Quantum Mechanics: Multiple Pathways Explained

[sirchick]

I recently got a starter home learning course on quantum mechanics and well its basically at the stage of explaining the simplistic basics of it.

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?

Or the other theory i was told was it takes all of them simultaneously and creates branches in the universe. But if the pathways cancel out - then wouldn't they have to have some kind of energy in the positive and negative to eliminate each other =/

It didn't go into depth on it but I've not heard of this before. I've only heard of the "it takes all possible paths".

 

[Ken G]

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).

 

[sirchick]

Is the lack of being able to measure which slit they go through due to limited technology?

Or is it literally impossible no matter how advanced our technology becomes?

 

[Ken G]

Is the lack of being able to measure which slit they go through due to limited technology?

No, we can certainly measure which slit they went through. The key point, though, is to do so requires a different experimental apparatus, and will result in a different outcome overall. For example, we won't get a two-slit interference pattern any more, if we detect which slit each particle went through. Nature shouldn't care whether or not we know something that it already knows, so since nature does apparently care if we detect which slit, this may well imply that nature itself does not know which slit unless it is determined by the experiment. That is certainly how some interpret quantum mechanics-- but not others (most famously, not deBroglie and Bohm).

Or is it literally impossible no matter how advanced our technology becomes?

What seems to be impossible is to measure which slit in each trial and still get the two-slit interference pattern over many such trials.

 

[sirchick]

That sounds a bit spooky.

So they have some ability to be aware of their surrounds that something or some one is observing.

And that very act removes both the wave thus resulting in a definitive path of where it will end up instead ?

Does it also mean no diffraction occurs when you measure which slit it goes through?

 

[Ken G]

So they have some ability to be aware of their surrounds that something or some one is observing.

And that very act removes both the wave thus resulting in a definitive path of where it will end up instead ?

Welcome to the spookiness of quantum mechanics! But note, it's not actually necessary to anthropomorphize the particles that way. Doing so does have the advantage of making it more colorful to picture, but I'd say a key lesson of quantum mechanics is that the "quantum domain" doesn't work like the classical domain, and anthropomorphizations are classical thinking. So I would prefer to just say that if a different apparatus establishes different facts about what is happening, then something different is happening. It's not "spooky" that different things happen when the apparatus is different.

Does it also mean no diffraction occurs when you measure which slit it goes through?

It means the only type of diffraction you get is single-slit diffraction. There's a common misconception that you don't get an interference pattern if you measure which slit, but what is really meant is you don't get a two-slit interference pattern, because you can't get interference between two things that are not consistent with the experiment. But you do get interference across the single slit, because passing through that slit is consistent with what the apparatus has established. Thus, it is still wave mechanics-- I hate language that suggests you have somehow turned the wave into a particle by measuring which slit, it's always a particle and it's always ruled by wave mechanics. The issue is, what goes into the wave mechanics, and the answer is, everything that is consistent with what the apparatus has established as fact.