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

Tags: causal, group wave, interference, noncausal, quantum entangled phase group, quantum theory, twist theory, vector field

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