**The Trouble With Physics**

## On the Nature of (ephemeris) Time

The FQXI contest is over. The big winner is Julian Barbour, but there are many other winners of lesser prizes. Unfortunately, my essay, “A Mystic Dream of Four,” is not among them. Too bad. I would have liked to have seen some sort of visible impact on the traditional thinking of the judges, given the unprecedented invitation to try to do so.

I’m sure Larson would have been able to pull it off. It’s an interesting thought to contemplate, but, still, a useless one too, since us lesser lights are left to carry on as best we can without him. It is interesting to note, however, how happy the judges were with Barbour’s “crystal clear and engaging” essay that argued for something called “ephemeris time.” This is the time that transforms Newton’s notion of absolute time into a set of vector motions described by energy conservation laws.

In his excellent treatment, Barbour was able to delight the judges by once again glorifying the venerated action principle, making it crystal clear that they still prefer that sort of thing over the type of innovative thinking that Larson was so good at. So, in the final analysis, maybe he wouldn’t have had any better luck than I had, in spite of his genius.

I guess it’s just too hard not to imagine that the change we call time is inextricably connected with the changing locations of heavenly bodies, even after all these centuries of mankind’s astonishing progress in understanding the structure of the physical world. You would think that the knowledge that we now have of the inherent oscillations of radiation and its constant speed of propagation, relative to all matter, would lead us to conclude that the space/time equations associated with it might be trying to tell us something about the nature of space and time in general that has nothing to do with the changing locations of heavenly bodies, but then that’s just me.

I expected Carlo Rovelli would win a juried prize, with his “Forget Time” essay, but he lost out to Barbour, Kiefer and Carroll, all of whom sought to find a way to transform time in their essays rather than to forget it. The remainder of the winners, were also, as expected, either professors, post docs, or grad students working on their PhDs under the tutelage of PhDs. As far as I can tell, not one prize was awarded to an “independent researcher.”

While this is understandable, given the community running the program, and the fact that so much noise accompanies the thinking of independent researchers, it nevertheless leaves us to ponder once again the wonder of mankind’s experience: The pace of our enlightenment seems to be governed by the birthing of gifted children more than the schooling of learned scholars.

Nevertheless, I’m grateful to FQXI for inviting the commoners to the festival.

## The FQXI Contest Update

Currently, my RST-based essay is ranked number 2 out of more than 70 essays submitted in the FQXI essay contest on the nature of time. This ranking is somewhat flattering, but also misleading in a way, because of the dynamics created by the contest rules.

Nevertheless, it’s been a worthwhile effort for many reasons, regardless of the contest’s outcome, even though, in the process of reading the essays and engaging in the discussions, I’m reminded of Henry David Thoreau’s acerbic, yet penetrating, social comment:

There are a thousand hacking at the branches of evil to one who is striking at the root, and it may be that he who bestows the largest amount of time and money on the needy is doing the most by his mode of life to produce that misery which he strives in vain to relieve.

While I wouldn’t go so far as to say that this sentiment applies perfectly to the troubled physics community, it clearly holds in some limit. Yet, paradoxically, I really feel that FQXI’s substantial contribution, marshalling the resources of the community willing to address fundamental issues, is striking a blow at the roots of the “evil” of theoretical physics, by leveling the playing field somewhat.

It is said that modern man does not face any philosophical challenge not already thoroughly explored by the ancient Greeks, and though many like to divorce physics from philosophy, in the end it cannot be done.

A case in point is clearly seen in the essay contest. The number 1 ranked essay by far is Carlo Rovelli’s essay, “Forget time.” However, the rationale for his injunction is motivated by the pursuit of a quantum gravity theory, which ultimately clashes with the essay by Peter Lynds, “Time for a Change - The Instantaneous, Present and the Existence of Time,” invoking the philosophical arguments of the ancient Greeks, concerning the paradox of the discrete and continuous notion of change. The point is, these two essays would never have been placed viz-a-viz, if it weren’t for the efforts of the Foundational Questions Institute, so maybe this is an exception to Thoreau’s conclusion.

In any case, Rovelli’s argument seems fundamental enough: General relativity shows that time is not absolute in the sense that it shows that the time of one system is a function of another’s time, or vice-versa. It doesn’t seem to matter, and, given this fact, it can be argued that a mechanical system, even a quantum mechanical one, based on a variational principle of action, can be formulated without a “special ‘time’ variable.”

