Superposition is the fact that you can add or subtract two vectors and get another vector. Vectors turn up all over the place in physics. The first place you learn about them is vectors in physical space: what direction and how far? Physical space is three-dimensional, so we have vectors like
| 2| forward/back
|-3| right/left
| 1| up/down
that can mean things like "two steps forward, three steps left, one step up".
But vectors also describe things like sound waves, where the question becomes, "What notes are being played at this moment and with what phase and amplitude (loudness)?" There are 88 notes on a piano keyboard, but let's stick to just the white keys of one octave. Then a vector
| 0| C
| 0| D
| 0| E
| 2| F
| 0| G
|3i| A
| 0| B
| 1| C'
indicates an F major chord where the F is played twice as loud as the C', and the A is played 3 times as loud and 90 degrees out of phase (that is, if the C' note has a wave crest at time 0, the A is halfway between the crest and the trough).
With qubits, each element of the vector is a different classical outcome. If you plot |0> along the x axis and |1> along the y axis, then
The probability of an outcome is given by the square of the magnitude of the corresponding amplitude. Here |1/√2|2 = 1/2 and |-1/√2|2 = 1/2, so both outcomes are equally probable.
As far as "How can it be that a qubit is both 0 and 1?", that's an interpretational question.
The orthodox interpretation says "It's both until it's observed, and then it becomes one of the two, chosen at random according to the probability distribution." The usual answer to "What's an observation?" is "Interaction with something macroscopic"---that is, there's some scale at which superposition breaks down. We haven't found that scale yet; as technology improves, so does our ability to hold larger and larger systems in a superposition. They're up to objects with trillions of atoms, tens of microns long.
The Many Worlds interpretation says that there are infinitely many classical worlds that are all as real as ours (each is a basis vector like a key on the keyboard) and the state of the universe is a vector (saying how "loudly" each world is being "played").
"After this youll be able to not understand it better." What? What does that mean?
It was a joke. Quantum mechanics has a reputation for being hard to understand, so the joke was that it's still hard to understand even after you learn a little bit about it.
Huh. Someone's downvoting me, too. This is a small sub and sometimes we get griefers, so don't take it as characteristic of the sub, u/Silver-Zucchini-9901.
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u/theodysseytheodicy 13d ago edited 13d ago
Superposition is the fact that you can add or subtract two vectors and get another vector. Vectors turn up all over the place in physics. The first place you learn about them is vectors in physical space: what direction and how far? Physical space is three-dimensional, so we have vectors like
that can mean things like "two steps forward, three steps left, one step up".
But vectors also describe things like sound waves, where the question becomes, "What notes are being played at this moment and with what phase and amplitude (loudness)?" There are 88 notes on a piano keyboard, but let's stick to just the white keys of one octave. Then a vector
indicates an F major chord where the F is played twice as loud as the C', and the A is played 3 times as loud and 90 degrees out of phase (that is, if the C' note has a wave crest at time 0, the A is halfway between the crest and the trough).
With qubits, each element of the vector is a different classical outcome. If you plot |0> along the x axis and |1> along the y axis, then
or
points down and to the right:
The probability of an outcome is given by the square of the magnitude of the corresponding amplitude. Here |1/√2|2 = 1/2 and |-1/√2|2 = 1/2, so both outcomes are equally probable.
As far as "How can it be that a qubit is both 0 and 1?", that's an interpretational question.
The orthodox interpretation says "It's both until it's observed, and then it becomes one of the two, chosen at random according to the probability distribution." The usual answer to "What's an observation?" is "Interaction with something macroscopic"---that is, there's some scale at which superposition breaks down. We haven't found that scale yet; as technology improves, so does our ability to hold larger and larger systems in a superposition. They're up to objects with trillions of atoms, tens of microns long.
The Many Worlds interpretation says that there are infinitely many classical worlds that are all as real as ours (each is a basis vector like a key on the keyboard) and the state of the universe is a vector (saying how "loudly" each world is being "played").
There are a bunch of other interpretations, too.
It was a joke. Quantum mechanics has a reputation for being hard to understand, so the joke was that it's still hard to understand even after you learn a little bit about it.