A Mystic Dream of Four by Douglas Bundy

Doug,

I don't see myself as cynical. Knowledge, just like everything else, is evolutionarily bottom up. Occasionally it plateau's, either because it doesn't have the wherewithal to continue and needs to marshall the facts to do so, or because the facts have abandoned it and it hasn't the initiative to reset, assuming the facts will eventually support it. There is no real way to know which the case is, until history has fully judged the situation. This can take a long time sometimes. Ptolomy's epicycles wouldn't have lasted for 1500 years if western civilization hadn't gone into hibernation between the fall of Rome and the end of the Dark Ages. Currently we have a large and well funded academic establishment which views the foundation on which it rests as solid, since it has produced many stunning technological advances, so that the supporting society isn't going to question its current state too closely, but sometimes strengths obscure weaknesses. I may sound frustrated in the last post, but I'd be perfectly happy to find where and which points I'm making are wrong. It's not like events go from being in the future to being in the past falls in the category of 'not even wrong." Tomorrow becomes yesterday is a fact, not a theory. "Not even wrong" just means not coherent enough to make a clear statement, whether right, or wrong. I think a large part of the problem is the academic necessity of publishing, or perishing, so those who find themselves in the business have to say something, even if they are winging it.

As for the point you are making, it seems to be of the issue whether reality is fundamentally dynamic, or fundamentally static. Are what we consider 'nouns' just transient nodes in the network of activity and there are simply opposing energies, or is activity simply the consequence of some underlaying essence. Physics is determined to find this essence, be it a TOE, god particle or whatever. My argument is this either/or question is moot. It is essentially a dichotomy, like my point about energy and information. You can't have one without the other, as information defines the energy which manifests this information. So when you pursue one or the other, it just gets tangled up. If you view it from the perspective of the dynamic, as QM mostly does, the information breaks down and blurs into fuzziness. While if you view it from the static geometry of Relativity, the dynamic is lost and you end up with things like 'block time.'

Regards, John

Dear Doug and John,the comment poster,

May i introduce some lightness in your intimate , intensive discussions through the following points:-

1. The Universe was created or it has always existed! if Bigbang is right it has been created. If so, what existed before. If it is perfect vacuum or the non-physical 'consciousness', then how it gave rise to the Universe that we apparently observe now?

2. Let us always remember that we humans are a negligible part of this entire Universe, full of its mysteries. Cosmology and Astrophysics have only provided limited measurements and that too with more limited accuracy.

3. Our mind is the only source that may provide access to the non-physical entity called 'consciousness'. Have we done something to train and control our mind! Normal life that we live, indicates that it usually runs wildly. In my own essay, i have hinted at the techniques of meditation and Yoga, through my personal experience, to be relevant in such a matter.

4. Nothingness, thoughtlessneses and silence appear to contain all the chaos, randomness and various dualities that we note in the Universe and not the other way around!

5. Besides the western philosophers, there exist a number of eastern philosophers both in ancient and modern times, who have gone into the 'inner depths' and have provided some postulates that may be worth the consideration in order to understand " The nature of Time " and how to about seeking reality. I have quoted two verses from Patanjali, the founder of Yoga techniques some 4000 yrs. back. These are profound as the first quote goes well beyond what Quantum Mechanics gave us now in the form of the observer/observed relationship!

Let us all have fun with seriousness that the topic deserves, as i myself am enjoying the essays contributed and am posting my comments on many of them, no offance or criticism implied. Love is truly our unifying nature as humans and we shall win if we constantly remember it in practice.

I read your 'Mystic Number Four' theory with interest.

I do agree with you that the Superstring Model is a wrong mixture of dependent measurements taken as they were independent (through the dispersing prism of motion); and the result is to dig a ditch between theory and concretion*.

That's why I follow you when you try to put order (with geometry), when you are isolating the mistake as a virus in a body; and why not ask Euclide or Pythagore to help you for that? Is C. Rovelli's trial so different? I am not sure that he does not pull the 'subtle' Time and the cognition parameters over because of the disorder Time is introducing in the 'Quanta Theory'. But Temperature is as biological or chemical as Time is.

But in my opinion your method is spoiled as string theory ideograms on this point: your eight squares and symetry drives you to deduce the facts from the theory as SM theoricians do. For instance: where is the point in the middle of your two dimensional cross coming from? Space or Time? Yourself? It is not clear.

(*Einstein's intuition was that the Universe was not an expanding Universe.)

Doug,

I have another question or two. In figure 1, you show deuterium composed of a proton plus a neutron but the proton in the graphic must be protium (hydrogen atom with one proton and one electron). Is the upside down triangle with the reddish border and -3 in the center of the proton supposed to be the electron?

The second question has to do with your new definition of motion. On page 4 you write:

"What this means, in the final analysis, is that we are able to define a multi-dimensional type of motion, differing from, but not replacing, the familiar definition of 1-dimensional motion. The familiar vector motion requires the change in an object's actual, or probable, location, for the purpose of defining a change in space over time, but under the new definition, a moving object is not required to define this change. We call this newcomer to the theoretical scene, scalar motion, a 3D, massless, motion, taking its place, by virtue of the definition of motion, along side the familiar definition of 1D vector motion, the motion of mass in one direction at a time."

Since physics is all about potential and kinetic energy doesn't this mean that you must redefine those two things as well? How can you do so without mass?

Thanks to commentors Narendra Nath and F. Le Rouge. Your comments are appreciated.