This leads Rovelli to posit that time is not a preferred physical variable of nature at all, and that there are no preferred thermodynamic equilibrium states a priori, but all variables of a physical system are equivalent. In contrast, Smolin argues, in a non-contest essay, that the unit space/time progression trips up this argument, from a practical standpoint (although not in those terms of course): His argument is simply that the universe is just too big to work in terms of Rovelli’s abstractions. The limits of communication due to the speed of light in 4D spacetime, and the limits of precision in measurements, ultimately defeat Rovelli’s mathematical model, according to Smolin.

In my case, the RST posits that all observables stem from the space/time progression, which implies that the ultimate equilibrium is the equilibrium between the increase of space and the increase of its reciprocal, time, as two different aspects of the same thing, a universal change. Since this approach preempts the notion of thermodynamic equilibrium, it refers the argument over the nature of time to an even more fundamental principle of cosmology.

For the ancients, this cosmological principle was based on a revelation directly from God:

And the Lord said unto me: Now, Abraham, these two facts exist, behold thine eyes see it; it is given unto thee to know the times of reckoning, and the set time, yea, the set time of the earth upon which thou standest, and the set time of the greater light which is set to rule the day, and the set time of the lesser light which is set to rule the night. Now the set time of the lesser light is a longer time as to its reckoning than the reckoning of the time of the earth upon which thou standest. And where these two facts exist, there shall be another fact above them, that is, there shall be another planet whose reckoning of time shall be longer still; And thus there shall be the reckoning of the time of one planet above another, until thou come nigh unto Kolob, which Kolob is after the reckoning of the Lord’s time; which Kolob is set nigh unto the throne of God, to govern all those planets which belong to the same order as that upon which thou standest. And it is given unto thee to know the set time of all the stars that are set to give light, until thou come near unto the throne of God.

Here we see that the ancient idea of order is expressed in terms of different units of time; that is, the “times of reckoning,” or the times of measurement, differ one from another in an ascending order. According to this really ancient view, established way before the ancient Greeks came on the intellectual scene, there is no absolute time of reckoning, but only a relative order of such times, which accords with the findings of general relativity.

How then can this idea be reconciled with the RST? This new system of theory posits absolute magnitudes of discrete units of space and time, and thus it not only seems to be in the same predicament viz-a-viz Peter Lynds’ essay, as is the timeless quantum gravity theory of Carlo Rovelli, but it also faces the challenge of general relativity and ancient revelation, wherein both assert that time magnitudes are not absolute, but relative.

I guess it brings us to that Clintonian moment when we must insist that the answer depends on what the word “absolute” means. I’ll try to address that in the New Physics blog soon. Happy Thanksgiving America!

## Columbus Day

The crisis in theoretical physics is only matched by the crisis on wall street. Funny thing is, many people are blaming physicists (especially string theory physicists) for both crises. However, in a paper just now submitted to the Foundational Questions Institute (FQXI.org), as submission to their essay contest on the nature of time, I make the point that string theory attempts to explain the forces of nature, as a property of motion, and its success in this regard cannot be easily dismissed.

The trouble is, string theory is not based on a symmetry group. Of course, the LRC’s development of an RST theory also views force as a property of motion, following Larson, but the good news is that it appears to fit into a mathematical group, even a mathematical field. In the essay, I tried to make this the central point, since it is symmetry, and its mathematical properties, that has come to play such a central role in theoretical physics.

It, turns out, however, that talking about mathematical groups makes people’s eyes droop with weariness. So, I had to use lots of graphics as an antidote of sorts. Even so, four out of four scientists that I asked to review it declined, one saying that he didn’t have the time nor the inclination to learn about another “theory of everything.” Since I didn’t use that phrase (I hate it), it must have been his own choice of words, after reading from the paper.

I can understand why it’s so hard for practitioners of normal science to take new ideas seriously, or even to take a serious look at new views, especially those offered from “uncommitted investigators.” It’s hard work, and people are so spread out, with hardly enough time to work on what they want to work on, let alone dive into completely unfamiliar territory, that they are very reluctant to help out.

So, today, I attended a lecture given by one of the scientists that turned me down, and listened attentively, while he reviewed all the scientific reasons why one should accept the “standard model” of cosmology. Yet, as each slide was presented and explained, I thought how the same data fits the non-standard cosmology of the reciprocal system just as well in most cases, and how true it is that our own conclusions are easily confirmed when that’s what we want.

Yet, without question, nothing we know today requires us to believe that the observed cosmic expansion implies that there was a beginning to the expansion. Indeed, the fact that evidence now suggests that there will be no end to the cosmic expansion, implies that there also was no beginning to it. If we entertain this notion, which the reciprocal system clearly urges us to do, we see that none of the data that we have gathered to date is inconsistent with the concept.

