Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken

Dr. E:

Isn't this just a copy of work published elsewhere? My understanding is that the contest essays are to be original.

Hello Excal,

The work has never been submitted to a formal peer-reviewed publication, and thus it has never been published in one. It hasn't even been posted on arxiv.org. But I hope to submit something soon! I'm looking forward to feedback on this forum, so as to further hone the theory.

I have shared variations of this work on the internet, and a very early version appeared in an appendix in my dissertation entitled "Multiple unit artificial retina chipset to aid the visually impaired and enhanced holed-emitter CMOS phototransistors."

However, this is the very first paper in which I lead with "Time as an Emergent Phenomenon."

The postulate that the fourth dimension is expanding relative to the three spatial dimensions (dx4/dt=ic) has implications across many realms of physics, and thus various papers could be written, including:

Time as an Emergent Phenomenon (the current paper--feedback would be greatly appreciated!)

The Unique Source of Quantum Mechanics' Nonlocality and the Relativity of Simultaneity

Unifying the Dualities--the Physical Reality Underlying the Space/Time, Wave/Particle, and Energy/Mass Dualities

Time's Arrows Unified: Entropic, Radiative, Cosmological, Quantum, and Pscyhological

Deriving Einstein's Relativity From a more Fundamental Postulate of a Fourth Expanding Dimension

Moving Dimensions Theory: Extending GR with a Fourth Dimension Moving independently of the Three Spatial Dimensions

Simultaneity and Nonlocality in Time: Ageless Photons are Forever Entangled

Time's Assymetries and the Fourth Expanding Dimension

The Gravitational Redshift and Slowing of Time Explained With a New Invariant: dx4/dt=ic

Why Radiation is Quantized and Gravition is Not

Relativity Does Not Imply a Block Universe, as the Fourth Dimension is Not Time, but ict.

Moving Dimensions Theory: A Physical Reality Underlying Quantum Mechanics, Statistical Mechanis, and Relativity

dx4/dt=ic : Underlying Einstein's Two Postulates of Relativity

Well, those are some titles for potential papers.

I'll look forward to your feedback on the current paper!

Thanks,

Dr. E :)

p.s.

there are also new ideas/concepts in the current paper "Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken" that have never been released anywhere else.

i'll look forward to your feedback! thanks!

dr. e :)

Thanks for that clarification. I started to read the paper, but having only recently discovered a similar paper on physicsmathforums.com, I thought I was reading the same one again.

Anyway, I will reread it soon. In the meantime, I do have some feedback for what it's worth. If the expansion of the fourth dimension is scalar, which it must be, then the radius of the spherical expansion is one unit of space in all directions, in one unit of time. Therefore, the radius of the sphere, r, is equal to ct = Äs/Ät * t = s = 1 (s = space), which makes ict = 2^1/2 = 1.414..., the radius, r', an imaginary value corresponding to the coordinate pair, [x, y] = [1,1], if we slice the sphere for simplicity.

But if we write dx4/dt = ic, aren't we writing di(s/t * t}/dt = is/t ? Then what is 'i*s' if not 1.414...? If it is 1.414... then ic is > c, correct?

Grrr, that umlauted A in the previous post was supposed to be the delta triangle.

Hello Excal--yes-I also posted the paper at physicsmathforums.com right after I submitted it here on 8/14/08. When did you read it first? I am trying to get as much feedback as possible, so I post it around. A great thing about the internet is it costs nothing extra to share an idea in different forums and get the word out. Indeed, I imagine scientific journals will evolve over time, so that ideas can propagate faster to a greater audience and with less expense.

Thanks for the feedback, but I'm not sure what you are saying.

dx4/dt = ic is what MDT states, which comes straight from Einstein's work.

x4 = fourth dimension

i = imaginary number

c = velocity of light

t = time

Suppose I told you x4 = ict and asked you to draw x4 at t=1, t=2, t=3 . . . etc.

Would you not draw x4 in different places for different t's?

Then, since Einstein and Minkoswki agree that the fourth dimension x4 = ict, does it not make sense that the fourth dimension moves over time?

Thanks.

Dr. E:

Clearly it does. However, what I'm saying is that, if, for velocity c = 1, we choose a unit of time (1 Planck time, 1 second, whatever) then that fixes a unit of space for the equation of motion, c = s/t = 1/1. Please see the attached diagram.

An expansion from the origin of the diagram, in all directions, at unit speed, ds/dt = 1/1 = c, will expand as the red sphere with radius r = 1, in one unit of time. But if the coordinates tangent to the sphere, at x = 1, and y = 1, are used to calculate the radius of the expansion, according to the Pythagorean theorem, the calculation would give the radius of the green sphere, r' = 2^1/2 = 1.414....

