Revisiting Kaluza-Klein Theory - Could it explain the Weak Interaction?

[metacogitans]

My personal take on Kaluza-Klein theory is to drop the "Cylindrical 5th Dimension" as an explanation for charge and instead view the intrinsic spinning/rotation of curved spacetime produced by a particle as being responsible for its charge.

 

While trying to visualize the intrinsic spinning/rotation of spacetime curvature around the particle geometrically, it seems the spinning/rotating curvature would have to have a polarity; that is, the spinning/rotation is faster along the "equator" of the spacetime curvature (can't think of what else to call it) and slower towards its poles -- assuming its spherical.

But if it has a polarity, then what's to stop it from flipping upside down and switching its charge? Then I thought that 'switching charge' is exactly what happens during beta decay with up & down quarks..

 

The 'polarity' of a quark flipping would change the orientation of the quarks, causing the spacetime curvature throughout the nucleus to change shape producing a 'ripple' in spacetime, and that 'ripple' might actually be the electron and anti-neutrino emitted by a neutron in the case of beta-minus decay.

 

What do you think?

 

Edit: Another thought - could W bosons actually just be anomalies in the Riemannian geometry of spacetime causing a quark's axis to wobble and possibly causing its poles to flip, causing beta decay?

 

Here's all of what I typed up earlier:

 

- 'Charge' can be conceptualized geometrically as the intrinsic curvature a particle produces in surrounding spacetime. Similar charges produce repulsion between each other similar to how two gears spinning in the same direction kick off each other. 'Rotation' or 'spin' might be what first pops in our head as a way to visualize charge - however, this is difficult to visualize in 3 geometrical dimensions. Assuming the curvature is spherical more or less, we might imagine that the spin/rotation of the curvature has a polarity, and the fluidic nature of spacetime helps to keep that polarity stable. Different hadrons could then be thought of as the various configurations between particles (quarks in this case) causing spacetime curvature with intrinsic spins/rotation and polarity.

 

- The interactions of the Weak Force could be thought of as taking place when the polarity of curvature produced by a quark is challenged; in the case of beta decay, the polarity of a quark's curvature is challenged successfully, thereby changing the orientation of its curvature relative to the other quarks, switching its quark flavor. The loose spacetime curvature resulting from the switch in polarity is what becomes the electron and electron anti-neutrino emitted by the neutron during beta-minus decay. A scary possible implication of this is that in a distant part of the universe, due to manifold geometry, the polarity of up and down quarks in the atomic nucleus could be in a completely different direction - their down quarks could be spinning in the same direction as our up quarks; magically teleporting to this hypothetical distant part of the universe would cause an eruption of weak force interactions, destroying whatever was teleported by turning the matter making it up into something completely different.

 

- For the geometrical explanation to return to gravity, the spacetime curvature produced by particles collectively should incidentally produce gravity at macroscopic scales. Now someone just has to draw what quarks curving spacetime in a hadron actually looks like, translate that drawing into tensor calculus with the curvature from electrons also, put 3.6 x 10^51 of those hadrons with about the same number of electrons in a simulated computer model which would be roughly the same number of hadrons that the Earth has, let it run, and see if stuff gravitates or not. However I don't think there even any supercomputers capable of running that; someone could try to estimate an average of curvature for a large number of particles, but that's what solutions for General Relativity already do and so that'd be back to square one.

 

Edit: Looking up whether or not a supercomputer could run the model or not, apparently there's a supercomputer capable of 10,000,000,000 Million Instructions Per Second, if the calculations performed are done in appropriate fragments instead of trying to emulate real-time, then the simulation should be able to run the equivalent of a few minutes in real-time if the computer is left to run it for a day or two. That's all you'd need to show whether it produced gravity or not - and if there's no inconsistencies between the simulation and real life measurements at any of the scales, it could be called a working unified theory. I don't know if the orientation of spacetime curvature produced by quarks in a hadron can even be described mathematically though; I'm pretty sure it's dynamic, and the quarks carry a unique frequency between each other that would affect the outcome of the simulation but is too much information to be calculated for each hadron in the simulation (I don't even think a computer could accurately simulate the dynamic frequency of even one hadron. It might unfortunately be non-mathematical, or at least uncomputable.

