# Light waves and Schrödinger probability waves

Ok, bearing in mind that I only have a brief understanding of quantum mechanics (no formal education, only from reading about concepts in books), so I could be way off here, I have a question regarding probability wave functions and light waves.

From my understanding, every particle of matter has a probability wave which fills the entire universe, that's to say the only reason a particle in my fingernail is in my fingernail is because that's where the highest probability of it being is (with the chance that it's anywhere else in the universe being infinitesimally small), so my question is what is a light wave? Also from my understanding, a light wave is simply a probability wave for the location of a photon, and only upon observation does that wave collapse and does the photon 'take on' a definite position in space, so if I compare a particle of matter to a particle of energy (a photon in this case), how come the particle of matter has a probability wave that fills the entire universe, and the photon have only a small defined wave which virtually makes up a straight line in space? Is the light wave just an area (straight line?) of space where the probability is magnitudes higher than everywhere else and the photon's probability wave is still permeating the rest of the universe, or is the photon's location definitely somewhere in the area of space defined by the light wave?

For example, could a photon that's part of a laser beam ever interact with a photon from a laser beam travelling parallel to the first beam? (Disregarding any other physical theories that could cause the two beams to converge through other means, I'm wanting to stay on the topic of Schroedinger probability waves)

I might well be completely misunderstanding/mixing concepts here, so that might be the reason for my confusion, if so, please enlighten me!

Let's take it a step at a time:

From my understanding, every particle of matter has a probability wave which fills the entire universe, that's to say the only reason a particle in my fingernail is in my fingernail is because that's where the highest probability of it being is (with the chance that it's anywhere else in the universe being infinitesimally small),

true

so my question is what is a light wave? Also from my understanding, a light wave is simply a probability wave for the location of a photon, and only upon observation does that wave collapse and does the photon 'take on' a definite position in space,

A light wave is also a particle, called the photon. Depending on the observation it can display its particle nature or its wave nature.

so if I compare a particle of matter to a particle of energy (a photon in this case),

a photon is a particle too, not different than other particles

how come the particle of matter has a probability wave that fills the entire universe, and the photon have only a small defined wave which virtually makes up a straight line in space?

A photon has the same behavior as any other particle, depending on the experiment: it either displays its wave nature, or its particle nature depending on the observation: through two slits shows interference, therefore wave properties, absorbed in an atom, particle. Both particles and photons behave the same.

Is the light wave just an area (straight line?) of space where the probability is magnitudes higher than everywhere else and the photon's probability wave is still permeating the rest of the universe,

a volume , and a very small one, like all particles

or is the photon's location DEFINITELY somewhere in the area of space defined by the light wave?

There is no definite in quantum mechanics. Only after the experiment the values are known. Only probabilities can be calculated for individual particles, photons or not.

For example, could a photon that's part of a laser beam ever interact with a photon from a laser beam travelling parallel to the first beam?

Here we are entering deeper into quantum theory, into what is called "second quantization". Yes, two photons parallel to each other in their probability paths can interact with tiny tiny probabilities by exchanging quanta of energy between them, these are carried by virtual particles covering the whole spectrum that is permitted by quantum number conservations.

Digressing into lasers: Lasers are another story, and are the result of the possibility that atomic physics allows to have coherent waves of photons. Coherent means "in step" in time and space. Atomic physics because the transitions between energy states in atoms happen with photon exchanges and interactions, and one can easily make a coherent beam of photons, all in phase with each other, as is the laser beam.

A way for a layman to understand the possibilities of the effects of coherence is the famous "soldiers crossing a bridge". In olden times, bridges were mainly stable because the arches held them up statically. The connecting mortar did not have much structural strength. Soldiers when crossing a bridge had to break step, otherwise the hitting of boots in phase could destroy the bridge by building up coherently large forces that the arch could not hold.

• Thanks! There's one thing I'm still not sure on though: Me - "Is the light wave just an area (straight line?) of space where the probability is magnitudes higher than everywhere else and the photon's probability wave is still permeating the rest of the universe," You - "a volume , and a very small one, like all particles" I'm not sure whether you're confirming what I was suggesting (apart from correcting my usage of 'area' to 'volume', obviously volume is the correct term here)? Is the volume defined by a light wave just a part of the entire probability wave where the probability is higher? – machinemessiah Apr 29 '11 at 21:00
• It is not true that every particle has a wave that fills the universe. What is true is that all the particles together have an entangled collective wave that fills a large chunk of the universe. – Ron Maimon Aug 20 '11 at 4:51
• @Ron Maimon Considering that electromagnetic and gravitational forces extend through the universe, even though extremely attenuated by the 1/r^2, the same is true of the solutions of the relevant equations, imo. It is only in idealized mathematical problems that one can have a localized solution. In the case of particles there will be exponential fall offs of the wave packet, for example infinitesimal probability of its being at infinity, but not zero. Should be the same for the particle incarnation of the photon, again imo. – anna v Aug 20 '11 at 13:15