Posts Tagged ‘group wave’

Defining a Unitary Rotation System Interaction

November 17, 2019

The new quantum interference interpretation described in previous posts provides a great connection between Newtonian physics, special relativity, and quantum mechanics.  I wrote a paper on it (group_wave_constant_speed), and then began working out a mathematical model that uses the main premise of the interpretation (particles form from a sum of instantaneous phase waves).  I’m taking some time from that work to post this progress report–a list of assumptions and structures I am assuming in this model, along with an effort to justify them.

The first question that has to be answered is whether the precursor waves (the instantaneous phase group wave described in the paper) can be modeled as single valued or can be superposed on each other in a linear combination.  Since I’m trying to construct a model representing the real world, I chose the E=hv relation to help answer this question.  This equation specifies that a given frequency can only have one energy for a quanta of that frequency, so that constrains the precursor field to just a single degree of freedom.  That strongly implies that a geometrical/mathematical model of a quanta must be a single unitary twist in some vector field.  In order to anchor this twist to a single rotation, there must be a lowest energy background state for the rotation, with a cost applied to any deviation from the background state.  This locks in the rotation to a single state.  If we allow the rotation vector to have a magnitude, we have too many degrees of freedom for E=hv to hold, so that means several things–first, that the rotation vector space is unitary, and secondly single valued–you cannot put two waves on top of each other in this field.  This has the additional effect that the field is blocking–you cannot pass information through a limiting neighborhood of a field without altering the vector orientation in that neighborhood.

The background vector state cannot exist in R3 without inducing a detectable dimensional preference in R3 (see Michelson experiment and similar), so I hypothesize a fourth imaginary dimension for it.  I realize that this violates the KISS (keep it simple) premise of science, but I believe it is required and so I assume a unitary four-vector field in R3 + I.  For the time being, time T will be independent of R3 + I but later I will bring in the necessary adjustments for special and general relativity.

With these assumptions in place, we are ready to define the mathematical basis for the precursor field, and make some more assumptions about how particles could interact.

It should be straightforward to define each element of this single-valued rotation field as a unitary three-vector, e.g., x = [xy_rot, xz_rot, and xi_rot] where ||x|| = 1.  Since this is a unitary vector field, no magnitude exists and a fourth vector element is not needed.

Let’s now consider two basic twist types in this vector field and determine a construct for how they will interact.  The first twist type is a linearly propagating twist, a quanta, of one complete cycle from the background state and back again.  The second twist type is a twist loop with one complete cycle (previous posts on this site describe how quantum interference will work to confine such a loop).  Can we propose a model interaction of these two types?  You can see why I propose a single-valued field–multiply-value fields cannot constrain the interaction, and in fact I believe that such a field would cause the two twists to fail to interact at all.  The blocking behavior of the single-valued field is necessary for interaction.

Now, both particles will have a fundamental wave frequency (see the paper for a more specific treatment), so let’s set up an interaction where the linearly propagating twist approaches a stationary twist loop.  We will use conservation of momentum to help constrain what happens.  The momentum of both particles is proportional to the fundamental wave frequency (E=hv, again), so if the linear particle is absorbed by the twist loop, the twist loop will emerge from the interaction with the same momentum as the propagating linear twist.

One promising way to make this momentum transfer work in our R3 + I vector field is to allow momentum transfer only when both particles have parallel vector alignment.  Then in that delta time, a delta momentum (which is inversely proportionate to the linear particle’s wavelength because the orthogonal rotation rate of the linear particle will vary as its frequency) will be exchanged.  Integrating over the time of the linear propagating particle, momentum will be conserved.  Note that only when the linear particle goes through the loop there will be a unique parallel vector alignment.  Nearby particles may have partial rotation absorption, however any virtual particle interaction such as this having an incomplete quantized rotation will fall back to the background state without having transferred a net momentum to the twist loop.

We have shown how the momentum exchange will produce a transfer inversely proportionate to the incoming particle’s momentum, but now we need to de-construct how the motion of the twist loop particle is affected  by this momentum change.  As this post is already too long, let’s start a new post for that…

Agemoz

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Why Does Quantum Interference Affect Particle Path?

June 11, 2019

I last posted on my discovery that any classical group wave will obey the observed constant speed property, a prerequisite (one of the two assumed postulates) for special relativity.  That is, if you throw a baseball, its speed will be some value v_p.  If you are standing on a train moving in the same direction at speed v_e, an observer on the ground will see the baseball move at speed v_p + v_e.  But, if you throw an object that is a linear sum of waves, such as a delta function group wave, it doesn’t matter what v_e (the relative speed of the thrower) is, the observer on the ground will always see it move at speed v_p.

The math and concept seemed bullet-proof, so I spent a couple of years writing a paper and trying to get it published.  I stayed away from any speculation and just wrote a proof that says classical group waves must appear to move at some constant speed v_p regardless of an observer’s frame of reference velocity v_e.  I made sure there was nothing in there that would make a reviewer immediately toss the paper.  I worked on getting the format and grammar acceptable for scientific publishing, had several reviewers check it for errors and conceptual problems.  They claimed it was good to go so then I submitted to several journals.  No luck–a bunch of rejections later and I finally gave up.  However, no editor wrote to disprove my math or the conceptual thinking, not sure they ever looked at that–it was always the paper doesn’t meet the quality standards of the journal or some such reason (if any).  In spite of my best skeptical analysis, I cannot find fault with the derivation, and I still think there’s some science here, so I decided to forget the publishing effort and just continue seeing what I could discover on my own.

