A Mystic Dream of Four by Douglas Bundy

Hi Matt,

Thanks for the compliments. Hamilton is the author of the sonnet on the tetraktys. He also is the one who discovered the quaternions (literally meaning "four"), coined the term "vector," and made many other contributions to math and science. The guy was a genius, but is, at the same time, roundly dissed by many lesser lights, on several accounts, especially for his attempt at poetry!

His term for pi/2 rotations, or ¼ rotation, was "quadrantal" rotation, which he identified with quaternion units of rotation, but Altmann, who is the widely acknowledged expert on the rotation group, shows that quaternion units are not units of 1/4 rotation, but units of 1/2 rotation!

Therefore, if we plot the changing volume of the oscillating pseudoscalar, we don't get a sine wave. We get a distorted saw tooth wave that looks like it has hysteresis. I don't know if this implies that the system is physical or not, but it's an intriguing sign. Meanwhile, the plot of the 2D pseudoscalar oscillation is very sinusoidal, and the plot of the 1D pseudoscalar looks like molar teeth! Plotting the resultant of all these, you get a distorted sine wave, with a pronounced negative bias.

I don't know what all this may lead to, but it's a fascinating study.

Hello Doug,

re:

[Hamilton] was a genius, but is, at the same time, roundly dissed by many lesser lights, on several accounts, especially for his attempt at poetry!

maybe sticking with math... ;-)

i'm not being terribly serious here, just trying to have a little fun with it. as i was with my quip about John's 'crazy idea' about light. i'd been considering the same thing so i have a frame of reference there. :-)

i notice Hamilton seems to have been most taken with '4', when the most notable feature of the tetraktys at first glance is the triangular configuration of which 4 is merely a subset of fairly equal value to 3, 2 and 1. curious.

looking into 'tetrakys' a little, i came across a devotional prayer of sorts in its praise (not written by Hamilton). there doesn't appear to be any counting in it.

re:

We get a distorted saw tooth wave that looks like it has hysteresis.

first thing that came to mind was Fourier Series, suggesting a compound wave formation - more than one function going on there. i'm not terribly strong on math and can't say i actually understand Fourier Series analysis of sine waves, but came across them looking for a solution to another trig problem (looking for a triangular wave form which i could control the specific angle of while translating it onto a curve - you'd think it would be easy. doing it as a mechanical drawing only took about a half hour, but coming up with a function... i've come close... forgot all about 'red shift' just trying to solve the illustration problem). i'm no expert, but Fourier Series might be useful in untangling threads there. you may well be aware of it already. (Fourier Series Sawtooth. there's other variations as well.)

re: the 1D pseudoscalar looking like molar teeth - sounds like a slight variation on a square wave - suggesting abrupt phase shifts of otherwise relatively constant states. since we don't have an electrical switch of any sort here, it's somewhat suggestive of Planck's discrete units...

sine wave's the easiest - you've got a frequency and an amplitude. but that's not terribly interesting or informative in itself. only in relation to the other two.

i've been looking at what you and Dr.D. are doing with interest. i like Einstein's work. i have the impression he may have quit a little too early, perhaps overcome with 'catastrophic success', as Bruce Springsteen has recently dubbed the condition, with his major contributions. it took him over 36 years to get around to looking at space, finally recognizing that it's got a remarkably long list of physical characteristics for 'nothing'. in Appendix A, added in the 1953 edition of his popular treatment of GR and SR, he talks a little about 'space'. arbitrarily placing a vector location in space and subtracting all extraneous influences, he concludes that what he has left is gravity.

a bit of a glimpse into how he thought about gravity.

what is gravity? something we don't appear to be able to see or find any particular particle for or any sort of 'radiation', but it's primary characteristic is that it imparts acceleration.

what is acceleration?

looks like ∆ to me.

x4=ict.

what is that? words... they can be remarkably troublesome.

looks like ∆ to me.

but then, i don't have any formal science training; all i can do is look at the patterns. looks like directional vectors to 'gravity' (innie and outie), emerging before 'time', instigating acceleration from which space, particles and time emerge (Einstein had said that matter is an extension of space). nicely accounts for observed relatively even distribution of matter in the universe, accounts for background microwave radiation without a big bang - it's just 'coming into existence' everywhere, we've got an 'innie' gravity, from here it looks like it's going backward in time accelerating outward (accounting for our local experience of the specific temporal arrow at a macro level and permitting light to manifest), dark matter's got an outie gravity, outwardly accelerating outward, so it doesn't clump together, can't be signaled from here (we'd say it's in the wrong time zone), light can't manifest, stays 'dark'. seems to nicely pull together a few loose ends.

but i don't have much of a science background. just looking at patterns, sort of like a jigsaw puzzle, how the pieces fit together or not. just having fun. i like puzzles.

our perceptions are fairly much a matter of pattern recognition. that's all we are capable of recognizing. we appear to be at the edge of the patterns here. that we are part of the patterns, what they spring from - what's behind them - seems beyond our physical ability even to contemplate. like asking what was before the 'big bang'.

matt.