Thus, the red sphere, with radius r = 1 is the real expansion, while the green sphere, with radius r' = 1.414..., does not exist, it is an imaginary sphere, projected we might say from the real one. Hence, the question I asked was, since r' goes from 0 to 1.414... in one unit of time, wouldn't the speed of expansion for the green sphere be s/t = 1.414/1, instead of 1/1?

However, after thinking about it, I realized that the answer is no, it is still equal to c, for the following reason. As soon as we choose a unit of time for c that fixes its unit of space, it also fixes a unit, albeit a different unit, for ic, because, no matter how finely we divide r, into 'a' intervals, for integration purposes, the corresponding, 'b', intervals that apply to r' will always be 41.4% larger than those of a, so when r reaches unity at a/a, r' will reach unity at b/b. I guess it's analogous to the apparent velocity of an EM wave in a waveguide.

The question is, though, if it's proportional to the red (real) sphere, why use the green one? I can see why it would be useful in quantum mechanics (it's the unit circle in the complex plane), and they need it for the phase space of gauge theory, but it seems to me that, the postulate that "time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c," is confusing, since expansion, by definition, is motion, ds/dt.

So, in a sense, to identify r' with the fourth dimension is not wrong, but to say it expands at the "rate" of s/t makes no sense, because it already represents a rate. For a rate to grow at a rate would turn it into acceleration. The radius r' expands, as the radius r expands, at the rate of c, but this is an expression of the s/t relation itself, one unit of space for one unit of time, the unit speed, which is a four dimensional ratio of 3 space dimensions over 1 time dimension.

Hence, in the equation of motion, the spatial expansion is defined in three, orthogonal dimensions, while the fourth dimension is time, defined in zero, orthogonal, dimensions; that is, the equation of motion for the spherical expansion is (s^3/t^0 * (tn^0 - t0^0). When n = 1, we get the spatial unit sphere inside the eightfold cube, but we also get the complex, imaginary, sphere, circumscribing the cube.

In other words, the fourth dimension is the time dimension, but it is the inverse of the three space dimensions, x1, x2, x3, on the unit circle, and x1', x2', x3', on the complex circle. At unit speed, s/t = 1/1, x4 = ct (r) and x4' = ict (r') represent unit expansion, which means that they can easily be mistakenly identified as a fourth spatial dimension, but in reality they only correspond to the real fourth dimension, t^0.Attachment #1: UnitComplexCircles.jpg

Hello Excal,

i think you may be making this a bit more complicated than it is . . . i hope the following might help!

real quick, before we get into it, could the expanding fourth dimension be the source of compactified kaluza-klein geometires? imagine points of x4 expanding in a spherically-symmetric manner:

http://www.diffusion.ens.fr/vip/images/10.11.jpg

http://www.asci.org/artikel945.html

(more on this later)

in his 1912 manuscript, Einstein wrote x4 = ict.

thus dx4/dt = ic

ergo x4 is moving relative to the three spatial dimensions. now this movement can be interpreted as an expansion. there are many, many parallel clues for this, from quantum mechanics, to relativity, to statistical mechanics, to cosmology, to all the arrows of time and their assymetries.

one simple clue for the concept of a moving or expanding fourth dimension is the propagation of a photon. an ageless, timeless photon, which remians stationary in the fourth dimension, is represented by a spherically-symmetric expanding wavefront of probability. ergo the fourth dimension may be represented by a spherically-symmetric expanding wavefront.

so in order to get the postualte "the fourth dimension is expanding relative to the three spatial diemsnions, we look at several clues:"

x4 = ict

dx4/dt = ic

the ageless photon

entropy

time's arrows

times assymmetries

qm's entanglement

relativity's simultaneity = inherent nonlocality of the fourth dimension

the only way to stay stationary in the fourth dimension is to move at c relative through the three spatial dimensions.

more clues are discussed in the paper, where towards the bottom of page 6, i write:

"Einstein definitively states x4 = ict, and time and ict are very different entities. Einstein

states, "One has to keep in mind that the fourth coordinate u (which Einstein sometimes writes as

x4) is always purely imaginary." It is imaginary because the expansion of the fourth dimension is

orthogonal to the three spatial dimensions in every direction, just as the radii of an expanding

sphere are perpendicular to its surface at every point."

note the i in the equation dx4/dt = ic.

if we considered a 2d plane, and an expanding 3rd dimension, we could write dx3/dt = ic which would manifest itself an expanding sphere of locality. in the 2d plane, this would appear as an expanding circle.

http://www.diffusion.ens.fr/vip/images/10.11.jpg

an expanding fourth dimension manifests itself as an expanding sphere in our three spatial dimensions.

http://www.diffusion.ens.fr/vip/images/10.11.jpg

MDT may provide a natural explanation for compactified dimensions.

