sirchick said:
Now one part of the lecture video mentions that if a photon has two possible pathways it can take. They cancel each other out and there for it takes neither path ? The video failed to explain why it won't pick either given i thought everything was based on probability, therefore it must take at least one of them?
Quantum mechanics isn't based on probabilities, it is based on probability amplitudes. That extra word makes a big difference, most notably because probability amplitudes can be negative (they are actually complex numbers, but their ability to be negative is the simpler way to think about it to get the basic idea). This is also the fundamental difference between how we used to think of waves and particles. We used to associate material objects (like particles) with probabilities of doing various things, like a rolling a pair of dice. Then the probabilities just add-- the more ways something can get rolled (like a 7), the higher its probability. But waves also work by adding up various sources, however waves have an "amplitude", and it can be negative. That means waves can experience what is known as destructive interference-- two wave sources can add up to no amplitude at some point (called a "node", like on a guitar string, where the two waves are waves moving in opposite directions along the string).
The big surprise came when it was found that particles can also exhibit wavelike effects, such as interference patterns. So it was realized that particles are also ruled by probability amplitudes, not probabilities-- just like waves are. This is called "wave/particle duality". So if there are two ways something can happen, we have to add up their probability amplitudes, not their probabilities, and then square the result (really, multiply by the complex conjugate) to get the actual probability. That won't always result in them canceling (called destructive interference), it might work out to increase the probability by a factor of 4 over each independent probability (called constructive interference). Working out how the amplitudes add up is a lot of what quantum mechanics is about.
You also raise the interesting question, if there are two contributing probability amplitudes to a final probability, can we tell which one of those is the one that actually occurred in any given instance of that event? When adding probabilities, like rolling a pair of dice, we can see how we got the "7"-- maybe it was a "1" and a "6", or a "3" and a "4", etc. But when adding probability amplitudes, it turns out very differently-- it is always fundamentally indeterminate which one actually happened, all you get to know is the final outcome. The classic example of this is the two-slit experiment, where you get an interference pattern in many trials. But in any single trial, it is fundamentally indeterminate which slit the particle went through-- you need both slits to be able to predict the pattern, but you never know which slit the particle went through in anyone trial. For many interpretations, this implies that nature herself is moot on the issue (but for some, who prefer a quasi-classical interpretation like Bohm gives, nature herself does know which slit but we don't get to know that).