What
might mean “more than impossible”? For example, that could be
what happens without any cause or that physical change which occurs
without any physical force (interaction) to act. Then, the quantity
of the equivalent physical force, which would cause the same effect,
can serve as a measure of the complex probability.
Quantum
mechanics introduces those fluctuations, the physical actions of
which are commensurable with the Plank constant. They happen by
themselves without any cause even in principle. Those causeless
changes are both instable and extremely improbable in the world
perceived by our senses immediately.
Even
more, quantum mechanics involves complex probabilities as forces
explicitly as follows. Any probability distribution may be
represented by its characteristic function, which is its Fourier
transformation and thus a complex function sharing one and the same
phase, i.e. a constant phase. The overlap of probability
distributions imposes a corresponding restriction of the degrees of
freedom in each space of events for the result in any of the
overlapped spaces is transferred automatically in all the rest of
them. That restriction of the degrees of freedom can be considered as
a generalization of the physical concept of force (interaction) as to
quantum mechanics. Indeed, any force (interaction) in the sense of
classical physics causes a special kind of restriction of the degrees
of freedom to
a
single one. Quantum force (interaction) also restricts, but to a more
limited probability distribution with less dispersion and entropy
rather than to a single one new value.
Particularly,
that consideration interprets negative probability as a particular
case of complex probability, which is what is immediately introduced.
The
understanding of probability as a quantity, corresponding to the
relation of part and whole, needs to be generalized to be able to
include complex values. For example, probability can be thought as
associable with the number of elementary permutations of two adjacent
elements for a given element of a limited series to reach its last
element (i.e. its upper limit) and more especially, to the ratio of
that number to the corresponding number of those permutations as to
the first element (i.e. the lower limit) of the series. Then, the
introduction of negative probability requires only the reversion of
the direction of elementary permutations from the upper limit to
The
narrow purpose of the paper is to be introduced negative and complex
probability relevant to special and general relativity and thus to
events in our usual perceptive world rather than to microscopic or
micro-energetic events studied by quantum mechanics (Section 3).
The
prehistory and background (Section 2) include the generalization and
utilization of ‘negative and complex probabilities’ in quantum
mechanics and probability theory, and Section 4 compares their use in
quantum mechanics and information, signal theory, probability theory,
and special and general relativity.
The paper (Video); a newer version as a PDF or as an item @ EasyChair or @ SocArxiv or @ AdvanceSage, or @ SSRN
The presenation (PDF, Video); also as slides @ EasCyhair
The paper (Video); a newer version as a PDF or as an item @ EasyChair or @ SocArxiv or @ AdvanceSage, or @ SSRN
The presenation (PDF, Video); also as slides @ EasCyhair
Related items
Negative and Complex Probability in Quantum Information - Paper (Presentation -YouTubeVideo)
The almost impossible worlds in quantum information (BloggerPost, WordpressPost, YouTubePresentation, PowerPointPresenation, PresentationPDF)
No comments:
Post a Comment