5Dst (4s + 1t) Dimensional Speculations Continued: A Possible Explanation for Virtual Particles and Quantum Entaglement

Excuse me if the following ideas are dis-pleasing, I simply wish to apply Occam's Razor to these points rather than get out Occam's Sword (currently needed desperately in G.U.T. theories), Occam's Long Sword and Shield, Occam's Mace or Hammer, and hopefully never Occam's Nuclear Weapon. Therefore, I require the services of a speculative Theoretical Mathematical Physicist to help or hinder the following approach if or before it gets much further.

1) Virtual Particles

We know yet are astounded that particles can spontaneously come into being in the vacuum. They live very short lives, thanks to Indeterminacy (Heisenberg's own word for his better known "Heisenberg's Uncertainty Principle", specifically the delta-E times delta-T version).

They briefly violate Conservation of Energy and Mass but not for very long as they are anti-particles to each other, and annihilate soon after birth.

How can this possibly be so?

Well, I will use a 3D (2+1) / 4D (3+1) analogy which can be expanded  to a 4D (3+1) / 5D (3+1) possible reality, which will require little thought in an extrapolatory sense, hopefully.

Think of "Flatland", a 2D space with and 1D of time (2Ds + 1Dt = 3Dst), say: a flat sheet of paper if you will. Imagine a circle intersecting it from "outside" that space (in our own an apparent 3Ds + 1Dt = 4Dst world).

At first we see nothing as the circle approaches. At the moment of contact our Flatlanders see a point. Then they see two points going away from each other. Then as the circle passes the halfway point, they come closer, ending in a point and disappearing.

The circle always remains a circle, the paper always flat, but the appearances are relative, and our poor Flatlanders remain confused until they grow the brains to understand the situation via their version of particle accelerators which in our world we call: "scissors".

2) Quantum Entanglement

The same would hold for QE, as our virtual particles (say an electron and positron) were actually part of the same particle, except the Flatlanders could not see that. Say: the circle is spinning. If so the direction of spin would be equal but opposite for the two "particles" as the Flatlanders measure them. Indeed if they measure the "spin" of one, they instantly know the "spin" of the other.

This may be so simple that's it's wrong, but is it at least possible?

Thoughts?

Best regards,

Steve Colyer

Happy Birthday Martin Gardner !

Martin Gardner of Tulsa Oklahoma turned 95 this month. HAPPY BIRTHDAY, Martin! I can't remember how many times he livened up my many boring study halls in high school thanks to the column he wrote for Scientific American (from 1956-1981).

Here's my favorite picture of him (yes, we were all young once):

Martin Gardner in the US Navy, 1942. Thank you for your Service, Dr. G !

Martin does not in fact have a Doctorate degree (and being the wonderful modest man he is he'd be the first to tell you), but in the hearts of millions he may as well. If he hasn't been awarded an honorary one that would be a crime. In my heart and home he has one, though.

One thing we remember Gardner for especially is turning us on to the game of "Life." What a beautiful diversion and seemingly Mathematics of a "Pure" variety, it actually has usage across a broad number of fields.

Click here to see Gardner's original article in Oct. 1970 Scientific American, and here to play the game. Pay attention to "Gosper Gliding Gun" and see if that doesn't get you excited. I'm actually working on a version of triangles, not squares, and looking for the "gun" in that scenario. Viva la Emergence !

 Gardner has a new book out. Click here to see its Amazon page.

Hey, Dr. Gardner. I have a question for you. We all know that i = the square root of negative one, such that i squared equals negative one. But tell me this:

WHAT is the square root of i ? Tough one, eh?

Oh. OK, fine. But can you prove it?

Well done!

I got that question and proof from a wonderful UK website: Murderous Maths

No, Gardner didn't answer that question or as far as I know had anything to do with that website. I just found out about that site by visiting his Wkipedia entry and following links.

The Cauchy–Schwarz Inequality in a Nutshell (or a "Quarkshell" if you're into that whole Number Theory "Integer" thing)

There are few equations as important in Quantum Mechanics (and therefore Physics in General) as this one from Mathematics. I will present a few bits from its entry in Wikipedia, here, then I'll have a few comments, following:

In mathematics, the Cauchy–Schwarz inequality (also known as the Bunyakovsky inequality, the Schwarz inequality, or the Cauchy–Bunyakovsky–Schwarz inequality), is a useful inequality encountered in many different settings, such as linear algebra applied to vectors, in analysis applied to infinite series and integration of products, and in probability theory, applied to variances and covariances. The general formulation of the Heisenberg uncertainty principle is derived using the Cauchy–Schwarz inequality in the Hilbert space of pure quantum states.

The inequality for sums was published by Augustin Cauchy (1821), while the corresponding inequality for integrals was first stated by Viktor Yakovlevich Bunyakovsky (1859) and rediscovered by Hermann Amandus Schwarz (1888) (often misspelled "Schwartz").

The Cauchy–Schwarz inequality states that for all vectors x and y of an inner product space,
where < . , . > is the inner product. Equivalently, by taking the square root of both sides, and referring to the norms of the vectors, the inequality is written as Moreover, the two sides are equal if and only if x and y are linearly dependent (or, in a geometrical sense, they are parallel or one of the vectors is equal to zero).

... OK, I'm back. If that looks like mumbo jumbo to you, then let me be the first to welcome you back to the wonderful world of Mathematics and Physics from the money fields of Finance, Accounting, and Law, and assure you that although you have a lot of catching up to do, this would be a good place to start.

