The Times They Are A-Changin'

I'd like to see a rule enacted which states that people who write articles about time must first define exactly what they mean when they use the word "time." Lack of specificity on this important fundamental point is a likely source of many of the woes of physics today.

We are left to assume that the authors probably are using the so-called "operational" definition of time; i.e., time is that which is measured by clocks. There is certainly nothing wrong with this definition, per se, so long as one then goes on to define what one means by a clock. These definitions of clocks (when such definitions are offered) typically go on about measuring regular repetitions of cyclical motions, but they typically fail to explain how one could determine whether a motion was "regular" or not without using a clock. Hmmm . . . .

This popular operational definition of time is not "wrong," but it is incomplete. It has allowed us to achieve many important advances in physics, but it has also lead us into some rather baffling puzzles. I believe that it would behoove us to look carefully for other ways of thinking about the nature of time, and I have proposed one such way in an essay which may be found here. Perhaps by somehow melding the operational definition of time with the sort of relational definition of time proposed in this essay we might be able achieve some worthwhile progress, but such a melding is a non-trivial task, and it has thus far remained beyond my ability to achieve. I'd like to think that it might succumb to the efforts of other, smarter people who would be willing to take up the challenge.

Time is non-dimensional.

The notion of multiple time dimensions strikes me as superfluous. If by "dimension" one means metric space coordinates (Weinstein does not depart from this convention) the Hilbert space allows infinite vectors. If the constraint is t = 0, the Riemann sphere C* as a compactification of C with a simple pole at infinity already accommodates a 2-dimensional analysis of the time metric -- the real time result is 1-dimensional, while the spatialized part (imaginary time) has as many dimensions as we like.

The zero constraint at infinity is unique, and its importance is underscored in the geometric intepretation of complex analysis: the expansion of pointlike space over an n-dimension field.

In my opinion the fly in the ointment never has been the failure to recognize more than one time dimension, but the persistent belief that PDE models can order real time evolution. I think that time reversibility in classical physics rules out such models. I don't see how we get to the physical meaning of time until we eliminate the need for boundary conditions -- imaginary time does that.

Tom

"understanding of what it means to be an observer ... I'm localized I can go here, or here, or here, and I can't be in two places at the same time".

Well, usual physics ignores several aspects of reality as did and do religions.

I also appreciate restriction to reasonable positive probability.

Eckard

A 12 dimensional theory with two times has some possibilities, but there are a number of hurdles which must be overcome. To see some of this it is necessary to look at string theory as it stands. The relevant dimensions are 26, 16, 11, and 10. The ten dimensional supersymmetric theory is 10 dimensions, 9 space plus time, which defines the 10 dimensional Supersymmetric Yang Mills (SYM) theory. This theory is a nongravitational theory which describes open strings, and the reason for 10 dimensions is that the Virasoro algebra has an anomaly cancellation property in this number of dimensions. The theory is not entirely satisfactory, for it is not renormalizable outside of compactification. We jump to the other end of these number to 26, which is the dimensionality of the bosonic string, where again this cancels anomalies at this dimension. I will avoid discussing the matter of the mathematics here, for that would digress too far into Virasoro algebras. However, these are vital to understand much about string theory. The relationship between the 26 and 10 dimensions involves the number of supercharges (charges which define supersymmetric fields), which contains 8 charges plus their superpairs --- 16 in total. This involves an interesting relationship between Clifford algebras and the Cayley numbers 1, 2, 4, 8, whereby if you add two to these you get 3, 4, 6, and 10. For a Cayley number n the supersymmetric theory is an so(n+1,1) group action on the Cayley or Moufang plane (the subspace where Trace(V) = 0 and we can define a density matrix in quantum mechanics). Again there is some machinery here which I will avoid. The paper by Dray and Manogue breaks some of this mathematics out. The Freudenthal Triple System (FTS) defines a 3-cycle which constructs a 10 dimensional theory. So given the Cayley number n = 8 (for supercharges) the theory is a CL_{9,1} = R[16](+)R[16]. (here the term (+) means oplus.

Now what about our 11 dimensions? That comes about from a 4-cycle. The FTS is due to an automorphism on the Jordan matrix algebra which defines a sum, trace of quadratic elements and a determinant. As with vector spaces the determinant of a matrix gives its eigenvalues. We can go one bit higher, a hyperdeterminant. The 3-cycle is a rule on fields (ψ*ψ)ψ =/= 0 then ψ(ψ*ψ)ψ = 0, which is a cohomology. The 4-cycle takes this into a spinor-vector rule with the product , which involves an antisymmetric system of elements which defines a hyperdeterminant. The result is this defines a Clifford algebra CL_{10,1} = R[32]. So this in a rule of thumb is where we add 3 to each of the Cayley numbers. I refer you to a paper by Baez and Huerta for this how 3 and 4 cycles determine Clifford algebras on Cayley numbers, with Clifford dimensions 3, 4, 7, and 11.. As for the extension to Jordan algebras and hyperdeterminants, that is work that I am engaged in now.

