4 ms·

An amplitude is kind of like a probability. I guess it's called an amplitude because it's used in complex quantum wave equations. But the rule to get a probabil

An amplitude is kind of like a probability. I guess it's called an amplitude because it's used in complex quantum wave equations. But the rule to get a probability from an amplitude is basically that you square its absolute value, which gives you a positive real number.

p1esk 7y ago
This doesn’t really help. How is this amplitude different from traditional probability? How can an event have negative amplitude? What does it even mean?
- empath75 7y ago
  Quantum mechanics makes a lot more sense if you don’t care about what it means and just learn the math.
- aeternum 7y ago
  The traditional probability = amplitude squared. An event can have negative amplitude, but due to the square the probability cannot be negative. I'm not sure why they don't just say that, it is the most straightforward part of QM.
  - wtallis 7y ago
    Amplitudes can be non-real, so simply squaring them doesn't ensure that you have a (non-negative) probability; you have to also take the absolute value. It's still a pretty straightforward process to derive a probability from an amplitude, but fully explaining that process is a bit of a distraction from making the point that amplitudes really aren't probabilities and shouldn't be thought of as equivalent to or even intuitively similar to probabilities.
    - a1369209993 7y ago
      To be more pedantic, it's actually the product of [amplitude] times [complex conjugate of amplitude][0]. Confusingly, this is sometimes called the "square" of a value - usually in contexts where complex-element vectors and matrices are involved, since most[1] real-element formulas calling for matrix transpose (dot products[2] are a special case of this) actually want conjugate transpose[3] but didn't notice because conjugate is identity on reals. 0: zz* = (z)·(z*) = (a+bi)·(a-bi) 1: Possibly all - I have yet to happen across a counterexample. 2: https://en.wikipedia.org/wiki/Dot_product#Algebraic_definition https://en.wikipedia.org/wiki/Dot_product#Algebraic_definiti... 3: https://en.wikipedia.org/wiki/Conjugate_transpose https://en.wikipedia.org/wiki/Conjugate_transpose
- mal808 7y ago
  Look at frequency and amplitude in sound, how different sound waves of different amplitudes interfere with each other. That'll help. Came across this while looking for an example: https://www.youtube.com/watch?v=CAe3lkYNKt8 https://www.youtube.com/watch?v=CAe3lkYNKt8
- pdkl95 7y ago
  Amplitudes were needed to easily describe wave-like behavior. To produce an interference pattern, we need something like a probability that can be negative to represent the negative half of a wave. Amplitudes are like probabilities that can destructively interfere when added. With traditional probabilities, if P(A) > 0 and P(B) > 0 the sum of the probabilities P(A)+P(B) cannot be zero. However, we needed to model observations like the two slit experiment where we observed that a location on the target that had positive probability of being hit by a photon in the two single-slit-only situations, that became zero when both slits were open.
  - rsp1984 7y ago
    Ok, so an "amplitude" is just like a PDF, only that it can also take on negative values and that adding "amplitudes" is a meaningful operation?
  - kitsuac 7y ago
    This was a very effective way to describe it, I've read a great deal about QM and you made it click much better.
  - p1esk 7y ago
    Isn’t it P(A|C) = P(B|C) = 0 where C is both slits are open? P(A)+P(B) is still > 0. The condition C modifies the marginal probabilities of A and B, does it not?

p1esk 7y ago

This doesn’t really help. How is this amplitude different from traditional probability? How can an event have negative amplitude? What does it even mean?

empath75 7y ago
Quantum mechanics makes a lot more sense if you don’t care about what it means and just learn the math.
aeternum 7y ago
The traditional probability = amplitude squared. An event can have negative amplitude, but due to the square the probability cannot be negative. I'm not sure why they don't just say that, it is the most straightforward part of QM.
- wtallis 7y ago
  Amplitudes can be non-real, so simply squaring them doesn't ensure that you have a (non-negative) probability; you have to also take the absolute value. It's still a pretty straightforward process to derive a probability from an amplitude, but fully explaining that process is a bit of a distraction from making the point that amplitudes really aren't probabilities and shouldn't be thought of as equivalent to or even intuitively similar to probabilities.
  - a1369209993 7y ago
    To be more pedantic, it's actually the product of [amplitude] times [complex conjugate of amplitude][0]. Confusingly, this is sometimes called the "square" of a value - usually in contexts where complex-element vectors and matrices are involved, since most[1] real-element formulas calling for matrix transpose (dot products[2] are a special case of this) actually want conjugate transpose[3] but didn't notice because conjugate is identity on reals. 0: zz* = (z)·(z*) = (a+bi)·(a-bi) 1: Possibly all - I have yet to happen across a counterexample. 2: https://en.wikipedia.org/wiki/Dot_product#Algebraic_definition https://en.wikipedia.org/wiki/Dot_product#Algebraic_definiti... 3: https://en.wikipedia.org/wiki/Conjugate_transpose https://en.wikipedia.org/wiki/Conjugate_transpose
mal808 7y ago
Look at frequency and amplitude in sound, how different sound waves of different amplitudes interfere with each other. That'll help. Came across this while looking for an example: https://www.youtube.com/watch?v=CAe3lkYNKt8 https://www.youtube.com/watch?v=CAe3lkYNKt8
pdkl95 7y ago
Amplitudes were needed to easily describe wave-like behavior. To produce an interference pattern, we need something like a probability that can be negative to represent the negative half of a wave. Amplitudes are like probabilities that can destructively interfere when added. With traditional probabilities, if P(A) > 0 and P(B) > 0 the sum of the probabilities P(A)+P(B) cannot be zero. However, we needed to model observations like the two slit experiment where we observed that a location on the target that had positive probability of being hit by a photon in the two single-slit-only situations, that became zero when both slits were open.
- rsp1984 7y ago
  Ok, so an "amplitude" is just like a PDF, only that it can also take on negative values and that adding "amplitudes" is a meaningful operation?
- kitsuac 7y ago
  This was a very effective way to describe it, I've read a great deal about QM and you made it click much better.
- p1esk 7y ago
  Isn’t it P(A|C) = P(B|C) = 0 where C is both slits are open? P(A)+P(B) is still > 0. The condition C modifies the marginal probabilities of A and B, does it not?