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About time for elementary particles

I assume some knowledge of the axiom of choice.
Let us start the set theory ZFU (with urelements, non sets)
with two infinite sets of urelements U1 and U2.
Mr Andreas Blass pointed out that their union is U, the usual
set.
Let physical space at the level of elementary particles be U1
and time be U2.
As U2 is not linearly ordered, there is no backwards time
causality.
In quantum mechanics, there are waves which go backward time,
see :
http://www.npl.washington.edu/AV/altvw08.html

But if U2 is time and is not linearly ordered, there is no
traveling backward time.
So, our notion of causality is less jeopardized than with backward time
causality.

May be using U1xU2 for space-time would be still better.

My idea is that Dedekind cardinals are cardinalities for space and for time.
For instance, the time ellapsed since 36 Big Crunches/Big Bangs ago is a
Dedekind cardinal.
The cardinality of the physical space of the previous universe (before the
Big Bang) is a Dedekind cardinal.

The negation of the axiom of choice is really true because it can be
applied in physics.
(Reminder : about space for elementary particles
We apply set theory with urelements ZFU to physical space, we consider
locations as urelements, elements of U.
Ui is a subset of U with number of elements n.
XiUi is the infinite cartesian product and a set of paths.
Let us consider the set of paths of all elementary particles-locations
which number is n.
If n is greater than m in CC(2through m), countable choice for k elements
sets k=2 through m, the set of paths will be the void set.
So, physical space would become void, the universe would collapse and a Big
Crunch would happen.
But the matter would have to go somewhere and indeed the Big Bang happened.
So, n is indeed greater than m.)
Adib Ben Jebara.
http://www.freewebs.com/adibbenjebara

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Does some prediction or explanation of observation/experiment follow from these thoughs?

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Surely you're joking, Mr. Zaphir smile


"Time is what prevents everything from happening at once" - John Wheeler
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Originally Posted By: rowenur
...Surely you're joking, Mr. Zaphir...
Maybe yes, maybe not - but it wasn't question for you.

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Oh, I see. I do beg your pardon, Mr. Zaphir.


"Time is what prevents everything from happening at once" - John Wheeler
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For Zephir,
An interpretation about space and time in quantum mechanics

There was a repeated experiment where at first, two protons are
joined and of opposite spins.
Then, the second is taken far away, and it is acted upon the first
to modify its spin.
The second proton will change its spin to keep it the opposite
of the spin of the first.
For further details :
http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_24.html#2.4.1

Now, if you will assume with me that we can apply the set theory ZFU
to physical space, U (urelements)) being physical space, you will see
that we get an interpretation of the experiment.

Indeed, as it is not possible to define a usual distance in U, the second
proton will not be any more far away from the first.

Also, if we consider time to be U, we cannot say that the protons
were separated a long time ago and that there should be no more
influence. [...]
There was another repeated experiment with a photon, expected to go one
way, going both two quite separated ways.
Here, again, if we assume something else about space, the two ways
would be not that much separated.
Regards,
Adib Ben-Jebara.

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Originally Posted By: Adib Ben Jebara
if ...we can apply the set theory ZFU to physical space, U (urelements)) being physical space, you will see that we get an interpretation of the experiment..
Maybe I'll see, maybe not. This is exactly the point, which requires some more detailed explanation for me. I can present my interpretation of F-C experiment in detail - but this is your topic and your theory - so I presume, we should hear the explanation of yours here.

Richard Feynman: "The first principle is that you must not fool yourself -- and you are the easiest person to fool".

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About every day life of the elementary particles (simplified)

This is what I think about some of elementary particles behavior,
avoiding much math.

The elementary particle jumps from one location to another with
the set of locations discontinuous and not linearly ordered.
What is far with the standard distance can be near with the jumps.

So, two particles can have an action one on the other after having
taken a "distance" one from the other.
The two particles could be within a limited number of jumps one from
the other.
Therefore, there could be an unexpected correlation.

Time itself is discontinuous and not linearly ordered.
So, there are no causality relationships unless time is ordered by
the observation set up.
Help is welcome for deducing other consequences of this behavior.

Adib Ben Jebara.

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Hi, Adib

This may be hair-splitting, but the particle itself doesn't jump, only the information about the particle. Does that make a difference to your ideas?

