Hello Brian,
Love your words!
You write--"When I sit here at my desk, my change in spatial displacement relative to the walls of the room is zero. Therefore my speed is zero, because the numerator in the speed calculation is zero. But time is still progressing. So my speed cannot really be zero, because the time in the denominator is still changing. This was addressed historically by adding the fourth dimension of ict. Two "events" can then be located in spacetime, and the separation between these events can be conveniently given by a calculation much like Euclidean distance. This is a clever device, but again does not seem truly fundamental."
Yes--the whole Minkowski spacetime is a great, clever device; but it has been built upon and used to obscure a more fundamental reality--the fourth dimension is expanding relative to the three spatial dimensions at c. Einstein and Minkoswki had this fact right there, staring them in the face, with x4=ict, implying dx4/dt=ic.
You're absolutely right above--did you know that there is but one velocity through spacetime? This velocity is c! It is impossible to move at any other velocity through our 4D spacetime. This is because the fourth dimension is expanding relative to the three spatial dimensions at c.
When matter is caught in the fourth expanding dimension, it moves at c relative to the three spatial dimensions and appears as photons. When matter is stationary in our lab, it is mostly propagating at c relative to the fourth dimension, which is only because the fourth dimension is expanding at the rate of c relative to the three spatial dimensions.
To move at c through the three spatial dimensions means to be stationary in the fourth dimension, as is the timeless, ageless photon. Ergo the fourth dimension is moving relative to the three spatial dimensions. The *only* way to stay stationary in the fourth dimension is to move at c. The instant a photon is measured, it is no longer timeless and ageless, as it no longer exists in a single locality defined by the expanding fourth dimension, whose expansion distributes locality.
Brian Greene has a treatment of this in the Elegant Universe, where he almost relaizes Moving Dimensions Theory, but falls just short:
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, at the rate of c.
You write, "So I don't think Einstein and Minkowski went far enough. They covered measurement, and how events in one reference frame would appear to an observer in another reference frame. That is quite useful in itself, but the real picture seems to be fundamentally much larger than what they covered. We need to go beyond Einstein and include temporal motion, which in turn requires a consideration of non-directional motion, speeds greater than light, non-locality, and so forth. Even better, we need to learn how to think in terms of "motional dimensions" directly, instead of space and time dimensions."
Yes! Feynman sought this mechanism for the ever constant motion of time! He sought source of time's arrows and assymmetries!!
And MDT provides this *physical* mechanism for time and all change, and a while host of other physical phenomena.
Indeed, MDT finally provides, in Feyman's words, "the thing that makes the whole phenomena of the world seem to go one way." Time has a definitive arrow because the dx4/dt=ic, or the fourth dimension is expanding relative to the three spatial dimensions at the rate of c. Ergo radiation, which is but matter caught upon the expanding nonlocality of the fourth exapnding dimension, expands outward, but never inward. Ergo time and all its arrows and asymmetries, as well as entropy, as more fully elaborated on in my paper.
Feynman stated, "Now if the world of nature is made of atoms, and we too are made of atoms and obey physical laws, the most obvious interpretation of this evident distinction between past and future, and this irreversibility of all phenomena, would be that some laws, some of the motion laws of the atoms, are going one way - that the atom laws are not such that they can go either way. There should be somewhere in the works some kind of principle that uxles only make wuxles, and never vice versa, and so the world is turning away from uxley character to wuxley character all the time - and this one-way business of the interactions of things should be the thing that makes the whole phenomena of the world seem to go one way. But we have not found this yet. That is, in all the laws of physics that we have found so far there does not seem to be any distinction between the past and the future. The moving picture should work the same going both ways, and the physicist who looks at it should not laugh."--(The Distinction of Past and Future, from The Character of Physical Law, Richard Feynman, 1965)
MDT has finally found "the thing that makes the whole phenomena of the world seem to go one way."
To be stationary in a lab means to move at c through the fourth dimension. So it is that absolute rest may be defined as maximal aging, but this can never be ascertained in an inertial frame cutoff from the surrounding environment, as time is measured relative to the velocity of light and distance, which are ultimately measured relative to time. This tautological definition of time and the velocity of light and the velocity of light and time is something Einstein noted.
Best,
Dr. E (The Real McCoy)