F. Le Rouge says: "I read your 'Mystic Number Four' theory with interest...but in my opinion your method is spoiled as string theory ideograms on this point: your eight squares and symetry drives you to deduce the facts from the theory as SM theoricians do. For instance: where is the point in the middle of your two dimensional cross coming from? Space or Time? Yourself? It is not clear."

Interesting question. The two-dimensional cross is the cross section of the eightfold cube, and the point is where the corners of the eight cubes in the 2x2x2 stack of one-unit cubes meet.

In order to observe a given, ongoing, unit, space/time progression, P, where space is 3D and time is 0D, a 3 1 dimensional reference location, x, y, z, t, must be selected in P. This location is necessarily zero, with respect to time, or t0, since all locations that are in the order before it is selected are at t0 - tn, and all locations after it is selected in the order will be at t0 tn, in the infinite order of P.

This is not a fact; it is only a logical and mathematical consequence stemming from the assumption of an infinite, discrete, space/time progression in four dimensions. The fact is, however, that given the assumption of the progression, the mathematical consequences reproduce the tetraktys, and the four spaces of the associated Clifford algebra, at tn - t0, when n = 1.

It is immaterial "when," or "where," the reference location is selected, the eightfold cube, the 3D pseudoscalar, will always be the result. This means that "when" and "where" really have no meaning until the reference location in P is selected.

What we can deduce from this, as far as constructing a physical theory, can only be verified to some degree of certainty that will always be less than 100%, by comparing the results with observation. Since it is possible to deduce consequences that have not yet been observed, the system possesses the power of prediction, making it falsifiable, unlike string theory, which appears to lack this property.

Hi Larry,

The answer to your first question is yes. Unfortunately, the error in this graphic is misleading. The word "proton" should be "protium" instead. The electron, composed of three "negative" preons (three "red" S|T units), neutralizes the three net "positive" charges of the proton, composed of one down quark, with one net "negative" charge, and two up quarks, with four net "positive" charges, which balances the protium atom, with four "negative" and four "positive" charges, as shown

Your second question is more difficult to answer. It has to do with the fundamental duality of the two systems. In the system of vectorial motions, the fundamental duality is that of potential and kinetic energy, where the total energy of the system is conserved. This is best illustrated in the swinging mass of a pendulum. At the top of the swing on either side, there is a point where the mass is stationary, so the kinetic energy must be zero at those two points, but at the bottom of the swing, halfway between these two points, the kinetic energy is at its maximum, and the gravitational potential energy is zero.

Now, what I will have to say about this below is based on Peter Rowlands analysis of the factor of 2 in fundamental physics

(see: http://arxiv.org/PS_cache/physics/pdf/0110/0110069v1.pdf).

We can compare this relationship between the potential and kinetic energy of the system, the symmetry of which incorporates the law of conservation of total energy, to geometry, because the area of a given right triangle is one-half the area of a corresponding rectangle:

A = (base x height)/2,

where two, dual, triangles are formed by bisecting a rectangle along a diagonal, each with area = A. The correspondence to kinetic energy is made by noticing that the diagonal, bisecting the rectangle, taken as the straight-line graph of velocity, v, multiplied by time, t, defining a uniform acceleration, determines the distance traveled, d, as the area underneath the line, or d = vt/2. When this accelerated motion is the acceleration of mass, the corresponding energy equation that applies has the dimensions of energy derived from the kinetic energy equation, E = ½ (mv)v, or momentum (mass time velocity) times velocity, or mass times velocity squared, divided by two (corresponding to ½ of the area of the rectangle, the area of the triangle.)

On the other hand, if the motion were unaccelerated, the area underneath the horizontal line of the rectangle (the top line of the rectangle), represents the distance traveled, or d = vt. When this unaccelerated motion is the velocity of mass, the corresponding energy equation that applies has the dimensions of energy derived from the potential energy equation, E = mv^2, or mass times velocity squared, not divided by two (corresponding to the total area of the rectangle, the area of both triangles combined.)

In general terms, then, there is a fundamental distinction being made here between continuous conditions (constant motion) and continuously changing conditions (accelerating motion,) and the distinction is made by a factor of two, because the continuously changing conditions invoke the Merton mean speed theorem, where the total distance traveled under uniform acceleration must equal the product of the mean speed and the time.

This reflects a very ancient foundational principle that incorporates what has been called the mediato/duplatio, or halving/doubling, basis for counting systems such, as the Mayan long count and other ancient counting systems, and there is much more to say about it than I can say here.

But briefly, recall that the fundamental duality in the new system, the scalar motion system, is the duality of spatial and temporal pseudoscalars, which also comes from a factor of 2, but the factor of 2 here is not related to the simple 1D geometric principle of the diagonal of the rectangle, which applies to the straight-line function of vt, or the space of 1D vector distance, but rather it is related to a much more complex 3D geometric principle of the diameter of the sphere, which applies to the function of v^3t, or the space of 3D pseudoscalar volume.

As Peter Rowlands shows in his paper, "...the factor 2 makes its appearance in molecular thermodynamics, quantum theory and relativity. It is, in a sense, the factor which relates the continuous aspect of physics to the discrete, and, as both these aspects are required in the description of any physical system, the factor acquires a universal relevance."

Hence, the relevance this factor has in the new system is the focus of our program of research. On this basis, we have been able to construct the toy model of the standard model illustrated in figure 1 of my essay, as well as the periodic table of elements, as shown here: http://www.lrcphysics.com/wheel

Our current goal, however, is the calculation of the atomic spectra. In this connection, it should be noted that the difference between the factor of 2 periods of the QM-based periodic table, and the factor of 2 periods of the RST-based periodic table, is a factor of 2! That is to say, in the QM-based theory, the periods are a 2n^2 cycle, while in the RST-based theory, the periods are a 4n^2 cycle.