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Originally Posted By: redewenur
...the particle itself doesn't jump, only the information about the particle...
The only problem remains, how to distinguish a particle from the information about it.. wink This is how the particle undulates in space by classical quantum mechanics (i.e. by numeric solution of Schrodinger equation) (it requires Java installation)



You can understand the AWT interpretation of quantum wave by using of the interactive DHTML applet herein. The motion of particles isn't jumpy, but it's not completely continuous, too. It's a mixture of jumps and undulations from certain perspective. It can be interpreted as a fast repetitive condensation and evaporation of density fluctuations of Aether.

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Hi,
There is uncertainty in what you wrote.
For me, the particle jumps.
Anyway, it should not make a difference to space and time not being continuous.
Adib Ben Jebara.

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Originally Posted By: Adib Ben Jebara
there is uncertainty in what you wrote. For me, the particle jumps.
This uncertainty follows from generalization of uncertainty principle. By my opinion the particle undulates in hidden dimensions - this makes the undulations choppy. You can imagine it as regularly rotating rod when projected to 2D ground-glass - this motion projected on ground-glass will not appear smooth because of partial lost of information about motion. The AWT considers all reality as a result of harmonic motion in infinite number of dimensions projected into 3D space (the similar concept arises from holographic model of Universe). We can even say, the particle isn't undulating itself, just the environment density is waving, so we are observing the location of particle in motion. All these stances are mutually dual and the most probable truth is somewhere inbetween.

Therefore the question isn't, whether the particle jumps in 3D space or not - but what we can deduce from this concept. If we can deduce nothing specific - it plays no role, whether the particle jumps or not and it has no meaning to waste time in discussions about it. Instead of this, the discussion about such concept becomes a religious war, where posters are holding their positions just from psychological reasons.

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Adib

Originally Posted By: Adib Ben Jebara
Hi,
There is uncertainty in what you wrote.
For me, the particle jumps.
Anyway, it should not make a difference to space and time not being continuous.
Adib Ben Jebara.

I suppose it makes no difference whatsoever to the falsifiability of your theories. We know that experimenters transfer quantum information from one particle to another by first establishing a causal relation, or entanglement, between them; but no quantum physicist, as far as I am aware, has ever claimed that a particle has been 'teleported' in the classical sense, i.e., moved to another location at superluminal velocity. Moreover, they deny that it's possible.

Insofar as I understand your ideas, which I confess is not very far, I respect your 'out of the box' thinking - it is interesting - but if you refute experimentally verified quantum theory and relativity theory without providing substantiating evidence, your theories will lack credibility.

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Originally Posted By: redewenur
...no quantum physicist...has ever claimed that a particle has been 'teleported' in the classical sense, i.e., moved to another location at superluminal velocity..
We shouldn't mix different concepts. The entanglement doesn't require the particle share some information by superluminal speed - they simply containing it already. We can illustrate such situation by lava lamp model, for example:

If we create a surface undulations on the some oil droplet inside the lava lamp and separate such droplet into two smaller ones, the surface undulations doesn't disappear. Both the resulting droplets will undulate "at phase" and if we connect them occasionally, the original surface vibrations will be restored again. By such a way, both oily droplets "knows" about it's entangled member at the distance, the surface mode of vibrations serves here as the simple analog "state memory".



With compare to entanglement phenomena, the concept of quantum evaporation and condensation is conceptually analogous to repetitive condensation and re-evaporation of water droplets in the rain. The people are having a problem to understand the Aether concept due the immense density of vacuum, because our Universe appears to be formed by extremely dense interior of dense star or black hole. Whole AWT is just an mechanical extrapolation of common processes to huge mass/energy density.


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I wasn't addressing you, Zaphir, I was addressing Adib...

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Originally Posted By: redewenur
I wasn't addressing you, Zaphir, I was addressing Adib...
I know, I'm just trying to demonstrate, some Adib's ideas aren't wrong, as they can be derived from Aether concept as well. They're forming an insight from special perspective. Even Einstein has talked about "spooky action at distance", after all - and mechanical concepts of vacuum aren't very new, too. So we can say, the entanglement is the result of mechanical action at the distance without problem - the only problem is, what we can deduce from such insight, if we are handling it so vaguely. We should describe the situation as exactly as possible and this requires a good working knowledge of reality. The knowledge of math theories wouldn't help you in imagination, if you don't know about their results in detail. I'm pretty sure, most of theorists never understood their theories, simply because they never attempted to draw their solution in 3D.