Doug,

The format here does not permit same posting on more than one essay. May i therefore request you to look at my last 2 postings on 'Forget Time' by Carlo Ravelli. The same are relevant to your essay too.

As a scientist who has worked both in the west and here in India, i find that we as scientists need not feel limited by the 'methodology' of conducting science that got built over the past 500 years of modern age. The expanding paradigms can come only if we expand our selves to all knowledge that exists and then rationalize our approach to develop path breaking precepts that may well lead to newer concepts that are able to cover much wider background than

covered earlier. For the nature can not be complex. It has evolved the Universe in a logical pattern. What happens when we cover a limited process/phenomenon in our theory, we limit ourselves unnecessarily. The failure or success of the current Super-string theory does not matter. We still need to follow an approach of a 'single' theory for all physical processes. One approach can come from the Unification efforts of the four force-fields where Gravity is holding on to itself presently. But this can be broken to unify the picture through some innovative 'thinking' yet to come! We need to emphasize excellence of 'mind' rather than just that of our intellect. Somehow i feel strongly about the closeness of interaction between the individual and the cosmic consciousness, as the latter is the storehouse of entire knowledge!

Thanks for the comments Matt. I'm just happy that there's a way to analyze the motion of the pseudoscalars. It wasn't apparent for a while how that the sine and cosine of changing angle could be used to describe the expanding/contracting pseudoscalars, but it turns out it works out well, especially since the expanding/contracting diameter of the sine is the reciprocal of the expanding/contracting diameter of the cosine, the one moving horizontally across the circle, the other moving vertically.

Your suggestion for using the Fourier series is right on. Our immediate objective is to calculate the atomic spectra, and, now that we have a spectra (!) to work with, the Fourier analysis will be the first tool we will want to use. It was Heisenberg's use of the Taylor series, following Kramer, which led him to the non-commutative multiplication that proved the key to quantum mechanics.

In the meantime, many people want to talk about cosmology more than particle physics, so I thought I would now turn the focus of the discussion in that direction. John's comments are especially inviting. He makes some excellent observations, but to lay the groundwork for the cosmological implications of our RST-based theory, I need to explain the fundamentals of space/time, as the new physical datum, replacing zero in a spacetime framework, with the one of the tetraktys.

That the tetraktys can be related to gravity will no doubt be a surprise to many, but we first have to understand how those ten dots relate to the faith that the early Greeks had in the integers. For them, the dots of the tetraktys represented their cosmology; not only did it reflect a profound truth about the first four numbers of arithmetic, but within its mystery, the principles of harmony, physics, and geometry all came together into a unified whole, enabling them to teach the meaning of life through a knowledge of answers to foundational questions, something 'que nos falta hoy dia."

To the Greeks, the monad was the father of all, the dyad was the mother of all, and their union in the triad was completed in the tetrad. Not only were these numbers found in the proportions of fundamental harmony, but they also figured in a fundamental way in the secrets of physics (the motion of heavenly bodies - through mediato/duplatio) and geometry, as well. Until, that is, the incommensurables were uncovered. The incommensurables such as the square root of 2 seemed to destroy the faith these ancients had in the integers. That numbers could exist that were not ratios of integers did as much violence to the beauty and harmony of their cosmology as the singularities of today's theories do to ours, and for the same reason: the discrete seems incompatible with the continuous, yet one cannot escape the compulsion to believe that because nature somehow reconciles the dichotomy, we should be able to do so too.

Einstein "plagued" himself over this, but had he and the Greeks realized the simple fact that nothing exists but motion, he would have easily overcome the difficulty. There is no incommensurable in the square root of 2, because, as any school child can discover, you can't square two symmetrical objects; that is, you can't arrange two symmetrical objects into anything but a line. No matter how hard you try, you can't arrange them into a square pattern.

In the case of the unit triangle, it's half of the unit square, but to understand the meaning of how the numbers of its sides relate to the number of its diagonal, it's necessary to understand the fundamental nature of distance: Distance is simply the space aspect of one-dimensional motion, nothing else. The length of the diagonal, the hypotenuse of the triangle, can't be drawn without BOTH space and time, or motion. But, as Newton clearly understood, the science of geometry has nothing to say about the origin of right lines and circles. They are input from without, based upon the science of non-geometric principles.