Now an interesting thing is that as the fourth dimension expanded, the entire surface of the sphere in the above figure would retain a locality, explaining both the non-locality in quantum mechanics' EPR paradox and entanglement, as well as the non-locality in relativity's simultaneity, where a phton remains local in the fourth dimension, no matter how far it travels. In both QM and realtivity, two photons emitted from a common origin can yet be considered to retain a locality (manifested in entanglement and agelessness), no matter how far they travel apart. Perhaps this arises from a fourth expanding dimension, which is inherently nonlocal via its very expansion, which would also account for free-will, time as we witness it, and entropy.

So it is that time, time's arrows, and time's assymetries may be viewed as emergent phenomonena in all realms, all originating from a common, underlying physical reality dx4/dt = ic, as elaborated on in the paper.

Well Excal, thanks for your feedback and I hope this helps! I hope I am adressing your questions and not being too redundant in trying to communicate the motivations for MDT.

Dr. E:

You are welcome to the feedback for what it's worth. I find that theoretical development is greatly dependent upon communication, and dialog versus monolog is an essential part of that communication, lest we end up convincing ourselves that our ideas are sound, but fail to convince others. So, I appreciate your patience.

My basic problem in trying to follow your thinking is this: Your identification of the fourth dimension as the radii of an expanding sphere, which are perpendicular to the three coordinate points on the surface of the sphere seems misguided to me.

The dictionary definition of the word "dimension" is: "A measure of spatial extent, especially width, height, or length." In mathematics this means: "The least number of independent coordinates required to specify uniquely the points in a space."

The least number of rectangular coordinates it takes to uniquely specify a given point on the surface of a sphere is three; the point's width, height, and length distances from the origin. The least number of polar coordinates it takes to specify the same point is three: the two angles theta and psi, and the point's distance from the origin, p. To me, what you seem to have done is taken the distance parameter, p, of the polar coordinate system and made it a fourth dimension in the rectangular coordinate system, as if it were a fourth dimension of space in the rectangular coordinate system, by virtue of its orthogonality to x, y, z.

If this is correct, then you are not following the definition of "dimension" that your readers follow, because the x, y, z, point can be uniquely identified with three measures of spatial extent. It is not necessary to use four dimensions to uniquely identify the point. If this is not correct and the fourth dimension is not a dimension of space, then it must be a dimension of time, which is something your readers could readily grasp, because one time dimension, in addition to three space dimensions, is the least number of independent coordinates required to uniquely specify a point in spacetime.

However, you state that it's a mistake to identify this fourth dimension as a dimension of time. You say it's an imaginary dimension. My question then is, "What is a dimension of the imagination? Is there more than one? If so, what do these dimensions specify?"

In putting the question this way, I'm not trying to be facetious, or mock you in any way, but simply trying to illustrate my confusion in regards to your work. To me, the fourth dimension, as ict, is always imaginary, because it specifies (being orthogonal to x', y', z' on the unit circle of the complex plane) a unique point on a circle that doesn't exist, as I've tried to explain above. The green circle of unit expansion in the diagram I provided as an illustration in the previous post is simply a geometric artifact of the real red circle of unit expansion.

If the red circle doesn't exist, then, like a shadow of an object, the green circle doesn't exist either. That is why Einstein insisted that it is always a purely imaginary quantity.

Having pointed this out, I don't wish to convey the idea that I think your work has no value. I just think there is more analysis required.

Thanks Excal,

Yes it is difficult to picture the fourth dimension. Some people over at Michio Kaku's forums have been kind in helping out with figures, and I'm currently working on some too:

http://www.mkaku.org/forums/showthread.php?t=1491&page=21

I quote Einstein a lot in the paper when it comes to the fourth dimension: "Einstein definitively states x4 = ict, and time and ict are very different entities. Einstein

states, "One has to keep in mind that the fourth coordinate u (which Einstein sometimes writes as

x4) is always purely imaginary." It is imaginary because the expansion of the fourth dimension is

orthogonal to the three spatial dimensions in every direction, just as the radii of an expanding

sphere are perpendicular to its surface at every point."

