Relativity and Cosmology

<Bows respectfully to superguru>

Some time ago there was some discussion that the universe might be toroidal rather than spherical, not that one can ever define such a shape from the outside! Does this impact on the thinking above, or is the toroidal universe concept now passé?

Hi PWS, no 'supergurus' around anywhere near here!

AFAIK, the WMAP data sets do not support a toroidal cosmos, which is a relief to me, because I have no idea how to model a cosmos based upon it.

-J

Hi Jorrie,

I couldn't get the link from [1] to work, can you check it.

I think it's worth mentioning that the energy of a photon is E=hc/λ meaning that the photon actually has less energy when it arrives then when it started.

Also, I'd like to hear your take on De Broglie waves and gravitational redshift. I've looked around and can't find anything discussing it but it must occur.

Roger

Hi Roger, tx for pointing out the broken link - fixed it.

Yes, the photons lose both linear momentum and energy as they travel. The 'lost' energy goes into expansion, I guess.

I think De Broglie waves may fit better under the next Blog topic that I'm planning - on particle energies in an expanding cosmos - but yes, there may be a link between the fact that particles lose momentum during cosmic expansion and the redshift of photons. A sort of 'particle redshift' in terms of De Broglie wavelengths. Interesting!

-J

A very 'enlightening' thread! I also bow.

"Yes, the photons lose both linear momentum and energy as they travel. The 'lost' energy goes into expansion, I guess."

Maybe you've discovered the Dark Energy. As the light (photons) get red-shifted they become 'dark'. Do we call this radiation pressure?

-S

Maybe. What bothers me about this is that no one appears to care. So either the explanation is so obvious (where the photon energy goes) that they (physics community) don't bother to explain it, or the magnitude of energy is so small that it is deemed unimportant (I have a hard time believing that since background radiation fills the entire universe), or no one cares.

It seems like a lot of energy to just ignore.

Hi Roger, as you noted, I tried to 'illuminate' the issue on my previous reply (to S). As far as the balloon analogy is concerned, there is no problem. In hyperspace, the photons have been 'lifted' to a higher energy plane - remember they lost kinetic energy in order to keep angular momentum constant, but they gained potential energy. That's why I originally blundered in saying "the 'lost energy' went into the expansion". Point is, they were 'lifted higher' by the balloon, not going there on their own accord.

It is somewhat equivalent to a particle orbiting a massive object in an elliptical orbit, continuously trading kinetic energy for potential energy (and visa-versa), while keeping the total mechanical energy constant. We know that photos cannot really orbit like that - even near black holes there is only one orbit, and that is circular and unstable. In the balloon analogy, we just force the photon's hand, so to speak. And so does the universe, apparently.

-J

Hi Jorrie,

In reply to what you wrote above, to what potential energy are you referring? From the standpoint of within the universe, the photons are losing energy but there is no potential energy gain as far as I can seeunless you are referring to gravitational? Can you clarify?

Also, I was wondering, have there been solutions done for an inhomogeneous universe? I ask not because I believe the universe to be inhomogeneous, but rather because I think it could elucidate local spatial effects. Local space is certainly inhomogeneous.

Roger

Hi Roger. The potential energy is most definitely gravitational here. Weird as it may seem, photons that are spread out more thinly (less radiation density) possess more potential energy than more dense counterparts. This is because radiation gravitates and it takes work to 'move the photons apart', so to speak. A static 'radiation only' cosmos would have collapsed under its own gravity and hence convert potential energy into shorter wavelength photons again. Perhaps it would disappear into a singularity, perhaps not...

There are various approximations for inhomogeneous universes. Local inhomogeneities are difficult to bring into the model, mostly done through perturbation theory. AFAIK, it is not possible to seamlessly match local solutions to Einstein's filed equations (e.g. the Schwarzschild solution) to the global solution, like Friedman's. I'm not too well clued up on inhomogeneous solutions though.

-J

Jorrie,

Thanks and Thanks. You're gravitational potential energy explanation seems reasonable. The energy of a photon is proportional to 1/λ (wavelength is just a distance) and the gravitational potential energy between photons is proportional to 1/r.

