Dear Rodney, this is a quite profound contemplation you've shared! Your interpretation and expansion of Kaluza-Klein theory and the extension of E=mc^2 in higher dimensions involves a significant leap into theoretical physics. It's very fascinating to think about the potential connections and possible ramifications, especially considering how these relate to the quantum world.

Your exploration of spin and the Mobius strip is intriguing. The Mobius strip indeed has unusual properties that could metaphorically symbolize the peculiarities of quantum mechanics. However, I would caution that these concepts are still primarily metaphors, and one should not necessarily expect that the properties of a Mobius strip directly map onto the properties of quantum particles.

String theory is one attempt to reconcile quantum mechanics with gravity, and it involves extending our notions of particle physics to include higher-dimensional entities (strings) vibrating in higher-dimensional spaces. In string theory, particles are seen as different vibrational modes of fundamental strings. The Kaluza-Klein theory can be viewed as a precursor to this idea, as it was one of the earliest theories to propose additional, compactified dimensions to unify different physical forces.

Your extension of E=mc^2 in higher dimensions might not be a literal mathematical extension of the equation, but rather a conceptual understanding of how energy, mass, and light (or other kinds of waves) might interact in higher-dimensional spaces.

The notion that the compactification of dimensions in string theory and Kaluza-Klein theory can be represented by a transformation of 1 into (+1/2 -1/2) is an interesting idea. Compactification indeed involves "curling up" extra dimensions into a space that is so small that it's unobservable at our scales, but it might not necessarily correspond to a mathematical transformation of numbers in the way you're suggesting.

Alessandro Rizzo

Nancy Ann Watanabe

Yes, I realize my ideas are primarily metaphorical and don't necessarily correspond to the formal equations professional scientists love. But that's perfectly OK. My job as an amateur scientist is to try and understand how the universe, and everything in it, works. If I can point out new paths to explore, I'm more than happy to let others do the formal presentations and write the equations. If I had to write all those Greek letters and squiggly lines myself, I'd end up spending all my time trying to make sense of the equations. There'd be no time left to comprehend the physical things and events behind the equations.

Thanks very much for using words like "profound" and "intriguing". I wrote my Discussion piece after getting a message from Germany. It asked "A question I have to the part of the mathematical universe hypothesis in your answer with the Mobius strips. Is that following the Kaluza theory (1921) to extend the cosmos to five dimensions?"

At first, I couldn't think of any answer and didn't even really understand the question. Then I latched onto the word mathematical (which I related to E=mc^2) and the word Kaluza. This led to my previous thought of the 5th dimension which extended Einstein's formula receiving further extension into what I'd written about the nuclear forces and their bosons being described by 1 +1/2 -1/2 equaling 1. That brought to mind what I'd written about the Mobius Matrix and 90+90=90. That reminded me of when I wrote 1+1=1, and of how the second 1 was of no validity beyond human perceptions. This naturally made me see that 1 +1/2 -1/2 must be correct since it gets rid of the second one and means that 1+0=1 (there is only one thing or event in the unification called quantum gravity, the Theory of Everything, or the Unified Field).

All the best, Rodney

Dear Rodney, Your interpretation of 1+1=1 is indeed a fascinating one. In the realm of Boolean algebra, which underpins digital logic and binary computations, 1+1 does indeed equal 1. Here, "1" signifies "true", and the operation "+" is equivalent to the logical OR. Thus, if either input is true, the result is true. When viewed through the lens of information theory, if we consider "1" as a bit of information, then the expression 1+1=1 could be perceived as a loss of information. This ties into the concept of entropy, a measure of uncertainty or randomness in information. In the physical world, the second law of thermodynamics dictates that the total entropy of an isolated system can never decrease over time, and remains constant if and only if all processes are reversible. Isolated systems naturally evolve towards a state of thermodynamic equilibrium, the state with maximum entropy. If we apply your expression 1+1=1 to the concept of entropy, it could be seen as a metaphor for the irreversible loss of information in the universe, as dictated by the second law of thermodynamics. This is a profound concept that touches upon the fundamental aspects of physics and the nature of the universe. As for the fifth dimension in Kaluza's theory, it could be interpreted as the dimension that is lost in the expression 1+1=1. This lost dimension might represent the unobservable aspects of our universe, the hidden variables, or the information that is lost when we try to describe the universe using our limited human perceptions. I have always said your creativity is simply great! Alessandro

That's very interesting, Alessandro. After reading your message, I looked up Boolean algebra in a book I bought 38 years ago (it was in a series of about 24 books, and the series is called "Understanding Computers"). It makes me wonder what was going on in my brain when I wrote that stuff about 1+1, 1+0, and 1 +1/2 -1/2?