In the context of these principles of non-geometric science, the geometric fact that the square of the hypotenuse is the sum of the squares of the sides is relevant. What matters, in drawing the hypotenuse that geometry studies, is that space increases in a one-to-one ratio with the increase of time. If this ratio changes, the slope of the line changes. In the non-geometric context, the hypotenuse of the right triangle, with unit sides, represents the number 1, not the square root of 2.

This fact is the phenomenon responsible for the principle of relativity, or covariance. There is no independent reference frame based on a fixed location, a zero reference, from which to measure motion. Everything must relate to 1, the unit ratio of changing space and changing time, the 1:1 ratio of the unit sides that PRODUCES the hypotenuse of the right triangle.

When we start with the right triangle of unit motion, or what we will call unit motion, there are two, and only two, possibilities to alter the motion: If the changing space aspect of the unit motion oscillates, this produces a spatial reference point in which only time continues to increase uniformly, effectively collapsing the triangle to a vertical line. If the changing time aspect of the unit motion oscillates instead, this produces a temporal reference point in which only space continues to increase uniformly, effectively collapsing the triangle to a horizontal line.

We can easily plot this on a spacetime chart, plotting time vertically and space horizontally. As long as the 1:1 ratio is maintained, the change of space, as a function of the change in time, or vice versa, is the diagonal slope, what we can call the unit slope, but the slope changes to the vertical, or horizontal, if the change in one aspect, or the other, is effectively nullified by continuous oscillation, like a soldier marching in place, he goes nowhere, even though he continues to move his feet. We can say that he is just "spinning his wheels."

Clearly, however, if instances of these two possibilities are combined, the result of the combination is unit motion, again, where the vertical change is contributed by the oscillating spatial component, and the horizontal change is contributed by the oscillating temporal component. These combinations will always move at unit speed along the diagonal relative to the temporal vertical line and the spatial horizontal line, which constitute fixed spatial, or temporal, reference frames relative to the diagonal, regardless of their position on the chart.

Small changes in the position of these fixed lines on the chart have little effect on the how the diagonals are plotted, while large changes will definitely affect it and so must be taken into account. One thing is clear, however: There is only one unit diagonal.

Every plot of ratios on the chart has to be equal to, greater than, or less than, this unit ratio. Thus, the values only range from the vertical (1:2 = zero effective spatial change) to the 1:1 ratio, or from the horizontal (2:1 = zero effective temporal change) to the 1:1 ratio. In numbers, we can write this range as a system of ratios: -0 à 1 ß +0, which, of course, is the inverse of the range: -1 à 0 ß +1, giving us a fundamental symmetry in which to work the laws of conservation.

In the former system of ratios, there is a continuous spectrum of magnitudes possible, analogous to the unit circle. In the latter system of ratios, the magnitudes form two, reciprocal, discrete numbers, which may be combined to form any discrete natural number. How these ratios give rise to irrational numbers is another, fascinating, story.

But that's enough for now. I have to go paint a house, before it gets too cold, more on this later.

Man, I hate the limitations of this editor. The strange symbols in the above post are supposed to be arrows:

-0 --> 1 0

Still didn't work. I guees backward arrows don't show. If only we had a preview capability.

There should be two, opposed, arrows separating the three numbers.

Though you can tell from the context easily enough, the sentence in the 14:35 post that reads,

"In the context of these principles of non-geometric science, the geometric fact that the square of the hypotenuse is the sum of the squares of the sides is relevant."

Should read "...irrelevant."

Doug

Hi Everyone,

With a basic understanding of the mathematical structure of the space/time | time/space progression established in the previous post above, we can continue the discussion of the cosmological implications of the new system.

However, the limitations of this forum's editor being what they are, it's better to post the entry on the LRC physics site, which can be previewed, edited and illustrated with graphics. Accordingly, a link to the entry is provided here, and discussion of it can be conducted there, or in this forum, as suits the reader.

Hello Doug,

Thanks so much for your Nov. 2, 2008 @ 00:08 GMT post in which you quote from Einstein's THE MEANING OF RELATIVITY.

It was great to see, as not only do modern physicists so often neglect foundational questions, but they also neglect foundational papers and works, while embracing and exalting multiverses, mysticism, m-theory, wormholes, tiny little vibrating strings which are safe from experimental tests, and time machines which nobody ever seems to have the time to build.

I hope that you have had a chance to read Einstein's work and realize that General Relativity treats dimensions as *physical* entities with *dynamical* properties.

