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

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Dr. E,

Thanks for the link. I have posted another reply on my thread.

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Dr. E,

I've ck'd your appended file and find that your calculations are not consistent with relativity. I don't know what theory you're using, but it's not relativity. Let me explain.

You're consistent with relativity in that ds^2 is the invariant interval, but you're inconsistent when you conclude dr^2 = ds^2 for a photon. The relativistically correct expression follows from ds^2 = 0 for a photon, i.e., photons follow null worldlines. The relationship between r and x4 for a photon is therefore dr^2 = -dx4^2. That gives dr^2 = -(i)^2*c^2*dt^2, i.e., dr/dt = +/-c (duh). So, according to special relativity, the photon's worldline has a component in x4, contrary to your assertion.

Are you trying to introduce a new theory, distinct from relativity?

Thanks,

Mark

[deleted]

Thanks Mark,

MDT agrees 100% with all of relativity. In fact, relativity is derived from MDT in my paper. The postulate that the fourth dimension is expanding relative to the three spatial dimensions at c is a necessary and sufficient condition for the derivation of all of relativity.

You have to agree with the fact that a timeless, ageless photon does not move through time, but only through space.

As you know, there is but one velocity for every object through our 4D spacetime--c, and a photon's motion occurs entirely through the three spatial dimensions, while it remians stationary in the fourth dimension. I quote Brian Greene commenting on this below.

I basically asked the question, "What if we approach the invariant interval from the photon's frame?" Surely the photon is not moving through the fourth dimension, while also propagating at c through the three spatial dimensions, as if it were also moving through the fouth dimension it would have to travel faster than c.

Now we all know that photons do not age. Ergo a photon does not move through time. All of a photon's motion is through space.

A timeless, ageless photon remains stationary in time. It remains stationary in the fourth dimension, while propagating at c through space.

All of a photon's motion is through the three spatial dimensions.

None of the photon's motion is through the fourth dimension.

A photon does not age.

Of course time passes for us in the lab frame, and we will agree that time has passed while a photon travels, as our watches tick.

But no time passes for the timeless, ageless photon. Ergo, in the photon's frame, the photon has not moved in time. And thus the photon has not moved in the fourth dimension.

As Brian Greene points out in the Appendix to Chapter 2 of The Elegant Universe, we note that from the space-time position 4-vector x=(ct,x1,x2,x3), we can create the velocity 4-vector u=dx/d(tau), where tau is the proper time defined by d(tau)^2=dt^2-c^-2(dx1^2+dx2^2+dx3^2). Then the "speed through space-time" is the magnitude of the 4-vector u, ((c^2dt^2-dx^2)/(dt^2-c^-2dx^2))^(1/2), which is identically the speed of light c. Now, we can rearrange the equation c^2(dt/d(tau))^2-(dx/d(tau))^2=c^2 to be c^2(d(tau)/dt))^2+(dx/d(tau))^2=c^2. This shows that an increase of an object's speed through space, (dx/d(tau))^2)^(1/2)= dx/d(tau) must be accompanied by a decrease in d(tau)/dt which is the object's speed through time, which also may be considered the rate at which time elapses on it's own clock d(tau) or the proper time, as compared with that on our stationary clock dt.

Ergo the faster an object moves through space, the slower it moves through time; but all objects always move at c through the four dimensions; and light has all of its movement through space, and thus is can have none of it through the fourth dimension.

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.

MDT agrees 100% with all of relativity. In fact, relativity is derived from MDT in my paper.

[deleted]

Dr. E,

"You have to agree with the fact that a timeless, ageless photon does not move through time, but only through space."

I disagree, as I stated before, ds^2 = 0 for a photon, that is invariant meaning dr^2 = -dx4^2 in all frames for photons. So, dr and dx4 can vary from frame to frame, but the only frame in which dx4 = 0 is in the frame that dr = 0, and that frame is of no interest to us (it's the photon's 'rest' frame). You're confusing coordinate time (contained in x4) with proper time (what the object's clock moving along the worldline reads). Proper time equals coordinate time for observers at rest spatially. Otherwise, they are not equal.

Your derivation of the magnitude of u = c (which follows from the fact that proper time is the parameterization along time-like curves) is based on ds^2 = -c^2*d(tau)^2. You include a step where you divide by d(tau)^2, therefore that calculation is not relevant for photons since d(tau)^2 for photons is zero. In fact, the magnitude of u along the photon's null path is zero.

Hope this helps,

Mark

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In 50 words, or less, please explain how your 4th dimension is motivated? Thanks...

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Thanks Mark,

I yet stand by my contention: "You have to agree with the fact that a timeless, ageless photon has no velocity component through the fourth dimension, but only through space."

Sure, as a light propagates our watches tick, but both teh velcoity of light and our ticking watches are powered by a fourth expanding dimension.