So what we have is a nice system in 10 dimensions, which is dual to something in 16 = 8+8 dimensions. In group theory this is SO(10) and E_8xE_8, where the last part is the infamous heterotic string, or closed string which carries 24 field elements that contain the "graviton." The SO(10) is our more well behaved (well except for renormalization) open string theory (eg type II) which describes things like the nuclear interaction. We also have this 4-cycle stuff, which pops us up one dimension and completes in some low energy approximation this thing we call M-theory. Within this structure for N = 4 supersymmetry the AdS/CFT theorem may be derived. This says the isometries of the boundary of an AdS spacetime contains the conformal structure of a quantum field theory.

So what about this business of two times? Well the AdS spacetime is a spacetime which is a hyperboloid solution in a higher dimension and two times. So this takes us into something involving F-theory. I. Bars has an interest in demonstrating that this additional time direction is not something which "flaps in the breeze" or that can be ignored, but plays a direct role in M-theory and strings. There are variations on this theme,with additional dilator or axion fields, or new degrees of freedom for these with respect to the type II string. This involves the trace of the 24 elements of the heterotic part which contains the dilaton field and popping it up one dimension. Most of the paper involves how this theory can break down into the SYM in 9 + 1 dimension, and the rest of the 3-cycle determined Clifford algebras. This can be seen in the paper by Bars & Kuo. The start of the paper centers around what appears to be a gauge fixing condition on the Majorana fermion fields of the theory. This from my early reading of things reduces the theory by throwing out field theoretic information, which might make the theory somewhat artifactual.

The idea is worth consideration of course. All the above that I set up above sits in one dimension higher, where AdS spacetimes are found from a reduction of a dimension, and there is no physics usually considered with this.

Cheers LC

Tom what is "imaginary time", where is imaginary time", how imaginary time is related to the physical change ?

Could you answer my questions.

yours amrit

in SR 4-th coordinate in NOT time

X4 = ict where t is "thick" of slock

TIME IS NOT DIMENSION

I'm deelpy imprest of how moch nonsense is dicussed in last few yers regarding time. The last one is that time is more-dimensional....it goes a bit on my nerves

yours amrit

tick.......(not thick)

WHY TIME IS NOT DIMENSION

1. there is no one experimental data in science time is dimension

2. with clocks we measure numerical order of material change i.e motion

3. X4 = ict where t is tick of clock

4. clock tick in space only, not in time

5. linear time "past-present-future" is not dimension in which we live, it is a mind model through which we experience life

6. space is timeless

7. in the universe past, present and future exist only as numerical order of change

8. universe does not run in time

9. time run in the universe as numerical order of change of the universe

10. if you do get 9 points than you know

ETERNITY IS NOW

Is there any hope someone will wake up in FQXI?

yours amrit

Imaginary time is a way of looking at instantons or quantum tunnelling states. The Schrodinger equation for a particle moving in one dimension with some potential V is

iħ∂ψ/∂t = -(ħ^2/2m)∂^2ψ/∂x^2 - Vψ.

If we consider a stationary case with a phase ψ(x,t) = ψ(x)exp(-iEt/ħ) the left had term just becomes Eψ, where E is the energy of the particle. Now let us rearrange things so that

-(ħ^2/2m)∂^2ψ(x)/∂x^2 = (E - V)ψ(x).

For a particle moving in space we set ψ(x) ~ exp(ikx), do the two derivatives and cancel out the ψ(x).

k^2 = (2m/ħ^2)(E - V).

The funny thing is that for V > E we have an imaginary k. This means that the kinetic energy is in a funny sense negative, which is not something you expect in classical mechanics. For a system of this sort it is in a classically forbidden region, and in more general systems there may be some dispersion ω = ω(k) = vk ... , this leads to an imaginary frequency. The phase for the system is exp(iφ) = exp(iωt). The imaginary quantity associated with the angular frequency ω may be reassigned to the time t, that is a mathematical triviality. So in some of these problems it is useful to use this and work with imaginary time, or what is sometimes called Euclideanized time.

Cheers LC

I don't think it will make a difference to you, Amrit, but let's pick up where Lawrence left off, at Euclideanized time.

You know that the flat Euclidean plane is two dimensional. When we do complex analysis, in two dimensions of the complex plane, points in the Euclidean plane become lines. The time metric is one dimensional, like a line. Real time is a one dimensional line in the real part of the complex plane. When we compactify the complex plane, C, with one point at infinity, we get C*, the complex sphere. Because the complex sphere has only this one simple pole at infinity, a metric beyond that point is entirely within the imaginary part of the complex plane; time is thus "spatialized." Hawking explains it as "north of the north pole." I.e., we know that one cannot, in ordinary space, go north of the north pole. In complex space, it is natural, and imaginary time is as natural as so called real time.

Tom

Spatial dimensions are static creations of our perception and basically describe the fact of the punctual observer. He stands at the center of a sphere of perception that simply and conveniently parts into x y z. But in this universe everything is dynamic and changing.

