So continuing on, what is difficult when you try to make sense of QM? What aspects make it difficult to see what QM is about?
I realised three posts wasn't going to cut it, but I'm still trying to keep things brief! Apologies!
A brief sketch of QM mathematically will help.
Quantum Mechanics describes the current state of the world as a set of amplitudes. Amplitudes are numbers that when you square them, they give the probability of some event occurring. Right now, since I'm not giving anything an interpretation, that's all they are.
So there's an amplitude for anything of the form:
Amplitude to see quantity A in region R have value V at time period T .
A concrete case would be:
Amplitude to see the Voltage in this wire be 4.5V between 10:40 and 10:50.
QM might give this an amplitude of -0.2, squaring makes it 0.04. So that's a 4% chance of this happening.
Just note that the amplitudes can be negative, however since we square them to get the probabilities, the probabilities won't be.
The final component is the uncertainty principle. Most quantities come in pairs, like position and moment, voltage and electric potential. When the amplitudes for one are concentrated around one value, meaning that outcome is very likely, the probabilities for the other become more spread out and uniform. Or put another way, as one element of the pair becomes more certain, the other becomes more random. Such pairs are called conjugate variables.
With this in place, I'll begin a list of problems, spread over some posts, before ending with interpretations.
1. What's a particle?
So QM presents a very detached and almost totally observation based picture of a particle. It is simply the case that there are certain "states of the world", that is lists of amplitudes, where a set of quantities co-occur (abstract, but just wait).
So an electron is just a case where the amplitudes say certain equipment will always detect a bit of spin with a bit of electric charge. To then conclude that there is an object, like a little ball, that travels around holding those properties is a mental picture that QM doesn't give any particular support to. This will get more extreme in the two cases below.
The silver oven: Let's say I've set up an oven that burns silver and I build a piece of equipment that can detect spin and charge. I then notice the oven makes the detector click every 30 seconds. So I say I have detected an electron, which the oven produces at a rate of one every 30 seconds. My detector is sensitive enough to narrow the location of the clicks down to the nanometer.
Now, without touching the oven, I go off and get a new detector that can narrow the clicks down to the femtometer and position it outside the oven. So I will continue to get clicks every thirty seconds, but sometimes it will be three clicks. Two with negative electric charge and one with positive. In a particle based view, I have seen two electrons and one positron.
Why though? The oven creating the particles hasn't changed, I've just made the equipment finer in resolution. Now the normal intuitive explanation is that the equipment, by probing so deeply, provided the energy to create the particles, but QM is silent on this. In fact it always presents there being a nonzero amplitude to detect three clicks in a femtometer sized region. The previous equipment just didn't have access to regions of that size, but QM always said the possibility was there.
So what is the oven actually emitting. It's hard not to conclude that its just "some charge and some spin" which will be packaged as single or multiple clicks depending on your equipment.
The beam of light:
Take a beam of light. The conjugate variables in the case of light is colour(frequency) and photon number. Hence the higher the probability for the light to be a single colour, the more spread out its probabilities are for photon number. This can be tested with Laser light. Lasers are states of the electromagnetic field that are highly likely to be observed having only one consistent colour. Consequently when you place a photon detector in front of them they have an equal likelihood of producing several values. The exact same beam of laser light could be measured as containing 10 photons one minute and 1000 the next.
Again how many particles are there? Is the possible conclusion that there is no such thing, simply probabilities for clicks?
Similar "uncertain particle count" occurs in all quantum mechanical system of sufficient complexity, for example most atomic nuclei have an indeterminate number of pions inside them. So to what extend can we say what anything is "made of", if particle count isn't fixed?
Ending on a brief point, even Hydrogen in QM is just a state with a set of amplitudes that "often" act like those of a proton combined with those of an electron. However some of the amplitudes for hydrogen events can't be parsed as a combination of those for a proton or an electron. So to what extend is it made of a proton and electron?
2. Interference:
In Quantum Mechanics possibilities can interfere. (If the mathematics below is tedious, skip to the bolded point)
Consider betting on a horse to come in various positions in a race, say 1st, 2nd, 3rd in a three horse race. The horse can be fed either Smithson horse food or Johnson horse food.
In the first case his chances of coming in the various positions are:
(0.1,0.4,0.5)
i.e. 10% chance of coming first.
In the second case:
(0.2,0.4,0.4)
If you don't know which of the brands of food the horse takes, you can combine the above to get:
(0.15,0.4,0.45)
So a 15% chance of winning when you aren't sure of which brand he took.
However in the QM case, since amplitudes can be negative, we could have for the first case:
(0.316,-0.632,0.707)
and for the second:
(0.447,0.632,0.632)
I won't go into how these are combined when the horse could eat either brand of food, but the main point is that the second possibility would cancel out due to the minus signs.
Hence a quantum horse has a chance of coming second if he eats one brand, a different chance of coming second when he eats another brand, but if he could eat either brand he has no chance of coming second at all. It is possible for an outcome to cancel out from two different sets of possibilities,even though it is possible in each of them alone.
This is why the double slit experiment is confusing. There are points on the detection screen that have a chance of being lit up when either slit is open, but not when both are open, because the two events of "particle goes through right slit and hits point A" and "particle goes through left slit and hits point A" have their probabilities cancel out.
If you see the probabilities as purely a reflection of your knowledge, it is very hard to see how this is possible. How by not knowing a binary outcome (Horse food A or B) do I remove something that can happen under either outcome?
It also leads to the next confusion....
Edited by Son Goku, : Bolding and spelling
Edited by Son Goku, : No reason given.
Edited by Son Goku, : No reason given.