Evolving Time's Arrow

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

Anil,

In my book - The Meaning of Time - A Theory of Nothing I introduce a new source for the arrow of time. I call it the intellectual arrow of time. The intellectual arrow of time is closely related to the idea of consciousness. The word consciousness is derived from the Latin conscientia, which may be literally interpreted as shared knowledge. The intellectual arrow represents our insatiable, relentless desire to understand the universe and our place within it. In other words, it represents an intellectual curiosity that, in spite of setbacks that have sometimes suppressed the shared knowledge of humanity, seems at all times to increase towards the future. There are three critical issues involved in defining this arrow of time.

The first issue is that the intellectual arrow of time may be associated with the liberal thinking that manifested itself in Franklin Roosevelt's New Deal and Lyndon Johnson's Great Society. It is this author's view that although purely governmental solutions to societal ills have their limitations, this philosophy represents a relentless trend in history toward the achievement of a more just, more tolerant, and more inclusive society. The future must lie in the direction of advancing ideas that expand the concepts of fairness and justice ─ not in the direction of their suppression.

The second issue is that there are forces in society that would like to stop or slow the intellectual arrow of time - sometimes with good reason. Change can be a destabilizing force in society, and not all change is beneficial or should receive widespread support. At darker times in history, however, the desire to suppress the expression of just ideals has been reactionary. During the Dark Ages, for instance, all the rich culture that had been developed by the Greeks, the Romans, and other nations was repressed by the ruling elite in an effort to control society. There have also been times when the forces of change have been fundamentally immoral. In recent history, for example, the actions of one demented madman led to the senseless death of millions; his agenda was essentially an effort to rewrite history in a way that justified these evil deeds.

And finally, as it ages every generation in some fashion laments the forces of change. This is particularly true in today's society. On the one hand, the ever-quickening pace of technological innovation has led to a more productive and prosperous society. On the other hand, this largesse has not come without a cost. Rapid change seems to leave in its wake the innocence of our youth. But there is no turning back; there is no way to return to an earlier time when events did not happen so quickly and everything seemed to be less complicated. We can influence the future but we cannot change the past.

Gene T. Yerger

"We can influence the future but we cannot change the past." Isn't the direction of causality always valid in nature in general? Just the so called laws of nature are invariant against shift and reversal of time.

I have to admit having confused Nobel laureates. Actually it was a Wilczek who avoided any comment while a 't Hooft pretended having not read my boring essays.

Eckard

Craig,

I just read your article in Scientific American 2010. It is very interesting. I fully agree. I´m a physicist. IMHO, I believe that life computes, and does it in the easiest direction. And I think that it is possible to demonstrate that this direction is from lowor to higer entropy. I wrote time ago a short presentation that, thank to your article now I´m extending. Most of the reasoning is paralell to your article here, and IMHO add some additional points realted with how life works. If this add a little clarification I would be very happy.

"Arrow of time determined by life´s easier direction for computation in space-time"

https://docs.google.com/present/view?id=dd5rm7qq_142d8djhvc8

"Arrow of time determined by life´s easier direction for computation in space-time"

Lets chat.

https://www.sendthisfile.com/Dsi1UcAS1T4nqej4a0zxk1TB

My clock converts a circular earth orbit into an eliptical one.

And the result is six minutes difference from sidereal time per year.

Approx we take this figure to 10,000 digits of pi accuracy as the formula uses Pi.

A cicular orbit can be in as many as 11 dimensions but these are unstable when an orbit is converted to an elipse it becomes stable in three dimensions plus one of time.

Thus you can reverse the equation to convert Einsteins 4D space time to 11 dimensions.

So you can convert String theory to Einsteins thoery and EInsteins theory back into string theory.

Some scientists believe Einsteins thoery cannot be expressed in 10 dimensions.

Others believe EInsteins thoery can be expressed in as many dimensions as you want to use...................

What do you believe can my thoery work to unify Einsteins thoery and string theory.

And is my clock time more accurate or just an error of six minutes per year rather than a more accurate measurement of time..........................................

Please help me with this problem.

Steve..................

Iam not answering the question myself what I have provided is background to the problem.

The central question is whether Einsteins 4D space/time can be converted to ten dimensions or not.