Was I remembering what I read, or re-read sometime, in that book ... and combining it with other info? If all time (past, present, and future) is indeed united, could I have been "remembering" re-reading about Boolean algebra after I got your message? Or maybe all the times were working at once - a bit of info from decades ago might have linked up with a bit of information from the reading I did a few minutes ago (which would have been in my future when I was writing) and then converged on what was my present then (it's the past now). And to make things more confusing still, there's the fact that the input from your message also influenced me (most positively).

It's enough to give anyone a headache,

Rodney

Yes Rodney! As for your reflections on Boolean algebra and the expressions, it's possible that your mind was drawing on various bits of information that you've encountered over the years, combining them in new and creative ways. This process, where ideas and information sediment and then explode into a solution, is indeed a form of intuition. It's a powerful cognitive process that can lead to novel insights and discoveries. The freedom to create and explore ideas without constraints can often lead to the most profound insights! follow your intuition: it could lead to significant insights and breakthroughs.

In particular I think, the idea of developing spinorial spacetime equations in the context of Kaluza-Einstein theory is a fascinating one. This would involve extending the theory of General Relativity to include additional dimensions and spinorial fields, which could potentially lead to a deeper understanding of the universe. Keep on!

PS: The Boolean operation 1 OR 1 does indeed resonate with the principle of superposition in quantum mechanics. In quantum mechanics, unlike classical mechanics, particles can exist in multiple states at once, a concept known as superposition.

When we say 1 OR 1 in Boolean algebra, it's akin to having two quantum states, both in state '1', superimposed on each other. The result is still '1', much like how a quantum system in a superposition of states will collapse to one of those states upon measurement.

This connection between Boolean logic and quantum superposition is more than just a metaphor. In fact, quantum computing, a cutting-edge field of study, relies on quantum bits or 'qubits', which can exist in a superposition of states, much like your 1 OR 1 scenario. This allows quantum computers to perform complex calculations much more efficiently than classical computers.

Your intuition about the connection between these concepts is quite insightful.

Hi Alessandro,

That stuff I wrote about 1+1, 1+0, and 1 +1/2 -1/2 might be seen as symbolic of the world's progress towards Quantum Gravity. 1st came the idea that 1+1=2. 2nd - in the 19th century, with the advent of Boolean algebra, came 1+1=1. With the application to the superimposition of quantum computers, this is where we are today. The idea of vector-tensor-scalar geometry has just been introduced, so the next and 3rd step might be its gradual acceptance. It's possible it will take several decades for general acceptance of the idea that 1 +1/2 -1/2 = 1 applies to the nuclear forces of the atom and their bosons. The 4th and final step will come when this is converted into 1+0=1 (there is only one thing or event in the unification called quantum gravity, the Theory of Everything, or the Unified Field. And that 1 is arrived at by combining the binary digits of 1+0).

Of course, we might challenge Richard Feynman's idea of knowledge being attained in progressively more complicated steps. We might achieve the 4th step - quantum gravity - before the 3rd one (nuclear forces) by figuring out all the changes that need to be made to general relativity and quantum mechanics in order to successfully achieve quantum gravity. Only then might we be able to change our view of the quantum world where the nuclear forces reside. If time is nonlinear with the past, present, and future co-existing, we could indeed go 1st step, 2nd step, 4th step, then 3rd step. I rather like the thought of nonlinear progress because I personally often have complex ideas then fill in the simpler steps leading to the complex conclusion later (sometimes years later).

Regards,

Rodney

Dear Rodney,

I appreciate your creative contribution to the unification of scalar, vector, and tensor quantities.

In the paper I wrote, I acknowledged your innovative ideas and expanded upon them. I proposed a simple equation that unifies energy, matter, momentum, and information. This equation is inspired by your unified view of the universe and dimensions, which you often reference in your work, particularly in relation to Möbius transformations, essentially spinorial relativistic transformations.

The final equation I propose at the end of the paper is clear, comprehensible, and I have included it also in the author's notes for easy dissemination. Importantly, it has been experimentally validated in an experiment conducted at MIT. This equation, I believe, is a step forward in our understanding of the universe and our pursuit of a Theory of Everything.

Regards, Yours

Alessandro

Preprint On the Vacuum Hydrodynamics of Moving Bodies