Fermilab

1. Does an unobserved, unmeasured (i.e. wave-like) photon exist as an electro-magnetic wave, or as a 'wave-function', i.e. a probability wave?

2. Is the 'wave' nature of an electron the same as speaking of it's wave-function, in other words does an unmeasured electron exist everywhere in space as a purely mathematical probability? Does an unmeasured electron not have any physical meaning at all then?

3. When performing Young's double-slit experiment with photons and electrons, what are the 'waves' that intefere with each other? Is is electromagnetic for photons and wave-function for electrons?

Thank you for your time. :)

Justin Leppan Glasgow, Scotland

Hi Justin,
Your questions are excellent, because they hide part of the answer, so it should not be difficult to reply.

Could you please help me with these basic questions:

1. Does an unobserved, unmeasured (i.e. wave-like) photon exist as an electro-magnetic wave, or as a 'wave-function', i.e. a probability wave?

Let me briefly explain the difference between an electromagnetic wave and a probability wave or as you call it a 'wave function'

When scientists first discovered that charged particles create an electric field around them , and that a wire with a current creates a different type of a field, called magnetic field, they quickly realized that these electric and magnetic fields (from now EM fields) could be time and space dependent, and sometimes this dependency is such, that the EM field travels in space, from one point to another one (carrying energy and information (see walkie-talkies)) and people started to call them EM waves. These waves were continuous propagation of EM fields.

Everybody was happy, until they (Max Planck) discovered some problems (thermal radiation of an object called black body). To solve his problem, he came up with a revolutionary idea, that the EM waves are not continuous, but QUANTIZED, that they propagate in little wave packets, called PHOTONS. And a baby quantum theory was born. :-)

Very smart physicists worked with his idea, and realized that EM fields are quantized as well and that excitations of the EM field can propagate in space time, and those excitations are the photons and these photons are described by something called wave functions from which you can get the probability of finding a photon in a certain space region at a certain time. (that is why the name, probability wave).

To make the long story short, the answer to your first question is : An electromagnetic wave is a classical, non-quantized description of a propagating EM field, A photon is a modern, quantized description of a propagating EM field. ( Notice, I carefully avoided saying that the photon is a particle or a wave! In the modern description, it has so called DUAL properties, sometimes it acts as a particle (when you have spots on your camera film) or as a wave, when you experiencing interference))

2. Is the 'wave' nature of an electron the same as speaking of it's wave-function, in other words does an unmeasured electron exist everywhere in space as a purely mathematical probability? Does an unmeasured electron not have any physical meaning at all then?

Before answering this question let me make the following remark. In the case of a photon, it was kinda "easy" to accept that it could act as a particle. However in case of electrons, it was very tough to accept that they could act as waves and be described by a wave function (probability wave) similarly as in the case of photons!!!!

So the answer to your question about the electron is YES, any unmeasured electron has its own probability being anywhere in the world.

About the physical meaning of an unmeasured electron.

It has its physical meaning, namely that with a certain probability it can interact with your eye here in the US and with a different, non-zero probability can interact with a proton in Australia, ... .

You are perfectly right if you think people have hard time to interpret the physical meaning of "unmeasured states" ( please remember the Schroedinger cat in a box problem).

3. When performing Young's double-slit experiment with photons and electrons, what are the 'waves' that intefere with each other? Is is electromagnetic for photons and wave-function for electrons?

I think this question had been answered above. In modern physics we describe every particle by their wave-function, and as I said, sometimes they act as pure particles, sometimes as waves.

I hope your questions got answered and you will keep wondering about these new and peculiar ideas.

Bye Arnold Pompos

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