Einstein writes, "One has to keep in mind that the fourth coordinate u is always purely imaginary."

i represents an orthogonality, so i would infer that i represents a perpendicularity--the fourth dimension is perpenidular to the three spatial dimensions.

now einstein also writes x4 = ict, so that dx4/dt = ic.

consider a 2D x-y plane and an expanding 3D sphere. the expansion of the sphere would appear as an expanding circle in the 2D plane. now, the surface of the sphere would be perpendicular to every point in the 2D plane. instead of writing the third coordinate as z, we could associate it with i--the imaginary number, which would represent the orthogonal surface at every point in our 2d plane.

now, let us consider the above with an extra dimension, so:

consider a 3D space and an expanding 4D surface. the expansion of the 4D surface would appear as an expanding sphere in the 3D space. now, the surface of the 4D surface would be perpendicular to every point in the 3D space. instead of writing the fourth coordinate as x4, we could associate it with i--the imaginary number, which would represent the orthogonal surface at every point in our 3D space.

now, 4D is a tough entity to envision, and i don't know if my theory improves on previous treatments.

but, it does do the following:

1. recognizes that time is not the fourth dimension, but x4 = ict, as Einstein and Minkowski agreed.

2. shows all of time's arrows from various realms derive from a common physical reality--the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic

3. shows all of time's assymetries from various realms derive from a common physical reality--the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic

4. derives relativity from a simple postulate/equation: dx4/dt = ic

5. presents a physical model for QM's nonlocality & entanglement, relativity's silumtaneity, and entropy

6. unifies the dualities with a common postulate: wave-particle duality, space-time duality, and matter-energy duality are all natural results of a fourth expanding dimension, which distributes nonlocality via its expansion. note that entanglement always occurs between two particles that were formerly in contact, and thus all nonlocality emerges from a common point or locality--another clue.

7. provides a physical model for time's fundamental assymetry in this universe

8. shows that time, as measured on our watches and witnessed in the world around us, emerges from a deeper reality dx4/dt = ic.

i am working on some more figures which i will be sharing soon.

thanks for your feedback & again i hope that the responses are helpful.

more figures soon.

also, Dr. John Baez writes at: http://www.qedcorp.com/pcr/pcr/baeztime.html

"The laws of physics do not distinguish the future from the past direction of time. More precisely, the famous CPT theorem says that the laws are invariant under the combination of charge conjugation, space inversion and time reversal. In fact effects that are not invariant under the combination CP are very weak, so to a good approximation, the laws are invariant under the time reverseal operation T alone. Despite this, there is a very obvious difference between the future and past directions of time in the universe we live in. One only has to see a film run backward to be aware of this." --http://www.qedcorp.com/pcr/pcr/baeztime.html

MDT presents a physical model that naturally distinguishes between the past and future, providing a model for entropy and time's arrows--the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic.

Dr E wrote (in the paper): "Consider the emission of a photon in free space."

When would this ever happen though? The only justification that immediately comes to mind (and I may be wrong, which is why I ask!) requires use of Feynman diagrams...but doesn't that kind of contradict what is being proposed?

(And why aren't we using our old friend the metric system in the paper?!)

Dr E writes:

"Consider the fascinating physical reality implied by Einstein's most famous equation--E=mc^2."

Uh wait this really is a special instance of the relationship $p_mu p^mu = (E/c)^2 - vec{p}cdotvec{p} = (mc)^2$ (if you will pardon my use of LaTeX) for relativistic systems.

This equation $E=mc^2$ is less general thus (speaking from a mathematician's perspective) *worse* because it is 0 for massless particles, but the dot product of the 4-momenta vector yields the condition $(E/c)^2 - vec{p}cdotvec{p} = 0$ for massless relativistic systems, which is sensible.

Just my concern as a mathematician and physicist...

"It is because the mass, which appears stationary in the lab, is yet propagating through space-time at the rate of c, as is every object, as the fourth dimension is expanding at c."

Uh wait don't you mean the world line of the body is "traveling" at $c$?

This argument doesn't really follow however since massless bodies also propagate at $c$ (consider photons!). So the cause is not mass...

The fact of the matter is that mass is seen as a sort of "potential energy"...the example I gave to a philosopher friend is the following: consider your wallet, you presumably have money in it. You can spend it willy nilly and buy whatever you want at the moment (this can be thought of analogous to kinetic energy); or you can invest it in a long period of time so it will last a great deal of time (this is analogous to potential energy -- you can change it to kinetic energy under certain conditions). Now (massive) particles have to invest a certain amount in a weird sort of potential which we call "mass", it is the cost of the particle even existing!

The third equation on page 7 is incorrect, it should read (in evil LaTeX):

$ int^{u}_{a}frac{dx^4}{du}dx^4 = ic(x^4(u)-x^4(a)) $

You are missing that value of $ic$...

If you instead had $dt/dx^4$ you may have something, but this is kind of mathematically fudgy what you are writing.

How do you deal with how well the notion of proper time works in relativity with your approach? It seems like this is overlooked completely...but I may be wrong.