 

Edited January 28, 2016 by metacogitans

[Mordred]

It seems to me from reading the above is that your visualization of particles are bullet like. This isn't correct. Particles are excitations in a field. The field itself can be zero or non zero. The excitation is a deviation from that field. The dimensions are mathematical descriptions of those deviations.

 

This webpage has a decent description of the extra dimensions in regards to Kaluzu Klien. Key note it's the number of coordinates to describe a location.

 

https://plus.maths.org/content/kaluza-klein-and-their-story-fifth-dimension

 

Terms such as axis, poles to flip etc may be the cause of how I read the above.

Edited January 27, 2016 by Mordred

[metacogitans]

Terms such as axis, poles to flip etc may be the cause of how I read the above.

Those were in reference to space-time curvature produced by the particle, not the particle itself.

 

I view fundamental particles as point particles, with the Pauli exclusion principle giving the illusion of occupying space.

Stable composite particles like protons I view as being a grouping of point particles that came within close enough proximity to each other that they're stuck at a scale removed from other particles -- most interactions with other particles affect the composite particle as a whole; its constituents can only be dispersed (as far as manmade interactions go) by forcing another particle into very close proximity, such as what takes place in a hadron collider.

 

I also view a particle's field as separate from the particle, with a particle's field being responsible for the wave-like behaviors of the particle -- the particle itself I view as being static, but capable of interacting with its own field. So I don't share the popular belief in wave-particle duality; I see it as readily explainable geometric phenomenon without all the spooky stage-tactics of pop physics.

 

Everything I ever learned in quantum physics about 'inherent uncertainty in the subatomic world', 'anomalous fluctuations', and 'inconsistencies being a guarantee' turned out to seemingly just be mankind's physical inability to make arbitrarily precise measurements, and the rules of causality are alive and well at subatomic scales (we just can't capture all the nuances behind causality).

 

Also, I think 'Cat State' Qubits are the 'Emperor's New Clothes' of the science world -- I think what they've actually made are just unorthodox transistors which harness wave phenomenon which seemingly defies classic mechanics, but is no more special than using electromagnetic waves to transmit TV signals.

 

If developing transistors that can be more than just on/off is what they want, there are different mechanical approaches to micro-architecture that could be developed and give the desired 'placeholder' effect of having more than one value; the unfortunate thing is no one needs them for anything; reconceptualizing micro-architecture to perform specific tasks has no application that wouldn't be simpler to just use regular microarchitecture for.

 

Optical processing on the other hand could lead to some worthwhile breakthroughs, but no one has the ambition or creative vision to pursue its potential who isn't already happy just settling for what we have now. Like a friend of mine told me, "20 years I've watched optical processing go nowhere". It would lead to technological breakthroughs though. As long as we're still going to see more advancement in the future and haven't actually just finished work on everything, then sometime in the near future we'll start to see things like true analog monitors (no more pixels) with the screen's display working like a projector, except using information stored optically and not film like a movie projector. Oh yeah, optical storage - for storing information made up of electromagnetic frequencies instead of binary. People are so hooked on binary though they can't understand why optical would be superior... I guess they don't like perfect sound and image quality and infinite room for file storage.

 

I've been trying to get my foot in the door and play the role of quacky inventor and bring some WIlly Wonka level game changers to the table, but there's no way to actually do that. I tried getting in contact with a few computer hardware companies asking for an internship and they could see where it goes, but I don't think they took it seriously. Corporate Heads of Research and Development know that it's not economical to change up everything anyways; it's better for the company to just milk the current paradigm, and only apply improvements ever so slightly. Otherwise, I just need money to be able to afford a patent. Pretty sure no one else has thought of optical displays yet; that's a billion dollar idea.. If I could afford a patent for that I'd sell it and use the profits to patent everything else I have in mind. I don't know how picky the patent office is but I bet if my jargon is different than their standards it will be declined and then possibly stolen. Well, at least I typed it here on this forum so there is some proof, if only for brag rights, that I thought it up first.

 

I don't know why my post became about quantum computers instead of Kaluza-Klein theory, excuse the tangent.

Edited January 28, 2016 by metacogitans

[Mordred]

Well unfortunately wave-particle duality is an extremely repeatable experimental certainty. Trying to seperate one from the other is akin to separating energy vs mass.

 

This has even been photographed to an extent.

