1,2,3D space

Jun 2016
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The things we rely on for our survival (often) have a 3D nature (Op C),
we have therefore evolved to be able to readily perceive and interpret things in 3D.

Mathematicians (Descartes) later created a formalized description of dimensions (Op A and B).

Later mathematicians recognized that (mathematically) they need not limit themselves to 3D,
Now they regularly consider n Dimensional Branes etc...
 
Mar 2019
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cosmos
@ Woody:
"The things we rely on for our survival (often) have a 3D nature (Op C),"
Yes. Thank you. Next step.
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This semi tramp heard the term "Plank length" many times. I feel it alike a "sub 3D space". People saw what "existence of sub matter" and the concept of "Plank length"/ "sub 3D space" occured?
 

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topsquark

Forum Staff
Apr 2008
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On the dance floor, baby!
@ Woody:
"The things we rely on for our survival (often) have a 3D nature (Op C),"
Yes. Thank you. Next step.
..........................................................
This semi tramp heard the term "Plank length" many times. I feel it alike a "sub 3D space". People saw what "existence of sub matter" and the concept of "Plank length"/ "sub 3D space" occured?
Given some natural constants there are three quantities that we can "derive."
The Planck length: \(\displaystyle L_p = \sqrt{ \dfrac{ \hbar G}{c^3} } \approx 1.616 \times 10^{-35} ~ m\)

The Planck mass: \(\displaystyle m_P = \sqrt{ \dfrac{\hbar c}{G} } \approx 2.176 \times 10^{-8} ~ kg\)

The Planck time: \(\displaystyle t_p = \sqrt{ \dfrac{ \hbar G}{c^5} } \approx 5.391 \times 10^{-44} ~ s\)

The Planck length and time are supposedly the smallest possible values that we can use. ie. there is nothing smaller than these. This obviously doesn't hold true for the Planck mass.

I don't know how many times I have heard that the Planck length is the smallest length scale in the Universe but I want to stress that nowhere and no one has ever derived these quantities in a theory. All they are is a jumble of constants that come out to the right units. There is no meaning given to them by theory or experiment.

-Dan
 
Mar 2019
924
50
cosmos
This case is an outstanding example of abusing of QM, I think. My humble opinion always is space and time dimension is continueos and integral. If some microscopic phenominia make people generate such concept of "sub 3D space", they should use other method to research it rather than doubt if the property of 3D space changes when it decline to such tiny scale.
 
Jun 2016
1,357
687
England
My feeling is also that space (and time) are continuous (with no smallest scale).
It is certainly believable that things can be no smaller that a certain size,
and that two individual things can be no closer that a certain distance (and still be considered as individual things)
but suggesting that space and time themselves are in some way discretised does not seem sensible.

Where I have seen people suggesting that the plank length is in some way a limit
they seem to have been taking the fictional idea of the universe being some kind of simulation on some vast super computer seriously!
This just seems silly to me,
This fictional super computer must then exist in some other universe
in which, presumably, space and time are continuous.
Unless that universe is also a simulation in an even bigger super computer in yet another universe,
and so on into absurdity.

I have seen the idea of a computer simulation of the universe in a couple of SciFi books
But the authors never intended it to be taken seriously...
 
Mar 2019
924
50
cosmos
@ Woody:
“It is certainly believable that things can be no smaller than a certain size..."
Don't be too certainly. The whole cosmos can contract to be a singurality.
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"...and that two individual things can be no closer that a certain distance (and still be considered as individual things)
but suggesting that space and time themselves are in some way discretised does not seem sensible."
Woody seems a gentleman...
Mass Point Dynamics ignores the substantial physical structure. I would rather push your idea one step forward:
"...and that two individual things can be close to a certain distance (and nolonger be considered as individual things)
but suggesting that space and time themselves are in some way discretised does not seem sensible."
I make a vivid analogy below:
When a fat lady got stranded at the door, is it the problem of space(the door) or the problem of object(the fat lady)?
 
Aug 2018
109
4
Neural Network of the Universe
My feeling is also that space (and time) are continuous (with no smallest scale).
It is certainly believable that things can be no smaller that a certain size,
and that two individual things can be no closer that a certain distance (and still be considered as individual things)
but suggesting that space and time themselves are in some way discretised does not seem sensible.

Where I have seen people suggesting that the plank length is in some way a limit
they seem to have been taking the fictional idea of the universe being some kind of simulation on some vast super computer seriously!
This just seems silly to me,
This fictional super computer must then exist in some other universe
in which, presumably, space and time are continuous.
Unless that universe is also a simulation in an even bigger super computer in yet another universe,
and so on into absurdity.

I have seen the idea of a computer simulation of the universe in a couple of SciFi books
But the authors never intended it to be taken seriously...
I wouldn't say, that Plank's lenght is a definitive limit of scale. We just don't need to operate on smaller scales at the current level of knowledge, so we treat it as a basic unit of physical space for our convenience. We simply don't know, how reality looks like at smaller scales - and we won't need to use a smaller unit of space, until we won't fully understand the mechanics of reality at observed scales...
 
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Aug 2018
109
4
Neural Network of the Universe
@ Woody:
“It is certainly believable that things can be no smaller than a certain size..."
Don't be too certainly. The whole cosmos can contract to be a singurality.
....................................................
I will personally send you 100$, if you show me a way to divide/compress/contract any value, other than 0 and end up with 0 at the end of equation. The only way, to get nothing from something, is through subtraction of an existing number...

When a fat lady got stranded at the door, is it the problem of space(the door) or the problem of object(the fat lady)?
Well, it probably depends, if you'll ask the stranded lady, or a nearby observer.... Subjective impression of an objective state - for me that's the heart of relativity...
 
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Mar 2019
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cosmos
@ Gatheringknowledge:
How old are you? Boy...dare to say something in this old pig (俺老猪)' thread?
作为年轻人,学会食古不化和随波逐流, 是没前途的。
 

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Aug 2018
109
4
Neural Network of the Universe
@ neila9876
That's a quite private question, but because today's date is: 2020 02.02 I feel in the mood to admit, that since last 3 days I'm 36...
My problem is, that I'm that kind of an ignorant, who doesn't get, what he does or doesn't suppose to dare. I think, the problem is, that we - the young ones - still consider a civilised discussion, as something healthy. I'm sorry, if my disagreement hurt this old pig's feelings. And of course, I absolutely wouldn't dare to imply, that you might have somekind of a problem with any hypothetical object :)
 
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