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Regarding quantum "leaps" or "jumps" (also known as atomic electron transition) -- do these leaps happen in what would appear to be random directions, or do they happen according to some rule, such as jumping from an area of lower gravity in the direction of higher gravity?

I ask this in the context of theories which include quantum jumps. I realize it's a is a topic of some debate, but for the purposes of this question I want to focus on the theoretical or empirical nature of quantum jumps (or whatever you want to call them) rather to debate their existence.

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    $\begingroup$ There are no "quantum leaps", hence one can't ask if they happen in random directions. Whether a quantum system is isotropic depends on the internal state of the system and external fields that it is subjected to, but for this one has to set up a density matrix description because even the quantum mechanical symmetries are not sufficient to make e.g. a radiating atomic system perfectly isotropic (photons are spin 1, hence the radiation pattern is that of a dipole, perfect isotropy can therefor only be achieved by a secondary stochastic distribution of atomic states). $\endgroup$
    – CuriousOne
    Commented Jun 12, 2016 at 2:23

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There are no quantum leaps. This is an errant notion from early theories that was latched onto by the public and continues to be popularized by 'pop science' programming. It is a misunderstanding of quantum mechanics.

There are discrete states for negative energy systems, but any Hamiltonian term that allows transitions between them does so continuously. In this sense, there are no discontinuities in time (ie, no jumping). The Hamiltonian system that allows for (continuous) transition between eigenstates is different (usually by the inclusion of a coupling term) than the system that admits true eigenstates.

Are the transitions random? No. Quantum mechanics is a fully deterministic theory, as far as wavefunction evolution is concerned. Transition amplitudes can be calculated/simulated, and will give the same result every time. The quantum evolution, while fully deterministic, only specifies the probability of measurement. Measurements themselves are understood to be predicted by treating $|\psi|^2$ as a random variable of measurement.

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    $\begingroup$ The states of, for instance electrons do change spontaneously/discretely; what is changing continuously is the wavefunction, the probability of the state occupation. $\endgroup$
    – Mario Krenn
    Commented Jun 12, 2016 at 1:29
  • $\begingroup$ @NiceDean It depends what theory you're using, but I don't disagree with your statement. My point is that these are continuous deformations of the wavefunction. I have also edited my answer for clarity. $\endgroup$
    – anon01
    Commented Jun 12, 2016 at 1:31
  • $\begingroup$ Read my answer carefully, I believe we are saying the same thing. The theory evolves deterministically. Measurements are not deterministic. $\endgroup$
    – anon01
    Commented Jun 12, 2016 at 1:34
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    $\begingroup$ @Hack-R Please provide a hyperlink. The Bohr model of the atom is proto-quantum: it was not well understood, formulated in firm ground, or even fully quantum mechanical in the sense we understand it today. It was a historical stepping stone to field theories of matter. $\endgroup$
    – anon01
    Commented Jun 12, 2016 at 1:40
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    $\begingroup$ @Hack-R: Bohr's model of the atom is outdated by almost a century now. It should not be taught, at all since it's virtually useless and misleading, as far as real physics is concerned. $\endgroup$
    – CuriousOne
    Commented Jun 12, 2016 at 2:18

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