"CHAPTER XXXII: THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY: According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of matter as being something that is known." --Einstein's Meaning of Relativity

Particularly, I hope you get to read chapter XXVII: THE SPACE-TIME CONTINUUM OF THE GENERAL THEORY OF RELATIVITY IS NOT A EUCLIDEAN CONTINUUM

Also read CHAPTER XXVII, "In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity. The motion of clocks is also influenced by gravitational fields, and in such a way that a physical definition of time which is made with the aid of clocks has by no means the same degree of plausibility in as in the special tehory of relativity."

Well Doug, I hope that you no longer deny the fact that as matter moves through space, it bends and twists the dimensions--and thus the dimensions can and do move.

Einstein himself states, in the Meaning of Relativity: "CHAPTER XXXII: THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY: According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of matter as being something that is known." --Einstein

One of the fun things that MDT is doing is going on back to the foundational papers and showing how MDT agrees with all of them--with Einstein, Dirac, Newton, Teller, Galileo, Bohr, Schrodenger, Feynman--while so many modern physicists do not agree with the Greats, nor *physical* reality; as physical reality has a tendency to get in the way of fiat empires and postmodern groupthink tryannies.

Best,

Dr. E (The Real McCoy)

Dear Doug,

i await your response to my posting of Oct.,31 as also an earlier post on your draft essay on a pre-existing FQXI site. The later demanded suggestions to finalize the essay draft. Both cover more or less the same material.NN

Hello Doug,

Over at http://www.lrcphysics.com/trouble-with-physics/?currentPage=2, your write, "John Baez is fascinated by the mystery of these numbers too, but, being in the midst of the "Madding Crowd," he can't see these eight 3D directions, as we are seeing them now. He sees them as Clifford first saw them,"

Does John Baez also reject Einstein's General Relativity and the fact that General Relativity is founded upon dimensions that can warp, bend, and move?

I am trying to grasp the meaning of your paper, but the fact that you reject Einsteins' GR makes it difficult to do so.

I understand that we live an an era where the Foundational Papers are being banned and deconstructed, and zero progress in physics has been institutionlized, but even so, rejecting Einstein's theory of General Relativity, which treats dimenisions as real, physical entities which can bend, warp, and move, seems rather extreme.

Your essay has received quite a lot of votes, so perhaps we can yet rid ourselves of Gravity, moving dimensions, and Einstein's General Relativity if enough people vote against it. I understand that Baez is in tight with the physics fanboy community, so seeing his name on your web-page is surely worth a few votes. But yet, it's hard to believe that there are that many people our there who oppose Einstein's General Relativity and dimensions that can bend, warp, amd move.

Einstein's General Relativity is founded upon a physical reality in which the *physical* dimensions can bend, warp, and move.

Your essay begins with, "The only observed relationship of time to space is a reciprocal relation, in the equation of motion. However, it seems absurd to think of space, defined as a set of points satisfying the postulates of geometry, as the inverse of time."

Now, if you are going to talk about time, space, and *geometry*, it makes little sense to refute Einstein's General Relativity--a well-tested *physical* theory which is built upon the fact that dimenions bend, warp, and move.

http://en.wikipedia.org/wiki/Tests_of_general_relativity

I hope that you get a chance to read Einstein's work "The Meaning of Relativity" and realize that General Relativity treats dimensions as *physical* entities with dynamical properties.

"CHAPTER XXXII: THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY: According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of matter as being something that is known." --Einstein's The Meaning of Relativity

Particularly, I hope you get to read chapter XXVII: THE SPACE-TIME CONTINUUM OF THE GENERAL THEORY OF RELATIVITY IS NOT A EUCLIDEAN CONTINUUM

Also read CHAPTER XXVII, "In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity. The motion of clocks is also influenced by gravitational fields, and in such a way that a physical definition of time which is made with the aid of clocks has by no means the same degree of plausibility in as in the special tehory of relativity."

Well Doug, I hope that you no longer deny the fact that as matter moves through space, it bends and twists the dimensions--and thus the dimensions can and do move.

Einstein himself states, in the Meaning of Relativity: "CHAPTER XXXII: THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY: According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of matter as being something that is known." --Einstein

One of the fun things that MDT is doing is going on back to the foundational papers and showing how MDT agrees with all of them--with Einstein, Dirac, Newton, Teller, Galileo, Bohr, Schrodenger, Feynman--while so many modern physicists do not agree with the Greats, nor *physical* reality; as physical reality has a tendency to get in the way of fiat empires and postmodern groupthink tryannies.

Best,

Dr. E (The Real McCoy)

I prefer to reserve this forum for the discussion of my essay. Therefore, I have posted responses to Dr. E's and Narendra's comments in their own respective forums, and prefer to discuss those issues there, rather than here.

