# Are Quantum Leaps instantaneous?

1. Mar 11, 2015

### Symmetry777

Are Quantum Leaps instantaneous?

Are Quantum Leaps faster than the speed of light?

Do you have a good source I can cite?

Last edited by a moderator: Mar 11, 2015
2. Mar 11, 2015

### Staff: Mentor

Can you clarify what you mean by quantum leap? Because my first thought is that there is no such thing as a quantum leap.

My guess is that you're not talking about something that actually travels, so what would it mean for it to have a speed?

Last edited: Mar 11, 2015
3. Mar 11, 2015

### Staff: Mentor

What's going on is the system is perturbed by something and that changes the systems state. States give the probability of something being observed. Before the probability of something was zero - after its non zero. Its different to the idea of something spontaneously (although see what I say later) changing. It's more like the idea you have a dice sitting there with say 6 face up. There is no chance of another face being up. If you observe it it will always give 6. Now someone comes along and throws the dice (that's like an interaction) so that when we observe it any of the other faces could be up. The quantum state changes from being such when you observe it it will always be 6 to one where it has a probability of being something else.

To do that perturbation theory is used:
http://www.pa.msu.edu/~mmoore/TIPT.pdf

If our math was good enough we could actually find the continuous change in the quantum state from the interaction - but it isn't that good - so we are reduced to this mathematical trick.

Spontaneous change is a bit trickier - its actually caused by fluctuations in the quantum vacuum - at least that's the explanation anyway - the vacuum itself doesn't really exist - its simply an artefact of the perturbation methods used.

So basically we use perturbation methods because we don't know how or its too hard to do it any other way, that explains what going on, but also introduces things like virtual particles and the vacuum that's not actually 'real' - its simply an artefact of those perturbation methods.

It's subtle and tricky - but there you have it.

Thanks
Bill

4. Mar 11, 2015

### Symmetry777

You wrote, "Spontaneous change is a bit trickier - its actually caused by fluctuations in the quantum vacuum - at least that's the explanation anyway - the vacuum itself doesn't really exist - its simply an artefact of the perturbation methods used."

Is the “quantum vacuum” contaminated given there is nothing that can block a magnetic force?

Source Sited:
Question

Is there any material that can block a magnetic force? Specifically does lead block magnetic fields?

Magnetic fields (forces are caused by magnetic fields) cannot be blocked, no. That is, there is no such thing as a magnetic insulator.

A major reason for this has to do with one of Maxwell's Equations:

del dot B = 0

Which implies that there are no magnetic monopoles. That is, where as you can separate electric monopoles (positive and negative charges) such that an E-field never has to terminate on the opposite charge, you cannot do this with magnetic poles. There do not exist any magnetic monopoles. There is no such thing as "magnetic charge." All magnetic field lines MUST TERMINATE on the opposite pole. Because of this, there is no way to stop them -- nature must find a way to return the magnetic field lines back to an opposite pole.

However, magnetic fields can be re-routed around objects. This is a form of magnetic shielding. By surrounding an object with a material which can "conduct" magnetic flux better than the materials around it, the magnetic field will tend to flow along this material and avoid the objects inside. This allows the field lines to terminate on the opposite poles, but just gives them a different route to follow.

“The quantum theory asserts that a vacuum, even the most perfect vacuum devoid of any matter, is not really empty. Rather the quantum vacuum can be depicted as a sea of continuously appearing and disappearing [pairs of] particles that manifest themselves in the apparent jostling of particles that is quite distinct from their thermal motions. These particles are ‘virtual’, as opposed to real, particles. ...At any given instant, the vacuum is full of such virtual pairs, which leave their signature behind, by affecting the energy levels of atoms.”

-Joseph Silk On the shores of the unknown, p. 62

5. Mar 11, 2015

### atyy

Quantum jumps are instantaneous. The results observed when a quantum jump occurs are real. The wave function collapse that accompanies a quantum jump is instantaneous and "faster than light" in the sense that it takes place on a surface of simultaneity. However, the collapse is a formal tool and not necessarily real, and can be assigned differently by observers with different assignments of simultaneity. Although the collapse is "faster than light", it cannot be used to transmit classical information faster than light.

http://arxiv.org/abs/quant-ph/9906034
Classical interventions in quantum systems. II. Relativistic invariance
Asher Peres

6. Mar 11, 2015

### Staff: Mentor

As I explained in my post its trickier than that.

The quantum vacuum doesn't really exist - its simply an artefact of the mathematical methods used.

'Virtual particles are not real. They are part of a diagrammatic method to calculate scattering amplitudes in quantum field theory. I.e., artefacts of the mathematics of perturbation approximations.'

Thanks
Bill

7. Mar 11, 2015

### Staff: Mentor

I don't think that's what's going on

Due to an interaction the state changes continuously - but the new state, when you observe it, now has other possible outcomes - that is what's interpreted as a jump.

Spontaneous jumps is caused by interaction with the vacuum - at least that the explanation in the pertubative formalism.

Thanks
Bill

8. Mar 11, 2015

### atyy

But the observation is instantaneous, or rather at some point, we or the formalism still has to pick when the outcome occurs. The outcome occurs at a definite moment, so it is instantaneous.