 

http://m.phys.org/news/2015-03-particle.html

 

Belief is well and good, but unless you back your modelling with the mathematics and experimental evidence does very little good.

 

So please feel free to show how your adapting Kalazu Klein coordinates to your viewpoint of a particle. How does Kalazu Klien provide the necessary degree of freedom to allow particles that don't interact with the weak force and how other particles do so. Please show how this interaction geometric dimension does so. (Mathematics) preferred.

 

Now as your viewing a particle as merely pointlike. (Like a ball). It seems your viewpoint of what spin is also requires clarification. I would suggest looking at

 

https://en.m.wikipedia.org/wiki/Stern-Gerlach_Experiment

 

it should be obvious from this that spin does not mean the particle is spinning like a planet etc. Which from your post above in your gears analogy you appear to describe.

 

 

For example ask yourself this fundamental questions.

 

Why can electrons only have two spin states 1/2 and -1/2? If they were truly ball like point particles they should be able to have as many orientations as a ball. (Take a ball place two dots on opposite sides). How many orientations can you place those dots? (Magnetic poles).

 

This is where the image of spinning point like particles breaks down.

 

An electron is either spin up or spin down. Not spin 20 degrees etc.

 

Another aspect is that it takes an electron or any other spin 1/2 particle 720 degrees rotation to return to its original quantum state.

 

Can you replicate this with that ball?

 

Lastly spin meaning angular momentum never changes for a Particle it never speeds up or slows down. It's an intrinsic property for a particle.

Edited January 28, 2016 by Mordred

[metacogitans]

Well unfortunately wave-particle duality is an extremely repeatable experimental certainty. Trying to seperate one from the other is akin to separating energy vs mass.

 

Not according to this article:

http://www.quantumlah.org/highlight/141220_wave_particle.php

 

"An international team of researchers has proved that two peculiar features of the quantum world – previously considered distinct – are different manifestations of the same thing. The result is published 19 December in Nature Communications.

Patrick Coles, Jedrzej Kaniewski, and Stephanie Wehner made the breakthrough while at the Centre for Quantum Technologies at the National University of Singapore. They found that 'wave-particle duality' is simply the quantum 'uncertainty principle' in disguise, reducing two mysteries to one."

 

 

 

Now as your viewing a particle as merely pointlike. (Like a ball). It seems your viewpoint of what spin is also requires clarification. I would suggest looking at

 

 

Let me clarify I do not view particles 'like a ball'. They can be viewed as point-particles because the Pauli Exclusion Principle allows for them to be viewed that way - as point particles, we escape the confusion of having to explain volume or occupying 'space'; the implications of the Pauli Exclusion Principle explains how particles are able to occupy space for us. No matter how close two particles are to each other, they can not occupy the same location simultaneously, and are therefore inherently 'side by side' at best - since this is a given, how particles occupy space results from their inability to occupy the same location simultaneously.

 

Point particles are just the easiest way to describe them in a few words without typing out an essay trying to give an explanation for what they actually are; whatever they actually are is intangible - we just know they have a relation to other particles. The most we can say really is there is a network of relations which we deduce the existence of particles out of. Kantian Metaphysics also attempted to explain this issue, positing that phenomenon as they appear to an observer are fundamentally dissimilar to the 'Thing In Itself'. It's more a philosophical debate whether it is correct to view fundamental particles as point particles.

Edited January 28, 2016 by metacogitans

[Mordred]

As far as the Pauli exclusion principles is concerned. This involves the wave functions of a particle.

 

"A more rigorous statement is that the total wave function for two identical fermions is antisymmetric with respect to exchange of the particles. This means that the wave function changes its sign if the space and spin co-ordinates of any two particles are interchanged."

 

Fermions being antisymmetric bosons being symmetric.

 

Sounds to me like your trying to change the probability functions in the entirety of QM.

 

 

Your definitely going to need some strong mathematical and experimental evidence for that.

 

 

Let me ask what do you think it means when it's stated a "particle has no internal structure"

https://en.m.wikipedia.org/wiki/Identical_particles

PS we can avoid these confusions with those mathematics.

Edited January 28, 2016 by Mordred

[metacogitans]

As far as the Pauli exclusion principles is concerned. This involves the wave functions of a particle.

 

"A more rigorous statement is that the total wave function for two identical fermions is antisymmetric with respect to exchange of the particles. This means that the wave function changes its sign if the space and spin co-ordinates of any two particles are interchanged."

