GENIUS FORUMS

By no stretch of the imagination can I be regarded as a trained, professional mathematician. When my life was transfigured by some insight into the wisdom of Plato, Plotinus, Advaita Vedanta and other great sources of Deep Truth, I thought: I am no mathematician; but if I attempt to cultivate my perception of Intellectual Beauty and achieve some progress therein, it will serve as a test for the practical use of the cultivation of deep philosophy. I can not claim that my achievements have been earth-shaking, but I seem to have had some insights into the prime numbers which no one else has noticed. I hesitate to publish my findings since I can not be sure that they have no relevance to cryptography and code-breaking. I feel that modern intellectuals are far too irresponsible about the effect of their discoveries on wider society. I think it unlikely that Wisdom Societies really existed in human history, but I find the idea attractive. Some knowledge should be withheld from the general public if society has not yet developed the institutions which will make that knowledge safe. But who are to be the judges in such matters? This question is, at least in part, behind my primitively formulated idea of a Supreme Court of Science as an institution responsible for the long-range development of human society.

I have had a profound respect for Albert Einstein all my life, but I regard him as essentially a tragic figure. That such a noble example of the best in human nature should have had a connection with the development of the atomic bomb! I was a child when Einstein was still alive in the early fifties. I remember a news report at the time in which Einstein had expressed the wish that he had become a plumber rather than a professional scholar. [the typical American reaction: television interviews with plumbers to get their opinion of Einstein's statement! "Well, the world needs plumbers, too...." As a friend of mine said: Americans trivialize the whole question of superficiality!] In the Germany of Einstein's younger years, the plumber was the paradigm of a blue-collar worker. As a child, I felt surprised and puzzled by his remark. Afterwards, I gradually came to understand it. In his later years, Einstein's personal and intellectual life had been marred by his becoming a focus of mindless adulation. For someone who is to make a significant advance in the life of the mind, the great essential is access to long periods of uninterrupted time which allows one to sink deeply into the contemplation of the questions which concern one. The modern university system seems to be diabolically arranged so that a scholar shall never have untroubled stretches of free time in which to be a true thinker. I think Einstein yearned for his years as a patent inspector when no one knew who he was and when he could do and think as he pleased. Warned by Einstein's awful fate, I have tried to lead an inconspicuous life and have considered time to be a treasure beyond all others.

It is therefore ironic that time has been one of the chief foci of my intellectual life. The common idea that time is like a flowing stream is clearly wrong. The special theory of relativity demonstrates that there is no objective "now" for all observers. This consideration led Einstein to the notion of a "block universe", an idea in which he apparently believed to the very end of his life. But quantum mechanics makes the block universe idea unviable. The irreducible non-locality of information in Einstein-Podolsky-Rosen experiments causes the block universe to be riddled with mutability as quantum wave functions collapse. John Wheeler came up with a striking example: Imagine a distant galaxy acting as a gravitational lens with reference to a yet more distant galaxy directly behind it in the line-of-sight from earth. Imagine that there is a fifty percent probability that a photon from the more distant galaxy will pass on the left side of the lensing galaxy and a fifty percent probability that it will pass on the right side, and be so registered on a photographic plate billions of years later on earth. This enormous indeterminacy in the path of the photon will remain unresolved for billions of years until the collapse of its wave function on earth! The block universe fails to have a deterministic structure.
Another strand in my thought derives from the notion of "advanced waves" in electromagnetic theory. This notion was first developed by Richard Feynman and John Wheeler and later taken up by a number of other people.