However, in regards to how our RST-based theory of gravity relates to Einstein's general relativity, or covariant theory, as applied to cosmology, and the standard model, the easiest way to understand it is through the difference between the definition of distance-based space, which is the set of spatial (x, y, z) locations that satisfies the postulates of geometry, and the definition of motion-based space, which is the inverse progression of the time progression, s/t = c.

Obviously, distance is only a measure of the space aspect of past, or contemplated, motion; that is, d = s/t * t. In the case of the motion of objects, this is necessarily one-dimensional motion. In the case of radiation, it is motion in more than one dimension, but the motion, in all but one of the dimensions involved, the dimension of propagation, is oscillatory motion.

This leads to what is called electroweak symmetry breaking, when EM motion is measured relative to a fixed reference system, but in relativity theory, there is no fixed reference system. There are only relative inertial frames, so how do we measure the oscillation of a propagating photon in isolation, to see if it's oscillating in only two dimensions, and not in the propagating dimension?

The only way an observer would be able to view an isolated photon in propagation is to be motionless relative to the photon, which requires the changing of the observer's location at the speed of light, something impossible to do.

Yet, if it were possible to do this, as Einstein used to like to imagine it were, what would the observer's speed be measured relative to? A stationary observer left behind? What, then, is the stationary observer stationary to? The departing moving observer?

Clearly, if the observer traveled with the photon, for a given unit of time, and then reversed course and traveled back to the stationary observer, at the same speed, the distance required to travel back to the stationary observer would have to be equal to the distance traveled out from the observer, which would equal half of the distance traveled by the photon, in the same amount of time.

Hence, in the time traveled by the photon, the total distance traveled by the moving observer is the same as the distance traveled by the photon, even though the distance between the stationary and the moving observers would be zero, while the distance between their location and the photon would be equal to the total distance traveled by the moving observer, out and back, in the same amount of time.

Certainly, we can represent these relative magnitudes of space, time and motion mathematically, and plot them on a graph. The speed of the moving observer and the photon is the same, c-speed. The distance traveled by the moving observer is the same as the distance traveled by the photon, but the direction reversal by the moving observer reduces the effective distance traveled, relative to the stationary observer, to zero. Yet, if we divide the time and distance traveled by the photon in half, it will equal the time and distance traveled by the moving observer in two directions. Therefore, the ratio of time to distance is the same, 2/2, in both cases, but in terms of the moving observer's roundtrip, it took two halves of the total time to complete the trip, or a ratio of 1 roundtrip to 2 halves of the total time traveled by the photon.

Now, instead of changing his location in space, what if the observer could change his location in time, in order to observe the propagating photon? To do this requires a stationary observer, but one stationary in time, not stationary in space, in order to measure the distance traveled by the moving observer and the photon in terms of temporal distance.

In this case, time would necessarily be defined as a set of temporal locations (x, y, z) satisfying the postulates of temporal geometry, and the speed of the photon would be defined as time per unit of space, t/s, instead of space per unit of time, s/t. The temporal distance between locations would then be a measure of the time aspect of the motion of an "object," given by d = t/s * s, which is, again, necessarily one-dimensional distance, in the case of the motion of these temporal "objects."

And, again, in the case of radiation, it is motion in more than one dimension, but the motion, in all but one of the dimensions involved, the dimension of propagation of the photon, is oscillatory motion. Thus, nothing has changed, except for the inversion of s/t to t/s.

Using the same analysis as before, then, we see that, again, the ratio of the time to distance, in terms of the moving observer's roundtrip, is 1 trip per two halves of the total temporal distance traveled by the photon. The ratio of temporal distance to space traveled by the photon is the same as the ratio of spatial distance to time in the former case: It is 2 units of temporal distance per 2 units of space, t/s = 2/2, which of course is unit speed in both cases.

So, what does this ansatz teach us, besides the perfect symmetry of space/time? Does it not teach us to distinguish between "space" as distance, and space entering into the speed of the photon? The fact that the temporal distance traveled by the moving observer in one roundtrip is equal to the temporal distance traveled by the photon in the same amount of space, and the spatial distance traveled by the moving observer in one roundtrip is equal to the spatial distance traveled by the photon in the same amount of time, are just the inverses of one another, suggests the possibility that time can be thought of as three-dimensional, as well as space, in the laws of motion.

The only difference is that, relative to the other, the moving observer's one-dimensional roundtrip, out and back, in one system, appears four times the "speed" of the other, no matter which system is selected as the reference, because the inverse of the magnitude of the space/time ratio 1/2 = .5 is four times the inverse time/space ratio 2/1 = 2, and vice versa.

