made exactly this point in my second post, in which I lamented that I probably couldn't arrange the empty-region scenario I want in a flat FLRW universe. In subsequent posts, I introduced the scenario of a very underdense universe with large negative spatial curvature. In that model, recession velocities can remain arbitrarily high for an arbitrarily long period of time. So it seems probable to me that a valid theoretical scenario can be arranged where two particles with Superluminal mutual recession velocity are embedded in a large but finite region containing no other matter.

I agree that regardless of how underdense it is, by definition an Einstein-de Sitter universe would not be entirely empty of matter. But I never suggested that the entire universe was empty; I was describing only a large but finite region which is either empty (other than the two test particles) or vanishingly close to empty. The existence of such a region in a very underdense universe "in the distant future" does not seem to offend the metric at all.

Please don't get me wrong, I'm not claiming to have "proved" a contradiction. I'm just saying that the logic suggests the possibility of a contradiction. This logic isn't limited to the special case where a region contains zero matter; a countervailing overall pattern emerges from the general metric. If we increase the matter density while keeping the Hubble rate constant, it becomes increasingly difficult to sustain superluminal recession velocities at all for any long period of time. One might have expected the opposite, if gravitational density is indeed the primary enabler of superluminal recession.

This countervailing pattern also raises the possibility that there may be NO satisfactory explanation available for the seemingly unprincipled nature of superluminal recession, other than that it is possible ONLY because of the expansion of space itself. But I think it's fair to say that current mainstream cosmology has not declared this to be the only reasonable answer, so why should we throw in the towel so quickly?

Jon

[Sundance]

G'day from the land of oz

Interesting reading on intrinsic redshift

http://arxiv.org/abs/astro-ph/0603169
Six Peaks Visible in the Redshift Distribution of 46,400 SDSS Quasars Agree with the Preferred Redshifts Predicted by the Decreasing Intrinsic Redshift Model

Authors: M.B. Bell, D. McDiarmid
(Submitted on 7 Mar 2006)

Abstract: The redshift distribution of all 46,400 quasars in the Sloan Digital Sky Survey (SDSS) Quasar Catalog III, Third Data Release, is examined. Six Peaks that fall within the redshift window below z = 4, are visible. Their positions agree with the preferred redshift values predicted by the decreasing intrinsic redshift (DIR) model, even though this model was derived using completely independent evidence. A power spectrum analysis of the full dataset confirms the presence of a single, significant power peak at the expected redshift period. Power peaks with the predicted period are also obtained when the upper and lower halves of the redshift distribution are examined separately. The periodicity detected is in linear z, as opposed to log(1+z). Because the peaks in the SDSS quasar redshift distribution agree well with the preferred redshifts predicted by the intrinsic redshift relation, we conclude that this relation, and the peaks in the redshift distribution, likely both have the same origin, and this may be intrinsic redshifts, or a common selection effect. However, because of the way the intrinsic redshift relation was determined it seems unlikely that one selection effect could have been responsible for both.


http://arxiv.org/abs/astro-ph/0409215

The Discovery of a High Redshift X-ray Emitting QSO Very Close to the Nucleus of NGC 7319

Authors: Pasquale Galianni, E.M. Burbidge, H. Arp, V. Junkkarinen, G. Burbidge, Stefano Zibetti
(Submitted on 9 Sep 2004)

Abstract: A strong X-ray source only 8" from the nucleus of the Sy2 galaxy NGC 7319 in Stephan's Quintet has been discovered by Chandra. We have identified the optical counterpart and show it is a QSO with $z_e = 2.114$. It is also a ULX with $L_x = 1.5 x 10^{40} erg sec^{-1}$. From the optical spectra of the QSO and interstellar gas in the galaxy (z = .022) we show that it is very likely that the QSO and the gas are interacting.

[jonmtkisco]

Hi Sundance,
Thanks for the reference to the papers. It's sobering to be reminded how much effort goes into distinguishing real phenomena from data selection biases.