The trouble is, in the QM-based theory, though the 1D motion concepts (electronic orbitals, angular momentum, electron spin, etc.), were conceived based on the experimental observations of energy transitions in spectroscopy, there are so many possible transitions, and the calculations get so complicated, that, to this day, the solutions of the wave equation can only be found "in principle," for most of the elements (see Tomonaga's "The Story of Spin").

We have similar problems in the new system, but the main difference between the two systems is in the treatment of mass. In the QM-based system, mass is a given, just like space and time, so the mystery remains, what is its origin? On the other hand, in the RST-based system, we know that the origin of mass has to be scalar motion, but how does this come about? Starting with space and time only, how does mass, energy and radiation emerge?

Well the factor of two introduced by the kinetic energy equation, where the potential energy term is twice the kinetic energy term, is found schematically in the toy model. The red circle of an S|T unit in the model represents the vibrating spatial pseudoscalar, while the blue circle at the opposite end of the black line that joins them, represents the vibrating temporal pseudoscalar, and since these two are inverses of one another, while the one expands, the other must contract, and vice-versa.

It is this inverse relationship, the redistribution of scalar motion, that is a striking analog of the redistribution of kinetic energy in an f = ma system, but since no mass is involved, only changing space and time, something else has to bind the two pseudoscalars together. It turns out that it is possible to show that this bond is a result of the continuous "flow" of space and time, thus completing the analogy of the relationship of potential and kinetic energy in the viral theorem. The scalar progression, t^0, of the spatial pseudoscalar oscillation, and the scalar progression, s^0, of the temporal pseudoscalar oscillation make it possible for them to combine, and, if two instances of them do combine, there is no event to separate them ever after.

I hope this is helpful Larry.

Hi Narendra,

Thanks for your wise counsel. You wrote:

"1. The Universe was created or it has always existed! if Bigbang is right it has been created. If so, what existed before. If it is perfect vacuum or the non-physical 'consciousness', then how it gave rise to the Universe that we apparently observe now?"

Good question. We are all familiar with the usual answers, but I assume that you ask the question here in the context of my essay. In the universe of nothing but motion, the space/time expansion does not require an extrapolation back in time to a singularity. Since in the new system of theory, matter is not introduced into the space/time structure independently, but consists of combinations of discrete units of scalar motion, it becomes clear that an entirely new cosmology emerges from the theory, which only requires that we apply the consequences of the system to deduce the physical structure of the universe.

(see Larson's The Structure of the Physical Universe, Vol III, The Universe of Motion)

Certainly, however, this does not solve the problem of the big bang, but only transforms it from the unanswerable question of what existed prior to the beginning of the big bang, to the unanswerable question of what, or who, initiated, or instituted, the motion of the space/time expansion. Then, instead of having to swallow a theory of inflation, we have to swallow a theory of "direction" reversals in space or time, which locally quantizes the spacetime continuum. The question then becomes, "By what mechanism does the expansion oscillate at certain locations, but not others?" The only answer is that whatever can happen, will happen, at some point in time or space.

These answers are hardly more satisfactory than the explanations of the hot big bang theory, but Godel's incompleteness theorem gets us every time. In the end, we seem to have to just choose our poison, I suppose. It's now clear to many that science cannot come up with anything but an approximation of the truth. How close the approximation of one approach is than another is something that is relative to what aspect of the truth one is partial to. The ancients were very good at some things that are still complete mysteries to us, even though the feats of our science and technology go far beyond theirs, in other aspects.

Thanks again for your comments. I liked your essay, by the way.

Thanks for the response. it is nice to like something but it is far more welcome to have queries/comments. I shall welcome the same from you on my essay, as i am an experimental nuclear physicist and a novice in cosmology! We acn all get to the depth of an issue even in modern times 'full of knowledge cum informatiom', provided we develop the capacity of 100 % living in the present moment. Mind requires some training of being 'kept quiet' in some of the moments. There is the role of meditation cum Yoga. Self experience is a must for grasping a problem at hand. External factors/opinions need self assimilation, otherwise these are mere words of little consequence. The longer the comments are the less significant these tend to become.

In his FQXI essay, Phillip Gibbs describes a crucial difference between time and space, in spite of their unification by Minkowski, through the symmetry in the Lorentz transformation. He writes,

"Time can distinguish itself from space in this way because the spacetime metric has a Lorentz signature that assigns a different sign in the time dimension versus the three space directions. Thus in locally flat Minkowski spacetime distances are measured by the invariant quantity

ds^2 = dx^2 dy^2 dz^2 - c^2dt^2

Part of the mystery of time is to understand where this signature comes from. Why three plus signs for space and only one minus sign for time? Even with this separation of dimensions there should remain symmetry under time reversal t -> -t, but the arrow of time breaks this symmetry. What is the origin of this arrow? From what bow did it take flight?"

One of the founders of FQXI, Max Tegmark, talks about the same thing here:

http://www.youtube.com/watch?v=2pLCOizNSLI

He says that, if it weren't for the minus sign in the above equation, it can be proven mathematically that there would be no point in having a brain even, because we wouldn't be able to predict things in the way we do.

Yet, the equation has a minus sign only because of the mathematics of an expanding sphere. Why should it be so amazing that the radius from the center of a sphere, expanding at light speed, should be equal to a point on its surface, defined by its rectangular coordinates? Isn't it clear from this that BOTH space and time are expanding? There is only one minus sign for time because it is the zero-dimensional expansion, whereas space expands three-dimensionally.