It feels like cosmic expansion is akin in many ways to a timelike gravitational well, which now that I think about it, is exactly what it is. A space like gravitational well means that as you move away from the well (out of the gravitational potential), the photon is redshifted because it's gravitational potential has increased.

Think about cosmic inflation in a similar way, except instead of moving through space, your moving through time. As time increases you are further and further outside of the gravitational well in the sense that your potential energy has increased, you have redshifted, hell, even the curvature of space has decreased (or is it increasing, I can't seem to get this straight).

How do you feel about such an interpretation Jorrie? It really seems right to me, I hope I'm explaining it well.

Roger, yes, " ...expansion is akin in many ways to a timelike gravitational well ..."

I'm not too sure what you mean by "timelike" and "spacelike" gravitational wells, but in a sense, the cosmos is expanding out of a gravitational well. There is one proviso though: the center of that well sits in a hyperspace dimension, never in a spatial dimension. The gravitational potential of the homogeneous cosmos is the same everywhere in space. It is only when 'lumpiness' is introduced that you have some local gravitational wells, but these are not part of the LCDM model. It may also be valid to view the gravitational well as sitting in a time dimension, but I am a bit wary of that.

The curvature issue seems to still cause some trouble! Remember that the cosmic balloon does not simulate cosmic curvature at all. The balloon's geometric curvature changes in the wrong sense, but it does not enter into any of the equations used, so it is irrelevant. It is perfectly valid to simulate a flat cosmos (with no curvature at all) by means of a balloon of arbitrary radius - all the calculations work perfectly.

-J

You wrote:"I'm not too sure what you mean by "timelike" and "spacelike" gravitational wells, but in a sense, the cosmos is expanding out of a gravitational well."

I guess what I was trying to say is not that the cosmos is expanding out of a gravitational well, but rather that it is a gravitational well and as we move forward in time we essentially are moving out of the well. Take a look at the diagram below:

I'm sorry the diagram is so messy. Basically the y-axis is the energy density (in the universe) and the x-axis is time. As we go forward in time the density decreases (as matter and radiation get spread out). Compare this with the gravitational well of a planet and it is very similar, except instead of Time on the x-axis, you would have space (radius r). I hope that makes what I'm trying to say clearer.

For the second part you wrote:"The curvature issue seems to still cause some trouble! Remember that the cosmic balloon does not simulate cosmic curvature at all."

I'm sorry, I wasn't thinking of the cosmic balloon when I was asking, I just couldn't remember which it did (I'm still unclear). In my mind, if big bang was a singularity then it seems like curvature should have decreased since then, but I have the nagging feeling you said that it actually has been increasing, which is why I'm confused.

To further clarify my point. Imagine we are a photon in space some distance from a black hole. We would expect as we increase our r (distance) from the black hole, that potential energy with respect to that black hole would increase, at the same time we would expect that our wavelength would be redshifted (because we are climbing out of it's gravity well)

I'm saying that this cosmological system is behaving the same way, except that instead of moving through space, the photon is moving through time. (I mean the photon is moving through space as well, but the redshift from cosmic expansion depends only on time). It's as though the Photon feels the gravity from the original singularity through time.

The cosmological constant thus would be a sort of measure against escape velocity of this singularity from back in time. Higher than 0 and the universe expands forever (light redshifts forever as it climbs higher and higher out of the gravity well). Lower than 1 and the universe eventually crashes back together in a big crunch. At 0 it doing neither, but such a position would be unstable.

Hi again Roger, you wrote: "We would expect as we increase our r (distance) from the black hole, that potential energy with respect to that black hole would increase, at the same time we would expect that our wavelength would be redshifted (because we are climbing out of it's gravity well)"

Qualitatively, yes. Quantitatively, no. The redshift around a black hole scales with √[1-2GM / rc²], while the cosmological redshift scales straight with 1/a, which is equivalent to 1/R for the balloon. So, be careful in not pushing this "analogy" to far - you may get seriously tangled!

"It's as though the Photon feels the gravity from the original singularity through time."

I suppose you can say that, but it's simpler to just consider that all the matter/radiation/vacuum energy of the universe set up a present time gravitational field and that photons and matter particles react to that.

