Complex Time.

[PatrickPowers]

It would be quite reasonable to represent time as a function of a complex number z^t. The imaginary part represents the frequency of the wave, and the norm |z^t| is the passage of time.

No difference mathematically from what we have now, but I like the concept of time as a spiral. If |z| > 1 then it does very well at describing the increase in the uncertainty of a particle, with the minimal uncertainty being 1.

[sandgroper]

Henri Poincarre proposed time was complex and bound to space in a 5D space-time. Minkowski simplified this idea by making time real and thus a 4D space-time. However, IMHO, time cannot be a dimension of space for a few reasons:

1. A dimension is a full degree of freedom and is not restricted in any way, whereas Time can only be a positive non-zero value (it cant go backwards - 2nd LoT).
2. Time is a meta-metric invented by ancient man to understand motion. Time doesn't physically exist outside the 'ever present now'. Past & Future are simply artifacts of the human mind.
3. Time has always been relative to some stable cycle - at the moment its atomic clock frequencies - so will always be affected by the things those cycles depend on.
4. Spacial dimensions must all resolve to the same units. Resolving seconds to metres by multiplying by C further obscures the fact that you are no longer working in a dimension with a sub dependency.

If you look at Time from an elementary view, its pretty clear the Time is a vector, not a dimension. So lets lock that in.

The next question that arises is what is Time a vector of? And the answer is just as obvious: Mass.

On this basis I am developing a model I call "Object Oriented Time", that also shows how extra spacial dimensions can and do co-exist in our ordinary 3D existence in everyday objects.

See https://plus.google.com/u/0/collection/8a4JU

[wendy]

No one ever said that dimensions have to be restricted. Vectors require direction, which gives space.

The models of the universe involving H (E2H = flat earth, S2H the spherical world), suppose that at some height H there is a transition between the human and devine. You might understand that any map of these realities are E2 and various distortions of S2, without a H component. Yet H is real.

Even though there is time's arrow and time's cycle, one might understand that there is a continuum of time, and that this sufficies to make a linear space. The actual nature of E3J (SRT) is that it has four real coordinates, but one axis is complex. The exact nature of the complex vector depends on the relative velocities, but this complex direction is the notion of time (aka ict).

You can of course, get quite interesting things out if you put cgs and mks units in and give it a bit of a whirl. These differ in formulae, and the difference in formulae are because certain constants are set to 1, where in the other system, they come to a value. The crank-theory-rage in the 1850s etc was that light was electromagnetic because there is a EM velocity constant of the same size. Maxwell showed the free-space solution to EM theory is waves traveling at the EM velocity, and speculated that light traveled in the same medium. More interesting is the spatial impedience, which accounts for a factor of 4pi. It corresponds to a partition of values which supposes that charge and matter have the dimensions of solid angle.

[PatrickPowers]

Time. How many dimensions?

Physical chemists keep a different proper time for each particle in a system. Relativity forces them to do this. I have been told that each particle adds six dimensions to the system, three spatial and three time. (For you GA fans this is a bivector basis.)

A system of N particles then has 6N dimensions in the mathematical sense. This overwhelming exponential increase is why Feynman came up with the idea of a quantum computer. It is the only conceivable way to solve systems such as large molecules.

Quantum mechanics is based on a "infinite dimensional rigged Hilbert space." It's infinite because the number of dimensions is so large it may as well be infinite. It's Hilbert if and only if all sums are finite. Rigging is some technical elegance I don't understand.

BUT all this being as it may, why do we say there is one dimension of time? It is because there is a system to convert one frame of reference to the other. We pick an arbitrary frame, make that the reference frame, and do all of our computation there. It is the only feasible way, I think.

BUT why do we think that there is an arrow of time? That time "flows" in a line like a river, always in one direction? This is true only in our macro world, of huge systems ruled by statistics. Time there is the same as entropy, which statistically flows in only one direction, that of increase. But the micro world of electrons and neutrinos and positrons has none of that. Electrons do not change at all. They may be created or destroyed, their state may change or be ambiguous, but an electron has no entropy. Statistics do not apply to a single body. In short, an electron has no arrow of time. Quantum mechanical equations are time symmetrical. PAM Dirac and Richard Feynman mined this view with great success. Richard saw a positron as an electron traveling backward in time. Why not? It could be.

That's a bit too radical for me right now, but one can very reasonably view time for an electron as traveling in a circle. An electron has a wavelength. That means to us it seems to have a tiny little one-handed clock spinning around with a very regular period. It isn't like our clocks in that there are no numerals on the dial. Revolutions are not counted. Every complete revolution is the same as every other. It cycles without cease until the end. So how can one say that linear time is going on? Linear is meaningful only in a system, in relation to other particles. For an isolated electron the arrow of time concept is not useful. So we can say that it doesn't have an arrow of time. It has its own little circle of time. Note that this circle is defined only relative to other circles. It is not "an observable."