 

Fermions being antisymmetric bosons being symmetric.

 

Sounds to me like your trying to change the probability functions in the entirety of QM.

 

I'm simplifying what it says, I'll give you that.

"Anti-symmetry of two fermion's total wave function" is tantamount to saying they can't occupy the same location or collide with one another. 'Occupying' and 'same location' aren't terms QM uses. 'Quantum numbers' is QM jargon. For electrons, two electrons can not be in the same orbitals with same angular momentum, with the same energy levels in a subshell, with the same spin angular momentum. I'll be honest that I'm not an expert on what each of those quantum numbers actually mean, but I know enough to know that an electron can not be in the same exact location as another electron because that would mean it shares all the same quantum numbers, which the Pauli Exclusion Principle says can't happen.

 

 

Let me ask what do you think it means when it's stated a "particle has no internal structure"

Was there somewhere in this thread I appeared to be saying the opposite? I thought I made it pretty clear, 'Point Particle', by saying it over and over.

 

I think I found where it sounded like I was talking about particles having structure; In the original post I said 'polarity of a quark flipping' - what I meant was "The 'polarity' of the spinning/rotating spacetime curvature produced by a quark flipping", and I edited that into my original post now. The reason I left it shortened to just 'polarity of the quark flipping' is because if I had to keep retyping "spinning/rotating spacetime curvature produced by a quark" every time that's what I was talking about, the post would have ended up unreadable.

Edited January 28, 2016 by metacogitans

[Mordred]

Fair enough, now that we've cleared some of the misreadings. I'm still uncertain how your proposing Kaluzu Klien in the weak interactions.

 

By the way I did some digging. Turns out this was tried already

 

"In order to unify gravitation, not just with electromagnetism but also with weak and strong interactions, it is necessary to generalise the five-dimensional theory of 5 1 to a higher-dimensional theory (Klein 1926, DeWitt 1964, Kerner 1968, Trautman 1970, Cho 1975, Cho and Freund 1975, Scherk and Schwarz 1975, Cremmer and Scherk

1977) so as to obtain a non-Abelian gauge group. In the five-dimensional case, an Abelian gauge group arose from the coordinate transformation"

 

http://www.het.brown.edu/people/danieldf/literary/eric-KKtheories.pdf

Edited January 28, 2016 by Mordred

[metacogitans]

Fair enough, now that we've cleared some of the misreadings. I'm still uncertain how your proposing Kaluzu Klien in the weak interactions.

With rotation/spin of curved spacetime being used to describe charge, flipping the pole of that rotating curvatures would not only cause a change in charge, but would cause spacetime curvature throughout the hadron to 're-adjust' into a different configuration - and curvature throughout the hadron would presumably be of a slightly different shape, as up quarks have a more significant charge (2/3 instead of 1/3) and are less massive than down quarks.

 

This change in shape means that some of the rotating spacetime curvature was lost, presumably expelled from the nucleus (what I referred to in the original post as a 'ripple' in spacetime). This lost curvature expelled from the nucleus into the space surrounding the hadron might form into the electron and electron anti-neutrino emitted during beta-minus decay.

 

It just seemed to fit together with the weak force - the geometrical assumption that flipping poles not only reverses charge but results in energy expelled from the nucleus (from the curvature changing shape) that's unaccounted for. Changing charges and expelling junk byproducts out of the nucleus sounded like it had to be beta decay, and couldn't be a coincidence.

Edited January 28, 2016 by metacogitans

[Mordred]

You probably didn't see the editted portion where I posted the pdf. The higher dimensions needed came later in string theory. Kaluzu Klein being a precursor.

 

Even then the mathematical side of Kaluzu Klein is well detailed.

Edited January 28, 2016 by Mordred

[metacogitans]

A cylinder-shaped 5th dimension present at every point in the universe seems pretty gimmicky to me.. It also defeats the point of trying to unify General Relativity with Electromagnetism in a way that's wholly geometrical.

Why even have a 5th dimension to explain charge? Charge might as well just be quantized, since that's basically what it's trying to do but taking unnecessary middle steps.

 

Besides that, the predicted measurements using Kaluza-Klein Theory with a 5th dimension were way off from observed measurements, which is why it was scrapped.