Of course, the implications of this symmetry are that there is a law of conservation associated with it, and that FTL limitation of objects only applies to objects with spatial extent. It would not apply to objects with temporal extent. But what in the world would an object of temporal extent be, anyway? Stay tuned for some thoughts on that, but in the meantime, it's important to note that there is no conflict with the concept of relativity theory's spacetime, as a four-dimensional continuum, and the concept of four-dimensional space/time, since the former is merely generated by the latter, when the idea of temporal and spatial distances are understood.

Dr. E,

As I've tried to explain to you over and over again, it's not Einstein's concepts that I reject, but your interpretation of them, so please stop trying to hide behind Einstein, at least in this forum.

Hello Doug,

I was actually referring to your paper in my above post:

"Your essay begins with, "The only observed relationship of time to space is a reciprocal relation, in the equation of motion. However, it seems absurd to think of space, defined as a set of points satisfying the postulates of geometry, as the inverse of time."

Now, if you are going to talk about time, space, and *geometry*, it makes little sense to refute Einstein's General Relativity--a well-tested *physical* theory which is built upon the fact that dimenions bend, warp, and move.

http://en.wikipedia.org/wiki/Tests_of_general_relativity

I hope that you get a chance to read Einstein's work "The Meaning of Relativity" and realize that General Relativity treats dimensions as *physical* entities with dynamical properties.

"CHAPTER XXXII: THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY: According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of matter as being something that is known." --Einstein's The Meaning of Relativity"

Dr. E,

As I posted in your forum:

"To me, it seems as if you listen only to yourself, repeating to yourself what you want to be true. Try listening to what I am saying, please.

"I don't have any problem with Einstein's theory, because I understand it, as far as the geometric concepts of warping, bending and moving the fabric of spacetime go (Shall I repeat that? I think I will.)

"I don't have any problem with Einstein's theory, because I understand it, as far as the geometric concepts of warping, bending and moving the fabric of spacetime go.

"What I have a problem with is your use of Einstein's concepts to justify your confused notion that the DIMENSIONS of spacetime are warped, bent and moved. Notice that, no matter how hard you try, you will not be able to find Einstein saying that the DIMENSIONS of spacetime are warped, bent or moved.

"Now, I've tried to articulate WHY this difference between your concepts and Einstein's concepts arise, but apparently you are not interested in discussing those arguments, but continue to repeat yourself over and over again, insisting that there is no difference between Einstein's concept of dynamic spacetime, and your concept of dynamic dimensions.

"Ok, if that's what you prefer to do, so be it, but please lay off me. Quit trying to make a case for my rejection of Einstein, based on my rejection of MDT. They are not the same, in spite of all your valiant efforts to make it so."

Let me just add to the above comment my summary of the problem: You have taken Einstein's dynamics of spacetime and tried to transform them into your concept of the dynamics of the dimensions of spacetime. This is a subtle, but important , distinction, because it allows you to take Einstein's fourth coordinate, the imaginary time variable, x4 = ict, and transform it into ic, by writing x4/dt = ic, and call it an expanding fourth dimension.

Well, the reason this is not even wrong, or is non-sensical, is that it conceives of the imaginary time variable, which Einstein employed to help make Minkowski spacetime into something more Euclidean-like, as a quantity, which changes over real time. Rejecting this nonsense is hardly tantamount to rejecting Einstein's general relativity, so please stop trying to say that it is.

The fourth dimension is the time variable, whether real or imaginary. It increases, or progresses, but not in relation to itself. In expands (moves) in relation to the three space variables, constituting the expansion of space, which is the definition of motion. If you could get past this conceptual hurdle, it would help you to make your case for the "moving" fourth dimension, in a sensible manner, I believe.

Doug,

"The fourth dimension is the time variable, whether real or imaginary. It increases, or progresses, but not in relation to itself. In expands (moves) in relation to the three space variables, constituting the expansion of space, which is the definition of motion."

Does motion cause time, or does time cause motion?

Doug,

To clarify my previous point; If two atoms bump into each other, it causes an event. While these atoms go from past event to future ones, the events go from being in the future to being in the past. Now if time is a fundamental dimension along which reality travels, then it is carrying these atoms from one event to the next. On the other hand, if time is a consequence of these atoms bouncing around and creating events, then time is these series of events which go from being in the future to being in the past.

Now all we really see and know, the basis and extent of our knowledge, is of the immediate past which is as close as our consciousness can process the sea of energy that exists as the present. This immediate past is rapidly receding into the more distant past.