Albert Einstein figured out how all the little clocks are related. Ultimately there is no solution. If you look at general relativity, in extreme cases the time concept is lost. There is no such thing, or is so altered as to be unrecognizable. The real fundamental property is a slippery Something Else that so far has defied simple description.

[Teragon]

It would be quite reasonable to represent time as a function of a complex number z^t. The imaginary part represents the frequency of the wave, and the norm |z^t| is the passage of time.

No difference mathematically from what we have now, but I like the concept of time as a spiral. If |z| > 1 then it does very well at describing the increase in the uncertainty of a particle, with the minimal uncertainty being 1.

t is not a function of z. Waves are a function of z and the independent parameter t.

[sandgroper]

Since my last post it has occurred to me that Henri Poincaré's complex space-time is a 5 dimensional reality.

Well ok, its patently obvious, and i even said as much, but what I have just realised is that Poincaré's 5D reality agrees with my assertion that space is 5 dimensional because the maximal volume of a unit n-sphere is that of the 5D hyper-sphere - adding more dimensions actually reduces the unit volume. Therefore space must naturally be 5D - because if pure energy is to explode in a "big bang" it will naturally want to fill 5 dimensions of space, not just 3. So where are the other 2 dimensions? Did Poincaré also realise that space must be 5D for the same reason?

According to string theory (in fact ST requires 11D) extra spacial dimensions are "curled up" at the plank length, but Poincaré may have discovered that not only could time replace spacial dimensions but it would need to be complex to make a 5D reality. Thus 3D+2D=5D.

Poincarre space-time is truly a great insight and its a shame that he has been overlooked as the original creator of space-time. If Poincaré was right and Minkowsky wrong then perhaps its little wonder that relativity fails at quantum scales. Perhaps all that is needed is to consider quantum space in terms of 5d Poincaré space-time as the great man originally proposed.

Has anyone encountered or done some investigation into this ? For example, does complex time help explain why the (eg) hydrogen electron can be found in some places but not others (see http://www.chemistry.mcmaster.ca/esam/C ... ion_2.html) ?

its also occurred to me that wherever time is squared the result is real. So accelerating in complex time (eg gravity) is always real but speed is not. Perhaps this explains why Einstein needed different approaches to special and general relativity, and why the latter fails at the quantum level. Poincaré was not a fool, whereas Minkowski is only famous for being one of Einstein's professors and his plagerisation/adulteration of Poincaré space-time. Einstein acknowledged his mate by referring to Poincaré Space-Time in 4D as Minkowski space-time.

This single act of cronyism by Einstein has distracted attention away from the original complex time, such that complex time is regarded by those ignorant of the history as "crackpottery". Yet Einsteins preference for 4d space-time instead of 5D complex space-time may well be the reason why general relativity fails in quantum space.

[sandgroper]

No one ever said that dimensions have to be restricted. Vectors require direction, which gives space.

Tnx Wendy. Time would appear to be a vector property of mass, and it's trivial to show that its direction is the centre of mass because General Relativity demonstrates how gravity is a time potential/ differential. Thus Time can equally be considered a vector associated with mass.

When Time is no longer a dimension things change. More importantly when associated with mass then low mass or massless objects no longer have a meaningful Time property.

IMHO

[sandgroper]

Time. How many dimensions?
PAM Dirac and Richard Feynman mined this view with great success. Richard saw a positron as an electron traveling backward in time. Why not? It could be. 

I agree with most of your observations, which are really important questions and insights.
Quantum physics is suffering from having to work with classical tools and ideas. Time cannot go backwards any more than the wind blows backwards. Thus time is a vector. More importantly, while you think of time as a dimension you will continue to believe that time can somehow go backwards and be less inclined to accept that time is a vector. We have to rethink Time completely so as to divorce ourselves from classical definitions of time.

Einstein showed that Gravity establishes a slower rate of casualty for a clock on the surface of a stellar mass than in free fall (faster).

This also means that gravity can be considered to be a time differential proportional to mass, but it's also relative to both masses. So if our clock is massive then that affects the rate of casualty it measures compared to one that is almost no mass. And so there will be a threshold mass smaller than which gravitational effects diminish to negligible, just as distance from the stellar mass diminishes gravity. Casualty for an electron is determined less by the local stellar gravitational field than it is by the atom it is attached to.

Time therefore cannot be a universal dimension. It is a vector property of mass in the form m = e / c^2 or t = 1 = sqr ( m / e ) * 3x10^8

This does not alter the maths of relativity. It simply explains why 4D space-time fails at the quantum level, namely because time is dependent upon mass and sub atomic particles do not have sufficient or any mass for time to have relevance. For a boson the above becomes t = 1 = 0 which highlights the problem. Einstein's mass energy equivalence fails unless you accept that the time constant t can be other than 1 or the speed of light can be other than 3x10^8 m/s.

IMHO :-)