Additions:
Additions:
Under Lorentz transformation, the order of interactions, ""I(xi)"", can be changed in the time-ordered product whenever ""xi − xj"" is space-like. Under the condition that the initial and final states are stable states of free particles, as in scattering experiments, the calculation of probabilities cannot be affected. The locality condition follows immediately.
Deletions:
Under Lorentz transformation, the order of interactions, ""I(xi)"", can be changed in the time-ordered product whenever ""xi − y"" is space-like. Under the condition that the initial and final states are stable states of free particles, as in scattering experiments, the calculation of probabilities cannot be affected. The locality condition follows immediately.
Additions:
**Proof:** We have (from [[rqgravity.net/Evolution#Stone’sTheorem Stone’s theorem]]), for any ""
"",
Deletions:
**Proof:** We have (from [[Evolution#Stone’sTheorem Stone’s theorem]]), for any """",
Additions:
**Proof:** We have (from [[Evolution#Stone’sTheorem Stone’s theorem]]), for any """",
Deletions:
**Proof:** We have (from above), for any """",
Additions:
The perturbation expansion can be interpreted directly as a quantum logical statement, meaning that any number of interactions might be found taking place at any time and any position if we were to do a measurement. The sums (including the integral sums) simply represent ""OR"" between possibities. In this interpretation, ""I(x)"" describes the possibility that an interaction might be anywhere. It is not a quantised “matter field” which is, in some undefined sense, everywhere. Similarly, Feynman’s [[http://en.wikipedia.org/wiki/Path_integral_formulation path integral]], or “sum over all paths” has as natural interpretation that the sum over paths is a logical ""OR"" between the possible paths that might be detected if an experiment could be done to trace the path (not that a particle passes through all paths in spacetime, as described by Feynman in [[http://en.wikipedia.org/wiki/QED_%28book%29 QED: The Strange Theory of Light and Matter]]). The time-ordered graphs give a pictorial representation of the same statement.
Deletions:
The perturbation expansion can be interpreted directly as a quantum logical statement, meaning that any number of interactions might be found taking place at any time and any position if we were to do a measurement. The sums (including the integral sums) simply represent ""OR"" between possibities. In this interpretation, ""I(x)"" describes the possibility that an interaction might be anywhere. It is not a quantised “matter field” which is, in some undefined sense, everywhere. Similarly, Feynman’s [[http://en.wikipedia.org/wiki/Path_integral_formulation path integral]], or “sum over all paths” has as natural interpretation, not that a particle passes through all paths in spacetime (as described by Feynman, e.g. in [[http://en.wikipedia.org/wiki/QED_%28book%29 QED: The Strange Theory of Light and Matter]]), but that the sum over paths is a logical ""OR"" between the possible paths that might be detected if an experiment could be done to trace the path. The time-ordered graphs give a pictorial representation of the same statement.
Additions:
The perturbation expansion can be interpreted directly as a quantum logical statement, meaning that any number of interactions might be found taking place at any time and any position if we were to do a measurement. The sums (including the integral sums) simply represent ""OR"" between possibities. In this interpretation, ""I(x)"" describes the possibility that an interaction might be anywhere. It is not a quantised “matter field” which is, in some undefined sense, everywhere. Similarly, Feynman’s [[http://en.wikipedia.org/wiki/Path_integral_formulation path integral]], or “sum over all paths” has as natural interpretation, not that a particle passes through all paths in spacetime (as described by Feynman, e.g. in [[http://en.wikipedia.org/wiki/QED_%28book%29 QED: The Strange Theory of Light and Matter]]), but that the sum over paths is a logical ""OR"" between the possible paths that might be detected if an experiment could be done to trace the path. The time-ordered graphs give a pictorial representation of the same statement.
Deletions:
The perturbation expansion can be interpreted directly as a quantum logical statement, meaning that any number of interactions might be found taking place at any time and any position if we were to do a measurement. The sums (including the integral sums) simply represent ""OR"" between possibities. In this interpretation, ""I(x)"" describes the possibility that an interaction might be anywhere. It is not a quantised “matter field” which is, in some undefined sense, everywhere. Similarly, Feynman’s [[http://en.wikipedia.org/wiki/Path_integral_formulation path integral]], or “sum over all paths” has as natural interpretation, not that a particle passes through all paths in spacetime (as described by Feynman, e.g. in [[http://en.wikipedia.org/wiki/QED_%28book%29 QED: The Strange Theory of Light and Matter]], but that the sum over paths is a logical ""OR"" between the possible paths that might be detected if an experiment could be done to trace the path. The time-ordered graphs give a pictorial representation of the same statement.
Additions:
We assume that we can define a Hermitian interaction density operator, ""I(x)"", having the same effect on a matter anywhere and at any time, as required by the general principle of relativity. By the identification of addition with quantum logical ""OR"", ""HI(t)"" can be written as a sum (as usual on this site, an integral represents a finite sum with enough terms that taking more makes no practical difference to calculation).
Deletions:
We assume that we can define a Hermitian interaction density operator, ""I(x)"", having the same effect on a matter anywhere and at any time, as required by the general principle of relativity. By the identification of addition with quantum logical , ""HI(t)"" can be written as a sum (as usual on this site, an integral represents a finite sum with enough terms that taking more makes no practical difference to calculation).
Additions:
We assume that we can define a Hermitian interaction density operator, ""I(x)"", having the same effect on a matter anywhere and at any time, as required by the general principle of relativity. By the identification of addition with quantum logical , ""HI(t)"" can be written as a sum (as usual on this site, an integral represents a finite sum with enough terms that taking more makes no practical difference to calculation).
"" i(x) can be represented diagrammatically as a vertex or node. The lines above the node correspond to creation operators, and those below the node correspond to annihilation operators. |
""
Deletions:
We assume that we can define a Hermitian interaction density operator, ""I(x)"", such that, if we were to determine the time and position at which the interaction takes place, the probability that it takes place at ""x"", is ""
"". The general principle of relativity implies that ""I(x)"" has equal effect on a matter anywhere and at any time. So, by the identification of addition with quantum logical , ""HI(t)"" can be written as a sum (as usual on this site, an integral represents a finite sum with enough terms that taking more makes no practical difference to calculation).
""| I(x) can be represented diagrammatically as a vertex or node. The lines above the node correspond to creation operators, and those below the node correspond to annihilation operators. |
""