-J

BTW, I've finished the particle 'redshift' (momentum decay) thread and has scheduled it to launch in a few hours from now. I've found the de Broglie wave interpretation very interesting (and have included it), but more difficult to work with than straight relativity.

Jorrie,

I really appreciating your indulgences on this subject. I want you to know that when you respond I think carefully about what you said, sometimes long after I've responded to you. I feel as though you really are helping me get an understanding of this subject. I'm ordering this book to read up some more.

As for you're caveat about redshift near a black hole, I agree. Lets say the analogy is more accurate the further you get from the black hole (where relativistic effects are less pronounced).

One side question that occurred to me when I was thinking about my timelike singularity (I should probably come up with a different name for this approximation, I'm open to suggestions).

Is there a rotating homogeneous universe cosmic model that you are familiar with? I'm just thinking that it would be an interesting twist (sorry about the pun).

Roger

Hi Roger, your diagram is just the wrong way round! Density starts out high and decreases as time goes on.

What you describe is akin to the so-called "kinematics model" of the universe. Jon and myself did quite a bit of work on that in this thread. It is useful to some level, but has a few serious problems. (i) It cannot handle the v > c recession velocities of the real cosmos. (ii) It does not agree with the accepted fact that time runs at the same rate everywhere in the homogeneous cosmos.

You must not equate the physical curvature of the balloon with cosmological curvature - they have nothing to do with each other. Cosmic curvature is an energy balance issue - if kinetic energy of expansion equals potential energy, the curvature is zero. If slightly off zero, it diverges farther from zero as time goes on. I have defined this reasonably well in that long thread on the design of the cosmic balloon (in a reply to S).

-J

Hi Jorrie,

You Wrote:"Hi Roger, your diagram is just the wrong way round! Density starts out high and decreases as time goes on."

You're right of course, sometimes I draw what I'm thinking rather than what I'm saying. What I put in that diagram was how energy density effected space, but I labelled it as energy level. Please disregard that diagram and give me a do over. I really fouled up what I was trying to say with that diagram, let me try again.

Here is a 3D representation of a black hole.

Let's call the position of the Singularity zero. As you move to the right from the singularity you climb out of it (lets not worry for the moment about if that's possible, or start above the event horizon if you can't take the impossibility of what I'm saying).

What I'm trying to say is when you're moving to the right, rather than moving through space, imagine you're moving through time. Each movement to the right is a movement further in time.

I'm saying this because cosmic redshift of radiation behaves exactly like the redshift experienced by a photon climbing out of a gravity well would. This is not the kinematic model you discussed before. This is a hyperspace model. It's just that it's a singularity in time rather than in space.

You Wrote:"You must not equate the physical curvature of the balloon with cosmological curvature"

I never think of the balloon ever when I think about this stuff. Ever.

You Wrote:"Cosmic curvature is an energy balance issue - if kinetic energy of expansion equals potential energy, the curvature is zero."

Lets just drop this. One of the difficulties of communicating by posts is that it's harder for me to assure you that I understand what you're saying. When I say I forgot which way the curvature went, I meant it literally, I just forgot. I remember now, curvature increases as we move forward in time (not smoothly I know).

Hi Roger, OK, I understand what you are trying here.

BTW: "I never think of the balloon ever when I think about this stuff. Ever." I'm afraid you do not realize what you miss. It's the only no-nonsense way (apart from serious mathematics) that I know of to make sense out of a difficult subject. I still have to find a general case that I cannot explain rather simply using the balloon!

Your "timelike singularity" probably just means that there was a spacetime singularity at some past time. I agree that you should find a better term for your idea. In any case, it does not look much different from the kinematics model, possibly suffering from the same issues that I listed previously.

Your diagram resembles Schwarzschild spacetime geometry. Yes, photons do redshift as they climb out of the gravitational well, but this is gravitational redshift, quite different (technically) from cosmological redshift. Inhomogeneities tend to look like Schwarzschild, but Friedman does not work with inhomogeneities. Good luck if you want to pursue this avenue!

"Is there a rotating homogeneous universe cosmic model that you are familiar with? I'm just thinking that it would be an interesting twist (sorry about the pun)."