Thanks for the comments Alex,

Yes--I used E=mc^2 as it is the more common form of the equation and we are also addressing a lay audience, but the results are the same! Mass is equivalent to energy because the fourth dimension is expanidng relative to the three spatial dimensions: dx4/dt = ic. The more formal approach is included in longer treatments of Moving Dimensions Theory, along with treatments of proper time, which jive perfectly with MDT. There's a 5,000 word limit on the current essay, so I had to drop a lot.

Moving Dimensions Theory fully supports Feynman diagrams and it actually provides a *physical* stage underlying Feynman's many-paths interpretations and Huygens' Principle in all realms.

"Consider the emission of a photon in free space," could apply to a photon being emitted from an atom or entity into an unobstructed area. Now I know one could argue there are no such things as a truly unobstructed area and that space is naturally abuzz with a quantum soup, but there again, we see that the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, so there is indeed a lot going on at every point throughout "free" space!

However, we can picture a photon emitted into this which propagates without crashing into anything, and that was how I was using the notion of a photon being emiited in free space. Perhaps I could have written "picture a photon being emitted from an atom or other entity into relatively free space where it does not crash into anything," but I feel most people get the drift of the shorter sentence, and there's a word limit. Perhaps the longer description will appear in future papers, so thanks!

Thanks for noting the dropped constant "ic" in the third step on page 7--I saw that and corrected it a couple weeks back. It got dropped in the transcibing, and it comes back in the next step and is there at the end; but perhaps I'll upload the corrected version. However, the conclusion remains the same: dx4/dt = ic --> the fourth dimension is expanding relative to the three spatial dimensions.

Have you ever thought about Feyman's "many paths" interpretations of quantum mechanics and why it is that a particle somehow "feels" out every path en route to its destination? Well, moving dimensions theory accounts for this.

How can a single point become a spherically-symmetric expanding wavefront?

It happens all the time in QED and nature, and it happens all the "time" in teh expansion of the fourth dimension.

Please see Huygens Principle, as clues are to be found in the Huygens-Freznel Principle:

http://en.wikipedia.org/wiki/Huygens'_principle : "The Huygens-Fresnel principle (named for Dutch physicist Christiaan Huygens, and French physicist Augustin-Jean Fresnel) is a method of analysis applied to problems of wave propagation (both in the far field limit and in near field diffraction). It recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed. This view of wave propagation helps better understand a variety of wave phenomena, such as diffraction."

MDT states that the expansion of the fourth dimension appears as a spherically-symmetric wavefront expanding through the three spatial dimensions.

Just like Huygens' Principle, which pervades all levels of nature, MDT recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed. The fourth dimension is expanding, manifesting itself as an expanding 3D sphere in our world, and each point on its surfcae obeys Huygens' principle, underlying Huygens' principle in all realms.

And thus MDT explains double-slit diffraction.

Wikipedia writes,

Huygens' principle follows formally from the fundamental postulate of quantum electrodynamics - that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. It is then the result of interference (addition) of all path integrals that defines the amplitude and phase of the wavefunction of the object at this given point, and thus defines the probability of finding the object (say, a photon) at this point. Not only light quanta (photons), but electrons, neutrons, protons, atoms, molecules, and all other objects obey this simple principle.

And so it is seen that MDT underlies Feynman's many-paths treatments and the fundamental postulate of quantum electrodynamics - that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. All paths have a probability of being followed because of the fundamental nature of a fourth dimension that is expanding relative to the three spatial dimensions. The probability distribution of the photon expands at the rate of c. After a photon is emitted, the spherical wavefront that defines its probability for being found at any point has a radius of 186,000 miles. This is the net result of billions and billions of quantum expansions of the fourth dimension, and during each expansion, the photon had an equal chance of being found anywhere on the surface of the net sphere, which is the sum total of billions upon billions of smaller spheres.

These diagrams illustrate the basis of Huygens' Principle, which pervades all of nature, providing clues for a fundamental reality from which Huygens' principle arises:

http://support.svi.nl/wikiimg/hugensPrinciple_2.png

http://cache.eb.com/eb/image?id=5704&rendTypeId=4

http://www.lems.brown.edu/vision/researchAreas/Shocks3D/Figs/fig4.jpg

MDT describes the fundamental motion of the unviverse, from which time and entropy arise--both which characterize the constnat motion of dx4/dt = ic.

From the simple postulate: "The fourth dimension is expanding relative to the three spatial dimensions," captured in the simple equation d(x4)/dt=ic, the following emerges:

Huygens' Principle: The fundamental postulate of quantum electrodynamics - that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point

Time

Entropy

Action at a Distance

Entnaglement

Double slit interference

Relativity

Length contraction

Time dilation

The equivalence of mass and energy: E=mc^2: Energy is but matter (momenergy) caught upon the fourth expanding dimension.