These and other considerations have led me to the metaphor of the "jello block universe", a block universe in which information, like vibrations, passes back and forth, up and down through the dimension which we call "time", causing the condensation and collapse of quantum wave functions into definite events. In this view, the ultimate history of the universe is as yet only partially determinate and will reach its final state only when the jello has finished vibrating.
Another metaphor is to imagine the True Universe as a brilliantly illuminated structure surrounded by a penumbra of increasingly dim and fuzzy universes; the dimmest and fuzziest would be vast in number and would represent all the possibilities for the history of the universe when the universe was born. As the shadow universes became brighter and more substantial they would resemble more and more closely the Final State of the universe, the One True Universe at the center of all these shadow universes. Our universe, the one which is the subject of our experience, is one of the intermediate universes, having a position between the dim, indistinct, unsubstantial universes which constitute the universe at the Origin of Time, and the unique Final State which is the expression of the End of Time. True Time in this metaphor is the progression from shadowy multitudes of universes to a single clear and distinct Final State, in which I am pleased to imagine that "even the grass is enlightened," as the Buddhists expressed it. But that thought is too close to religious wish-fulfillment, so I try to keep it at arms-length.
The similarity between the dream-like shadow universes and the maya of Śankara is obvious.
Surprisingly, there is a remarkably good literary rendering of these odd ideas. When I say "good" I am referring to the rendering of the ideas; the literary style of the novel is horrible; it always makes me cringe when I read it; but if you can endure that, it is worth reading. The novel is The End of Eternity by Isaac Asimov. It is about as good a rendering of quantum phenomena as you can expect in a literary medium, and in many ways it approaches my conception of the nature of time. I read it as a teenager long before I started to evolve these notions. I have seen no evidence that anyone else has ever looked at the novel in the way that I look at it ---even the author, Asimov. This seems to be a common phenomenon: the universe produces a message whose meaning is unperceived by most people, usually even by the "author" of the message, and reveals itself to just those people for whom it was "intended." In my view, "information" [or should I say "data"?---I think we need a new term here, for what is passing up and down through time does not reach the thresh-hold of constituting a "message"] is constantly passing up and down through ordinary Minkowski space-time, "causing" ordinary emission and absorption events to condense in tandem out of the apparent indeterminacy of the quantum vacuum. I will drag in one last metaphor here: I think Einstein's "spooky action at a distance", and quantum correlations in general, are similar to what happens in a rug or membrane which is warped. There is a bulge in the rug; you press it down with your foot and "it" pops up again in another part of the rug. The bulge has not travelled from point A to point B; rather, strains have passed through the entire fabric of the rug [which represents all of Minkowski space-time in this metaphor] which create a new bulge which preserves certain features of the original bulge [in the case of an electron which "travels" from A to B, those features are spin, mass, and charge].

You may ask: does Plotinus have any concrete results that support these rather fanciful notions? Over the years, my ideas have themselves condensed out of a misty fabric of many confused speculations, cloudy intimations, and half-sensed correlations. One thing has been my guide out of the Minotaur's labyrinth of doubt and speculation: the golden string of intellectual beauty, which I have been laboriously winding up into a ball for many years. Always I have striven to keep the far-flung fabric of my personal Net of Indra in balance, sought to keep all of the jewels polished and bright, each reflecting every other jewel in the net. Another goal has been important to me: accuracy. I felt that I could not afford to be satisfied with approximations. All my figures are accurate to within the measured uncertainty of the physical constants; this usually means an accuracy out to six or seven decimal places. Some of my figures are more precise than the presently measured experimental values. They constitute a test of my ideas. In particular, I have a rather precise value for the gravitational constant, G. Also, many years ago I came up with a value for the temperature of the Microwave Background Radiation to a degree of precision greater than that measured at the time. Since then, the COBE satellite has confirmed my value. I have a number of physical values which await confirmation or denial; I even have a derivation for the fine-structure constant, which in my view is a logarithm related to the amount of information in a volume. Twenty or so years ago I got a value for the information content of the universe out to the event horizon: 10¹²¹ [actually My figure is more precise than this]. About six or five years ago Seth Lloyd had an article in Nature Magazine in which he derived the same figure as the maximum computational capacity of the universe, if we consider the universe to be analogous to a computer. Some of his arguments were similar to those which I had come up with.

This communication is becoming too long, but I will mention one idea which I have been pursuing: the minimum quantum of energy. I find it astonishing that everyone understands that the Planck energy is the maximum energy which can be involved in a single quantum event, but no one gives a thought to the minimum amount of energy which may be involved in a single interaction. Yet such a minimum quantum of energy is obvious if one thinks for a moment. It is Planck's constant divided by the age of the universe. There could be no smaller well-defined energy. Interestingly, if one divides the mass of the observable universe by this energy minimum one gets the 10¹²¹ units of information mentioned above. The ratio of the Planck energy to the energy minimum is the square root of that figure. Also, each quantum of the energy minimum has an uncertainty of temporal location equal to the age of the universe. This means that the sum total of all 10¹²¹ units is enough uncertainty to affect the entire mass of the universe all the way back to the Big Bang! My calculations are that it is precisely enough uncertainly. I regard the entire history of the universe to be a superposition of these 10¹²¹ quanta and that they account for enough uncertainly to affect the history of every single particle in the universe!

Well, that is probably enough eerie, dream-like irreality for now. If there is any truth to it, one wonders how such an insight might have affected the history of extra-terrestrial civilizations. Their approach to life and action in the universe might be very different indeed from what we are familiar with here on earth.
I still have some important outstanding questions. Einstein thought, as do I, that quantum mechanics is an incomplete theory. He was determined that his block universe be determined! He and I would probably be in agreement that Leibnitz's Principle of Sufficient Reason is always true. It seems to be valid for every process in the universe, with the glaring exception of the standard formulation of quantum mechanics. I think the great limitation of standard quantum theory exists in the structure of the Schrödinger equation and in all other formulations equivalent to the Schrödinger equation. In this basic equation of quantum mechanics, time is an independent variable, and the equation develops deterministically through time. I feel that this is inconsistent with the spirit of quantum mechanics. I seek a formulation in which time loses its privileged status and becomes just another dependent variable. I have not yet achieved this formulation.

