Witt

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Originally posted by jpbrooks
.....the successes of geometry (and the sciences that make use of it) seem to give us no reason to believe that space-time is not a continuum.
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From PhysLink.com:

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The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning.

And roughly equal to 1.6 x 10^-35 m or about 10^-20 times the size of a proton.

The Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10^-43 seconds. No smaller division of time has any meaning. With in the framework of the laws of physics as we understand them today, we can say only that the universe came into existence when it already had an age of 10^-43 seconds.
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Hi excreationist,

I think is is absurd to say that 10^-43 things are not divisable and (10^43)+1 things are divisable.

In the absense of Zeno's paradox, it cannot be inferred that there are atomic parts of space or time.

We presume that space and time are real number qualities, because it satisfies more queries.

We cannot assume that there is a finite value of the smallest space-time thing, for there cannot be a smallest.

The compactness of numbers, that there are infinitely many numbers between any two, shows that there is no next (space) or next (time) is there?

We make these units of measurement, they are not properties of the things.

It is false to say that an infinite number of finite terms is necessarily infinite.


The concept of 'limit' eliminates the infinitesimal.

Witt

Nowhere357

Why? It would be divisible into the Planck length and the +1 part, whatever that is.

And then given Zeno's paradox, such inference can be made?

Yes. Leading us to Zeno.

But we could if there is, and isn't that the question?

I think this points to the difference between the theoretical number system, and the reality of space/time, and not of necessity to the continuous nature of space/time.

This sounds right.

Why? How can an infinite number of anything not be necessarily infinite?

Why?

I hope someone who understands the Planck length would explain where the value comes from - why is that the length at which classical physics breaks down? Am I anywhere close in my assumption that it is related to the energy levels of an atom?

Now why the hell am I getting a headache? This stuff is not that hard, is it? :/

Witt

Witt
I think is is absurd to say that 10^-43 things are not divisable and (10^43)+1 things are divisable.
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Why? It would be divisible into the Planck length and the +1 part, whatever that is.


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In the absense of Zeno's paradox, it cannot be inferred that there are atomic parts of space or time.
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Nowhere357
And then given Zeno's paradox, such inference can be made?

Yes, and that's the problem with paradoxes. That is, they cannot occur!
Logic abhors contadiction, there are no such events at all.

When apparent paradoxes occur, we can be sure we are using language wrongly.


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We presume that space and time are real number qualities, because it satisfies more queries.
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Nowhere357: Yes. Leading us to Zeno.

Not at all.
Zeno's paradox occurs when you believe that the limit of (1 + 1/2 +1/4 + 1/16 ..) is different from 2.

Even though each term (1/(n^2)) > 0, it is false to say that the infinite series of finite terms does not converge at the number 2.


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We cannot assume that there is a finite value of the smallest space-time thing, for there cannot be a smallest.
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Nowhere357: But we could if there is, and isn't that the question?

We need to agree as to whether space-time is represented by real numbers or not.
Someone on this thread has already implied that sqrt(2) can be expressed as a distance in physics.
Do you doubt that irrational numbers do represent reality? (eg. pi, epsilon etc).

Even the complex numbers and hypercomplex numbers have representation in physics.


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The compactness of numbers, that there are infinitely many numbers between any two, shows that there is no next (space) or next (time) is there?
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Nowhere357
I think this points to the difference between the theoretical number system, and the reality of space/time, and not of necessity to the continuous nature of space/time.

We can not talk about a reality that we cannot understand.
Absoluteness in this context seems to me incorrect.

All that we can know is what we can show.

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We make these units of measurement, they are not properties of the things.
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Nowhere357: This sounds right.

At last, an affirmative response.

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It is false to say that an infinite number of finite terms is necessarily infinite.
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Why? How can an infinite number of anything not be necessarily infinite?

Convergence happens, in those cases.

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The concept of 'limit' eliminates the infinitesimal.
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Nowhere357: Why?

The derivative of Newton and of Leibnitz are explained in virtue of limits without any reference to infinitesimals.

Nowhere357
I hope someone who understands the Planck length would explain where the value comes from - why is that the length at which classical physics breaks down? Am I anywhere close in my assumption that it is related to the energy levels of an atom?


Nowhere357: Now why the hell am I getting a headache? This stuff is not that hard, is it? :/

Yes it is more complex than expected.


Witt

jfryejr

I didn't mean Zeno's Paradox to be used as an actual argument for time necessarily being discrete. Merely as an analogy to the difficulty of understanding how the concept of a continuum is difficult to understand.

I never actually wrote that I thought time was discreet, just that most of our universe functions in a discrete manner.

Here's an ok web page describing the Planck Constants:

http://zebu.uoregon.edu/~js/glossary/planck_time.html

At the Planck length, according to modern physics, not me (necessarily) spacetime becomes quantized. Enter String Theory and the uninterpretable, unimaginable, etc...

excreationist

Apparently there is scientific evidence for that and it is widely accepted by physicists.

This Planck time thing would be based on evidence rather than just being an arbitrary assumption. Though I don't understand what it is all about.

So then that means that the infinite divisibility of numbers doesn't automatically prove that space and time are infinitely divisible.

No it's not (I think). e.g. what about an infinite series of integers or odd numbers...? You just said there was an "infinite number of".

Yeah... that is what "discrete" things (like integers) are all about. The words "quantum" and "quantized" have a similar meaning.

It seems things that are smaller than the planck length and planck time can exist, but they just don't follow the rules of larger-scale physics. They'd behave weirdly but I'm not sure if they'd be fundamentally discrete or continuous.

jfryejr

I think on scales smaller than the Planck length, everything is quantized (according to modern theory). This would imply they are fundamentally discrete.

Albert Cipriani

Nowhere and Jafryejr are correct. Whereas Witt is a two syllable word that starts with “dim.” He is full of what rhymes with “it” and that means he is full of nothing but assertions.

Let me count the ways:
1) Your nonsense is appalling
2) I have 0 tolerence for any religious individuals
3) The concept of 'limit' eliminates the infinitesimal
4) It cannot be inferred that there are atomic parts of space or time.
5) All that we can know is what we can show.

Dear Dim (We are on a first name basis, aren’t we?) you have a serious condition of assertive-itis. The only known antidote is massive doses of humility. But first you must induce vomiting to rid yourself of all that irrational bile you harbor. Then, just maybe, we’ll be able to dialogue. – Sincerely, Albert the Traditional Catholic

sophie

Nowhere357 : They wer'nt intentionally meant to baffle, honestly, they are only a different view of the 'world'. Existence itself is represented as dt (a rate of change exactly as Professor calculus described). The t which represents time is obtained through the availability of dt. With every t can possibly have a dt except at the regress point where t is dt and dt is t (somewhere beyond quantum mechanics). With every dt there is a t, since dt supports the notion of t. (lots more to say but...)


To start I would have to say that classical physics runs off the steam of atomic physics and atomic physics runs off the steam of quantum physics. This is why there are differences between the systems which are hard to reconcile. The t which atomic physics realises through its own dt, becomes the dt under which wee enjoy our daily t. Then the dt of atomic physics (perodic table) is provided by the t of quantum mechanics. If you notice the dt which supports the t of quantum mechanics is not substantially known.

I hope this is a little more confusing.

Nowhere357

You have the heart of a poet, think. Poetry confuses me.

Philosoft

Okay gang, Albert's religion is of zero issue here. Please allow him to respond to the points at hand without adding unecessary jabs at Catholocism. Such arguments are to be taken to GRD if you wish them pursued.

Thanks.

Philo