Feynman, Einstein, Relativity, Quantum
Hi I am currently reading "The Elegant Universe" by Brian
Greene. (Which is a fantastic book.) He refers to Feynman's
formulation about the double slit experiment, which says that there
is a probability that an electron can travel infinite paths to get
through both slits. This means that information can travel faster
than the speed of light, which Einstein says is not possible. Am I
missing something or is this another inconsistency between
Relativity and Quantum Mechanics?
I suggest picking up a copy of QED, The Strange Theory of Light and
Matter, by Feynman. It is a short text of about 150 pages and written
in terms a non-expert can easily grasp. Chapter 3 presents an eloquent
explanation of the double slit experiment, but please read the first
two chapters to get a foundation. The discussion of light reflected by
a mirror (in which ray diagrams show the angle of incidence equals
angle of reflection) is explained within the context of an infinite
number of possible paths. You will find that there is no conflict
between relativity and QM. Personal note: I like Brian Greene's stuff
very much, but I find his discussions to be sometimes disjointed and
assume a level of understanding inconsistent with the presumed target
Hope this helps.
Congratulations, you answered your own question :)
This is another inconsistency between Relativity and Quantum Mechanics.
Perhaps you can be part of the effort to solve the problem.
Feynman's path integral techniques do not mean that an electron travels
through one slit and then goes back to travel through the other. The
electron, like all particles, also has wave properties. If there is no
way to tell which slit the electron passes through, then the electron
interferes with itself like when light waves and sound waves pass
through double slits. The electron passes through both slits together,
as a wave rather than a particle. If you do have a way to tell which
slit the electron passes through, then the electron can go through only
one of the slits, and interference doesn't happen. If something is
measured in quantum physics, then it has only the quantity measured. If
it is not measured, than it has all possible values. Measurement forces
one of the possible values to be "chosen". For relativity, a particle
is always a particle, and a wave is always a wave. For quantum physics,
each item has properties of both.
As for the term "infinite paths", this means an infinite number of
paths, not paths if infinite length. Each electron final position has a
certain probability of happening. Only one final position happens for
an electron, but you cannot predict what it will be. After sending many
electrons through, the most likely final positions will have received
most of the electrons.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012