The Times They Are A-Changin'

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?

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."

"The present is the coincidence of multiple signals in one point called the observer."

"Spacetime is a correlation of distance and duration using the speed of light as a conversion factor, rather than a fundamental structure of reality."

Bing, you guys have nailed it. I've tried to make these point on several threads, perhaps less eloquently, but it didn't fly with the few people on here who reject special relativity. It seems that some people just need to think of the universe as a giant shooting gallery of photons ontologically zooming from here to there for billions of "universe-years," like tiny wayward space travelers wondering where they will end up. Even most popular-science magazine articles depict the Cosmos this way. The sooner we realize that this is a false, anthropomorphic view of reality -- a human projection of the "true" universe onto a context that makes intuitive sense to us -- the sooner we'll have a realistic, workable definition of time and what it really means.

Karl,

The irony is that the linear narrative that is the dimension of time, is profoundly anthropomorphic.

Basically Einstein rejected Newton's "God's view" of an absolute flow of time for a subjective understanding, where the individual perspective determines what can be observed. What gets overlooked is that since there is no "God's view" in the first place, what was being rejected was an anthropomorphization of objective reality, rather than an actual attempt at objective reality. The presumed universal narrative was being rejected in favor of the individual narrative, without considering that the very quality of narration might not be fundamental. So that "universal flow" from past to future was replaced by a four dimensional spacetime geometry, in order to incorporate the fact that clocks are inherently subjective. The simple basic fact though, is that similar processes will evolve at different rates under different conditions, as opposed to there being some fundamental geometry of spacetime telling them how fast to evolve.

"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,"

It only becomes a dimensionless point between the past and the future if we fail to recognize and understand that particular times are identically equivalent to and are completely defined by, and only by, particular configurations of the universe. The universe always has some configuration, and this configuration changes; it evolves. We, as sentient beings, are able to observe this evolution, and we have given it a special name: "the flow of time."

This word "time" is a human invention, and it is the source of a great deal of mischief and confusion. The existence of this word and the ways in which we use it tend to blind us to the fact that we are simply using the word as a tool to describe the environment in which we find ourselves as it rearranges itself. In our sometimes inelegant and imprecise way of communicating with one another, we have all tacitly agreed to describe various arrangements of the universe which we observe by referring to them as various "particular times." The universe is dynamic; its configuration changes in more or less predictable ways which we strive to understand and which we have dubbed the laws of physics. Unfortunately, our word "time" has become inextricably tangled up with physics in ways which ultimately may not serve it, or us, well. We need to rethink our use of this word and the concept with which it is linked.

I have attempted to offer a more thorough explication of this in the essay which may be found here.

Karl, John,

Let's not forget the partition of the different truth systems. That I can see at the same time both the Sun and the Moon in the sky remains a truth for me, the observer and his truth system. What we talked about and agreed with above is another truth system that belongs to the ontology of the universe. What I am saying is that within a specific truth system the truths do not agree with other truth systems, this is normal and logical. No one is wrong if he specifies to which truth system the absence of choice a.k.a. facts a.k.a. truths it belong to. Many arguments and paradoxes are eliminated by recognizing this partition.

Marcel,

flow of time is flow of numerical order of materal change running in a timeless space