However, to entertain the possibility that a new concept is as consistent with observations as what we already believe requires some work on the part of investigators to understand how the new concept explains the data. If we contend that a logical process that explains the origin of matter exists that doesn’t include the highly concentrated energy and density of a common event, the burden is on us to explain how, but it’s impossible to do that if those who are to be convinced are thinking in terms of the familiar concept, while they consider the claims of the new theory.

The mastery of the new concept must come first, so that’s why we begin at the begin, with a new definition of space and time, as the two, reciprocal, aspects of scalar motion. It cannot be denied that this implies that the nature of the observed progression of time is that it is just the inverse of the observed progression of space, and that might be startling, and therefore difficult to entertain, but once it’s understood that it goes on to reveal an entirely unknown sector of the universe, as a heretofore unknown player in the drama, which we see unfolding before our eyes, there is just no going back. It’s like the discovery of the new world beyond the sea. Once that happens, the race to explore and colonize the new territory is on.

But try to explain that to an Italian scholar in 1508, who never heard of Chris, and who is convinced that it’s not worth his time to read a sailor’s fanciful tales of a new world, full of gold and treasure, when he has lessons to prepare for students, letters to write to his colleagues, and funds to raise for his work.

## Is Our External Physical Reality a Mathematical Structure?

This question was addressed recently by Max Tegmark in an interview published in Discover Magazine. Peter Woit is not too happy with Tegmark’s thinking on it, but he’s fascinated with the question. The trouble is, Peter feels, Tegmark does not recognize that all mathematics is not equally important. In other words, it’s important to understand that there exists a fundamental mathematics that somehow relates to fundamental physics. Peter writes:

…the evidence is that the mathematical structure we inhabit is a very special one, sharing features of the very special structures that mathematicians have found to be at the core of modern mathematics. Why this is remains a great mystery, one well worth pursuing from both the mathematician’s and physicist’s points of view.

The truth seems clear to me that it is both a mathematical and physical fact. Indeed, one can begin with 0 directions in 0 dimensions, and work up to 8 directions in 3 dimensions, looking at the mathematical and physical relationships that come from that study and find a lifetime of work cut out for oneself.

It turns out that a good example is found in the Discover interview. In it, Tegmark regards abstract mathematical structures, such as the integers, as existing independently of time, statically, all at once, from the outside point of view, so-to-speak, but then they can also be regarded from an inside point of view, within time, he thinks, as when Einstein combines the three dimensions of space and one dimension of time. He explains:

The integers are not a mathematical structure that includes time, but Einstein’s beautiful theory of relativity certainly does have parts that correspond to time. Einstein’s theory has a four-dimensional mathematical structure called space-time, in which there are three dimensions of space and one dimension of time…the important thing to remember is that Einstein’s theory taken as a whole represents the bird’s perspective. In relativity all of time already exists. All events, including your entire life, already exist as the mathematical structure called space-time. In space-time, nothing happens or changes because it contains all time at once. From the frog’s perspective it appears that time is flowing, but that is just an illusion. The frog looks out and sees the moon in space, orbiting around Earth. But from the bird’s perspective, the moon’s orbit is a static spiral in space-time.

For Tegmark, the passing of time is just an illusion. He attributes the fact that the universe is not predictable not withstanding this, except on the basis of statistics, to quantum mechanics:

If the history of our universe were a movie, the mathematical structure would correspond not to a single frame but to the entire DVD. That explains how change can be an illusion…[However,] things are more complicated than just relativity. If Einstein’s theory described all of physics, then all events would be predetermined. But thanks to quantum mechanics, it’s more interesting.

But then the interviewer interjects the natural question arising from our experience with using mathematics to understand physics: “Why do some equations describe our universe so perfectly and others not so much?” To which Tegmark responds:

Stephen Hawking once asked it this way: “What is it that breathes fire into the equations and makes a universe for them to describe?” If I am right and the cosmos is just mathematics, then no fire-breathing is required. A mathematical structure doesn’t describe a universe, it is a universe. The existence of [my] level IV multiverse also answers another question that has bothered people for a long time. John Wheeler put it this way: Even if we found equations that describe our universe perfectly, then why these particular equations and not others? The answer is that the other equations govern other, parallel universes, and that our universe has these particular equations because they are just statistically likely, given the distribution of mathematical structures that can support observers like us.

Of course, this drives people like Woit up the wall, but he and Smolin are in the minority. Woit contends that the only reason Tegmark can get away with this nonsense is due to the fashionable status of speculative science today. Again, I’m on Woit’s side, but for a very specific reason that won’t be found on any of the blogs discussing mathematics and physics, fashionable or not.