Jon

[Sundance]

G'day from the land of ozzzzzzz

jonmtkisco said

Hi Sundance,
Thanks for the reference to the papers. It's sobering to be reminded how much effort goes into distinguishing real phenomena from data selection biases.

How do you distinguish?

[Chaos' lil bro Order]

In your car analogy, the foot on the gas Is dark energy. An analogy that fits a universe without acceleration of the expansion would be closer to this:
Start with a car initially moving 100kph, coasting and with your foot on the brake. Then ease up on the brake as time goes on. The car continues to slow as time goes on, but the rate at which it slows decreases.

This analogy matches what we would expect to see in a universe without dark energy. The decreased effect of gravity is something fully expected. In fact, this is what was bieng investigated in the study that first indicated the acceleration. They were, in essence, trying to determine how fast the universe was "letting up on the brake". What they found was that the universe apparently also had its "foot on the gas".

So while your analogy does fit the presently understood situation, it doesn't "explain" dark energy, because it doesn't explain were the "foot on the gas" comes from.

Ok Janus, now you are just confusing me. Unlike many cosmologists, I don't find it offensive or incorrect to say that the Big Bang was an 'explosion' that was comparable to how a spherical shaped charge of C4 explodes. However, unlike C4, the fragments of the big bang were of such high density during the first few seconds after the explosion that they gravitationally dampened the massive expansion. As the explosion grew, the proximity of one fragment to another fragment diminished, and thus gravity's inverse square law dictated that the gravity 'felt' between any two fragments also weakened. And weakened and weakened and weakened. The Universe 'appeared to be speeding up' in its expansion, but in reality it just had less gravitational breaks slowing it down. Anyways, that is the theory as I understood it. I am not expert enough to judge it on its consistencies or inconsistencies with cosmological data, so I defer this to smarter people than I, like Janus and Marcus. Help :)

I think its also important to note that we have no idea if the Universe big banged into a medium that would have caused any friction or other effects on the accelerating Universe. Clearly a C4 explosion which takes place in air, explodes with its highest velocity upon ignition and its fragments then decelerate according to earth's gravity and the friction caused by earth's air.

If I'm understanding it right, it is quite a nice theory and worthy of consideration. Some questions come to rise: Do cosmologists know or have limits set on the Universe's accereration rate? If so, is the Universe accelerating faster or slower than the square law (ex. 1,4,9,16,25...). If faster, clearly the weakening of the gravity breaking alone could not achieve this, so one then adds another force to the Universe as an additional boost to the Universe's acceleration. Dark energy, Quintessence, etc. Or, one could imagine a Universe that exploded with an intrinsic force that is accelerative in its very nature and that the gravity breaks have never stopped the Universe's accelerated expansion, but they merely have dampened it less and less over time.


Janus, Marcus what contradicts this theory?

[jonmtkisco]

Hi Sundance,
G'day from the land of ozzzzzzz
How do you distinguish?

Well, the two articles you referenced show examples of how cosmologists try to approach the issue. For example, if you have two independent data sets obtained through different techniques, the likelihood of both having the same data selection bias may be reduced. Known selection biases can also be subtracted out. And sometimes people just make judgements from the shapes of the curves, as to whether a selection bias seems plausible or not.

At the end of the day, increasing the amount and diversity of data sources is the way to figure it out. That may take years or sometimes decades.

Jon

[jonmtkisco]

OK, here's another idea for explaining superluminal recession without resorting to the notion of expanding space.

So far, I have overlooked one obvious fact: that 100% of the superluminal recession velicities we currently observe are in our universe's past. They may or may not remain superluminal in our universe's present. The higher the z value, the further back in time these redshifted images originated. Since that time, considerable gravitational deceleration has occurred. If Lambda were 0, it might be the case mathematically that NO contemporaneous superluminal velocities would be calculated if we extrapolate the distant galaxies' decelerating recession velocities to what their present values are. We can calculate this with straightforward math (I haven't tried yet). Lambda of course threatens to distort this conclusion, particularly in the distant future. But let's try to tackle a simpler universe with Lambda=0 before we take that one on.