The central question is whether there is 4D. And there is not. I will give you a clue, here is a quote from Lorentz 1892 (para 5), this is how it started:

"I have sought a long time to explain this experiment without success, and eventually I found only one way to reconcile the result with Fresnel's theory. It consists of the assumption, that the line joining two points of a solid body doesn't conserve its length, when it is once in motion parallel to the direction of motion of Earth, and afterwards it is brought normal to it. [The factor being] p2/2V2 . Such a change in length of the arms in Michelson's first experiment, and in the size of the stone plate in the second, is really not inconceivable as it seems to me".

Paul

The key is distance in/of space as it relates to the consequences of touch/motion in (and with) time. The extremes of size, motion, and energy/force have to be equivalent/balanced in conjunction with space manifesting as gravitational/electromagnetic/inertial energy -- as inertia, gravity, and electromagnetism are all key to distance in/of space. (This is the prescription for quantum gravity too.) Fundamentally balanced/equivalent inertia and gravity (both at half strength/force) balances attraction and repulsion.

I have demonstrated all of this in/as dream experience; and, moreover, I have shown the dream to be a linked center of body experience as well. All of us originate at/from the center of the HUMAN body.

Eckard Blumschein wrote: "Hence the first premise is untenable. Yes, if Callender is honest then he has to hint at the false premise."

The second premise (Einstein's 1905 constant-speed-of-light postulate) is untenable:

http://www.ccsenet.org/journal/index.php/apr/article/download/10410/7432

Applied Physics Research Vol. 3, No. 1; May 2011, One-Way Light Speed Determination Using the Range Measurement Equation of the GPS, Stephan J. G. Gift

"In particular the one-way determination of light speed using the range measurement equation of the GPS establishes in (7) that a signal sent eastward travels at speed c minus the rotational speed of the Earth v at that latitude giving c - v. The GPS data also shows in (13) that a signal sent westward travels at speed c plus the rotational speed of the Earth v at that latitude giving c plus v."

Pentcho Valev pvalev@yahoo.com

Dear Pentcho,

Thank you for your hint to Gift. While I am not familiar with the matter and he did not give error bars, the values 14ns for the distance NY SF and 207ns around the equator might be realistic. Doesn't the ECI frame move during the light travel by several meters? So the c+v westward and the c-v eastward correspond to smaller and enlarged, respectively distances. This reminds me of Foucault's 1852 pendulum. Incidentally Foucault was also the first one who measured c by means of mirrors.

Following Maxwell's theory of light as an electromagnetic wave and in agreement with Van Flandern, I see the GPS data rather a confirmation of c as the speed of light but at odds with SR. I read several books on SR. We cannot deny that high energy accelerator experiments confirmed c as a limit which is to be expected for waves. So I am naively ready to accept electrons as waves but not SR as correct.

Electrodynamics is obviously not covariant under Galilei transform. Incidentally, as Schroeder wrote, Michelson said to Einstein in 1931, he regrets that his work gave rise to the monster of Einstein's theory of relativity (G. Holton, Am. J. Phys. 37,968(1969)

Perhaps, SR cannot be rescued unless one restricts the consideration to closed systems that are free of uncertain or unseen influences which I consider the essence of reality in contrast to theory. This explains why Einstein necessarily admitted to Popper sharing the (abstruse) philosophy of Parmenides, and why he, Hilbert, and others denied any role of the now and even of the arrow of time. Science is still suffering from this implication.

Regards,

Eckard

While reading in recent years about the conundrum of 'dark energy' it occurred me that since Minkowski it has conventionally been simply assumed that the metric of scale of time to be same as for space. While we cannot look to anything in particular to establish a universal system of scale as absolute, it is quite arguable that as real physical properties the length of a span of duration in the dimension of time is covariant with a commensurate length of a span of directional dimension in space. As illustration, any intersection of time and space would establish the relative scales of length of each for that dynamic locality. In an intersection of a shorter dimension of time with a longer dimension of space, time would be induced to extend producing a corresponding expansion of space in leap-frog fashion until the extensional covariance produces a self-replicating proportion, such as the Golden Mean. If time and space were invariant in scale time would not need extend at all but exist as a static appearance of space. An intersection of a longer span of time with a shorter one of space would induce time to contract with a corresponding dynamic wherein that locality would diminish out of existence. Thus the 'arrow' of time is one of only extension as a physical property.

This is conjecture, of course, as it is difficult to imagine any experimental protocol to support it as hypothesis. Conjecture is therefore a dangerous thing if it satisfies, but not outside the legitimate realm of philosophy which is the discipline of Prof. Callender.