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

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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 becuase 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?

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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. :-/

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Stranger

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

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ahrkron

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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.

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Eh

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jackle

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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?

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jackle

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drag

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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.

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arivero

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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)?

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

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jackle

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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?

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

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

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arivero

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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.

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