Readers will have to read our New Physics and New Math blogs to get the details, but it has to do with a different understanding of numbers, dimensions, time and space. When Hamilton redefined number in his Algebra as the Science of Pure Time, and when Larson redefined space in *The Structure of the Physical Universe*, it opened the way to understand the four dimensions of space and time, not as one possibility in an endless array of static mathematical structures, but as an inevitable, dynamic, mathematical structure of evolving space|time. The new structure takes us back to the crossroads of math and science history, when the introduction of a symbol for the square root of two and the *ad hoc* invention of the imaginary number, propelled us into the modern age of perplexing physics and floundering mathematics.

It starts us down a new path, one in which the square root of 2, derived from a triangle of unit sides, does not lead us to the mysteries of infinity and real numbers, but the 1:1 ratio of the same triangle’s sides, derived from a progression of inverse integers, leads us to the enlightenment of integers in four dimensions. Indeed, it leads us to a whole new structure of mathematics and physics, one for which, as we saw in the previous post, Einstein pined. Here we find the fundamental relationship defining both mathematical and physical structure: Each dimension of our reality has two directions. From this fundamental symmetry, all the rest of mathematics and physics follows.

## Larsonian Physics and Einstein's Plague

A friend called me the other day and asked, “What is ‘Larsonian physics,’ as distinguished from ‘Newtonian physics?’” To compare the two systems (see here), it is helpful to understand Hestenes’ description of Newtonian physics. He writes: ^{1}

Newtonian mechanics is, therefore, more than a particular scientific theory; it is a well defined program of research into the structure of the physical world…. [The foundation of the program to this day is that] a particle is understood to be an object with a definite orbit in space and time. The orbit is represented by a function x = x(t), which specifies the particle’s

positionx at each time t. To express the continuous existence of the particle in some interval of time, the function x(t) must be a continuous function of the variable t in that interval. When specified for all times in an interval, the function x(t) describes amotionof the particle.

This continuous function, representing the motion of an object from one location to another over time, which “expresses the continuous existence of a particle” and forms the foundation of Newtonian physics, is replaced in Larsonian physics, as developed here at the LRC, by a progression of space and time, independent of any object. When either the space or time aspect of the space|time progression oscillates, at a given point in the progression, a point in space (or time) is established, the position x of which is represented by the continuous function x = x(t) = 0 (or x = x(s) = 0); that is, the point’s spatial (or temporal) position, in the progression, no longer changes with the progression, due to the oscillation. In other words, it becomes stationary (non-progressing) in space (or time); Its fixed position, relative to the progression, is actually generated and maintained dynamically by its oscillation (as a 1D analogy, we can think of a stationary fish swimming against the current of a flowing stream.)

Thus, in the LRC’s Larsonian physics, the continuous function expresses a spatial or temporal location that had no prior existence, while in Newtonian physics, the continuous function expresses a change between pre-existing locations. Subsequently, the change that Einstein introduced into the Newtonian program replaced Newton’s ideas of absolute time and absolute space, so that spatio-temporal locations are no longer pre-existent in the Newtonian system, but are dynamically generated from a gravitational field in general relativity.

Of course, the fixed background of locations in Newton’s concept is still necessary to define motion in the quantum field theory of particle physics, where only Einstein’s special relativity is employed and his general relativity is ignored, causing the immense trouble with the attempts to unify modern physics, which is the subject of this blog: The theory of gravity generates the space and time continuum, while the theory of matter pre-supposes it, even though they are both field-theoretic constructs.

However, the important thing to understand about the LRC’s Larsonian physics is that the dynamic creation of points out of the space|time progression provides the basis for a physics of the discretium, without the need to resort to the continuous field concept, or, as Einstein would have expressed it, it provides a basis for an algebraic physics, as opposed to a physics of the continuum, or a geometric physics.

Though it’s not widely known, Einstein actually would have preferred a discretium based, or algebraic physics, but was unable to find a way to get to such a system. He was convinced, as today’s physicists are too, now, after pursuing unification as diligently as he did (even though he was mocked for doing so at the time) that the space continuum is “doomed,” as Witten puts it.^{2} In fact, according to Arkani-Hamed, “The idea that [the space continuum] might not be fundamental is pretty well accepted…”^{3}^{ }in the legacy physics community.