Time's radiative arrow

Time's thermodynamic arrow

Time's qunantum Arrow

And finally, the goal of physics is ultimately to describe physical reality. We live in a universe whose physical reality is that the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic, from which relativity may be derived and which provides a physical model underlying entropy, entanglement, Hugens' principle time's arrows, and father time himself.

Hello again Alex--your comments brought to mind this discourse on a passage from Brian Greene's Elegant Universe.

MDT & Brian Greene's Elegant Universe:

In An Elegant Universe, Brian Greene almost characterizes Moving Dimensions Theory's deeper reality:

"Einstein found that precisely this idea--the sharing of motion between different dimensions--underlies all of the remarkable physics of special relativity, so long as we realize that not only can spatial dimensions share an object's motion, but the time dimension can share this motion as well. In fact, in the majority of circumstances, most of an object's motion is through time, not space. Let's see what this means." Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49

Right here Brian almost grasps MDT. But time is not a dimension. Time is an emergent phenomenon that arises because the fourth dimension is expanding relative to the three spatial dimensions at the rate of c. Let's rewrite Brian's paragraph with MDT's insights:

"Einstein found that precisely this idea--the sharing of motion between different dimensions--underlies all of the remarkable physics of special relativity, so long as we realize that not only can the three spatial dimensions share an object's motion, but the fourth dimension, which is moving relative to the three spatial dimensions, can share this motion as well. In fact, in the majority of circumstances, most of an object's motion is through the fourth dimension, not the three spatial dimensions. Let's see what this means." Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49

Most objects are traveling far less than c through the three spatial dimensions. Thus most objects are traveling close to the rate of c through the fourth dimension. To be stationary in the three spatial dimensions implies a velocity of c through the fourth dimension. Ergo the fourth dimension is expanding relative to the three spatial dimensions. To be stationary in the fourth expandning dimension, as is the timeless, ageless, nonlocal photon, implies a velocity of c through the three spatial dimensions. Ergo the fourth dimension is expanding relative to the three spatial dimensions.

dx(4)/dt = ic

Brian Greene continues:

"Motion through space is a concept we learn about early in life. Although we often don't think of things in such terms, we also learn that we, our friends, our belongings, and so forth all move through time, as well. When we look at a clock or a wristwatch, even while we idly sit and watch TV, the reading on the watch is constantly changing, constantly "moving forward in time." We and everything around us are aging, inevitably passing from one moment of time to the next. In fact, the mathematician Hermann Minkowski, and ultimately Einstein as well, advocated thinking about time as another dimension of the universe--the fourth dimension--in some ways quite similar to the three spatial dimensions in which we find ourselves immersed." Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49

What Greene misses is that the time measured on your watch--the ticking seconds--is not the fourth dimension, but it is a phenomenon that emerges because the fourth dimension is expanding relative to the three spatial dimensions. The time measured on a clock or watch relies on the emission and propagation of photons, be it in the context of an unwinding clock spring or an oscillating quartz crystal, or even the beating of a heart. And photons are matter that surf the fourth expanding dimension. As time is so inextricably wed to the emission and propagation of photons, and as photons are matter caught in the fourth expanding dimension, our notion of "time" inherits properties of the fourth expanding dimension. But the fact is that time emerges from a deeper physical reality--a fourth dimension that is expanding relative to the three spatial dimensions.

Brian Green continues on, heading off in the wrong direction that just misses the central postulate of MDT:

"Although it sounds abstract, the notion of time as a dimension is actually concrete."

But it is not. Can you move to where your watch reads three seconds back in time? Or can you move to where your watch reads an hour back in time? We can walk left or right. We can climb up or down. We can move forwards or backwards. But we can't move through time like we can through the three spatial dimensions. This is because time, as measured on our watch, is not the fourth dimension, but it is a construct we have devised which is based on the fundamental fact that the fourth dimension is expanding relative to the three spatial dimensions, governing the emission and propagation of photons, by which time is known and measured on our watches.

Brian Green continues on,

"When we want to meet someone, we tell them where "in space" we will expect to see them--for instance, the 9th floor of the building on the corner of 53rd Street and 7th avenue. There are three pieces of information here (9th floor, 53rd Street, 7th avenue) reflecting a particular location in the three spatial dimensions of the universe. Equally important, however, is our expectation of when we expect to meet them--for instance, at 3 PM. This piece of information tells us where "in time" our meeting will take place. Events are therefore specified by four pieces of information: three in space and one in time. Such data, it is said, specifies the location of the event in space and in time, or in spacetime, for short. In this sense, time is another dimension."

