Evolving Time's Arrow

The CMB exists without inflation. It is predicted by the standard FLRW spacetime model of the big bang. What inflation does indicate is how the CMB is smooth with small anisotropy. It also tells us how different regions of the CMB originated from the same initial conditions.

The quantum aspect of inflation is the vacuum energy stretched out space enormously, about 63 efolds. The vacuum energy just defines an energy density

T_{00} = Λg_{00} = (8πG/c^2)ρ,

for ρ the energy density of the vacuum. So the vacuum energy provides the energy for the dynamics of space, where that dynamics is purely classical.

Cheers LC

Lawrence,

What would light be that has been completely redshifted far beyond the visible scale? Wouldn't it resemble the black body radiation of CMBR?

Wouldn't it also have small distortions around where the emitting source is located, like ripples in a stream around a submerged rock?

Anil Ananthaswamy wrote: "Unfortunately, physics treats time rather differently. Einstein's theory of special relativity presents us with a four-dimensional spacetime, in which the past, present and future are already mapped out."

Equivalently, Anil Ananthaswamy could have written, referring to Banesh Hoffmann's text below: "Unfortunately, Einstein resisted the temptation to account for the null result of the Michelson-Morley experiment in terms of particles of light and simple, familiar Newtonian ideas":

http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768 "Relativity and Its Roots" By Banesh Hoffmann "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd... (...) And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

The CMB has a thermal or blackbody distribution of frequencies. This peaks in the microwave region. We identify infrared with heat because the blackbody distribution peaks for most hot sources in that region. There is actually nothing fundamental about that. A blackbody curve can peak in the extreme gamma radiation frequency range, and in fact did so during the rather early universe.

Other galaxies outside our local group will red shift increasingly. In 10 billion years they will only be observed in the IR band. However, the distribution of frequencies from these sources will not be Gaussian or blackbody. As this occurs however, the time of arrival rate for photons will decrease, their wavelengths will increase and it will becomes very difficult to detect them.

Cheers LC

Lawrence,

Just in theory, assume there are infinite numbers of galaxies in infinite space. So that even radiation from much further than 13.7 billion lightyears away eventually reaches us. Wouldn't that distribution of sources fill in all the gaps and result in a black body radiation below the infrared and in the microwave?

" ... assume there are infinite numbers of galaxies in infinite space ..."

Why?

Why not:

Olber's Paradox

I am answering this in a new text box.

An infinite universe is plausible. The RxR^3 topology of the universe may not have the same vacuum structure everywhere. There may be these zones where the vacuum energy Λ_0 >> Λ, where Λ_0 and Λ are the bare vacuum and the broken vacuum cosmological constant. So our observable universe may have a sort of barrier, where signature of that might exist on the CMB. This is the Linde pocket universe model, and these bubbles are due to the physics of Coleman --- called bubble nucleation. There some good reasons to think this is the case.

However, we can assume the vacuum is the same for the entire R^3. Any observer looking out will see galaxies and objects further out move at increasing velocity, indeed faster than light. If the space is infinite the velocity as one looks out to infinity becomes infinite. I outline how this works below. So if that happens then any photon emitted sufficiently far out is not just red shifted to the IR or into the radio wave band. It red shifts beyond the horizon length ~ 10^{10} light years. Again I illustrate what the horizon is below. So this quells the Olber's paradox, for anything sufficiently far out is redshifted to such low frequencies that it is not very observable. Further. anything that far out emits photons along our light cone from behind the CMB opaque region. This means such photons are swamped by that boundary This would not be the case if these quanta are in the form of neutrinos. In principle with neutrinos we could observe the universe at a time far earlier than the CMB. Gravitons similarly could permit us to observe right to the quantum gravity event. These gravitons would be red shifted into long wave length gravity waves which might perturb the CMB in so called B-modes.