If you view time as a fundamental dimension, then it accords with the idea that is a fourth dimension expanding relative to the three static dimensions of space. On the other hand, if you see it as a consequence of motion, than all there is, is this sea of energy which is creating the events which constitute our knowledge and are represented by the three dimensions of space. So than it is this energy which is the constant and the three dimensions which are collapsing rapidly(at the speed of light) into the past. That there is some stability to our world is a function of some of this energy maintaining some consistency of form, aka, mass.

So, do you think motion is the basis of time, or time is the basis of motion?

Doug,

You write,

"What I have a problem with is your use of Einstein's concepts to justify your confused notion that the DIMENSIONS of spacetime are warped, bent and moved. Notice that, no matter how hard you try, you will not be able to find Einstein saying that the DIMENSIONS of spacetime are warped, bent or moved."

This is getting funny.

In THE MEANING OF RELATIVTIY, Einstein writes, "the geometrical properties of space are not independent, but they are determined by matter." Egro mass bends spacetime dimensions. Ergo spacetime dimensions bend and move.

And this is backed by empirical evidence:

http://en.wikipedia.org/wiki/Tests_of_general_relativity

As a mass moves through space, it warps and bends the dimensions. The dimensions bend and move around it.

I hope that you get a chance to read Einstein's work "The Meaning of Relativity" and realize that General Relativity treats dimensions as *physical* entities with dynamical properties.

"CHAPTER XXXII: THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY: According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of matter as being something that is known." --Einstein's The Meaning of Relativity

Here is an awesome video, starring David Duchovney playing Brian Greene, in which you can see the dimensions moving!

http://www.youtube.com/watch?v=0rocNtnD-yI

Start it at 6:15. When the sun is introduced onto the spacetime at approx 6:22, watch the dimensions move! This is produced by Columbia University, NSF, and one of the world's leading string theorists! Surely they would not mislead us about moving dimensions!

Then watch the Harvard physicist talk, and at around 6:35, you can see that as the earth moves through spacetime, it stretches the dimensions! Ergo dimensions can move!

Then, my favorite part--at 7:20 David Duchovney makes the sun dissapear! And how the dimensions move and then some! Look at the dimensions bending, warping, and moving!

And then, at about 0:36 into this next video, watch the dimensions themselves bend and move as the masses move through them!

http://www.youtube.com/watch?v=fxwjeg_r5Ug&feature=related

And if ths sun ceased to exist, watch what would happen to the dimensions--they would warp, bend, and move!

http://www.youtube.com/watch?v=T884m5_QzWM&feature=related

And check out the movement of the dimensions around two oribiting stars!

http://www.youtube.com/watch?v=sUyrPDmh4rI&feature=related

As you might know, Joseph Taylor won the Nobel Prize for observing such orbiting stars and finding more experimental evidence supporting the fact that dimensions can bend, warp, and move! I had Taylor for experimental physics at Princeton, but did not know that his middle name is Hooton:

http://en.wikipedia.org/wiki/Joseph_Hooton_Taylor_Jr.

"Taylor has used this first binary pulsar to make high-precision tests of general relativity. Working with his colleague Joel Weisberg, Taylor has used observations of this pulsar to demonstrated the existence of gravitational radiation in the amount and with the properties first predicted by Albert Einstein. He and Hulse shared the Nobel Prize for the discovery of this object."

Again, this is kindof boring after all the cool animations above with David Duchovney, but you can see how the earth would curve spacetime--how it would make the dimensions curve and move, as it revolved about the sun, tramping through spacetime.

http://en.wikipedia.org/wiki/Spacetime

http://commons.wikimedia.org/wiki/Image:Eclipse-test-of-relativity.jpg

Please do not ignore this experimental evidence and all of Einstein's hard, grueling work in developing General Relativity, by stating that "dimensions" cannot bend, warp, and move. It is rather insulting, when you think about it, to Einstein. GR demonstrates irrefutably that dimensions are capabale of motion and that dimensions move.

If you really, really believe that "dimension is an adjective," I would encourage you to free your mind by reading about General Relativity, starting with Einstein's The Meaning of Relativity and progressing to:

http://www.amazon.com/Gravitation-Physics-Charles-W-Misner/dp/0716703440/

http://www.amazon.com/Journey-Gravity-Spacetime-Scientific-American/dp/0716760347/ (I highly recommend this book Doug! It is writen for laymen and a more general audience & too, my name is in the acknowledgements--the only time I have ever shared a paragraph with Einstein--haha)

You are refusing to watch, listen, think, read, and understand; preferring word games, and yet, I have faith that you might grasp the fact that dimensions can bend, warp, and move!