Time for example is dynamic. It has many dimensions but they are not static dimensions. They are dynamic dimensions. What the heck is that? Well, time passes at a certain rate and that is your baseline. That is the nature of time. And we know that this rate varies from place to place like in a gravitational field. This rate varies in the ball at the moment you accelerate it and throw it away. So the rate of time passing can have different values, change from one value to another etc. These are the actual dynamic variations of time. They are made of the various time variations (derivatives) of this rate, positive or negative.

Lets recap. Time is dynamic and therefore its dimensions are dynamic as well. You have the base rate with a variable value. You have its change of value, increasing or decreasing. Even increasing and decreasing will have different values of acceleration. And you finally have all the other time derivatives up to Nth ...

Now, the time rate in one place cannot change forever. This is why increasing time is connected with its opposite conjugate that brings it down back. A lump of increasing time rate has to be connected to an equal and opposite lump of decreasing time. This simple situation can be created spontaneously into the "vacuum" as short lived directionless dip and dimples (above or below the local base rate). If you match the opposite dips and dimples then you get a wave with direction! This is because this conjugate of dip and dimples is "motion" for lack of a better word.

When one superimposes a model of time rate variation of the EM wave, as above, over the classical electro-magnetic model .. one gets an interesting rule of correspondence. The magnetic vector is the time rate in the process of changing. The electric field is where this change in the time rate changes direction; from increasing to decreasing or vice-versa. This is up to par with the known rules of induction.

The field from your bar magnet or the static electricity from your comb are just different dynamic dimensions of time...... This is no surprise if you understand that the whole universe, by reason of logic, must be made of only one thing of one nature. If this thing is dynamic then you have all its variations as bonus ... which makes for a more interesting emerging universe.

Marcel,

Marcel you wrote: Time for example is dynamic. It has many dimensions but they are not static dimensions. They are dynamic dimensions. What the heck is that? Well, time passes at a certain rate and that is your baseline. That is the nature of time.

That is philosophy, no physics, no data foe what you say.

Wiht clocks we measure numerical order of change.....this is wahat time is.

Yours amrit

Every point is the center of its own three dimensional coordinate system and every clock is its own dimension of time. Why? Because dimensions are a modeling tool, not the basis of reality.

Einstein said space is what we measure with a ruler and time is what we measure with a clock. Well, a ruler can only measure one dimension at a time, so it takes three rulers to measure three dimensions of space, but a clock has two components, hands and face. Relatively speaking, while the hands go past to future, against the face, the face goes future to past, against the hands. So that would make two balanced directions,,er,, dimensions of time.

So, do we travel the fourth dimension from the past into the future, or does the constant rearrangement of what is, turn the future into the past?

"So, do we travel the fourth dimension from the past into the future, or does the constant rearrangement of what is, turn the future into the past?"

The rearrangement of "what is" turns the present into a new and different present. The future does not exist, nor does the past. The past (i.e., a previously objectively real configuration of the universe) formerly existed but has evolved into the configuration which we currently perceive and which we call the present. We infer that the present configuration will evolve into new configurations which we think of as the future, but these hypothetical future configurations have never been objectively real.

Correction: when I wrote "The past (i.e., a previously objectively real configuration of the universe) formerly existed but has evolved into the configuration which we currently perceive and which we call the present."

I should have written, "The past (i.e., previously objectively real configurations of the universe) formerly existed but they have evolved into the configuration which we currently perceive and which we call the present."

The remainder stands as written. Apologies for any confusion.

J.C.,

I basically agree with your position, but I'm thinking part of the problem with physics is we get a little too demanding of what's real and what's not. We agree past and future do not exist, but then we turn around and try to define the present and it becomes this dimensionless point between past and future, but that doesn't work because there would be no duration to affect the change that both creates and replaces the configuration. Then when we try to understand duration, we're back to past and future.

The problem is that time is an emergent effect that if we look too closely at, begins to fade, much as the effect of temperature begins to evaporate when we get to the level of individual activities.

Past, Present, Future

There is no "overall present". The present is the coincidence of multiple signals in one point called the observer. Look at the Moon and it is a second away in time. Look at the Sun (not directly!) and it is about 8 minutes away. Everywhere you look around you is the past. Because the speed limit of light is a limit also for everything ... this distance in time is EFFECTIVE, OPERATIONAL and final. There is no NOW between you and the Moon or Jupiter or even your computer screen... It does not make sense to ask "what is the weather like now on Mars". We may find out in minutes and hours the answer but, .. this is a trick of consciousness and memory and some language thrown in... The observer on Earth and Mars were never part of the same moment or "now". Past and future are equally .... Block ideas ... and time travel suggests moving between two of these blocks that do not exist ...

Marcel,

Marcel,

I fully agree that the effect of time can be entirely explained in the context of motion and the projection of events as a dimension is only a narrative model and not physically real in any way, shape or form. Spacetime is a correlation of distance and duration using the speed of light as a conversion factor, rather than a fundamental structure of reality. The problem is this does create problems for current physics models and it's easier to reject it than consider the consequences.

As a friend once said, when I pointed out that time is actually the future becoming the past, rather than movement from the past into the future, "Stop it. You're hurting my head."