The problem with an infinite universe with a single vacuum is that it means our past light cone extends infinitely outwards. In order to have a finite time it means the initial inflationary period involved an infinite expansion. That is a bit of trouble. So to prevent some problems the Linde pocket universe idea (eternal inflation etc) is a better candidate. However, the whole R^3 contains an infinite number of these pockets expanding out at an extremely rapid rate. So in some sense we have pushed the problem out to another level. So this R^3 might have started out as a three sphere S^3 where a point was removed and that topological information is involved with quantum information of these bubbles that are finite in number. Further, for reasons I will go into right now, that huge vacuum these bubbles are contained in may run down, which would also mean the creation of pocket cosmologies is finite and of brief duration.

The expansion of the universe is described by a scale factor a(t). Given a radial distance r the scale factor a(t) gives a new radial distance r'(t) = a(t)r. I will use Newtonian mechanics and gravity, for it turns out that this gives the same thing as general relativity for flat space, but curved spacetime. General relativity is somewhat complicated to work with. We have for Newtonian mechanics with gravity that the kinetic energy of a moving object is (1/2)mv^2 and that the potential energy is -GMm/r. The total energy is the sum of these. The velocity is determined for our situation by the scale factor so that r(t) = a(t)r and v(t) = (da/dt)r. A little bit of calculus is entering in here. So the total energy we can set to zero, and we have

(a')^2 = 2GM/a, a' = da/dt

We then have M = (4π/3)d (ar)^3, for d = density of matter in a spherical region of radius r' = a(t)r. We then write this dynamical equation as

a'^2 = 8π Gd a^2/3,

where the Hubble factor is H = a'/a. Now if I assume that the density is constant then this is a differential equation a' = Ka, for H = sqrt{8πGd/3}, and the solution is

a(t) = (1/H}exp(Ht).

So the scale factor expands exponentially. This is approximately a de Sitter spacetime configuration.

The Hubble factor for small time gives v = Hr, for r a small radius out related to a time t. For v = c one can compute the radius where that occurs and we have r = c/H which is the cosmological horizon distance

R = 1/sqrt{8πG/3c^2} = sqrt{3//\}

Where /\ is the cosmological constant. This horizon distance is about 10 billion light years.

This event horizon is not a barrier to our ability to observe things. It is similar to the event horizon of a black hole, but it is analogous to looking out into the exterior world from inside a black hole. It is a barrier to our ability to send a signal to anything beyond this distance. A galaxy with a z > 1 is beyond this event horizon, and the CMB has z ~ 1000. What happens with galaxies disappearing is that they will accelerate away and become highly red shifted. In about 10 billion years all galaxies outside our local group will be red shifted out of the optical band. An intelligent life form could observe other galaxies if they use IR or microwave instruments. The CMB will recede into the radio wave band and to long wavelength frequencies.

LC

Tom,

If redshift is a function of distance and not recession, then that black body radiation is the light from those infinite numbers of stars. It has just fallen off to the microwave spectrum.

Tom,

Lawrence's post, 5/23, at 13:46;

" As this occurs however, the time of arrival rate for photons will decrease, their wavelengths will increase and it will becomes very difficult to detect them."

From my essay in the recent contest;

"As the light from a star expands out to fill the volume around it, it necessarily grows

more diffuse, as the same amount of energy must cover ever more volume. The further

away that star is, the smaller it appears and the fainter its light gets. Since the smallest

measurable quantity of light we can detect is what will trip that electron, eventually it

reaches the point that barely enough is reaching our detectors to even trip one atom on

the detector. Beyond that and the duration between the detections start getting further

apart, so that the resulting wave pattern created by the continuing process of measuring

these photons will have longer wavelengths."

I find it much easier to accept many worlds, than an infinite R^3 universe.

Infinite red shift freezes observation on the horizon, so even though the horizon is not a barrier, it is a boundary. If we want a continuous model with boundary conditions (I do), to me it seems more plausible to fix the radial length 1 of R^3 on the S^2 manifold embedded in the S^3 topology. /\ can retain its value of very near zero, and quantum mechanical unitarity holds on all time scales calculated in R^2 (in other words, quantum configurations in the Hilbert space can be shown to have correspondence to physical space without regard to locality). This boundary condition allows an R^n universe with no assumption of infinite distance from the origin -- a complete inversion of the general relativity model from finite in time and unbounded in space, to one finite in space and unbounded in time. It makes Einstein's quasi-Euclidean model fully Euclidean.