The true symmetry Gibbs is unwilling to sacrifice is preserved in the independent reality of the union of space and time, just as Minkowski predicted it would be, but then, if this is true, why should we look for symmetry in something that has no independent reality, like time, or space, apart from motion? Neither can have any meaning without the other.

As Tegmark observes, this one-way nature of time is indisputable mathematically, so Rovelli urges us to "forget time" and Gibbs declares, "Temporal causality has to go," when all that is really necessary is to recognize that the symmetry of space/time is reflected in the binomial expansion of the tetraktys: Three dimensions are the inverse of zero dimensions and these four are joined together, reciprocally, just as surely as space and time are joined together, reciprocally, to the extent that neither has any meaning apart from this union.

Thus, both the symmetry of space/time and temporal causality can be reconciled through the four dimensions of the tetraktys. There is no need to give up either of them. The mystic dream of four becomes an independent reality, when the 3 of space and the 1 of time are recognized as the two, reciprocal, aspects of the same underlying reality, motion.

This is clear when space, or time, is quantized by unit vibration. Writing the equations for the cycles of the respective unit pseudoscalars, and their product, clearly shows this:

f = 1/t = 1/2, and fbar = s/1 = 2/1, so s/t = f * fbar = 1/2 * 2/1 = 2/2 = 1/1 = 1,

where the radius, r = ct, expands, then contracts, in 2 units of time. We can write it as eight units out and eight units back and get the same result:

s/t = f * fbar = 16/2 * 2/16 = 32/32 = 1/1 = 1,

or, in terms of the unit sphere,

s/t = f * fbar = 2π/2 * 2/2π = 4π/4π = 1/1 = 1.

Certainly, succumbing to the demands of symmetry, by looking to the intuitive concept of motion, in which the inverse of this independent reality requires the admission of 3D time 0D space, seems much more reasonable than insisting that we should give up causality and invent extra dimensions.

Doug,

"Why should it be so amazing that the radius from the center of a sphere, expanding at light speed, should be equal to a point on its surface, defined by its rectangular coordinates? Isn't it clear from this that BOTH space and time are expanding? There is only one minus sign for time because it is the zero-dimensional expansion, whereas space expands three-dimensionally.

The true symmetry Gibbs is unwilling to sacrifice is preserved in the independent reality of the union of space and time, just as Minkowski predicted it would be, but then, if this is true, why should we look for symmetry in something that has no independent reality, like time, or space, apart from motion? Neither can have any meaning without the other."

Forgive my essential ignorance, but the logic of this has always eluded me and I can never seem to get a clear answer as to why; If space has no independent reality from motion, then presumably the most stable description of distance we have is c, so how can it be said that space expands at c? If space is actually expanding, wouldn't that mean that c would be increasing proportionally? Example; If two points are x lightyears apart and space expanded to twice its size, would that make them 2x lightyears apart, or would they still be x lightyears apart, since c increased as space expanded?

If they are 2x lightyears apart, that would seem to be an increasing distance of a stable measure of space, not expanding space. If they are still x lightyears apart, how do we know they are really expanding?

What determines c, if it is a measure which pre-exists this "expanding sphere" of space?

Thank you for your answer, Doug. I guess it is not an accident if this answer is based on quantas : "The DEGREE of certainty is always less than 100%". But I made an objection on the starting point, not on the 1 %.

For whatever it's worth, my vote for a single FQXI essay, of all that have been submitted so far (excluding my own of course!), would be Peter Lynd's essay. This is because he argues, very cogently, that the only independent reality that can exist logically is continuity, or constant change (i.e. motion). Yet, at the same time, his favorite quantum gravity theory would have to be Rovelli et al's loop quantum gravity (LQG) theory, which requires the definition of discrete units of space and time!

He writes to Carlo:

"I very much enjoyed your essay. Naturally, I very much agree with its general drive too. I have a question though. As a proponent (and founder) of Loop Quantum Gravity, are you not assuming the existence of time by asserting that time (and space) are quantized, and come as minimum, indivisible atoms in LQG? I think one can see this just in general, but also that by asserting the existence of indivisible, minimum time and space intervals, one is also assuming the existence of instants in time and spatial points (things that would constitute the building blocks of time and space and which certainly do not exist) to bound and determine such intervals. I naturally have no problem with Planck time and distance - intervals beyond which clocks and rulers can no longer have meaning - but this does not mean that continuity ceases beyond this point, not (sic) does Planck time and distance require the existence of instants and spatial points.

Best wishes

Peter

PS: I should note that, considering its emphasis on background independence and its adherence to 4-d, I find LQG the most promising current approach to quantum gravity. It is just the "atoms of time and space" that I have a real problem with. I'm not sure if LQG could be reformulated without this feature and still be 'LQG' however."

This opinion is very pleasing to me, of course, because any RST-based theory MUST be background independent and adhere to 4D. However, Carlo's response to this was also very interesting. In essence it's the same trick Einstein employed when dealing with the aether concept: He wants to just change the name of spacetime to gravitational field! Einstein did this when he changed the name of the aether to spacetime, giving it different properties (length contractions and time dilations,) and now Carlo wants to change the name of spacetime to gravitational field, giving it different properties (space points and time instances.) He explains to Peter:

"Einstein great discovery, of course, is that the two things are in fact the same. The two things are: on the one hand, the gravitational field, and on the other the two "entities" that Newton put at the basis of his picture of the world, and called "space" and "time". Now, when you discover that mister A and mister B are the same person, you can equally say that mister A is in reality mister B, or that mister B is in reality mister A. Books like to say that the gravitational field, in reality, is nothing but the spacetime, which happens to curve and so on. I prefer the opposite language: namely that the entities that Newton called "space" and "time" are nothing else than the gravitational field, seen in the particular configuration where we can disregard its dynamical properties, and assume it to be flat."