This idea gives rise to another idea. As Whiting suggests (and the Lewis & Barnes radar ranging paper also implies), gravitational redshift may be a component of cosmological redshift. As we discussed in an earlier thread, gravitational redshift can be validly interpreted to mean that nothing physical has occurred except a change in clock rate. Faster clocks make electromagnetic frequencies look slower (lower), i.e. redshifted.

If cosmological redshift also includes a Doppler element as Whiting suggests, perhaps the decline in the cosmic recession velocity (Hubble rate) over time can also contribute to a cosmic clock speedup, like it does in SR (think of the Twins Paradox).

This raises the possibility that in some "external" non-comoving sense (I know I'll get critisism for that terminology), the Hubble clock (uniform to all privileged observers comoving in the Hubble flow) in our observable universe has been speeding up over time. In the very early universe, both gravitational density and the Hubble rate were very high compared to now, so the comoving clock might have been running much faster (relative to non-comoving time) than it would if those conditions had not existed. In current times, the density and Hubble rate have dropped dramatically, so the relativistic suppression of a comoving clock's pace has been greatly reduced. If this relationship is valid, then the comoving clock was moving astoundingly slowly immediately after the big bang; the inflation era could have lasted for eons (according to an observer not participating in the Hubble flow).

The obvious question then becomes, what is this "external" clock against which you measure our Hubble clock's variance? Isn't time always relative? Well, an answer is easy to describe if one can take the liberty of using a model of the universe in which all of empty space pre-existed the big bang, and the big bang itself originated at some arbitrary point "in" pre-existing space.

Here's a toy model to play with: Place a massless, electrically neutral test particle in freefall at an arbitrary coordinate origin in otherwise empty space. Gather a very large number of protons (hydrogen ions) and use an enormous external force to compress them into a very tight ball centered at the test particle. An observer located on the test particle gives the signal to release the external containing force, allowing each proton to accelerate away from all of the other protons very rapidly. After a while, the acceleration rate will drop asymptotically toward zero, and the protons' velocities will flatten out, let's say into a range of recession velocites (relative to the test particle) from 0 to .499c.

The observer on the central test particle has a clock that keeps constant time, which we'll call "central time." Other observers comoving with the protons keep their own clocks, which we'll call "comoving time". All comoving observers AND the test particle observer experience the same gravitational density at every point in time (declining as a function of time), but comoving observers have a range of different comoving velocities relative to the test particle. So if relative velocity contributes to clock variance, the comoving clocks will run more slowly than central time. The freefalling clock at the center experiences maximal aging. The comoving observers will perceive the recession velocity of other comoving protons to be faster than the central observer perceives, simply because their comoving clocks are slower -- more events occur in a given tick of their clocks. Note also that the comoving observers will mostly not agree with each other on a universal comoving time. Comoving observers who are relatively close to each other will show very small disparities in their clocks; the clock disparity will increase with distance. The central observer experiences the same relative clock disparity proportional to distance.

This toy model suggests that only velocity differential can contribute to contemporaneous clock differentials. On the other hand, the decline in gravitational density can also contribute to non-contemporaneous clock differentials, because the only photons observers can see from distant galaxies are those emitted in the distant past when clocks ran slower. So contemporaneous and non-contemporaneous clock variance are two different, but not mutually exclusive, possibilities to think about.

As I described in an earlier post, the FLRW metric does not recognize the possibility of differential clock rates for comoving observers. Clock rates are universally the same for all privileged comoving observers, and with respect to both the past and future. If this were viewed as an incomplete aspect of the FLRW metric (or at least in the way it is normally applied), it might help provide an explanation for superluminal recession without depending on the expansion of space itself.

I don't claim to have proved anything, just brainstorming out loud. Comments are appreciated.

Jon

[jonmtkisco]

I should clarify that my prior post suggested 4 ideas which are more or less separate but cumulative. They are listed in order of increasing speculativeness:

1. Superluminal expansion does not exist as a contemporaneous phenomenon, we see it only because we're looking into the past. I played around with the Morgan calculator, and this one is tough to make work. For a matter-only universe with omega=1, it eliminates superluminal velocities in the "Speed away from us now" category only up to z=3. If you set omega=2, then it eliminates all superluminal recession "now" up to at least z=1089, the CMB surface of last scattering.