But, in his day, Einstein suffered alone, “plagued” with his thoughts that the assumption of a space and time continuum was probably the wrong approach, given that physical phenomena are quantized. Nevertheless, all the while, he is celebrated as the champion who revolutionized continuum physics. John Stachel, of the University of Boston’s Center for Einstein Studies, who first discovered this other side of Einstein,” explains: ^{4}

If one looks at Einstein’s work carefully, including his published writings, but particularly his correspondence and reminiscences of conversations with him, one finds strong evidence for the existence of

anotherEinstien, one who questioned the fundamental significance of the continuum. His skepticism seems to have deepened over the years, resulting late in his life in a profound pessimism about the field-theoretical program, even as he continued to pursue it.

What Einstein would have discovered, had he lived to study the algebraic physics that we are developing at the LRC, is that, while the continuum is something that can be conceived by the human mind, it isn’t necessary to conceive of it as an a priori construction needed to develop a discrete set of points, which was the great obstacle that baffled him. As Stachel points out, Einstein wrote to Walter Dallenbach, confirming that his former student had also correctly grasped the “drawback” of the continuum, which drawback is essentially that it seems that one needs to have a continuum in order to have a discontinuum:

The problem seems to me [to be] how one can formulate statements about a discontinuum without calling upon a continuum (space-time) as an aid; the latter should be banned from the theory as a supplementary construction, not justified by the essence of the problem, [a construction] which corresponds to nothing “real.” But we still lack the mathematical structure unfortunately. How much have I already plagued myself in this way.

Of course, the mathematics of the time were still going the opposite way. Mathematicians were happily following Dedekind and Cantor in constructing a continuum (infinite sets and smooth functions) from a discontinuum (discrete numbers). In fact, Stachel, speculates that Einstein’s doubts about the reality of the continuum stem, in part, from his reading of Dedekind, from whom he borrows his oft used phrase “free inventions of the human mind,” that did anything but endear him to Larson. Dedekind argues against the continuum by insisting that discontinuity in the concept of space does not affect Euclidean geometry in the least:

For a great part of the science of space, the continuity of its configuration is not even a necessary condition…If anyone should say that we cannot conceive of space as anything else than continuous, I should venture to doubt it and call attention to the fact that a far advanced, refined, scientific, training is demanded in order to perceive clearly the essence of continuity and to comprehend that besides rational quantitative relations also irrational, and besides algebraic, transcendental quantitative relations, are conceivable.

Of course, it was highly unlikely that Einstein was aware that Dedekind’s intellectual journey into irrational numbers and infinite sets began some fifty years previously with his exposure to Hamilton’s work, who had defined irrational numbers, but in the context of numbers derived, not from the abstract notion of a set, but from the intuition of the progression of time. And while Hamilton’s work on irrational numbers in his “Algebra of Pure Time,” is little regarded today, who could have known that it would have been eventually synthesized by Clifford with the Grassmann numbers as an “operationally interpreted” number, leading to Hestenes’ pioneering work in the recognition of geometric algebra as the unification of geometry and algebra through the geometric product.

While the bottom line can only be sketched at this point, all indications are that the mathematical structure, which Einstein pined for, that would enable him to be able to define a discontinuum, without the aid of a continuum, appears to be at hand. To be sure, he outlined major conceptual obstacles with both concepts in his letter to Dallenbach:

Yet, I see difficulties of principle here too. The electrons (as points) would be the ultimate entities in such a system (building blocks).

Are thereindeed such building blocks? Why are they all of equal magnitude? Is it satisfactory to say: God in his wisdom made them all equally big, each like every other because he wanted it that way? If it had pleased him, he could also have created them different. With the continuum viewpoint one is better off in this respect, because one doesn’t have to prescribe elementary building blocks from the beginnning. Further, the old question of the vacuum! But these considerations must pale beside the overwhelming fact: The continuum is more ample than the things to be descibed.

Thus, Einstein was left to plague himself with these thoughts, but now with a knowledge of Hamilton’s “algebraic numbers,” Larson’s “speed displacements,” and Clifford’s “operational interpretation” of numbers, and his multi-dimensional algebras, there is much more to work with than there was in Einstein’s day. Perhaps, it’s time to now stand with the legendary icon of physics and say:

I hope my friend would understand.[O]ne does not have the right today to maintain that the foundation [of physics] must consist of a field theory in the sense of Maxwell. The other possibility leads, in my opinion, to a renunciation of the space-time continuum and to a purely algebraic physics.

Logically, this is quite possible: The system is described by a number of integers; “Time” is only a possible viewpoint, from which the other “observables” can be considered - an observable logically coordinated to all the others. Such a theory doesn’t have to be based upon the probability concept…