While the unphysical concept of the aether was called upon to explain the propagation of radiation, Einstein did away with this requirement by calling upon the properties of Maxwell's concept of the electromagnetic field and the principles of invariance, enabling him to eliminate Newton's concept of absolute space and time in the process.

Taking it a step further, he was able to eliminate the concept of the aether altogether, by calling upon the properties of a hypothesized gravitational field and the principles of covariance. Thus, Einstein eliminated the concept of an unphysical aether, by substituting for it a different concept of physical fields, which for physicists, at least, "are as real as the chair they sit on," to use the words of the genius himself.

Of course, a field is continuous, not discrete, and, in the case of the hypothesized gravitational field, the continuity consists in the smooth change of 4D spacetime, which in the absence of matter, would be flat in Einstein's theory, so Carlo argues that what Newton conceived of as absolute space and time, and what Maxwell conceived of as continuous aether, are, in reality, only a set of electromagnetic and gravitational fields, before matter is introduced into the theoretical picture; that is, without matter, only spacetime and light are conceivable.

But we know that light is quantized, which means that the electromagnetic field must be quantized, and, if the electromagnetic field is quantized, then the gravitational field must be quantized as well. This means, then, that all observables are simply functions of the various field interactions.

Well, in quantum field theory, the quanta of the electromagnetic field is the photon, while the quanta of the gravitational field is the graviton, so what's the problem? Why can't we just turn out the lights and go home?

The reason is, in a word, renormalization. Renormalization is the key that opened up the escape hatch for quantum field theory faced with the absurdity of singularities, but because of the weakness of the gravitational force, renormalization in connection with the graviton, at high energy, doesn't work. A work-around for this is a concept called "effective field theory," in which a non-renormalizable theory is regarded as merely a theory in which these high-energy interactions are highly suppressed.

Nevertheless, the scales, at which these effective field theories would be able to do their magic, are woefully out of reach from the human scale, so that approach seems literally out of reach.

Yet, the problem Peter has with LQG is even more fundamental than that. His paper shows how, logically, there can be no discrete interval of duration in which there is no change, which prevents the quantization of the G field a-priori; that is, there can be no "atoms of time and space," because if there were, it would require that change, or motion, would have to be non-existent, during that interval, no matter how small the interval might be. If this is the case, how can gravity be explained in terms of "atoms of space and time," even if their names are changed?

Larson never let this bother him. He simply asserted that the required change during the natural interval proceeded, from one boundary to the next, smoothly, crossing boundaries as if they weren't there. Though no one ever challenged him on this, they should have and Peter would have been able to do so quite handily, in my opinion.

So, if Carlo can't get away from this well articulated, philosophical, objection to the quantization of spacetime, what about the RST-based theory? How does it deal with this deepest of all physical mysteries: How DOES nature manage to be discrete and continuous, at the same time?

I'll take a stab at it in the next post.

In the previous post above, I promised to deal with Peter Lynds' (indirect) question, as to the mystery of discrete and continuous space and time, but first, I want to address the comments of John and Le Rouge that have been posted in the meantime. Their comments and questions focus on the same thing, actually. Le Rouge questions the origin of the eightfold cube, while John questions the space/time expansion of the sphere it contains.

John asks:

"If space has no independent reality from motion, then presumably the most stable description of distance we have is c, so how can it be said that space expands at c?"

The answer is that c is a velocity, a space/time ratio, defining the expansion of its space aspect relative to its time aspect. To measure the expansion requires a point of reference to be established relative to one aspect or the other of the space/time expansion. If we choose to measure the time aspect, we must "stop" the space aspect's expansion and vice-versa. Thus, "stopping" the progression of the space aspect, say by imagining that instead of continuously increasing, the space expansion alternately increases/decreases, yielding a net spatial increase of zero (spinning its wheels so-to-speak), a reference point in the spatial expansion is established that enables us to measure the passage of time, which continues increasing uniformly, 1, 2, 3, ...n, as a dimensionless scalar.

On this basis, the spatial pseudoscalar reverses its "direction,"at the boundaries of 0 and 1, meaning it reverses from inward to outward, at 0, and, again, from outward to inward at 1, creating the oscillating unit sphere (max circumference = π).

Notice, now, that the radius of this unit sphere is also the x4 = ict coordinate of Dr. E's MDT expansion, which, while it is unit distance (d = s/t * t = s) from the origin, just reaching a point, x, y, z, on the surface of the sphere, it is also equal to the unit time interval (the i term is due to the use of the Pythagorean theorem to define the length of the radius, in which the square root of -1 is employed in the equation showing the equivalence of the polar and rectangular coordinates. When this equivalence is compared, by subtracting one from the other, the result is 0.)

Hence, the minus sign is no big mystery. It's just the result of the procedure used to talk about the radius of the unit expansion. The really big deal is that the radius is equal to both ct and t! To see the significance of this important detail, we have to understand that the pseudoscalar DIAMETER expands by two units, for every 1 unit of time increase.