Here it is: group_wave_constant_speed

Unlike many of the ideas I post here, which are guesses how things work and are borderline science fiction, I thought this work was a small breakthrough, it says several important things.  First, if this is true (represents reality), it shows why special relativity exists in our universe.  All the research I have done shows that no one has determined why we assume the constant speed of light postulate holds and thus why we have special relativity behavior.  Second, it shows that every particle and exchange particle must consist entirely of some kind of a wave summation, otherwise it would violate special relativity–thus giving an important clue how to mathematically define subatomic particles.  And third, it shows that any quantum particle composed of waves must phase shift the waves at a causal rate–but there can be no time-dependent component to the phase-shift along the length of the wave.  In other words, the entire wave component shifts non-causally, albeit at a causal rate.  This is important because now the Aspect experiment makes sense–if entangled particles are emitted in opposite directions, the particles stay coherent–perhaps as a orthogonally complex double helix going to oppositely placed detectors.  They oscillate their states, back and forth, until one detector captures and absorbs the momentarily real portion of the double helix, instantaneously leaving the orthogonal (imaginary at that moment) helix intact for discovery by the other detector at a later time.

This work provides a novel set of tools for looking at various quantum particle interactions.  I’m going to discuss some of what I’ve discovered on this website.  I am trying to be clear what is provable (stuff in that paper) or science fiction (these posts, for the most part, are guesses how things work and aren’t really provable at this point).  I will try to make a good case for my science fiction, that is, why I find my ideas attractive possibilities.

One example is the famous two-slit experiment.   When a single particle hits a barrier with two openings in it, it interferes with itself and only will land at certain target locations on the other side of the barrier.  Paradoxically, if you close one of the openings, now the particle will land on any target location.  I have considered the question: why does the second opening cause an alteration to the particle’s path?

The second Bohm interpretation (the leading contender of valid quantum interpretations) suggests that the particle is preordained to go through one or the other slit, but is guided to an interference controlled destination by the particle’s extended wave property going through two slits.  In this Bohm interpretation, when determining the time/space evolution of the particle wave function, a complex exponential (representing the wave from the second opening) is added to the particle wave function to mathematically guide the particle to the interference pattern target.  Two spherical waves will combine to produce various interference patterns–see the figure:

interference_pattern

The big problem with this interpretation is that work is done to move a particle.  If the particle was ordained to go through one opening to a target that is blocked when the second opening is opened, but instead goes to a nearby interference defined location, the Bohm interpretation says that the waves going through the second slit is somehow expending energy via some force being applied to the particle.   There is no evidence for such a force in nature.

There are no forces needed when using the group wave interpretation approach described in my paper.   The particle is merely defined by where the wave components sum to produce a localized group wave delta function or similar construct.  Interfering waves simply change the possible places where the “particle” will appear, and in fact the concept of particle region is set by how a detector absorbs the group wave.  In the region of the barrier, the concept of a particle becomes very ambiguous, but no waves are absorbed by the barrier .  Instead, they all pass through the openings, so a Fourier composition must reform the particle somewhere after the barrier that will eventually hit the target detector region.  No funny or weird alterations to the wave function are needed.

There are many more ideas like this that follow from assuming a group wave interpretation–one of the most important being that group wave particles will appear to be moving at constant speed regardless of the observer’s frame of reference–a foundation for special relativity.  Do you agree why the group wave concept is a cleaner approach than the Bohm interpretation?  I don’t think this is science fiction, but I couldn’t get any journal editors to see things the way I am….  😦

Agemoz

PS:  I use wave and wave functions interchangeably in this post–the concepts shown here are valid for both physical waves and probability distributions.

 

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Noncausal Interactions, part II

December 11, 2012

I want to clarify the previous posting on how I resolve the noncausal paradox in unitary twist field theory–after all, this is the heart of the current struggle to create a quantum gravity theory.  Here, I’m continuing on from the previous post, where I laid out the unitary twist field theory approach for quantum interactions.  In there, I classified all particle interactions as either causal physical or noncausal quantum, and quantum interactions fall into many categories, two of which are interference and entanglement.  These two quantum interactions are non-causal, whereas physical interactions are causal–effects of physical interactions cannot go faster than the speed of light.

Many theories have attempted to explain the paradoxes that result from the noncausal quantum interactions, particularly because relativity theory specifies that no particle can exceed the speed of light.  The Copenhagen interpretation, multiple histories, string theories such as M theory, the Pilot wave theory, etc etc all attempt to resolve this issue–but in my research I have never found anyone describe what to me appears to be a simple solution–the group wave approach.

In my previous posting, I described this solution:  If every particle is formed as a Fourier composition of waves, the particle can exist as a group wave.  Individual wave components can propagate at infinite speed, but the group composition is limited to speed c.  This approach separates out particle interactions as having two contributors:  from the composite effect of changing the phase of all wave components (moving the center of the group wave) and the effect of changing the phase of a single fundamental wave component.  If the individual wave components changed, the effect is instantaneous throughout spacetime, but there is a limitation in how quickly the phase of any give wave component can be changed, resulting in a limitation of how quickly a group wave can move.

It’s crucial to understand the difference, because this is the core reason why the paradox resolves.  Another way to say it is that when a change to a wave component is made, the change is instantaneous throughout R3–but the rate of change for any component has a limit.  An analogy would go like this: you have two sheets of transparency paper with a pattern of parallel equally spaced lines printed on it.  If you place each sheet on top of each other at an angle, you will see a moire pattern.  Moving one sheet relative to the other will move the moire pattern at some speed limited by how quickly you moved the sheet.  But note that every printed line on that sheet moved instantaneously relative to every other line on that sheet–instantaneous wave component movement throughout R3.  Note that the interference pattern changes instantaneously, but the actual movement of the moire pattern is a function of how fast the sheets are moved relative to each other–exactly analogous to what we see in real life.  This is the approach that I think has to be used for any quantum gravity theory.

Agemoz

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