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Is it safe to assume photons really are not waves, per se? It would seem to make more sense if the electric and magnetic fields surrounding the photon are responsible for "wavelike" character, but in "reality" there is no wave action taking place. Would that be reasonable to assume? That begs the question, when a single photon is sent through a slit experiment, it can be assumed it does not interact with itself to produce light and dark wavelike pattern, but rather something else is going on?

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It's a rite of passage to attempt, and inevitably fail, to explain Young's double slit experiment - so here's my ill-conceived take on it all:

When a beam is shot through the double-slit, a wave-like interference pattern is measured on the screen. However, if we "measure" which slit each item travelled through then instead a particle-like pattern is projected onto the screen. Clearly this beam is neither exactly wave-like or particle-like.

The double-slit experiment. This image is in the public domain and is in the Wikimedia Commons.

Mathematically our beam can be described by a quantum mechanical wavefunction - a probability amplitude describing our system. In this regime, saying that a photon passes through a slit is misleading. The notion of a definite position does not exist for our photons. Instead we must ask "If I made a measurement, what is the probability that the photon is at some position?".

Not measuring the slits:
We have a wavefunction describing our system and we ask "What are the probabilities of the beam hitting each position of the screen?". The beam hitting the screen is our measurement. Many photons hit the screen randomly and eventually the interference pattern corresponds to our probabilities.

Measuring the slits:
Taking a measurement is a well-defined operation is quantum mechanics. We ask "What is the probability that a photon passes through slit A THEN hits the screen at position X?". This constrains our setup to one in which each photon definitely passes through one of the slits.

In the first case noted that the wavefunction doesn't correspond to any definite position. In the second we impose that it definitely passed through one of the slits. It's this requirement that changes the interference pattern.

That may or may not have been useful, but it's how I interpret the results. Now onto answer specific parts of your question:

Is it safe to assume photons really are not waves, per se?

It depends on what you mean by "safe". Light certainly exhibits behaviour unbecoming of a wave, but that doesn't mean that it is a particle either.

electric and magnetic fields surrounding the photon are responsible for "wavelike" character

The double slit experiment seems to have the same mysterious behaviour for all items that we send through it: photons, electrons, etc. Whilst photons can be thought of as oscillating electric and magnetic fields, electrons cannot. Therefore this cannot be true.

when a single photon is sent through a slit experiment, it can be assumed it does not interact with itself to produce light and dark wavelike pattern, but rather something else is going on?

From the perspective of quantum mechanics there is no interference whatsoever. Instead we have a superposition of all of the possible outcomes, this makes no mention of number of particles. One photon passing through the experiment will only hit one location but it's probability density is the same as the one that produces the interference pattern that we saw with our beam.

Hopefully that shines some light on the problem for you. It's useful to keep in mind that in matters regarding quantum mechanics, your intuition learned from the macroscopic world may not provide any sufficient analogies to describe a phenomena.

Two more mathematically complex answers that I found particularly enlightening on this site are:

The Wikipedia article Double-slit experiment is also quite good if you are looking for more basic information about the experiment itself. How one understands this phenomena is somewhat dependent on their interpretation of quantum mechanics. For an introduction of these interpretations see the Wikipedia article Interpretations of quantum mechanics.

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  • $\begingroup$ Good stuff. Having a tough time wrapping around - "From the perspective of quantum mechanics there is no interference whatsoever. Instead we have a superposition of all of the possible outcomes, this makes no mention of number of particles." - it seems there needs to be a more sensible answer. $\endgroup$ – therr Apr 14 '18 at 0:54
  • $\begingroup$ Vielbein and @therr, why the interaction of the edges with the photons is not taken in account? The light has a magnetic and an electric field component and the surface electrons of an edge have too. physics.stackexchange.com/q/158105 $\endgroup$ – HolgerFiedler Apr 14 '18 at 6:04

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