The eightfold cube forms by virtue of the dimensionality of the pseudoscalar, but the 1D motion of the radius is a 1:1 ratio; that is, in 2 units of time, at c-speed, the radius is d = s/t * 2t = 2s, or d = s/t * nt = ns, for any number, n, of unit time expansion. The 2D area of the pseudoscalar is (2n)^2s/t * nt = 16s, when n = 2, and the 3D volume is (2n)^3s/t * nt = 64, when n = 2.

What this means is that c remains constant in terms of a single direction (a selected radius of the expanding sphere), defined in terms of three dimensions, from the origin, because the space/time ratio remains at 1:1, in this 1D direction, no matter how long the expansions continues.

In your example, taking a lightyear as one unit, two points x lightyears apart, expanding for two lightyears, as measured from one of them (i.e. one is at the origin), would not be 2x, or x, lightyears apart, but they would be 2x x lightyears apart.

As for your question of what determines c = s/t = 1/1, the answer is that the value of the ratio, the speed, is observed relative to all matter (which is composed of these oscillating pseudoscalars recall), but the space and time units are assumed to be revealed in the Rydberg constant, as explained in my essay. These discrete units are constant. They do not change, only the length, area and volume of the pseudoscalar changes, according to the dimensionality of the tetraktys.

Admin: Please delete the previous two posts. I was trying to hurry because my wife just informed that the basement is flooding, just when I was doing the cutting and pasting and I didn't do it right. I'm sorry for the mess. Please help.

This is the errata comment that I've been trying to post:

Opps, sorry guys. I'm in too much of a hurry. The equation of the radius of the progression is d = s/t * t, but that's not the equation of the space/time progression. The equation that yields 16s and 64s, when n = 2, is

(2n)^2s/nt^0 * nt^0 = 16s, and

(2n)^3s/nt^0 * nt^0 = 64s,

as shown in my preliminary paper, discussed earlier in this forum. My mistake. So sorry.

Doug,

" These discrete units are constant. They do not change, only the length, area and volume of the pseudoscalar changes, according to the dimensionality of the tetraktys."

It still seems to me what you are describing is increasing distance in stable units of space, as opposed to space itself expanding.

To put this in the context of my own thinking, if space is ultimately flat, with areas of gravitational contraction balanced by the seeming apparent expansion of the field of space itself, then there is no overall expansion, since this field effect is absorbed into those gravitational sinks. When we measure redshift, it is of light that has crossed large expanses of space and not fallen into intervening gravity sinks, until it falls into our telescopes. Since this space is effectively expanding for the light crossing it, the redshift is compounded so that the further it travels, the faster the source appears to recede. Eventually this recession exceeds the speed of light, creating a horizon line for visible light. This doesn't mean the source is actually moving away, only that the path the specific light travels is growing, much like running up a down escalator doesn't mean the levels of the building are moving apart. Gravity curves space around gravitational sources and this causes the source of that light to appear to move as it travels behind the source, but that doesn't mean the actual source is moving, only the light traveling from it is bent. So is there a way that light could be redshifted by the effects of extreme distance, much like it is bent by gravity?

The idea of "tired light" was dismissed because any effect which would slow the passage of photons would also scatter them and distant star wouldn't be nearly as clear. What if light really doesn't travel as particles of light, but as waves and it's only when it contacts something is it quantized? For one thing, it would provide a far more effective mechanism for transmitting light over the distances required and not having their clarity compromised, while it would also provide a reasonable explanation for how they lose energy, as the volume of space increases exponentially with distance, so the energy of the wave is reduced. When striking our telescopes, the energy of individual photons is the same, since the quanta of light are a function of the absorption, but their number is reduced.

Mass and energy are interchangeable, but what is the mechanism? If light expands as a wave, but is absorbed as particles, or units of energy, it would seem this quantization of light is the first step of energy being converted into matter. Plants do it all the time.

Eventually this structure ignites through chemical reaction or pressure and radiates back out, continuing the cycle.

So the expansion is a function and consequence of the unitary wave nature of light, while gravity is the collapse of this wave into discrete units. That would explain how nature can be both continuous and discontinuous.

This way, we can have expanding space, without having to explain the entire universe expanding from a point. Since it is a property of energy and space, it amounts to a cosmological constant, not the result of a singularity and there is no need for "dark energy."

John,

Please pardon the delay in my response. I've had to contend with a flooded basement, among other distractions. In trying to hurry under duress, I've only managed to mangle the stream of thought in this forum, by inadvertently posting the same comment three times!

What I would like to do, to get back on track, is to note that the major threads of thought developing here are actually related. We were discussing the discrete vs. continuous essay of Peter Lynds, related to his comments in Rovelli's forum on LQG in the context of the discussion of the arrow of time there.

In addition, we were discussing Gibbs' point on the need to give up causality for the sake of symmetry, in string theory, insisting that it's not really necessary to do this, and also to resort to string theory's extra dimensions, when we recognize that the symmetry of motion, not space, not time, meets the requirement for spacetime symmetry without sacrificing causality and adherence to 4D.

To summarize, with our RST-based system, we get background independence in four dimensions, maintaining causality, through the symmetry of discrete magnitudes of space/time and time/space. Yet, there remains the need to explain how motion can be discrete, in the face of Peter's challenge of LQG, showing the logical contradiction inherent in the concepts of discrete and continuous units of space and time.

In the meantime, you write:

"It still seems to me what you are describing is increasing distance in stable units of space, as opposed to space itself expanding. To put this in the context of my own thinking, if space is ultimately flat, with areas of gravitational contraction balanced by the seeming apparent expansion of the field of space itself, then there is no overall expansion, since this field effect is absorbed into those gravitational sinks."

