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ZENODO
Preprint . 2024
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2024
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2024
License: CC BY
Data sources: Datacite
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Dirac Equation form -Et+px?

Authors: Ruggeri, Francesco R.;

Dirac Equation form -Et+px?

Abstract

In (1), we argued that spatial and temporal resolutions of hbar/p and hbar/E follow from degenerate values of A=-Et+px. In particular, t and x absorb the information of E and p through 1/E and 1/p making A=0 or removing all information from A. We argued that even though this degeneracy only appears in A=-Et+px (not in ctct -xx or -EE + pp = momo), -Et+px links (p,E) and space time (x,t) for mo, v=0 at x=0 with all constant --v frames. Given the degeneracy points n*hbar/p and n*hbar/E, where n is an integer, we suggested in (1) creating a periodic function exp(-iEt+ipx) which represents a kind of probability, i.e. the quantum free particle wavefunction. The use of this periodic function, however, removes the need for t,x in -Et+px, leaving only linear E,p which must be linked to mo. In this note, we first argue that -Et+px really represents the idea that there are setsof (p,E) equivalent to (0, mo) of the rest frame. The fact that one links space-time (x,t) with (E,p) allows one to pull E and p into resolutions of x and t and remove all information from A, i.e A=0. The question we ask here is: Can one use -Et+px to create an equation which directly yields exp(-iEt+ipx)? To do so, we first note that it is really the set (p,E) which defines the physical state as x,t may be any value in -Et+px, even non-trajectory values. This suggests an equation in (p,E) and maybe mo alone and we have already suggested this idea in a previous note. Here, we suggest that -Et+px yields the resolution gradations hbar/p, hbar/E key to the function exp(-iEt+ipx) by pulling E and p information into t and x. Normally, x and t would be independent of E,p. To use E,p,mo to create an equation yielding exp(-iEt+ipx) we suggest pulling t and x information into E and p, the exact opposite procedure. We do not set E=1/t or p=1/x because E and p are fixed values, but we do replace E and p with space-time derivatives d/dt partial and d/dx partial. As a result, a linear equation linking E,p and mo with space-time appearing through derivatives d/dt partial and d/dx partial should be able to yield a solution of exp(-iEt+ipx). We note, however, that (E,p,mo) in a linear equation represents an operator acting on exp(-iEt+ipx). If one multiplies this operator by itself one should obtain an operator equation yielding -EE + pp =momo for consistency. If this is to be the case, then there is more happening than just exp(-iEt+ipx), one has to introduce matrices in exactly the manner shown by Dirac. Dirac, however, started with -EE+pp=momo and used E=-id/dt partial, p=-id/dx partial without obtaining these from -Et+px. He then decided that the a priori goal was to obtain a linear equation in E, p and mo. We suggest that a link may be made by using -Et+px as a starting point.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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