2. Apparent superluminal velocities need to be adjusted for #1 above; in addition a clock adjustment is needed to account for a non-contemporaneous (time-dependent) comoving clock differential caused entirely by the changing comoving gravity density.

3. Apparent superluminal velocities need to be adjusted for #1 and #2 above; in addition a clock adjustment is needed to account for a non-contemporaneous (time-dependent) comoving clock variance caused by the changing Hubble rate.

4. Apparent superluminal velocities need to be adjusted for #1, #2 and #3 above; in addition a clock adjustment is needed if the universe has a historical centerpoint, to account for a contemporaneous comoving clock variance because different galaxies have different recession velocities relative to the historical centerpoint.

Jon

[Sundance]

G'day from the land of ozzzzz

Two points:

The Big Bang theory states that the bang did not occur at one point, but varies point throughtout the universe.

Thus no centre to the universe.

Some say the known universe is about 90 Gyrs across others say 180 Gyrs across. You can google for the diffefence.

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

This link is most interesting:

The Magnetospheric Eternally Collapsing Object (MECO) Model of Galactic Black Hole Candidates and Active Galactic Nuclei

Authors:
Robertson, Stanley L.; Leiter, Darryl J.

Publication Date:
00/2006 Origin: ADS


Abstract
The spectral, timing, and jet formation properties of neutron stars in low mass x-ray binary systems are influenced by the presence of central magnetic moments. Similar features shown by the galactic black hole candidates (GBHC) strongly suggest that their compact cores might be intrinsically magnetic as well. We show that the existence of intrinsically magnetic GBHC is consistent with a new class of solutions of the Einstein field equations of General Relativity. These solutions are based on a strict adherence to the Strong Principle of Equivalence (SPOE) requirement that the world lines of physical matter must remain timelike in all regions of spacetime. The new solutions emerge when the structure and radiation transfer properties of the energy momentum tensor on the right hand side of the Einstein field equations are appropriately chosen to dynamically enforce this SPOE requirement of timelike world line completeness. In this context, we find that the Einstein field equations allow the existence of highly red shifted, Magnetospheric, Eternally Collapsing Objects (MECO). MECO necessarily possess intrinsic magnetic moments and they do not have trapped surfaces that lead to event horizons and curvature singularities. Their most striking features are equipartition magnetic fields, pair plasma atmospheres and extreme gravitational redshifts. Since MECO lifetimes are orders of magnitude greater than a Hubble time, they provide an elegant and unified framework for understanding a broad range of observations of GBHC and active galactic nuclei. We examine their spectral, timing and jet formation properties and discuss characteristics that might lead to their confirmation.

And

http://th-www.if.uj.edu.pl/acta/vol39/pdf/v39p1501.pdf
EXPANSION OF THE UNIVERSE — MISTAKE OF
EDWIN HUBBLE? COSMOLOGICAL REDSHIFT AND
RELATED ELECTROMAGNETIC PHENOMENA IN
STATIC LOBACHEVSKIAN (HYPERBOLIC) UNIVERSE


7. Conclusions and remarks
On the basis of a three-dimensional real Lobachevskian geometry, we
presented a geometrical analysis from which cosmological red-shift and related
phenomena follow in natural way. The presented equations give correct
numerical values for their respective physical quantities. The new Eqs. (15)
and (16) which relate red-shift to aberration might be useful in astronomical
observations.
Our presentation of Lobachevsky–Hubble cosmological redshift (5), the
Lobachevskian–Doppler effect (7), and aberration was done in rigorous way on a purely geometrical basis of Lobachevskian three-dimensional real geometry with all entities clearly defined. At present, the widely adopted view explains cosmological red-shift using the vague concept of physical space inflation.
For example, observations tell us that space within galaxies, which are rather diffuse objects, do not expand.