Here is a proof that photons remain stationary in the fourth dimension:

a) a photon travels at c through the three spatial dimensions, for all observers

b) if a photon had any velocity component in the fourth dimension, then its velocity would be greater than c through 4D space-time

c) nothing can travel faster than c through our 4D space-time

d) ergo a photon's velocity in the fourth dimension must be 0

Another similar proof:

a) a photon travels at c through the three spatial dimensions, for all observers

b) if a photon had any velocity component in the fourth dimension, then its velocity would be greater than c through 4D space-time

c) a photon travels at c through 4D spacetime

d) ergo a photon can have no velocity component in the ofurth dimension

One last proof:

a) the only velocity through our 4D space-time for all objects is c

b) if a photon, which is always measured to travel at c through the three spatial dimensions by all observers, had any velocity component in the fourth dimension, then its velocity would be greater than c through 4D space-time

c) ergo a photon can have no velocity component in the fourth dimension

d) ergo a photon's velocity through the fourth dimension is 0

I went back to Einstein's Relativity tonight, and you were mostly right Mark in saying, "You're consistent with relativity in that ds^2 is the invariant interval, but you're inconsistent when you conclude dr^2 = ds^2 for a photon. The relativistically correct expression follows from ds^2 = 0 for a photon, i.e., photons follow null worldlines. The relationship between r and x4 for a photon is therefore dr^2 = -dx4^2. That gives dr^2 = -(i)^2*c^2*dt^2, i.e., dr/dt = +/-c (duh). So, according to special relativity, the photon's worldline has a component in x4. . ."

But yet, as we have just shown above, it is impossible for a photon to have any component of its velocity in the fourth dimension x4. Otherwise it would travel faster than light through our 4D space-time.

Now when we consider the invariant interval for light,

0 = ds^2 = dx1^2 + dx2^2 + dx3^2 + dx4^2 where x4 = ict

the t above is not a device which measures a photon's velocity through the fourth dimension, which is 0. Rather, the t above is what is measured on our watches in our frame, and x1,x2,x3 represent the distances measured in our frame. So as this time passes on our watches in our frame, we can easily conclude that the photon is "moving through time," and since many confuse time with a fourth dimension, they can conclude that "a photon is moving through the fourth dimension." But as we have proven above, it is quite impossible for the photon to have a velocity component in the fourth dimension. Rather we are witnessing a photon travel at c as t ticks on our watch, but the fact is, the photon is staying at but one place in the fourth expanding dimension.

The only way to stay stationary in the fourth dimension, in fact, is to move at c through the three spatial dimensions, as does the photon.

The t in the equation:

ds^2 = dx1^2 + dx2^2 + dx3^2 + dx4^2 where x4 = ict

is an emergent parameter which arises because the fourth dimension is expanding relative to the three spatial dimensions, carrying the momenergy of the photons in our local watches' and clocks' unwinding springs and quartz crystals and circuitry, which exists in the foruth expanding dimension.

Because the velocity of light is measured relative to time, and because time is inextricably wed the propagation of energy, which propagates at c; the velocity of light is always measured relative to the velcoity of light in all frames, and this tautological, symbiotic definition of light and time means that c is thus measured to be the same to for all observers, and this velocity c is set by a more fundamental universal invariant-the fourth dimension is expanding relative to the three spatial dimensions at c.

Consider the timeless, ageless photon.

Relativity tells us that it stays in the same place in the fourth dimension. Again--the proof:

a) the only velocity through our 4D space-time for all objects is c

c) ergo a photon can have no velocity component in the fourth dimension

d) ergo a photon's velocity through the fourth dimension is 0

Quantum Mechanics tells us that a photon's motion is described by a spherically-symmetric probabilistic wavefront expanding at c.

While staying in the same place in the fourth dimension, a photon is also manifested as a spherically-symmetric probabilistic wavefront expanding at c.

Ergo the fourth dimension is expanding at c, distributing locality as a spherically-symmetric wavefront.

Hence entanglement, as two intially-interacting photons yet share a unique locality in the fourth expanding dimension, which distributes locality. Hence quantum mechanics' nonlocality.

Einstein already demonstrated that dimensions can bend, warp, amd move in General Relativity, and MDT extends this fundamental *physical* principle in a simple and natural manner--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, or dx4/dt=ic.

No other theory comes close to uniting entropy, entanglement, and relativity in a simple *physical* model, which celebrates a fundamental *physical* universal invariant, while providing a physical mechanism for time and all its arrows and assymetires across all realms.

Why does radiation manifest itself as expanding spherical wavefronts, but not as contracting ones? Because dx4/dt=ic--the fourth dimension is expanding relative to the three spatial dimensions.

"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.

Best & thanks for your words and insights!

Dr. E (The Real McCoy)

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Dr. E,

I'll try one more time to explain why you're not doing SR.

"Relativity tells us that it stays in the same place in the fourth dimension. Again--the proof:

a) the only velocity through our 4D space-time for all objects is c

c) ergo a photon can have no velocity component in the fourth dimension

d) ergo a photon's velocity through the fourth dimension is 0"

a) is only true for time-like worldlines, photons follow null worldlines.

b) confuses four-velocity with three-velocity. A photon's 4-velocity has magnitude zero, its three-velocity is c, therefore it must have a component in x4. Just look at M2, the photon's path is at 45 deg!

c) & d) only apply in the rest frame of the photon, not in general. ds^2 = 0 for a photon is what you must satisfy, not necessarily dx4 = 0 (good thing, that's an impossible frame for us to occupy!).