"According to Einstein's general theory of relativity, mass and energy warp spacetime. The undulations then affect the trajectories of passing objects, producing the effects we call gravity. In Einstein's theory, spacetime is a stretchy, dynamical entity." --http://focus.aps.org/story/v14/st13

Spacetime is a dynamical entity in Einstein's theory. Ergo, dimensions move.

So it is that MDT is small extension of something we already knew! The fourth dimension is expanding relative to the three spatial dimensions at c, in units of the Planck length!

With an heroic spirit, MDT takes us back to origin of modern physics--to the original papers on relativity and QM, and it humbles itself upon that mountaintop. And when it comes on down, off the shoulders of relativity and QM's giants, MDT presents us with a fundamental view of reality that conforms to all experimental evidence, while not only resolving the paradoxes of the non-locality of the EPR effect and seemingly frozen time in Godel's block universe, but also unifying the resolution of both physical curiosities within a simple physical postulate--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic. In a sense, this is the first theory to predict QM's nonlocality and entanglement, by postulating that the fourth dimension is inherently nonlocal via its expansion--an empirical fact that the timeless, ageless, nonlocal photon agrees with, as the photon surfs the fourth expanding dimension. And not only does MDT predict this, but it also provides a *physical* model for entropy and time and all its arrows and assymetries throughout all realms. And finally, all of relativity may be derived from MDT's simple postulate, as it is in my paper--the fourth dimension is expanding relative to the three spatial dimensions--dx4/dt = ic. A postulate and an equation representing a novel *physical* feature of our universe--a fourth expanding dimension--and the natural, subsequent prediction of all of relativity, qm's nonlocality, entropy, time's arrows and assymetries in all realms, and quantum entanglement.

The great thing about Moving Dimensions Theory is that it allows us to keep all of relativity while also granting us free will and liberating us from the block universe.

Wish I could buy everyone a beer to celebrate our newfound free will! Perhaps now they can no longer argue that string theory and loop quantum gravity are our fate for the next four thousand years, as they are pre-embedded in the future of our block universe.

And too, in addition to exploding the block universe myth and unfreezing time, MDT provides a *physical* model accounting for change, entropy, relativity, quantum mechanics' nonlocality and entanglement, and time and all its arrows and assymetries across all realms. Furthermore, Huygens' principle, which manifests itself in all realms from classical waves to Feynman's many-paths interpretations of quantum mechanics, is given a deeper foundation--a raison d'etre--a fundamental source--and this is the same fundamental source underlying relativity and quantum mechanics' nonlocality and thus QM's probabilistic nature, as the fourth expanding dimension distributes locality.

MDT's great uniter and unifier is a fundamental invariant of the universe that has hitherto been unsung--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic.

Too, too many postmodern theories suggest that we should get rid of time, free will, nonlocality, causality, change, and even space! Yes--too, too many modern theories suggest that we should get rid of *physics* and *physical reality*, so that we can keep funding bureuacracies! Too, too many postmodern physicists have long ago given up trying to explain entanglement, nonlocality, entropy, and time and all its arrows and assymetries with a *physical* model. Too, too many physicists have chosen to ignore Godel's problems with the block universe and time, while losing the sense of wonderment when considering action-at-distance, nonlocality, and the EPR Paradox.

"The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed." --Albert Einstein

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 emchanics--in statistical mechanics and entropy.

Hello John,

You write,

"So, do you think motion is the basis of time, or time is the basis of motion?"

The fourth dimension is very, very real.

All motion rests upon its fundamental expansion relative to the three spatial dimensions: dx4/dt = ic. Every object moves at but one speed through space-time--c. This is because space-time moves at but one speed through every object--c. Catch up with the fourth expanding dimension, and you'll be going close to c relative to the three spatial dimensions. Remain stationary in the three spatial dimensions, and you'll be traveling at close to c relative to the fourth dimension. And isn't it cool that the faster an object moves, the shorter it is in the three spatial dimensions? This is because it is physically being rotated into the fourth dimension--the fundamental source of all motion by its never-ending motion, which sets the universe's maximum velcoity at c.

Relativists oft imply a frozen, timeless, block universe. But as Galileo said, "Yet it moves!" *Why* is this? Because dx4/dt = ic! And the spherically-symmetric expansion that the expanding fourth dimension manifests itself as--this smearing of locality--jives perfectly with the motion of a photon as well as its nonlocal properties, setting its velocity to c independent of the source and rendering it timeless and ageless--stationary in the fourth expanding dimension, which would also explain entanglement with other photons with which it once shared a common origin! And we also get a *physical* model for entropy and time.

Well, I hope this helps! Thanks for the questions!

MDT shows that time, and all motion, emegres from a more fundamental universal invariant. The fourth dimension is expanding relative to the three spatial dimensions at the rate of c.

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.

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