Thus, where is the “border line” in space which divides expanding space from non expanding space?

Next, we are told that inflation itself is due to some rather mysterious event, which was sarcastically named by Fred Hoyle (to ridicule the whole concept), as the big bang.

Instead, we offer an alternative solution based on simple Lobachevskian geometry. We believe that looking at experimental data and Eq. (5), a much simpler solution (minimum complexity solution) is to admit that the space between distant sources and our spectrographs is negatively curved, i.e. it is a Lobachevskian three-dimensional space causing the recorded shifts. In other words what we see through our telescopes is the fundamental formula of Lobachevskian geometry: Eq. (3). Experiments confirm our model.

From the analysis performed, the importance of the range of applicability of some mathematical notions follows. For example, someone who only saw a map of the Earth as in Fig. 2, and had no prior knowledge where this map came from, and what mechanism was used in mapping process, will in good faith believe that Greenland is as big as the USA. His or her conclusions about geography made from the distorted image will be necessarily
false.

Similarly, making conclusions about the geography of the universe based on the so called “relativistic” formulas in the form of RHS expression in Eq. (7) (and Eq. (6) as well), is misleading since we did not know that we were looking at distorted formulas of a precise Eq. (3) of non-Euclidean geometry projected into Euclidean space–space in our vicinity! Conclusions based on a distorted formula will inevitably lead to the inconsistencies and/or paradoxes for projections from regions of high distances d ≃ 1 in space or high distances ≃ 1 in velocities space. Of course, as long as we stay “close to equator”, (which means going local, i.e. d ≪ 1, ≪ 1) distortion will be negligible within the required range of precision. Nevertheless we have to be aware that we are still dealing with the distorted images.
This rises the serious question of applicability of the Special Relativity in the range d ≃ 1, ≃ 1.
One may ask a legitimate question of how the experimentally detected cosmic microwave background radiation (CMBR) is related to Lobachevbreak skian geometry (Lobachevskian universe)?

The answer is that in Lobachevskian space, CMBR is identified with the homogeneous space of horospheres which is dual [7,9] to Lobachevskian space. In our work [3] we showed that a horosphere in Lobachevskian space, as far as physics is concerned, is a surface of constant phase of an electromagnetic horospherical wave. In other words, it is a horospherical wavefront.

Radiation represented by horospherical wavefronts homogeneously fills the entire Lobachevskian universe. Therefore, assuming a hyperbolic universe, we have to have CMBR with its properties of homogeneity and isotropy! It follows “automatically” from Lobachevskian geometry.

Horospherical waves are solutions of the Laplace–Beltrami operator (wave operator) in Lobachevskian space. Their properties are well known and well understood. Thus, there is entirely no need to associate CMBR with the big bang — an event which itself cannot be understood and deliberated in scientific terms.

In Lobachevskian space filled only with radiation CMBR would be perfectly isotropic. In the presence of matter however, which on local scales is distributed rather randomly, a small anisotropy in the properties of CMBR might be present due to local conditions. This was already recorded by COBE. More about the space of horospheres can be found in [7, 9].
The author wishes to acknowledge Vadim von Brzeski for his invaluable
comments.

[Sundance]

G'day

Missed a link
http://adsabs.harvard.edu/abs/2006ndbh.book....1R
The Magnetospheric Eternally Collapsing Object (MECO) Model of Galactic Black Hole Candidates and Active Galactic Nuclei

[George Jones]

G'day

Missed a link
http://adsabs.harvard.edu/abs/2006ndbh.book....1R
The Magnetospheric Eternally Collapsing Object (MECO) Model of Galactic Black Hole Candidates and Active Galactic Nuclei

As far as I can tell, the links given in your last two posts(in this thread) have nothing to do with cosmological redshifts, and thus nothing to do with this thread,

This series of papers by by Leiter and collaborators tries to establish that black holes don't form, but for good reason, Leiter has been having trouble getting these papers published in reputable journals.

Timelike geodesics don't suddenly become lightlike geodesics. See

http://www.physicsforums.com/showthread.php?t=123988

[marcus]

I played around with the Morgan calculator, and this one is tough to make work...