The only reason I think that /\ is not exactly zero, is the necessary condition for dissipation of thermodynamic information over n-dimension manifolds. Necessary, because continuation of the time metric over S^n implies exchange of energy and therefore entropy production. /\, then, is the universal gravitational constant in a sphere kissing model.

This model also answers the sticky problem you raised:

"So to prevent some problems the Linde pocket universe idea (eternal inflation etc) is a better candidate. However, the whole R^3 contains an infinite number of these pockets expanding out at an extremely rapid rate. So in some sense we have pushed the problem out to another level. So this R^3 might have started out as a three sphere S^3 where a point was removed and that topological information is involved with quantum information of these bubbles that are finite in number."

Indeed, the S^3 topology in an S^n model, by the generalized Poincare conjecture and Perelman's proof, eliminates singularities. The "other level" is then continuation of the time metric over S^n, asymptotic to length 1.

Tom

Tom,

That seems more like a statement of preference, rather than an argument against infinite space. With many worlds, you just kick the can down the road, with infinite numbers of bounded spaces. Presumably they are connected.

Just as practice, wouldn't it be possible to consider what a universe of infinite space, subjectively bounded by horizons, might look like?

Yes, it might make a lot of current theory superfluous, but if it works, it would provide a more solid foundation for further mathematical modeling.

As I indicated the cosmological horizon is not a barrier to observing the universe beyond it. It prevents one from ever sending a signal to anything beyond it. Anything beyond it will recede away faster than any light signal you might try to send to it. One might think of the cosmological horizon as similar to a black hole horizon for an observer inside the black hole. As you observe further out the velocity of objects will increase to infinity. This means your past light cone will "splay out" in the distant past and cover an infinite R^3. Equivalently inflation was divergent. Of course we have quantum gravity issues, where maybe it does not actually "cover to infinity," but within a Planck time from the initial R^3 it might then stop. This would be something similar to a stretched horizon in the distant past, within sqrt{Għ/c^5} ~ 10^{-43} sec of the initial spatial slice. So we might think of this as looking at the cosmological horizon from the other side. Maybe, the idea I have been kicking around for a while, where maybe this is equivalent to the rapid flattening of a sphere S^3 after the removal of a point. The hole almost instantly expands to infinity. This would be that huge inflation. For a number of reasons I am not sure how happy I am with this idea though.

The cosmological constant does have to be nonzero for there to be an accelerated expansion of the universe. The horizon distance d = sqrt{3/Λ}. If Λ = 0 then the horizon is at "infinity," or maybe better put not defined. During the inflationary period of the universe Λ was 100 orders of magnitude larger than it is now.

Cheers LC

Lawrence,

I agree with you about the rapid flattening (Euclideanization), except that I find it cannot occur on S^3. I find ("time barrier" fig. S2.2, p. 34) that two Chi = 2 2 S^2 manifolds (which is topologically equivalent to S^3), split from the removal of a vertex point on S^9 (10 dimensions), where that configuration is unstable (by the Banach-Tarski construction).

This more supports my conclusion that the four dimension horizon of S^3 is identical to the 10 dimension limit (S^9). The real significance, though, is the unitarity (assuming scale invariance) of the time metric on the classical scale.

Tom

I have to accept somehow the many word hypothesis. Ours is a Planck value universe. There are most likely other universes with h+n h-n Planck values

n being any number .. with which we do not interact, like our neutrinos living on the fringe of our Planck universe....

Is there a quantized n values/step between universes? and what is this number?