The common problem of contemporary scientists and many physical enthusiasts is, they're just describing the same reality from many different perspectives via abstract models, so they're not willing to understand, they're describing the same things due the priority concerns. As the result, they're not willing to collaborate, even though their concepts are apparently dual (the string and LQG theorists as an example). I'm sure, we can understand the physics much more effectively, if we would focus to the common/dual parts of theories, not to their differences.

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redewenur,
Zephir,
You have knwledge but in research you have to look at the things differently even when mentionning experiments because experiments could have more than one interpretation or even conclusion.
How can you be sure that space and time at the level of the elementary particles are continuous ?
Adib Ben Jebara.

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Originally Posted By: Adib Ben Jebara
..experiments could have more than one interpretation or even conclusion..
Well, exactly. If some experiment can lead to the more theories, it means, all these theories are valid as well from their perspectives. For example, I can describe the gravitational lensing both from relativity perspective (where the space deforms and the light speed remains constant), both from Aether theory perspective (where the space metric is fixed and the light speed doesn't remain constant). And both these models are correct, in fact - they just describing the reality from different perspective (inner/outer in particular). Therefore to discuss differences between theories has no meaning - we should target to their similarities, to their common message which can lead us to the more general level of understanding. It requires to cooperate, not to fight.



Originally Posted By: Adib Ben Jebara
..How can you be sure that space and time at the level of the elementary particles are continuous?..
We cannot, but the space continuity concept is necessary with respect to causality. We should consider, every piece of space between particles is filled by density gradients of another particles, recursively to avoid the "spooky action" at distance. At the case, the difference between densities/sizes of particles is large, it can lead to the illusion of empty space. But for example the wave character of energy spreading is demonstrating, here must be some "elastic" environment. Without it the elastic properties of common matter could be explained by elastic properties of space, which isn't apparently correct. The elasticity and wave spreading are fundamental attributes of common matter, because their constants (permitivity, permeability...) are depending on properties of particles, not the space, which fills the gaps between particles. The space as such has no attributes, which could be changed from experiment to experiment.

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Originally Posted By: Adib Ben Jebara
....How can you be sure that space and time at the level of the elementary particles are continuous?....
The point of recursive particle concept of AWT is, it can explain the discontinuous character of space-time (which we can really observe at Planck scale and I've no problem with this) by continuous character of underlying sub-space. And this insight remains compliant with concept of nested rotators in Hilbert space, as postulated by matrix interpretation of quantum mechanics. It has even its direct mechanical analogies: a nested condensation inside of dense supercritical foam/fluid, where every droplet is formed by density fluctuations of another droplets.



The behavior of such system is nontrivial and it's hard to describe mathematically, I admit - but it's still imaginable a we can confront it with human scale experiments and cosmological observations. At least three basics plural models/concepts can be used for its description: the nested vortexes, the nested foam and the nested particle clusters concept.

Each approach brings a specific insights and predictions - but in fact, they're all mutually equivalent each other, although their math differs significantly. And of course, they can be combined freely. They enable us to understand, why the vacuum appears so ambiguously with respect to liquid-gas, vortex-wave, space-time, energy-mass, particle-wave, relativity-quantum mechanics, quantum strings - quantum loops etc.. dualities.

We can discuss them later in details, but we should begin with the definition of space and time concepts first, as they're most relevant for further understanding.

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It is rather impressive as you write about so many things, but it
is not very clear. Why not moderate the scope of the discussion so that people may follow better ? Thanks.
For me, space and time are defined as sets of urelements which
are in set theory with urelements (non sets).
They are defined mathematically.
And the "experiment" I refer to to know whether it fits reality is the Big Bang (which happened as forecasted by my "theory").
Adib Ben Jebara.

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Originally Posted By: Adib Ben Jebara
...space and time are defined as sets of urelements...
Hi, Adib. You should be always prepared to assign a number of dimensions and/or space-time metric to these sets. Is it principally possible? If not, then the set of "elements" cannot serve as a model of space or time, because it cannot comprehend all physical attributes of these concepts, assigned so far by another theories. By another words, you should use the definitions of space and time, which are backward compatible with existing concepts/definitions, so they can be reconciled with them on the background of correspondence principle.

