Fluid Dynamics of Sub-Planck Lengthed Particles

[KALSTER]

I was provided with a link to Einsteins View on the compatibility of an aether with relativity on another site. It has made me think a bit further on the nature of the proposed aether. Einstein says that for the aether to be consistent with Relativity it can not be thought of as existing of individual particles in relation to which motion can be measured. But then how can it have the needed properties for electromagnetic radiation and gravity to exist? Logic dictates that everything is infinitely devisable, for when you choose to stop dividing after any number of divisions you could still in principle divide to yet another level. So if you take it to the limit (pun intended) mathematically, you will be left with a particle with dimensions that tend toward zero.

 

The seperation between these particles would also tend towards zero, but slight variations in these seperations would allow for any kind of 3D dynamics on the makro scale.

 

The question is: How would the fluid dynamics of these particles (strings maybe :?: ) be affected when the particles and seperations are on a sub Planck length scale?

[Edtharan]

Logic dictates that everything is infinitely devisable,

Actually Logic does not dictate this, that is an assumption, not a logical conclusion based off of evidence.

[KALSTER]

Ok. Maybe not everything. If you keep on cutting something into pieces you'll eventually end up with fundamental particles, which, as far as we know is not devisable. Someone on another forum directed me towards the fact that this premise of mine has the essence of Zeno's_paradoxes at heart. As a purely mathematical/philosophical consideration it certainly does hold water. The invention of Calculus has provided a means to circumvent the paradox, but it has not gone away fully. The hypothetical particle system I am investigating here does not need any kind of proof for it to be logically consistent.

[Edtharan]

sub Planck length scale?

The Planck length, according to current understandings of Quantum Mechanics, is the smallest distance possible. This means you can't have a sub-Planck length at all and no particle can have a dimension smaller than the Planck length.

 

The hypothetical particle system I am investigating here does not need any kind of proof for it to be logically consistent.

"Logically Consistent" does not mean "Actually Exists". It is possible to show that Pink Unicorns are logically consistent, but it does not mean that they exist.

 

The error does not lie in the logic, but instead in the initial assumptions that was used to derive the conclusion.

[bascule]

Einstein is describing the fabric of spacetime itself as a sort of ether. That said, general relativity cannot ascribe properties to spacetime on the sub-Planck scale... only quantum mechanics and modern physics inspired by it can do that.

 

That said, different theories within modern physics give remarkably different views of how space looks on scales below the Planck length, but they seem to fall into some distinct categories:

 

Logic dictates that everything is infinitely devisable

 

That space is continuous and thus infinitely divisible is but one of three pictures of how space operates below the Planck length. This, I believe, is how space is modeled by string theory, aside from approaches involving "string bits", which I haven't heard outside of Lee Smolin.

 

That said, Smolin used to paint a rather different picture: space is discrete, composed of chunks which are not divisible. He wrote an entire book on how spacetime is best modeled as an evolving network of relationships, best described in structures called "spin networks" or "spin foam".

 

There exists a third picture, somewhere between the previous two. This involves modeling space as a self-similar structure, somthing akin to a fractal. I can't really speak of theories of this nature as I don't know any of the specifics.

[KALSTER]

I didn't know they moved it here, oh well.

 

"Logically Consistent" does not mean "Actually Exists". It is possible to show that Pink Unicorns are logically consistent, but it does not mean that they exist.

 

The error does not lie in the logic, but instead in the initial assumptions that was used to derive the conclusion.

Very true. That is why it has tie up with observation, experimentation, and verified predictions. Then after this it can make predictions of its own (with the aid of appropriate mathematics) that can be tested. If these pan out, it can call itself a proper theory, while still being inherently falsifiable. The initial assumptions are my attempt to provide a bridge between QM and relativity, explain wave-particle duality, and maybe even bring back logical consinstency to QM (explain H Uncertainty, non-locality, true chaos, etc) by elucidating the exact processes involved.

 

There exists a third picture, somewhere between the previous two. This involves modeling space as a self-similar structure, somthing akin to a fractal. I can't really speak of theories of this nature as I don't know any of the specifics.

You mean other than what i have been considering as an explanation for forces (excluding gravity)? Do you maybe have a link?

[Norman Albers]

I have used, as a common generative idea, the idea of 'vacuum' space as necessarily an availability of polarization, which is to say polarizability. This is certainly 150 years in our understanding, to a point (sic), but for me it yields both localized (and thus possibly quantized) photons, and electrons. Furthermore, we can see gravitation as the scalar thickening, relatively speaking, of the vacuum availability. I figure all the higher energy states (mass or whatever) follow. I guess, to me, the game is to represent what is as the genesis from common field. Now when you figure the Schwarzschild radius of an electron, you're looking at 10E-57 meters. This says to me that things in the small must be modelled basically as having much attitude as far as spin, which is the only thing common in all quantum mechanics, and as far as charge. So far I have no need to go deeper, but what the <bleep> do I know?

[KALSTER]

You know, I have been considering something similar HERE on another forum. Some of the ideas has evolved somewhat while still keeping with the initial premise, which is the possibility that all of the universe (matter and forces) are geometric distortions of an infinite (and lately superfluid) medium.

 

I want to satisfy Einstein's requirements for an aether to be compatible with SR, which is that it can not be thought of as existing of individual particles in relation to which motion can be measured. A primary reference frame if you will. So a way to circumvent this requirement, I thought, was if the particles in question were sub Planck-lengthed. Trying to consider them in relation to anything on the macro scale becomes meaningless. So in that way it can become a truely continuous medium maybe?

Edited May 30, 2008 by KALSTER

[Norman Albers]

Simply describable, as far as we feel we need to, but bearing the necessary potentialities. "A FEW CONSTANTS, AND A FEW GEOMETRIES".

[KALSTER]

Sorry, I don't understand what you are saying?