塞 翁 失 馬

Julian Barbour's The End of Time (1999) is an attempt to formulate physics without time as a variable. He tries to disabuse the reader of traditional notions of time and presents a case that time itself is nonexistent.

plotinus wrote:But quantum mechanics makes the block universe idea unviable. The irreducible non-locality of information in Einstein-Podolsky-Rosen experiments causes the block universe to be riddled with mutability as quantum wave functions collapse.

That mutability does not invalidate the block universe idea. "Collapse of wave functions" does not need to be considered in the transactional model, at least not in the usual sense. (The collapse happens along the entire transaction; it is a wave interference effect.)

John Wheeler came up with a striking example:
Imagine a distant galaxy acting as a gravitational lens with reference to a yet more distant galaxy directly behind it in the line-of-sight from earth. Imagine that there is a fifty percent probability that a photon from the more distant galaxy will pass on the left side of the lensing galaxy and a fifty percent probability that it will pass on the right side, and be so registered on a photographic plate billions of years later on earth. This enormous indeterminacy in the path of the photon will remain unresolved for billions of years until the collapse of its wave function on earth! The block universe fails to have a deterministic structure.

I don't see that as a problem. It's consistent with Feynmann's "sum of all pathways" approach. The "photon" goes on both sides of the galaxy; what of it?

It seems like billions of years in our frame of reference. But can we talk about the photon's frame of reference...?

Another strand in my thought derives from the notion of "advanced waves" in electromagnetic theory. This notion was first developed by Richard Feynman and John Wheeler and later taken up by a number of other people.

Consider two particles exchanging a photon (in the transactional model). One is at position one (x1, y1, z1, t1) and the other is at position two (x2, y2, z2, t2).

A photon travelling from position one to position two is exactly the same as an anti-photon travelling from position two to position one, but going backward in time. But an anti-photon is just a photon. In the photon's frame of reference - travelling at the speed of light - no time passes. The travel from position one to two, or from two to one, is instantaneous; so there can be an "advanced wave" and a "retarded wave" that are really simultaneous. A photon is exchanged because there is some sort of resonance between the two points; resonances arise whenever you have waves.

Waves are fundamental to the nature of the universe; therefore, resonance is also a fundamental concept. (When something stops being a wave, and is instead considered a particle, is a matter of perspective and frame of reference.)

At Planck-length scales, the universe is time-symmetric. The asymetry we see in time at macroscopic scales is due to entropy.


This is all highly speculative, of course...

In my view, there is no contradiction between the "transactional interpretation" of quantum mechanics and the "jello block universe" model. However, the mathematical apparatus which I have been blessed to perceive arose out of questions concerning the universe as a whole, rather than individual quantum interactions.

The paradox of Schrödinger's Cat may be sharpened by considering the problem of "Wigner's friend":

http://en.wikipedia.org/wiki/Wigner%27s_friend

The mixed state of the wave function of the cat in the box can only be collapsed by an interaction with the outside world. This interaction is often, though not necessarily, represented by the observation of a person, conveniently called "Wigner's friend." A paradox arises because a strict interpretation of quantum mechanics requires that the collapse of the wave function of the cat create a new mixed state consisting of the cat and the observer! The new state can only be collapsed by an interaction from outside, and so on.... Ultimately, this mess can only be resolved by the collapse of the wave function of the entire universe! The problem is that an external source to initiate this collapse is impossible, since, by definition, there is nothing external to the universe!

This problem has had an influence on the development of my ideas. In fact, I have a mathematician friend who was a friend and colleague of Eugene Wigner, so, in a sense, I am a friend of Wigner's friend.

I am in agreement with Julian Barbour that time, as we normally perceive it, is an illusion. However, there are strong reasons to regard change and dynamism as very real. Unfortunately, the most rigorous exposition of this view is contained in the unpublished papers of an associate, and therefore I am not at liberty to discuss them.

For anyone who is interested in these questions from a philosophical point of view, it is of value to read the writings of Plotinus, the foremost philosopher of the Neo-Platonic school of thought. A modern person may have difficulty in mastering the technical vocabulary of Plato and Plotinus. It is also not easy to feel at ease with their way of thinking. As someone said, "the past is a foreign country; they do things differently there." However, what they say is not nonsense. as many think who read them without care.

塞 翁 失 馬

Plotinus,

I was going to skip your initial post because it was long and looked crazy at first glance, but saw some things that caught my eye and ended up reading it all. I was pleasantly surprised to find that you seem to be doing interesting work. With amateur cosmology, there's a fine line between interesting and kooky, with most of it falling on the former side.

I think we need more original thinking in astrophysics. Stuff that is well outside the mainstream, but hopefully without falling into Time Cube territory.

This guy made a mark a few years ago by getting published in a major journal with no academic qualifications. He has some interesting ideas about time, which you might be interested in.