The communication problem here, I believe, is that you are thinking in terms of space, not in terms of motion. When we realize that space can have no independent meaning outside its relation with time, we see that it cannot expand, anymore than it can warp, because it has no properties independent of those it has in its union with time. The concept of "flat" space makes no sense, and the only reason that we can think of "flat" spacetime is that the spacetime concept incorporates the expansion of spacetime, as the only independent reality.

While physicists such as Gibbs and Tegmark are intrigued with the single negative coordinate of time in spacetime, Dr. E, is captivated with its identity as an expanding dimension, but I don't think its possible to understand space or time, unless we recognize that the only meaningful way to approach either is as the two, reciprocal, aspects of motion.

Space is a measure of motion, either past or contemplated. It is not something that can be treated as if it existed between two or more points, as one, two, or three-dimensional magnitudes. But here is the rub, isn't it? How do we relate points to lines, areas and volumes? Peter's point is that, while this may be trivial in geometry, it's clearly not the case in physics, where change is the central concept. Newton recognized this long ago, when he said that:

"...if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved. To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from mechanics; and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principles, brought from without, it is able to produce so many things."

The key is "those few principles, brought from without." Today, we can design and build mechanical devices upon those non-geometrical principles of math and physics that can recreate even the roughness of nature with great accuracy, let alone the smooth figures of right lines and circles. But what we discovered along the way, is that, no matter how we try, we cannot escape the delimma that has plagued and vexed the intellectuals of mankind from the beginning of time: What is the meaning of a point?

A point has no dimensions, it has no extent. How then can it be charged? How can it spin? How can it be the basis of changing magnitude? Obviously, nature's magnitudes are infinitely divisible. How can this be? Sure, we can intellectually start with an empty set, and then we can count this empty set as a member of a non-empty set, but let's face it, we are only fooling ourselves for the sake of getting a grip on something practical. The ancient Greeks have the last laugh. In the end, we are just as perplexed by the physical point as they were.

So, while I really would like to discuss your ideas, some of which are very consonant with my own, I first have to deal with this most fundamental challenge of all: How does nature reconcile the seemingly irreconcilable dichotomy inherent in the discrete versus continuous concepts, so handily? Unless we are able to solve that problem, in a background-independent, four-dimensional, context, nothing else matters, really.

Hello John & Doug!

Great conversations here! I'll be re-reading Doug's paper on the treadmill in a few minutes.

John--above you write to Doug, "You propose something similar to Dr. E's theory of the expanding fourth dimension. As I pointed out to him, if, as he seems to suggest, this expanding wave is light, or represents light, than according to Einstein, light is the constant and gravity is actually shrinking the three dimensional geometric space, relative to this standing wave."

Where did Einstein state this? That's awesome, as it's exactly what MDT states in the attached mini-paper! If you can give me the source for "according to Einstein, light is the constant and gravity is actually shrinking the three dimensional geometric space, relative to this standing wave", that would rock!

John--I think this is what you've been trying to say to me above and in the forum for MDT.

In the attached mini-paper, I show how the gravitaional redshift and the gravitational slowing of clocks both arise from a more fundamental invariant--the fundamental invariant which also happens to define Planck's length and the velocity of light: The fourth dimension is expanding relative to the three spatial dimensions at the rate of c, manifesting itself as a spherically-symmetric wavefront in our 3D, which has a wavlength of Planck's length. This is the "invariant standing wave!"

Please see the attached mini-paper to see how MDT explains the gravitational slowing of clocks, the gravitational slowing of light, and the gravitational redshift; with simple diagrams superimposing an invariant, standing wave over space which can strecth! with these diagrams, MDT explains why clocks run slower in stronger gravitational fields where space is stretched. It shows that time, as measured on a clock, is also stretched, but only because of an underlying invariant which is never stretched--the expansion of the fourth dimension relative to the three spatial dimensions--which manifests itself as a standing sine wave in the figures. For even though time and space are stretched, the expansion of the fourth dimension remains invariant: dx4/dt = ic. And too, it shows that space is continuous, and all quantization arises from the quantized invariant expansion of the fourth dimension relative to the three spatial dimensions, or dx4/dt = ic. The invariant wavelength of the fourth expanding dimension, which is Planck's length, chops measurements of space--of time, energy, and momentum--into units of the Planck length, while providing the fundamental wave nature that gives rise to Heisenberg's Uncertainty Principle in all realms, as well as Hugens' Principle in all realms.

So it is that the absolute invariance of the expanding fourth dimension, whose wavelength and rate of expansion never changes, when superimposed on continuous space that can be stretched by a mass, results in clocks ticking more slowly in stronger gravitational fields.

Yes--entanglement, entropy, time, nonlocality, Huygens' Principle, relativity--how mysterious are all these! And yet if you ask foundational questions such as *why* entanglement, *why* entropy, *why* time, *why* nonlocality, *why* Huygens' Principle, *why* relativity, the richest, wealthiest establishment in the history of physics, which also happens to be the establishment which has contributed the least (perhaps money cannot buy physics and philosophy?), sends forth anonymous postdocs and grad students to launch the snarky, ad-hominem attacks they perfect under the guidance of their pseudo-physicist political mentors.

But hey--everyone's got to make a living.

Behold MDT--the great unifier and invariant source underlying all these *physical* phenomena--in relativity and quantum mechanics--in statistical mechanics and entropy.

For the first time in the history of relativity, *change* has been *physically* woven into the fundamental fabric of spacetime, with dx4/dt = ic. And that's where change needs to be! For can you name any branch of physics in which change, and time, do not exist? Without change, no measurement can be made.