What the urelements are supposed to be from physical point of view? Can we derive something testable from such assignation?

From Aether Wave Theory perspective the definition of space and time is very simple. The causal energy spreading can occur only along surfaces of Aether density gradients in transversal waves. After then the space dimensions are the directions, along which energy spreading occurs. And the time dimensions are the rest directions, which are perpendicular to space dimensions.



For example, the water surface can be considered as a local space-time for mechanical wave spreading. After then the space dimensions are the directions plan-parallel with water surface and the time dimension is the direction perpendicular (normal) to these directions, i.e. the direction of water surface gradient itself. It's easy to comprehend definition and it brings surprisingly high number of testable insight/predictions into Aether model. You can try to explain your definition of space/time on background of my definition, as I suppose, the physically relevant definitions should be always compatible.

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There are at least two posssinilities for dimensions, I am still
thinking about if we should have U1xU2 for space and time or
U1xU2xU3xU4.
As for urelements, they are "objects" which do not contain anything and which are undistinguishable, which fits space and time.
As for the lack of compatibiliity with other theories, it would be seen by critics.
May be you can help.
Adib Ben Jebara.

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Originally Posted By: Adib Ben Jebara
...as for elements, they are "objects" which do not contain anything and which are indistinguishable, which fits space and time...
I can see nothing very useful in this concept. The Aether Wave Theory (AWT) is using so called the "unparticle concept", which was proposed independently here. But the Unparticle physics is still nothing, what cannot be derived from common particle physics directly - it's just another view to it.

The AWT is using a following trivial insight: everything what we can see from the gas aren't the particle itself, but a density fluctuations of it. It means, during condensation of dense gas, we couldn't never see its particle itself, just a density fluctuations. And the AWT idea is: WHAT IF every particle, which we can see is just a density fluctuation of another particles, i.e. without any exception? It means - here's no upper or lower limit of particle size, every particle can be considered as a dense cluster of another particles: from gravitons to whole observable Universe itself. It means, here are no "fundamental particles" - simply because here's no meaningful physical reason to have some. Everything can be explained at the scope a few adjacent particle generations, which we are living in and it has no mean to ask about limits of such structure - simply because we would be required to explain them, after then.

Only practical limits (for example the speed of energy spreading) limits the size and the fractal dimension of the observable structures. Here are another limits given by curvature of the space-time, mediated by such structure: after some number of generation the space perceived would become formed by its own distant fluctuations (a sort of Uroboros or Klein bottle model) by the similar way, like the space formed by nested foam (i.e. foam, where each bubble is formed by another bubbles, recursively). But these small bubbles aren't small, in fact - they're just a very distant one.

In this model the observable structures are of limited size and they're created by itself. A practical realization of such system can appear like interior of black hole, which contains another black holes, recursively.

Motto: "if you don't about reason of reasons, don't ask about them".

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Particles theory is the challenge not unparticle theory which does not explain well particles and is not even clear enough.
Adib Ben Jebara.

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Originally Posted By: Adib Ben Jebara
..unparticle theory which does not explain well particles and is not even clear enough...
The unparticle physics was "guessed" as an ad-hoc theory by the same way, like LQG or string theory, but from AWT perspective they're all steps by correct direction, because the scale invariant density fluctuations in heavily compressed particle matter are both spin loops, strings and unparticles at the same moment.

The AWT is based on the assumption, the Universe is completely random, but the number of states is limited due the limited speed of information (transversal wave spreading), so that the randomness of the directly observable system is always violated due the finite number of states in it.

It's like the observation of set of infinite many numbers - we have no chance to observe some regularity in it. But at the moment, the number of states in the set is limited, we can observe a multinomial distribution between similar members. It's like the throw of dice: if the dice would be of infinite wall number, we cannot detect any regularity between individual throws. But when the the number of walls will be limited by polyhedra, we cen observe a sequences of multinomial distribution: ...1101011010100011010111... We can observe "something".



For example, the system of colored points, where the colors are limited by finite set can be never fully homogeneous: it exhibits a colored spots: a fluctuations of color density. And these fluctuations are scale invariant, they're behaving like "unparticles". It doesn't matter, in which scope these colors spots will be averaged: they'll always exhibit the color spots of the same distribution,

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