The reason many of us left Maths + Physics in the first place was due the weirdness of Quantum Mechanics, specifically Indeterminacy also known as Heisenberg's Uncertainty Principle. The Cauchy–Schwarz inequality is key to understanding it.

Uncertainty is taught SO badly to undergrads by Physics professors it is mind-boggling. It got me to quit my boyhood love of Math and Physics, and I'm not the only one. It seems unbelievable that such an important and fundamental thing in its field would be taught so badly, I know, but it's very much taught in a most horrible fashion. Compounding the problem is another unbelievability which I feel is best expressed by Lee Smolin's honest comment that half of all PhD's in Physics aren't sure they believe it, and every crackpot scientific theory also slams it and calls it flat out wrong.

But it is true. It's true, experiment backs it up.

Good luck, and may the Schwartz be with you!
A photograph of actor Rick Moranis as Darth Helmet in Mel Brooks' film, "Spaceballs", reacting to his Physics professor's comment "Shut up and calculate!" in response to Darth's probing question re Uncertainty. The Schwartz was not with him that day.

Augustin-Louis Cauchy (1789-1857)

Victor Bunyakovsky (1804-1889)

Hermann Schwarz (1843-1921)

Werner Heisenberg ( 1901-1976)

YIN, YANG, and YONG

To continue the 3 Universes discussion …

Most of us are familiar with the intertwining paisley shapes that describe the Eastern symbol of duality called Yin and Yang (Male and Female), but what if there were three … let’s call them Yin, Yang, and … Yong (I submit).

Could three intertwining Universes describe what we see in the one we inhabit?

Perhaps.

One basic problem (and solution) would be the difference in gravity between all three. Consider if you will that one has a much stronger gravity than ours, and the other much weaker, and further consider this may be a “relative” thing.

More specifically, if we could magically travel to the heavier Gravitic Universe, then our universe, the one we just left, would be the Lighter Universe because in the Heavier Universe, we would be of "normal" gravity there, relatively speaking. Once in the Heavy-verse, the Lighter-verse (in our Normal-verse) would appear heavier.

How could this be! I don’t know, but it would create a tension between all three Universes. The tension would exert itself then as a “pull” in each Universe from its relatively heavier neighbor-verse, around and around.

How this might manifest itself is “matter” in the form of say, a Higgs boson, the particle that Standard Modelers hope will explain mass, since the simpler versions of the Standard Model cannot account for that. The attraction would exert itself along the 5th dimension (4th Spatial dimension) that connects the Universes. Neutrinos would be pulled with the least strength, Black holes the strongest.

There are two established speculative models in Physics that may assist in understanding this, and which I intend to explore in greater Mathematical detail. They are:

- Randall-Sundrum model (5D Gravity Brane theory)
and
- Ekpyrotic Universe

There are no "problems," only ... "challenges."

Remember that for the rest of your life, please.

Lisa Randall of Harvard University

Raman Sundrum of John Hopkins University

 

Paul Steinhardt of  Princeton University

Neil Turok of The Perimeter Institute

SU(4) Spin(6) Identity Analysis

My current mathematical fetish, I'm currently working on this and will present when I'm finished and not before.

But aw, that's no fun! Click here for a serious hint and here for an impish hint.

If it's not obvious, well here's another clue for you all ...

{{familytree/start}}
{{familytree| | | | |TOE| | TOE=Theory of Everything }}
{{familytree| | | | | |!| | }}
{{familytree| |REL|-|^|-|GUT| | REL=[[Gravity]] | GUT=[[Electronuclear force]] ([[Grand Unification Theory|GUT]]) }}
{{familytree| | | | | | | | |!| | }}
{{familytree| | | | |QCD|-|^|-|-|EWT| | QCD=[[Strong interaction|Strong force]]
[[Special unitary group|su(3)]] | EWT=[[Electroweak force]]
[[Special unitary group|su(2)]] x [[Unitary group|u(1)]] }}
{{familytree| | | | | | | | | | | | |!| | }}
{{familytree| | | | | | | | |WNF|-|^|-|EMF||WNF=[[Weak force]]
[[special unitary group|su(2)]]|EMF=[[Electromagnetism]]
[[Unitary group|u(1)]]}}
{{familytree| | | | | | | | | | | | | | | |!| | | | | | }}
{{familytree| | | | | | | | | | | |EF|-|^|-|MF| |EF=[[Electric force]]|MF=[[Magnetic force]] }}
{{familytree/end}}

... the Walrus was Paul.

No!

I'm not trying to solve T.O.E., The "Theory of Everything", partly because such as a thing may not exist, or it does but our species lacks the IQ to understand it, but if it does anything that gets us one step closer in understanding is a good thing, and I intend to give it my best shot. I strongly suggest we work on a G.U.T. before tackling T.O.E., but it never hurts to look a bit ahead, and try hard not thinking about Gravity ... I don't think that's possible. :-)

I told you about strawberry fields
You know the place where nothing is real
Well here's another place you can go
Where everything flows.
Looking through the bent backed tulips
To see how the other half live
Looking through a glass onion.

I told you about the walrus and me-man
You know that we're as close as can be-man
Well here's another clue for you all
The walrus was Paul.
Standing on the cast iron shore-yeah
Lady Madonna trying to make ends meet-yeah
Looking through a glass onion.

I told you about the fool on the hill
I tell you man he living there still
Well here's another place you can be
Listen to me.
Fixing a hole in the ocean
Trying to make a dove-tail joint-yeah
Looking through a glass onion.

... John Lennon (1940-1980), Accidental Physicist

John Lennon, circa early 1970's, exploring the Universe from the ground up