No, I have never heard of such a model that works and observations seem to rule it out (we do not see any 'twist').

-J

Hi S, you wrote: "Maybe you've discovered the Dark Energy. As the light (photons) get red-shifted they become 'dark'. Do we call this radiation pressure?"

I think my "The 'lost' energy goes into expansion, I guess" was maybe a bit misleading.

Photons do not create pressure that can expand the universe - any 'radiation pressure' would have been randomly distributed in all directions and cancel out. Photons simply act as gravitating energy that tries to collapse the universe.

For the first 50 thousand years or so, radiation energy was the dominant energy doing the 'braking' on expansion. Then the radiation energy density dropped lower than the particle energy density and normal matter (light and dark) took over as the 'braking force' on the expansion.

Dark energy only took over some 7 billion years later, both as a 'brake' and as an 'accelerator', with the accelerator winning, it seems. By that time, radiation energy density only made up some .02% of the total energy density, so it made a negligible impression - even less today.

So, where did the 'lost energy' go? OK, maybe still into expansion, but it was never used to cause expansion. Inflation caused the initial expansion (we think) and then the expansion coasted, 'thinning out' all the other energy forms (reducing densities), while keeping the overall total cosmic energy constant.

-J

Jorrie, concerning your link in footnote 1: I like it. Now if only we could convince marcus in the physics forum that space expands. Then maybe we could all get on the same page. Like that's gonna happen. This is another example of the illogicalness that's pervading cosmology these days.

Wikipedia uses H for the Hubble parameter instead of h. Which one is used more? So the paper should have used H₀ instead of h and should have called it the Hubble constant instead of the Hubble parameter? That's what I am getting. It's all quite frustrating.

I got the following from this source. What do you think of it?

1. Redshift with Distance

It is a remarkable coincidence that there are actually two ways that you get a redshift with distance (and strangely only the big bang explanation was considered which is the most complicated explanation, the most simple explanation was never considered).

Fig.1 - In Big Bang cosmology, the universe is all that exists, thus to prevent it gravitationally collapsing an expanding universe was proposed. The discovery of the redshift with distance seemed to confirm this, where the redshift is assumed to be a Doppler effect of receding motion due to an expanding universe.
The problems with the Big Bang theory are obvious!

What is a 'Big Bang' and how does it create Space, Time, Matter and Motion?

What is outside the expanding universe?

Fig.2 - In WSM Cosmology, the observable universe is just a finite spherical region of infinite eternal space. We can only see and interact with other matter in this region. Thus there is no need for an expanding universe, as other matter around our observable universe prevents it from collapsing. This is the equivalent of Einstein's Cosmological / Antigravity constant, but it is just normal gravity of matter outside our observable universe within infinite space.
So why the redshift with distance?
Because as we look at matter farther away from us, we find that we share less overlap of a common finite spherical observable universe. And this means that there is less energy exchange, which equates to a redshift with distance.

See The Cosmological Redshift Explained by the Intersection of Hubble Spheres
This article shows that each wave center 'particle' is the center of its finite spherical observable universe (Hubble Sphere) within infinite Space. As two wave center 'particles' move apart there is less overlap of common Hubble spheres / observable universes, thus less wave interactions with increasing distance, thus less energy exchange which then provides a simple sensible explanation of the redshift with distance.

-S

Hi S,

"Wikipedia uses H for the Hubble parameter instead of h. Which one is used more?"

I don't know which Wiki-article you are referring to, but if that's what it says, it's simply wrong. H is called the 'time varying Hubble constant', also sometimes explicitly denoted by H(t). I do realize that it is sometimes erroneously called the 'Hubble parameter', but the cosmological convention is that a parameter is a dimensionless entity, which H is not. I use the Peebles 1993 conventions. It is also clear that the paper that you referenced last time uses h in the standard way.

I'll respond to the rest of your reply later...

-J

Hi Jorrie,

I think I could have found worse quotes than the ones you posted. I couldn't make sense of a sphere around a distant particle (like it could observe us). And it said their explanation was the simple one! Ha, yours is far more simple. It has to be if I can understand it! One for the trash can, I think.

-S