I think every physicist, whether real or amateur or crackpot, goes through the exercise of trying to work out a geometry for the field that particles reside in. This is the heart of many issues, such as why is there a particle zoo and how to reconcile quantum theory with relativity, either special or general. There are many ways to approach this question–experimental observation, mathematical derivation/generalization, geometrical inference, random guessing–all followed by some attempt to verify any resulting hypothesis. I’ve attempted to do some geometrical inference to work out some ideas as to what this field would have to be.
Ideas are a dime-a-dozen, so throwing something out there and expecting the world to take notice isn’t going to accomplish anything. It’s primarily the verification phase that should advance the block of knowledge we call science. This verification phase can be experimental observation such as from a collider, mathematical derivation or proof, or possibly a thorough computer simulation. This system of growing our knowledge has a drawback–absolute refusal to accept speculative ideas which are difficult or impossible to verify (for example, in journals) can lock out progress and inhibit innovation. Science investigation can get hide-bound, that is stuck in a loop where an idea has to have ultimate proof, but ultimate proof has become impossible, so no progress is made.
This is where the courageous amateur has some value to science, I think–they can investigate speculative possibilities–innovate–and disseminate the investigation via something like a blog that nobody reads. The hope is that pursuing speculative ideas will eventually reach a conclusion or path for experimental observation that verifies the original hypothesis. Unlike professional scientists, there are no constraints on how stupid or uninformed the amateur scientist is and no documentation or credentials that says that science can trust him. The signal-to-noise is going to be so high that it’s not worth the effort to understand or verify the amateur. The net result is that no progress in our knowledge base occurs–professional scientists are stuck as publishable ideas and proof/verification become more and more difficult to achieve, but no one wants to bother with the guesses of an amateur. I think the only way out is for an amateur to use his freedom to explore and publish as conscientiously as he can, and for professionals to occasionally scan amateur efforts for possible diamonds in the rough.
OK, back to the title concept. I’ve been doing a lot of thinking on the field of our existence. I posted previously that a non-compressible field yields a Maxwell’s equation environment which must have three spatial dimensions, and that time is a property, not a field dimension as implied by special relativity. I’ve done a lot more thinking to try to pin down more details. My constraints are driven primarily by the assumption that this field arose from nothing (no guiding intelligence), which is another way of saying that there cannot be a pre-existing rule or geometry. In other words, to use a famous aphorism, it cannot be turtles all the way down–the first turtle must have arisen from nothing.
I see some intermediate turtles–an incompressible field would form twist relations that Maxwell’s equations describe, and would also force the emergence of three spatial dimensions. But this thinking runs into the parity problem–why does the twist obey the right hand rule and not the left hand rule? There’s a symmetry breaking happening here that would require the field to have a symmetric partner that we don’t observe. I dont really want to complexify the field, for example to give it two layers to explain this symmetry breaking because that violates, or at least, goes in the wrong direction, of assuming a something emerged from nothing.
So, to help get a handle on what this field would have to be, I’ve done some digging in to the constraints this field would have. I realized that to form particles, it would have to be a directional field without magnitude. I use the example of the car seat cover that is made of orientable balls. There’s no magnitude (assuming the balls are infinitely small in the field) but are orientable. This is the basic structure of the Twist Field theory I’ve posted a lot about–this system gives us an analogous Schroedinger Equation basis for forming subatomic particles from twists in the field.
For a long time I thought this field had to be continuous and differentiable, but this contradicts Twist Theory which requires a discontinuity along the axis of the twist. Now I’ve realize our basis field does not need to be differentiable and can have discontinuities–obviously not magnitude discontinuities but discontinuities in element orientation. Think of the balls in the car seat mat–there is no connection between adjacent ball orientations. It only looks continuous because forces that change element orientation act diffusely, typically with a 1/r^2 distribution. Once I arrived at this conclusion that the field is not constrained by differentiability, I realized that one of the big objections to Twist Field theory was gone–and, more importantly, the connection of this field to emergence from nothing was stronger. Why? Because I eliminated a required connection between elements (“balls”), which was causing me a lot of indigestion. I couldn’t see how that connection could exist without adding an arbitrary (did not arise from nothing) rule.
So, removing differentiability brings us that much closer to the bottom turtle. Other constraints that have to exist are non-causality–quantum entanglement forces this. The emergence of the speed of light comes from the fact that wave phase propagates infinitely fast in this field, but particles are group wave constructions. Interference effects between waves are instantaneous (non-causal) but moving a particle requires *changing* the phase of waves in the group wave, and there is a limit to how fast this can be done. Why? I don’t have an idea how to answer this yet, but this is a good geometrical explanation for quantum entanglement that preserves relativistic causality for particles.
In order to quantize this field, it is sufficient to create the default orientation (this is required by Twist Field theory to enable emergence of the particle zoo). I have determined that this field has orientation possible in three spatial dimensions and one imaginary direction. This imaginary direction has to have a lower energy state than twists in the spatial dimension, thus quantizing local twisting to either no twists or one full rotation. A partial twist will fall back to the default twist orientation unless there’s enough energy to complete the rotation. This has the corollary that partial twists can be computed as virtual particles of quantum field theory that vanish when integrating over time.
The danger to avoid in quantizing the field this way is the same problem that a differentiable constraint would require. I have to be careful not to create a new rule regarding the connectivity of adjacent elements. It does appear to work here, note that the quantization is only for a particular element and requires no connection to adjacent elements. The appearance of a connection as elements proceed through the twist is indirect, driven by forces other than some adjacent rubber-band between elements. These are forces acting continuously on all elements in the region of the twist, and each twist element is acting independently only to the quantization force.  The twist discontinuity doesn’t ruin things because there is no connection to adjacent elements.
However, my thinking here is by no means complete–this default orientation to the imaginary direction, and the force that it implies, is a new field rule. Where does this energy come from, what exactly is the connection between elements that enforces this default state?
Oh, this is long. Congratulations on anyone who read this far–I like to think you are advancing science in considering my speculation!
Agemoz
Agemoz's Physics Blog 