What Are the Effects of Quantum Time on Mathematical Differentiation?

[Einstiensqd]

Is there a quanta of time? I do believe that there is a quanta of time, and i think it would be a one-dimensional particle, and much to my dismay, this enforces superstring. The reason that i chose a one-dimensional particle was because one dimensional particles cantravel at infinite speeds because of its near non-dimensionalism. Also, while typing this, I thought that mabeye anti particles were one-dimensional, and this could explain their short life span, or permenant existence in one moment in time.

 

[climbhi]

Are you saying time is a particle? And what do you mean a point is "near non-dimensional" I thought the definition of a point was that it is non-dimensional?!

 

[Funkee]

Climbhi, then you mean that a point does not exist. Nor would anything less than 3 dimensions that we know it. For it not to have a width or height would be pretty rash, to assume. For no matter the most infentessimely small size that it may be, it does exist. The same condition exists with a point, or anything else. If that holds true, and the superstring theory of 10 dimensions does as well, then we must say that every particle has a total of 10 dimensional properties that describe it. Now whether these dimensions exist as change, forces, or spatial properties is up for grabs, but indeed for the dimension to decrease to 0, then the particle will no longer exist, hence removing any concept of other dimensions. It may approach 0, becoming so small that it reaches the Planck length, or whichever may be the smallest measurement that exists in quantum mechanics.

 

[Einstiensqd]

Also climbhi, a non-dimensional object would be the singularity described in the big bang.

 

[climbhi]

People, points have no dimensions. They are dimensionless.

From mathworld.wolfram.com: A 0-dimensional mathematical object which can be specified in n-dimensional space using n coordinates. Although the notion of a point is intuitively rather clear, the mathematical machinery used to deal with points and point-like objects can be surprisingly slippery. This difficulty was encountered by none other than Euclid himself who, in his Elements, gave the vague definition of a point as "that which has no part."

The basic geometric structures of higher dimensional geometry--the line, plane, space, and hyperspace--are all built up of infinite numbers of points arranged in particular ways.

This does not mean that points do not exist. They exist, and are zero dimensional!

From Funkee: For it not to have a width or height would be pretty rash, to assume. For no matter the most infentessimely small size that it may be, it does exist. The same condition exists with a point, or anything else. If that holds true, and the superstring theory of 10 dimensions does as well

So since you are wrong about points having dimensions, and because you state that superstring theory is valid if points have dimension, does that mean that superstring theory is wrong?

But off that, how on Earth do you come to the conclusion that if points have dimension then superstring theory is true? Shouldn't the test of whether a theory is true or not be based on if it correctly describes how nature acts? By your token here any theory which predicts that points have dimensions would be true; obviously this is absurd! If a theory made no sense at all, but predicted that points had dimension would it still be true? NO! Then how can you make a claim that string theory is true if points have dimension?

 

[Funkee]

Well, it depends what you mean by point? Is a point a description of a part of a object? Does a line describe an object? Or can you define an object as a point or line?

The way I pictured it, is the latter. I just realized this now, but if you do use the term to describe a part of an object, then I guess it can make sense.

I assumed the latter, and so the superstring theory wasn't logical. I just applied the rule of 10 dimensions, or however many there may be if the superstring theory was false, that every dimension, in that an object must have a value in every dimension. But then, a dimension is a value. When you mean line, you mean length, don't you? Then yes it is valid.

I hadn't thought about it that much. Sorry. :-/

 

[Stranger]

I read that time is considered to be made up of particles that have been named 'chronons'...

 

[ahrkron]

Originally posted by Stranger
I read that time is considered to be made up of particles that have been named 'chronons'...

That's a nice name. However, it is far from being a standard idea.

The closest concept you can find in theoretical physics today to a "quantum of time" is probably in the Spin Network models. Basically, spacetime is seen as a 4D grid in which areas and volumes are quantized. There is no quantization of lengths or times, but some combinations of time and length may be.

(you can google search for Carlo Rovelli, Spin Networks, Loop Variables, Loop Quantum Gravity, Alejandro Perez).

Carlo Rovelli has a nice article on the nature of time measurements, and how their quantization works.

 

[Eh]

A one dimensional object would not be able to travel at infinite speeds. Take something like a one dimensional string, and shake it. The vibration will move down the string at the speed of light. Likewise, this object will still travel at a speed depending on it's rest mass. I have no idea why the 1D aspect of a particle would somehow change that.

 

[jackle]

Gravitons have been predicted (respectable science) and have a close relationship with the curvature of space and time.

I often wondered if space and time could exist in different structures at a microsopic level. This is similar to matter, which is smooth until it reaches molecular lumps and then atomic lumps and finally sub-atomic particles. Perhaps there are always 3 quanta of space bonded with a unit of time to make 4 dimensions?

 

[jackle]

Does anyone know anything about the Planck time, some sort of minimum possible length of time? And Planck length, minimum units of space?

 

[drag]

Greetings !

I suppose Plack time can be considered as
a form of time quntization because it's the
smallest period of time which "makes sense",
below it time ceases to exist as we know it.

Einstiensqd,
Anti-matter is almost the same as ordinary matter.
What's with all the dimension stuff ?

Live long and prosper.

 

[arivero]

Plank time is just an scale, not a constant. It is got from Newton constant by putting it in area units, then doing the square root, the multiplying times lightspeed. But there are not a mathematical theory using Plank time as a physical constant (except, in a trivial way, classical Newtonian gravity, of course).

BTW, this relation between areas and lengths in quantization has always puzzled me. What object is the quantised one? take for instance the original Energy-quantisation rule.

E= h 2pi/ T, where T is the period of the wave.

Does it quantise E or does it quantise (T * E)?

 

[damgo]

^^^ Quantizes E, for a wave of some specific frequency/period.

Time isn't quantized in regular QM, because it's not a Hermitian observable like E or p or x.

 

[jackle]

What are the mathematical implications of temporal quantum? For example, what would happen to differentiation if instead of v=dx/dt we returned to first principles of differentiation and had:

limit[(delta t)->(planck time)] instead of limit[(delta t)->0]

Would there be a noticable effect on v and under what circumstances?

 

[arivero]

Originally posted by jackle
What are the mathematical implications of temporal quantum? For example, what would happen to differentiation if instead of v=dx/dt we returned to first principles of differentiation and had:

limit[(delta t)->(planck time)] instead of limit[(delta t)->0]

Would there be a noticable effect on v and under what circumstances?

If you consider H(J, th), the hamiltonian in function of the action-angle variables, then discrete differentiation is exactly the Born-Heisenberg-Jordan quantum principle.

If you consider H(x,p), or any f(x,p), then the discrete differentiation at plank time implies some commutation relations (seach for Kauffman) but is not exactly related to quantum mechanics.

If you consider x(t) for the functions x(t) where the path integral concentrates, then the derivative actually diverges. This is the same effect than in stochastic mechanics for Brownian paths. So here a time cutoff smooths this divergence.

More research is to be done.