First time I've heard of someone having trouble with Morgan calculator. Thanks for telling me! Maybe others have had trouble and not mentioned it!

Suggest you type in standard parameters first
Omega_matter = 0.27
Lambda = 0.73
Hubble = 71

then put in your redshift and tell it to compute.

Morgan makes you type in those three parameters first. And what she means by Omega is the matter fraction Omega_matter.
Once you have those three numbers loaded they will stay in, so you don't have to retype unless you want to try variations.

[jonmtkisco]

Hi Marcus,
First time I've heard of someone having trouble with Morgan calculator.

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.

I was saying that my attempt to relegate all superluminal recession to the universe's past is difficult to achieve: This result occurs only out to z=3 when Omega=1; it occurs more completely when Omega=2. In all cases I have set Lambda=0.

Jon

[sketchtrack]

Maybe rather than the doppler shift being the reason that light red shifts, maybe it is due to light actually moving faster than C due to gravitational effects. We have found it to be true that light can be sucked into a black hole which proves light is subject to gravity even if much less than mass is. Perhaps light leaves it's source at C, but as it begins to recede from a galaxy, all the mass of the galaxy is in the opposite direction of the photons movement. The gravity of the galaxy may slow the light down as it recedes, thus blue shifting it. Then at the halfway point from one galaxy to the next, it would be back at C, and then as it begins to come closer to the new galaxy which is in the direction of the photons movement, it would redshift.

Probably stupid thing to suggest, but I wanted to say it just so I can get a response that will sober me because I can't seam to figure out how to rule the idea out on my own.

[jonmtkisco]

Hi sketchtrack,
Maybe rather than the doppler shift being the reason that light red shifts, maybe it is due to light actually moving faster than C due to gravitational effects.

The most fundamental cornerstone of relativity is that light always travels at the same speed, c, in its local frame. Photons get blue- or redshifted instead of changing their speed. If you dig into the Scwarzschild metric for black holes, you will find that the locally measured speed of an infalling photon never exceeds c; the photon just becomes infinitely redshifted at the event horizon. It is possible to calculate the metric in the coordinate system of an infinitely distant observer, which says the photon exceeds the speed of light inside the event horizon. But this is believed just to be one of those unfortunate mathematical singularities that occur in any metric; it is not believed to be physically real. As I said, the singularity vanishes when different coordinates are used.

Thanks for suggesting the idea, but it's more radical than anywhere I'm willing to go for this thread.

Jon

[sketchtrack]

Hi sketchtrack,

The most fundamental cornerstone of relativity is that light always travels at the same speed, c, in its local frame. Photons get blue- or redshifted instead of changing their speed. If you dig into the Scwarzschild metric for black holes, you will find that the locally measured speed of an infalling photon never exceeds c; the photon just becomes infinitely redshifted at the event horizon. It is possible to calculate the metric in the coordinate system of an infinitely distant observer, which says the photon exceeds the speed of light inside the event horizon. But this is believed just to be one of those unfortunate mathematical singularities that occur in any metric; it is not believed to be physically real. As I said, the singularity vanishes when different coordinates are used.

Thanks for suggesting the idea, but it's more radical than anywhere I'm willing to go for this thread.

Jon

Thanks for the response.
just for fun

Imagine two galaxies A, and B. They are x far away from each other. A photon is somewhere in between A and B. A is equal in mass and density to B. The maximum gravitation force of B or A would depend on X because of the ability for A and B to gravitationally cancel each other. Therefore, X would determine the amount of blueshift and redshift the photon experiences given that gravity is capable of accelerating a photon. So in other words, red shift would be proportional to distance.

It is too bad it isn't that simple.

[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

[kev]

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 travelling twin in the twins paradox, the travelling 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 travelling twin to undergo a Lorentz contraction in the direction of motion, but that does not mean that the non-travelling twin observes the travelling 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 (Dthen + Dnow)/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 occurance 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 (Vthen + Vnow)/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