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Unidempicity
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OK, so this question really digs into the heart of determinism in the realm of quantum mechanics, specifically the standard model.
First let's expose my limited understanding as it exists at the moment: There are known quantities that must be conserved such as mass charge momentum etc, and force laws such as gravitation and the other three (which to the best of my knowledge are formalized en formula as symmetries on or fields proportional to specific properties). These forces are fundamentally described as particle exchanges and transformations which are fundamentally geometric. There is uncertainty in as much as the physical apparatus of measurement creates necessity of it. The current best interpretation for how these interactions occur on a particle exchange level is a probability distribution over all possible interactions.
My question is this: what is the meaning of all "possible" interactions. Does this mean: the uncertainty in the current known state means that there is a distribution over when and in which direction a photon will be emitted, OR does it mean: the only way to know which way a photon will be emitted in a PERFECTLY known state is to count up every way in which all known conservation laws are obeyed and that is all we can say about what will happen, OR in a PERFECTLY known state there is only ONE outcome that will obey all conservation laws, OR is it theorized that there are conservation laws that are in effect that are not presently known, so due to our lack of knowledge, we can only posit probability distributions, but even if stochastically sampled, they still obey all presently observable phenomena.
[OR (worst case) once the distributions over all possible conservation law compliant states (sequences?) are made, they need to be further pruned so as to obey force laws?]
A PROBLEM: It seems as if it were so that photon emission were the only means of transferring electromagnetic force, and if position and momentum vectors were perfectly continuous, and emission was only determined by the complete state of the omitter and anything that made precise contact with it, then the odds of anything actually interacting would be infinitesimal. Is this not an issue? Are particles not points? If not what are they? Wave packets? What does one wave packet do when it fuzzes into another wave packet? Are there laws for this kind of thing?
Do we know anything more than "Um this thing can come out of this other thing sometimes maybe I couldn't tell you when but um this gravity thing is ALWays true sometimes I think on the large scale at least something to do with probability I guess I really couldn't tell you.."
THE REAL QUESTION: Is there and extant theory which can take the EXACT state of a system in terms of its most basic KNOWN components and properties and then give its EXACT state at a later point in time? Is it theorized that no such equation exists that could produce such a result, even if it were possible to measure the actual state at a given time to such an accuracy? Is this only a quantum mechanical flaw? Are there equations that currently work with atoms as their primary abstraction that can simulate events on that scale to a degree close enough to observable reality to be useful? Are these models simply built from observations of Atoms with no underpinnings in Quantum Mechanics?
Thank you for your consideration and understanding.
P.S. Please fill in any gaps in my understanding, or perhaps explain why these problems are more superficial than they seem because there are ways of explaining observable phenomena without resorting to the exact motions of the fundamental particles which are inherently unknowable anyway, even with entanglement.
OK ONE LAST QUESTION! Does conservation of energy mean anything sensible from a quantum mechanical framework?
First let's expose my limited understanding as it exists at the moment: There are known quantities that must be conserved such as mass charge momentum etc, and force laws such as gravitation and the other three (which to the best of my knowledge are formalized en formula as symmetries on or fields proportional to specific properties). These forces are fundamentally described as particle exchanges and transformations which are fundamentally geometric. There is uncertainty in as much as the physical apparatus of measurement creates necessity of it. The current best interpretation for how these interactions occur on a particle exchange level is a probability distribution over all possible interactions.
My question is this: what is the meaning of all "possible" interactions. Does this mean: the uncertainty in the current known state means that there is a distribution over when and in which direction a photon will be emitted, OR does it mean: the only way to know which way a photon will be emitted in a PERFECTLY known state is to count up every way in which all known conservation laws are obeyed and that is all we can say about what will happen, OR in a PERFECTLY known state there is only ONE outcome that will obey all conservation laws, OR is it theorized that there are conservation laws that are in effect that are not presently known, so due to our lack of knowledge, we can only posit probability distributions, but even if stochastically sampled, they still obey all presently observable phenomena.
[OR (worst case) once the distributions over all possible conservation law compliant states (sequences?) are made, they need to be further pruned so as to obey force laws?]
A PROBLEM: It seems as if it were so that photon emission were the only means of transferring electromagnetic force, and if position and momentum vectors were perfectly continuous, and emission was only determined by the complete state of the omitter and anything that made precise contact with it, then the odds of anything actually interacting would be infinitesimal. Is this not an issue? Are particles not points? If not what are they? Wave packets? What does one wave packet do when it fuzzes into another wave packet? Are there laws for this kind of thing?
Do we know anything more than "Um this thing can come out of this other thing sometimes maybe I couldn't tell you when but um this gravity thing is ALWays true sometimes I think on the large scale at least something to do with probability I guess I really couldn't tell you.."
THE REAL QUESTION: Is there and extant theory which can take the EXACT state of a system in terms of its most basic KNOWN components and properties and then give its EXACT state at a later point in time? Is it theorized that no such equation exists that could produce such a result, even if it were possible to measure the actual state at a given time to such an accuracy? Is this only a quantum mechanical flaw? Are there equations that currently work with atoms as their primary abstraction that can simulate events on that scale to a degree close enough to observable reality to be useful? Are these models simply built from observations of Atoms with no underpinnings in Quantum Mechanics?
Thank you for your consideration and understanding.
P.S. Please fill in any gaps in my understanding, or perhaps explain why these problems are more superficial than they seem because there are ways of explaining observable phenomena without resorting to the exact motions of the fundamental particles which are inherently unknowable anyway, even with entanglement.
OK ONE LAST QUESTION! Does conservation of energy mean anything sensible from a quantum mechanical framework?