But again, time is different from the three spatial dimensions. Time is inextricably wed to our sense of the past--the order stored in our memory, long with our ability to imagine and dream of future events. The present is where we put our dreams into action. However, the time defined by past, present, and future is not a dimension akin to the three spatial dimensions, but rather it is a phenomenon that emerges because the fourth dimension is expanding relative to the three spatial dimensions.

Dr. E,

Expansion implies contraction. How might that extend your conceptual model? Put it in the context of a convection cycle, where energy radiates out, while structure contracts inward. Not only does this describe the basic relationship that defines our physical situation, but may describe the relative nature of time as well. Just as the present moves from one unit of time to the next, these units go from being in the future to being in the past. To the hands of the clock, the face moves counterclockwise. Yes, reality only moves into the future, but the events of which this reality consist go from being in the future to being in the past. Tomorrow becomes yesterday, as we go from yesterday to tomorrow. So the expanding energy goes into the future, as the defined contracted, reductionist structure it manifests as, goes from future potential to past circumstance. The energy doesn't collapse, but the information created by it must, in order to be information. Order condenses out of the energy.To paraphrase, 'Bit from it.'

Thanks for your comments John,

Indeed energy does tend to radiate outwards, and MDT accounts for this with a *physical* model--as the fourth dimension is expanding relative to the three spatial dimensions at c, and as photons (energy) are but matter caught on the fourth expanding dimension, the photon appears as a spherically-symmetric expanding wavefront, as it surfs the expanding fourth dimension. All of nature rests upon this fundamental reality, and all of time's arrows and entropy derive from this simple premise, as does nonlocality, entanglement, and the agelessness of the photon.

I would highly recommend "Time's Arrow and Archimedes' Point: New Directions for the Physics of Time" by Huw Price

Wikipedia writes:

http://en.wikipedia.org/wiki/Wheeler%E2%80%93Feynman_absorber_theory

"The Wheeler-Feynman absorber theory is an interpretation of electrodynamics that starts from the idea that a solution to the electromagnetic field equations has to be symmetric with respect to time-inversion, as are the field equations themselves. The motivation for such choice is mainly due to the importance that time symmetry has in physics. Indeed, there is no apparent reason for which such symmetry should be broken, and therefore one time direction has no privilege to be more important than the other."

But, in our reality, time has a definitive arrow. We all know this, we all see this, we all experience this, time afeter time, and empirical evidence never stops supporting time's relentless arrows.

What has brought us all here is "why?"

There is nothing permanent except change - Heraclitus. But why?

Relativity implies a block, timeless universe. "And yet it moves," as Galileo said. "Eppur si muove"

http://en.wikipedia.org/wiki/E_pur_si_muove!

And yet, we continue to ask questions--those questions which keep us up at night, searching for a *physical* reality and model that might answer them.

Why entropy? Why time's arrows? Why time's asymmetries? Why is c the maximum velocity and why is c independent of the source? Why the dualities? Why does physics present us with the mass-energy, space-time, and wave-particle dualities? Why entanglement, length-contraction, nonlocality, and time dilation? Why *time*? All of these phenomena can be traced to a simple principle--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c: dx4/dt = ic, from which Einstein's relativity is derived.

I remember when Wheeler came out with his "it from bit" publication--it was a small pamphlet with the picture of a sphere on the cover, covered in ones and zeroes--trying to find a cover photo/picture of it on google--if you find one, let me know! Thanks!

Dr. E,

Relativistically speaking, from the perspective of this expanding dimension which is carrying light, or is light, it is the three spatial dimensions which are shrinking. If, as Einstein said, time doesn't exist for the photon, it would seem this wave is the constant, not the three spatial dimensions. In fact it was because his theories described gravity as shrinking space to a point that Einstein felt compelled to add the Cosmological Constant, a factor which he subsequently rejected, but has been resurrected to explain dark energy, which does appear to cause space to expand. So from Einstein's original perspective, it would seem time is contracting space to that gravitational absolute, yet we seem to have lost sight of that as we have tried to understand the expansion of space and energy. Could there be some larger relativistic equilibrium that hasn't been recognized? According to measurements by COBE and WMAP,the expansion of space is roughly balanced by the contraction of gravity, resulting in overall flat space.

Entropy refers to useable energy in a closed set, but what if the very concept of "set" is a subjective concept necessary to define "information?" So that energy is just traded around, collapsing into sets as particles and expanding back out as waves, which collapse back into particles when we try to measure the energy, ie. define the informational content.

Yes, time has an arrow, but it is moving against a relative context, which is therefore going the opposite direction, as events go from being in the future to being in the past. Reality exists as this quantum field, of which macroscopic reality is an emergent phenomena. That's why I think it's more logical to understand time as an emergent property of this field, like temperature, thus time is the flow of created events from future potential to past circumstance, as this field fluctuates. One of the rebuttals raised to this is that quantum mechanics isn't intuitive, so conventional logic doesn't apply. My response to that it is the description of time as a dimensional projection which moves from past events to future ones that is intuitive, as our individual, biological perception of time is of a linear narrative from beginning to end. The same logic used to describe time as a dimensional projection of space could also be used to argue that temperature is another parameter of volume, since their relationship to measuring energy is similar.