Marcel,

The idea is that some "blob" of vacuum energy from "elsewhere," say some other spacetime cosmology or maybe equivalently from a Dp-brane interaction, quantum tunnels into a new inflationary manifold. At the critical point the S^3 is topologically changed into R^3, and the point which is removed carries the unit of Euler index number or Betti number which manifests itself as topological fields on the manifold. The reason why it would start out as S^3 is a quantum fluctuation of some vacuum energy must be finite, so some volume with a vacuum energy density is involved with the quantum tunneling.

The S^3 is a quantum wave functional, such as a solution given by the Wheeler DeWitt equation. The topological change stretches the S^3 - pt into R^3 and this process is an inflationary spacetime with Λ ~ 10^{120}GeV^4, which is at the Hagedorn temperature, and this topological dynamical change at R^3 has a vacuum state with Λ ~ 10^{100}GeV^4 and the generation of matter fields from the topological quantum number induced from S^3 -- > R^3. This is the space our pocket universe is contained in, where this is a region of symmetry breaking. Then after about 63 efolds from there the cosmological constant exhibits a rapid drop in a bubble of nucleation so Λ ~ 1GeV^4, where this is our "pocket universe." The vacuum at this lower energy is one of broken symmetry, and this is a phase transition which results in a form of latent heat. This latent heat marks the reheating period and is responsible for the thermal "bang" in the big bang.

There are some technical problems with this though, but it has always struck me as having some attractive features. Maybe if I get the time I will return to this to see if I can make a go of it.

Cheers LC

Our tense-less time scale from eternity to eternity is a mistake that can be attributed to the bible and maybe Descartes rather than to Einstein. Already Oliver Heaviside introduced the fictitious split of the not yet existing future into an even and an odd component. Not just Tom and LC are still convinced to solve the most foundational imperfections by means of mathematics. I do not share this attitude.

Among the first who admired Einstein's SR was a coworker of Max Planck: Max von Laue. He was born in 1879 as also was Einstein. He discovered compelling evidence for radiation to be an electromagnetic wave, he supported SR, and he got the Nobel price in 1914. Why did he not realize or at least not admit that Poincarè's synchronization is logically flawed?

Eckard

Eckard Blumschein wrote: "Our tense-less time scale from eternity to eternity is a mistake that can be attributed to the bible and maybe Descartes rather than to Einstein."

Let us only concentrate on the properties of time that deductively follow from Einstein's 1905 constant-speed-of-light postulate. Craig Callender, Lee Smolin, John Norton seem to reject those properties without questioning the postulate, an approach that is not very fair. If you don't accept the consequences, you should declare the premise false, no matter what catastrophe in mainstream science might occur.

Pentcho Valev pvalev@yahoo.com

A Nobel price winner of Polish origin, I forgot his correct name, maybe Wilczek or so, called my essay to long and boring. Perhaps, my reasoning is too simple as to be taken seriously. My starting premise is causality of reality. In reality, future processes did simply not yet have any effect. I see this a strong argument against Einstein's first postulate.

His constant-speed-of-light postulate is the second one, and I do not see any reason for sharing the widespread doubt on the correctness of his second one. If light has the same properties as have other waves than this includes a maximal speed. I do not overvalue the attempts to enforce an interpretation of failed experiments for pinpointing a hypothetic ether relative to which the earth was thought to move. The speed of electromagnetic waves can be measured, and propagation of signals faster than light proved impossible.

On the other hand, apparently nobody objects against the seemingly reasonable first postulate. I may be the first one who disagrees: Even if we do not question that the differential equations of physics will remain valid in future processes too, the reality corresponds to cumulative influences from the past, and the belonging integral relationships cannot be shifted. Future processes do not yet exist.

Accordingly, Poincaré's method of synchronization is not fair. With reference to the moment of reflection, the moments of emitting the signal and of receiving the reflected one are located in the past and the future, respectively. Hence, such procedure is not always correct in reality.

Paradoxes may be valuable indications of mistakes. It would not be honest if I signed the petition concerning the interpretation of the twin paradox. I see it one of several indications for the inconsistency of Lorentz transformation.

Incidentally, while Tom referred to "Olber's paradox" I consider Olbers' mistake simply an indication of naive thinking.

Eckard