 

The original goal of unifying two forces geometrically is what inspires me.

 

On the topic of string theory, it seems too similar to just inventing a new dimension each time you need to explain-away something. It's too much fantasizing about multiple dimensions and not enough practical science.

[Mordred]

Dimensions in these cases is analogous to coordinate systems or degrees of freedom.

 

lets take a simple example. Space Dimensions is 3, then add coordinate dimension of time. Now take each particle interaction. Charge, color, flavor, assign them a seperate coordinate system. The first spacetime dimensions being well described by GR. However the interaction coordinates may be better represented by rotational symmetry, or translational symmetry etc.

 

Each dimension represents different coordinate systems or degrees of freedom. Not all coordinate systems need to be like flat sheets of paper. Some can be like a cylinder, others rotational

 

 

This is essentially how Kalabu Klein works.. he describes gravity by the usual 4d dimensions which does well for energy/momentum but shows the symmetry to the electromagnetic degrees of freedom via a coordinate system for the electromagnetic.

 

(Loosely put) it's simply adding another degree of freedom into the metrics of GR

 

Ppl get confused on the dimension elements Fundamentally they are merely representative on added degrees of freedom within the mathematics

For example start with gravity 4d

Add charge+2, color+3, flavor+3.

 

Wow 12 dimensions, remind you of anything? With Kaluzu you can lower charge to 1 dimension =11

Edited January 28, 2016 by Mordred

[metacogitans]

Dimensions in these cases is analogous to coordinate systems or degrees of freedom.

 

lets take a simple example. Space Dimensions is 3, then add coordinate dimension of time. Now take each particle interaction. Charge, color, flavor, assign them a seperate coordinate system. The first spacetime dimensions being well described by GR. However the interaction coordinates may be better represented by rotational symmetry, or translational symmetry etc.

 

Each dimension represents different coordinate systems or degrees of freedom. Not all coordinate systems need to be like flat sheets of paper. Some can be like a cylinder, others rotational

 

 

This is essentially how Kalabu Klein works.. he describes gravity by the usual 4d dimensions which does well for energy/momentum but shows the symmetry to the electromagnetic degrees of freedom via a coordinate system for the electromagnetic.

 

(Loosely put) it's simply adding another degree of freedom into the metrics of GR

 

Ppl get confused on the dimension elements Fundamentally they are merely representative on added degrees of freedom within the mathematics

If properties like charge, color, spin, etc.. don't cohere with 3 geometrical dimensions, why not just quantize them? Why bother adding more sets of coordinates if they don't cohere with the 3 geometrical and 1 time? What's the benefit?

 

Furthermore, why did everyone just give up on trying to fit them into 3 geometrical dimensions and 1 of time?

 

I understand what you're saying though; instead of trying to cram charge, color, spin, etc. into the first 4 dimensions which are already tedious to calculate, you can just add a fresh set of coordinates and save yourself some time. But what's the benefit of having coordinates for them instead of just leaving them quantized? Why are coordinates needed?

Edited January 28, 2016 by metacogitans

[Mordred]

We describe all particle interactions via coordinates. However some coordinate changes are better described by different symmetries.

 

On unification metrics it's sometimes more convenient showing those.

 

For example the SO(3.1) Lorentz group alone has 255 degrees of freedom. However this reduces down to 11 partial derivitives. That's just GR alone. Now add the various charges.

 

The mathematics can get mind boggling. Figuring out how to simplify these possibilities of the numerous interactions is highly sought after.

 

Twistor theory is one of the better adept at it from what I understand, though I understand little of twistor theory except in principle

https://en.m.wikipedia.org/wiki/Dimension

 

Although mathematically intense this resource I often find handy

 

http://arxiv.org/abs/hepth/9912205: "Fields" - A free lengthy technical training manual on classical and quantum fields

I forgot to add if you add up all the interactions of the standard model elementary particles you have 196 degrees of freedom. Simplifying and reducing this number is highly sought after. ( though that number will vary depending on which gauge theory your using..SO(5), SO(10) etc

Edited January 28, 2016 by Mordred

[ajb]

Mordred has already pointed out that people have looked at non-abelian versions of KK theory, I will also point out that super versions have also appeared in the literature (I forget who and when).

 

Anyway, the bottom line is, as always, build some models and show us how the weak interaction is related to KK theory.