Volume and distances/dimensions are descriptions of the vacuum. Time and temperature are consequences of the fluctuation.

Dr E,

The one question on the MDT that I don't see any answer to yet is, "What is the fourth dimension?" If it's not time, then it has to be space, but there is not a fourth spatial dimension, orthogonal to the three observed spatial dimensions, that can be observed.

And even if there were an unknowable fourth dimension, it would have to be an unknowable dimension of space, since everything else is eliminated.

It seems to me that calling it an imaginary dimension is not very scientific. At least the imaginary number 'i' was a number, but how do you get an imaginary dimension? Every dimension has two directions, or no directions. There is no in between. A scalar, like time has no direction, while each spatial direction has two directions. The three spatial dimensions define the direction of any one of the radii of an expanding sphere, like two spatial dimensions define the direction of any one of the radii of an expanding circle. The radius is not an independent dimension, by any stretch of the imagination, as far as I can tell.

Hello Excal,

Thanks again for your insights/questions.

MDT agress 100% with Einstein's and Minkowski's relativity. The fourth dimension is a direction that is orthogonal to the three spatial dimensions. All that MDT states is that the fourth dimension is expanding relative to the three spatial dimensions. In his 1912 paper Einstein just states x4 = ict. MDT begins at a more fundamental level: dx4/dt=ic, which also provides a physical model accounting for entropy, entnaglement, quantum mechanics' nonlocality, and time and its arrows in all realms, in addition to relativity.

MDT contends that the fourth dimension is very much like the spatial dimensions, except that it is expanding relative to them! dx4/dt = ic.

Now, regarding i, i does not imply "imaginary" in the sense of "it doesn't really exist." But rather i implies a very real perpendicularity.

i is an imaginary number, but it can define very real entities!

For instance, in a complex plane, we can designate the x axis to be real and the y axis to be imaginary. This is a mathematical tool, but the y axis is very real! Imaginary numbers are very useful in describing oscillations and rotations. When we solve an equation and we see one, that is math's way of lettig us know--"hey there is something going on here that is perpendicular to where you started."

If we were called upon to draw i, we would draw it perpendicular to the real number line. i^2 would be -1 on the real number line i^3 would be -i--it would point "south" along the y axis. And i^4 is 1 on the real number line. So multiplying by i rotates something by 90 degrees! Multiplying by i makes something perpendicular to its former self! Now although i is "imaginary," the y-axis is a very real entity. So i has a reality to it.

So if we're solving an equation, and an i pops out, all of a sudden we need to start thinking of an orthogonal space.

Now the way I interpret x4 = ict is that x4 is perpendicular to the three spatial dimensions, and that as t advances on our clock or watch, it moves.

Consider a 2D x-y plane and an expanding 3D sphere. We could then say that the sphere will also expand in the imaginary direction, which is directed along the z axis. The expansion of the sphere would appear as an expanding circle in the 2D plane. Now, the surface of the sphere would be perpendicular to every point in the 2D plane. instead of writing the third coordinate as z, we could associate it with i--the imaginary number, which would represent the orthogonal surface at every point in our 2d plane.

Now, let us consider the above with an extra dimension, so:

consider a 3D space and an expanding 4D surface. The expansion of the 4D surface would appear as an expanding sphere in the 3D space. now, the surface of the 4D surface would be perpendicular to every point in the 3D space. instead of writing the fourth coordinate as x4, we could associate it with i--the imaginary number, which would represent the orthogonal surface at every point in our 3D space.

more clues are discussed in the paper, where towards the bottom of page 6, i write:

"Einstein definitively states x4 = ict, and time and ict are very different entities. Einstein states, "One has to keep in mind that the fourth coordinate u (which Einstein sometimes writes as x4) is always purely imaginary." It is imaginary because the expansion of the fourth dimension is

orthogonal to the three spatial dimensions in every direction, just as the radii of an expanding sphere are perpendicular to its surface at every point."

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 obeject--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.

Relativity implies 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! Thansk for the questions--the onus is on me to answer them.

Best,

Dr. E

Dr,

In your reply to Excal above, you seem to be making the point that this fourth dimension is the quantum constant, so it is the three spatial dimensions which are shrinking/moving into the past. ?

That does seem to accord with the impression that the present is the constant and time is the procession of events which recede into the past as each one is replaced by the next, as each is created and consumed by this energetic constant.