MDT is unique in that it offers a *physical* model underlying entropy, entanglement, and nonlocality, and too, all of relativity can be immediately derived from its simple postulate and equation, as can the gravitational slowing of clocks and light, as well as teh gravitational redshift.

I expect MDT to bring additional boons for years to come!

Thanks for the conversations, and thanks for the reference, John! Would love to see where Einstein states, "light is the constant and gravity is actually shrinking the three dimensional geometric space, relative to this standing wave.""Attachment #1: MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf

In continuation of my earlier post some days back, may i refer your self to a postings made on Oct.26 and 28 on the essay of Carlo Rovelli ' Forget Time'. It deals with 'consciousness' and 'quantum' aspects while discussing 'gravitation'. The involvement of physical concepts/parameters along with the non-physical concept of 'consciousness' provides the expanding paradigms indiscussing the Nature of Time.As a propounder of MDT aspect, you may like to respond to my postings, as i expect to get enlightened.

Thanks for the comment, Dr. E. I'll come to your forum to post a response, as soon as I can make time to do so. In the meantime, I'm trying to get to the discussion of the discrete vs. continuous issue raised by Peter Lynds' essay.

People have been asking me to clarify the concept of binary oscillation, or rotation by ð, as opposed to quadrantal oscillation, or rotation by ð/2. The best way to do this, I think, is to refer to my discussion of it here, and then, if there are any questions concerning it, I'll be glad to entertain them in this forum.

The entire foundation of quantum mechanics rests upon the principles of rotation, but the mathematics of rotation employed in the theory is based on complex numbers, which are made possible by the ad hoc invention of the imaginary number, "i." The complexity of the approach is compounded by the role that Lie groups and Lie algebras play in applying the concepts of rotation to gauge groups, but in essence, the idea is this: Rotation enables us to view the continuous spectrum of magnitudes in terms of discrete units, marked out by units of rotation, which is, by definition, a continuous change.

In quantum mechanics, this takes the form of the U(1) group of rotations, or 1D rotations in the real unit circle, the SU(2) group of rotations, or 2D rotations in the complex unit circle, and the SU(3) group of rotations, or 3D rotations in the complex unit circle. By means of the properties of these Lie groups and the interactions of their Lie algebras, modern physicists have been able to construct the standard model of particle physics, as the basis for the electroweak theory (U(1) & SU(2)), and the strong nuclear force theory (SU(3)).

The great advantage in using complex numbers in the SU groups of rotations, over the real numbers in R(n) groups of rotations, is that additional degrees of freedom are attained that enable physicists to incorporate quantum variables in their theories, such as 720 degree spin, for instance, which would be impossible to do otherwise.

Of course, the nature of scalar motion excludes the concept of rotation, altogether, since it requires something to rotate. Larson tried to get around this by using a concept of rotating scalar vibrations, in his RST-based theory, but this has been replaced by the concept of pseudoscalar vibration in this development of an RST-based theory.

It turns out, though, that the expanding/contracting pseudoscalar is isomorphic to binary rotation, or rotation by pi, but, since we are talking about scalar vibration, and not vector rotation, the principle involved is new. Recall that in the pseudoscalar oscillation, the diameter of the sphere contained within the eightfold cube expands from 0 to 2 in one unit of time, and contracts from 2 to 0, in the next unit of time.

At first glance, it doesn't seem possible to compare such an expansion/contraction to rotation, binary or quadrantal, but when we recognize that, in the dual direction property of dimensions, we have an analog of Newton's third law of motion, that conclusion must be revisited. The fact is, that for every direction in a dimension, there is an equal and opposite direction.

This means that, just as soon as we choose a reference point in the rotation of a radius in the unit circle, any subsequent degree of displacement from that mark may be matched by an equal, but opposite, displacement, in the other direction; that is, a chord of the circle is defined at every point in the continuous spectrum of points making up the circumference of the unit circle.

As the rotation of the radius continues around the circle, then, a reciprocal radius rotating in the opposite direction, marks the second point, defining the chord's length, at any given instant, across the circle, which reaches its maximum extent after ð/2 radians of rotation, when the two, reciprocal, radii are diametrically opposed, coincident with the diameter of the circle.

Since two rotations of ð/2 radians are required to reach this point, one in each direction of rotation, this is a total rotation of ð radians. As the rotation continues from this point, the length of the chord, demarked by the two radii, decreases, as they converge at the ð radian point. Arriving at the ð radian point, the two radii are coincident with each other, meaning that they then rest on the same point of the circumference, effectively defining the zero-length diameter of the contraction for one instant of change.

As the two, reciprocal, rotations continue, back to the starting point, the chord length again expands, from zero, to maximum, at the 3ð/2 mark, and contracts as before, to zero again, at the 2ð mark, where the radii are once more coincident, together having rotated a total of 2 * 2ð = 4ð radians in the completed cycle.

Consequently, we not only see the equivalent of binary rotation in the oscillating pseudoscalars, but we also see a simple, physical, equivalence of 720 degree "spin" per cycle of rotation. Not only this, but we also see the definition of a point, with zero extent, in the coinciding radii, defining a discrete interval of change between them.

To my mind, this resolves Peter Lynds' philosophical issue, by showing that the discrete interval, defined by its boundaries, is, in fact, an interval of continuous, reciprocal, progression, a progression of zero-dimensional, extentless, points, rather than a succession of non-zero, extended, space and time intervals, during which no change can take place.