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June 30, 2014

How Big Is a Photon? The Conceptual Foundation of Quantum Mechanics

[From an October 2004 post on the Ultranet@topica.com email list.]

Daniel asked:
>Finally, here's the question: what's the width, if any, of a photon of
>visible light?

I wondered myself in classical electrodynamics what the physical location of the
Poynting vector was within a wave - how is the energy distributed within the wave?
In experiments the energy interaction happens at one spot which can be localized
to any degree required so long as the phenomenon used to register the interaction
propagates with a small enough wavelength. When the "screen" used to register
interactions has more resolution than the waves of the particles it is measuring,
the individual interactions are each well localized on the screen but appear randomly
within the region defined by the impinging waves.

Photons, like all quanta, are not objects but interactions. Elementary entities are
waves when they are going someplace and particles when they get there. All individual
observations are of particles, the wave propagation can only be inferred statistically
from the distribution of particle interactions. Interactions, since they are not
objects, do not themselves have a size. Everything about a given interaction is
specified by what happened in a single instant and therefore what happened at a
single point*, and the amount of this knowledge is restricted by the initial information
content of the interacting particles and the fundamentally limited information conveyed
by the particles resulting from the interaction.

The informational limits imposed by the necessity that two states must either be
distinguishable or indistinguishable with respect to any given interaction lead
to the necessity of quantitization - things that differ must do so by at least one
bit. This limited information conveyed by the particles resulting from the interaction
also requires that a given system must have a maximum information capacity and if
one attempts to get more information out of an interaction with the system then
the results of the interaction become fundamentally unpredictable. For some reason
this unpredictability varies regularly in complex waves and their interference.
Since a system may have multiple parts, it is possible for the information content
of some multi-part system with respect to some interaction to stiil be only one
bit. Independent, separated interactions with different parts of the composite system
with respect to that bit will logically be interdependent - this is entanglement.
The bits transferred by an interaction are all there is ever to be known about it.**

One cannot go back to an given individual interaction and measure it again, such
measurements would be interactions distinct from the original. Therefore observers
cannot compare independent measurements of a given interaction and the notion of
its size is undefined beyond whatever bits were gained from the particles resulting
from the interaction.


*The point-junctions of the particle world-lines in Feynman graphs are being replaced
by junctions with extent in more dimensions, similar to pipe junctions, for example.
I think the gradualness of the separation of two such pipes (superstring world-sheets),
is equivalent to the rate of decoherence of a state into two incompatible possibilities.
This might be regarded as the "size" of the particle interaction.

**See "A Foundational Principle for Quantum Mechanics" by Anton Zeilinger

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