It's as if you're trying to map the time-like realm of M4 into E4 such that the null cone becomes three space and you've gotten rid of the space-like realm of M4. Is that right? If so, you're not doing SR, but it might be interesting.

Mark

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Thanks Mark!

It's fun waking up to see an informed rebuttle.

Please read Brian Greene who refers to Einstein on page 50 of an Elegeant Universe, "Here's the leap: Einstein proclaimed that all objects in the universe are always traveling through spacertime at one fixed speed--that of light." Egro all objects travel at c through spacetime at the speed of light, including light, for if all objects travel at one fixed speed through space-time at the speed of light, how could light travel at any other speed other than the velocity of light.

Here is the passage in Greene's An Elegant Universe:

http://www.amazon.com/gp/sitbv3/reader?asin=0393058581&pageID=S020&checkSum=SnkcwiUHFdGzyu9TGO5bJrIZynDqD6MxeREjPv5dsGM=

The book has been read by literally millions, and vetted by countless experts. Is there something in the passage that seems wrong to you?

In light of what Brian Greene and Einstein state, I am going to have to stick with my contention: a) the only velocity through our 4D space-time for all objects is c

Here it states that "For photons the four-velocity is not defined since dx*dx=0 , i.e. there is no frame in which a photon is at rest." http://www.mth.uct.ac.za/omei/gr/chap2/node2.html

This also states that for photons the four velocity cannot be defined: http://books.google.com/books?id=qhDFuWbLlgQC&pg=PA52&lpg=PA52&dq=photon's+four+velocity&source=web&ots=tbfFNlyaWA&sig=84KUmU3QSpV_ttYSk6j9GP--F2c&hl=en&sa=X&oi=book_result&resnum=7&ct=result

Ergo it appears that we cannot say that a photon's four velocity is zero.

Nor can we conclude, in any way shape or form, that a photon travels at any speed other than c through our the 4D of our spacetime.

Photons define c and c defined photons.

One of the central postulates of relativity is:

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

Light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.

Relativity tells us that the photon stays in the same place in the fourth dimension. Here's a proof:

a) the only velocity through our 4D space-time for all objects is c (stated by Brian Greene/Einstein)

b) if a photon, which is always measured to travel at c through the three spatial dimensions by all observers (a postulate of relativity), had any velocity component in the fourth dimension, then its velocity would be other than c through our 3D space.

c) ergo a photon can have no velocity component in the fourth dimension

d) ergo a photon's velocity through the fourth dimension is 0

Well relativity is indeed subtle, and I think you may be letting certain interpretations of subtle math try to trump the physical reality.

But I will have to stick with Einstein/Brian Greene and the physical reality of the photon, which stays in but one place in the fourth expanding dimension!

How else would one provide a *physical* model for quantum mechanics' nonlocality and entanglment, while also providing a simple postulate for a *physical* reality underlying time and all its arrows across all realms, as well as entropy, while also providing a foundation for all of relativity? What would your equation and postulate be? Is not the point of physics to make everything as simple as possible but not moreso? Is not the point of physics to unify disparate *physical* phenomena with simple *physical* models and mathematics?

Consider a photon emitted from a source. Quantum mechanics describes the photon's propagation as a spherically-symmetric wavefront of probability expanding at c.

Relativity tells us that the photon does not age--it stays at the same place in the fourth dimension.

Ergo the fourth dimension is nonlocal via its expansion--it is expanding relative to the three spatial dimensions at c. Ergo the spherically-symmetric wavefront of probability expanding at c, which describes the photon's propagation, yet represents a locality in the fourth dimension.

This fits perfectly with Einstein's 1912 paper, where he wrote x4 = ict, or dx4/dt = ic. As you can see, the fourth dimension is expanding relative to the three spatial dimensions at the rate of c.

Now, in light of this (no pun intended), is it no wonder that two initially-interacting photons remain entangled? For even though they propagate in opposite directions, they yet remain ageless, and in the same place in the fourth expanding dimension!

Best,

Dr. E (The Real McCoy)

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Hello Myke,

You write, "In 50 words, or less, please explain how your 4th dimension is motivated? Thanks... "

Well, in its simplest case, MDT is motivated by the photon, as was quantum mechanics and relativity.

Throughout all this, the photon has been my best friend, providing clues as to the nature of the fourth expanding dimension via both its behavior in quantum mechanics and relativity.

I would recommend that you read one of the books on Einstein's Annus Mirabilis, as he was motivated by the photon in both his conetemplations on quantum mechanics and relativity! While he won a Nobel for his work on the photoelectric effect/quantum mechanics, he never won a Nobel for his work on relativity. How ironic that he never quite accepted quantum mechanics. . .

http://www.amazon.com/Einstein-1905-Greatness-John-Rigden/dp/0674015444/

Consider the timeless, ageless photon.

Relativity tells us that the photon stays in the same place in the fourth dimension. Again--the proof: