I QM & Motion: Is There Consensus?

[Zelebg]

Is there consensus on the stance of QM in regards whether motion is actually continuous or not?

 

[PeroK]

Is there consensus on the stance of QM in regards whether motion is actually continuous or not?

In orthodox QM, a particle is represented by a continuous wave-function. In that sense, the probability that you find a particle at a particular location is a continuous distribution. But, there is no sense in which the particle follows a specific trajectory $x(t)$, with the position of the particle being well-defined for every time $t$.

The expectation values, however, do generally follow classical laws. This is Ehrenfest's Theorem. For example:

$\langle p \rangle = m \frac{d \langle x \rangle}{dt}$

This says that the "expected" position of a particle at time $t$ is related to the expected value of its momentum according to the classical formula.

PS If, however, you question was: "does a particle move continuously from A to B, or jump from A to B in a sequence of discrete steps?"; then, neither of these is an accurate interpretation of QM.

 

[Zelebg]

PS If, however, you question was: "does a particle move continuously from A to B, or jump from A to B in a sequence of discrete steps?"; then, neither of these is an accurate interpretation of QM.

It's a question I had from a long time ago, so I forgot exactly where and what, but some QM descriptions seemed to imply electron would simply appear at point B, sometimes even before disappearing from point A, but in any case would appear at new position without actually traversing the distance.

 

[PeroK]

It's a question I had from a long time ago, so I forgot exactly where and what, but some QM descriptions seemed to imply electron would simply appear at point B, sometimes even before disappearing from point A, but in any case would appear at new position without actually traversing the distance.

A free electron is best described as a "wave packet", which corresponds to the probability distribution of the electron's position. The wave packet itself moves with a given velocity. But, it doesn't define a definite position or a definite velocity for the electron at any time. If you measure the velocity of the electron at any time, again you get value taken from the probability distribution.

The key to understanding QM is to understand that the quantities you measure are governed by probabilities. You can only say an electron is at point A if you measure it and find it at point A. You can't measure an electron to be at point A and point B at the same time.

 

[EPR]

Motion of what? This question is just too Big. There is no consensus what moves in qm(knowledge, probabilty, nonlocal fields, nonlocal guiding waves, etc.).

What moves in the delayed choice quantum eraser(a variant of the double slit experiment)?

QM is a theory of measurements via the Born rule - it is slightly more correct to assume motion is non-continuous.

For some profound reason classicality plays a big role in the quantum world, as long as you probe with classical sized devices.

 

[vanhees71]

In QM there's nothing noncontinuous. The time evolution is given by a differential equation and thus there cannot be "quantum jumps" in the literal sense.