As for the perturbative formalism, one can ignore that, since basically everything is smooth and just unitary evolution until the observation.

9. Mar 11, 2015

### Staff: Mentor

Sure - its exactly the same as the usual measurement problem. In interpretations with collapse that collapse happens instantaneously - but not all interpretations have collapse.

Thanks
Bill

10. Mar 11, 2015

### atyy

Yes, there's no quantum jumps in interpretations without collapse.

11. Mar 12, 2015

### vanhees71

There's no such thing as "quantum jumps" and there's nothing "instantaneous". You must always distinguish between the levels of description of a physical situation. On the most fundamental quantum level, the time evolution is continuous. On a macroscopic time scale sometimes you have things that appear to be happening instantaneously like the emission of a photon from a "spontaneous" decay of an electron from an excited energy level to a lower one, but there's nothing in the quantum formalism that's instantaneous here. It's the interaction of the atom with the electromagnetic field, and this is described by a continuous unitary time evolution operator in QED.

12. Mar 12, 2015

### atyy

But you need either hidden variables or many-worlds in order not to have quantum jumps.

13. Mar 12, 2015

### vanhees71

Why? I need states and operators representing observables and the matrix elements and expectation values to make contact to (macroscopic) observables. All this develops continuously with time. There are no quantum jumps. This is a notion from the socalled "old quantum theory" aka the Bohr-Sommerfeld atom, where transitions where explained as ad-hoc "quantum jumps". In the full theory (QED in the case of atomic transitions) the spectral width of observed spectral lines is small, and thus the transition necessarily anything else but "instantaneous" (according to the energy-time uncertainty relation).

14. Mar 12, 2015

### atyy

Oh, if that's what you mean. Peres uses quantum jump more or less synonymous with collapse, which is part of the quantum formalism unless one uses something like hidden variables or many-worlds.

http://arxiv.org/abs/quant-ph/9906034
Classical interventions in quantum systems. II. Relativistic invariance
Asher Peres

15. Mar 13, 2015

### atyy

It looks like there are two definitions of a quantum jump. One is the informal "old quantum theory" idea about electrons jumping between energy levels, and used more recently by Dehmelt as a heuristic. This is not really a jump in the quantum formalism. However, some, like Peres in http://arxiv.org/abs/quant-ph/9906034, use it for the collapse which follows a definite outcome and is instantaneous in the formalism. I think Plenio and Knight talk about these two meanings in http://arxiv.org/abs/quant-ph/9702007.

"From a quantum mechanical point of view, however, one has to be very careful, as the emission of a photon is not well defined. It is the detection of a photon in the radiation field which is a real event."

"So far we have discussed the quantum jump approach for the description of single radiating quantum systems. The main ingredient in the derivation was the assumption of time resolved photon counting measurements on the quantized radiation field. The resulting time evolution could be divided into a coherent time evolution governed by a non Hermitean Hamilton operator which is interrupted by instantaneous jumps caused by the detection of a photon and the consequent gain in knowledge about the system."

More or less the same reasoning is mentioned in Daley's more recent review http://arxiv.org/abs/1405.6694.

"If we are able to make perfect measurements and we see a photon appear in the time window t, then we know that a jump has occurred, and that the state of the atom should be projected on the ground state. On the other hand, if we know that no jump has occurred, then the corresponding evolution of the system is an evolution under the effective Hamiltonian Heff . Already here, we see a key piece of physics that will recur multiple times: knowing that no jump has occurred means that we gain information about the system, just as knowing that a jump has occurred gives us information that the atom is projected into the ground state.

Last edited: Mar 13, 2015
16. Mar 14, 2015

### vanhees71

There is no "instantaneous jump" in the detection of a photon, although I absolutely agree that this after all is what a photon is, namely the detection of a certain excitation of the electromagnetic quantum field via interaction with the detector material. Why should this represent an "instanteneous jump"? Microscopically it takes quite some time to establish such a detection event. On a macroscopic scale, we cannot resolve this, and it appears instantaneous, but that doesn't mean something is instanteneous in the microscopic description. Also, I still don't like to call a detection event "collapse". Fortunately usually nothing collapses, when a photon is absorbed in a photodetector or the em. cals. of the various detectors at experiments like the LHC.

17. Mar 14, 2015

### atyy

But in the formalism, the detection always takes place at a specific time. Is there such a thing is an observable that is smeared in time? In the Heisenberg picture, one writes for an observable O(t), and t is a sharp time. Basically, an observation is always conceived as a spacetime event, so it is real and sharp and localized. The collapse is not necessarily real, but one takes a simultaneity assignment and the wave function collapses instantanously across the surface of simultaneity when the observation occurs.

Last edited: Mar 14, 2015
18. Mar 14, 2015

### TrickyDicky

To be fair this is not the complete story. During the renormalization process nonunitarity(non-inversibility)is clearly introduced.

19. Mar 14, 2015

### atyy

The renormalization is unitary term by term. If one takes a QED to be a lattice theory, the theory is exactly unitary.

Some renormalization processes are irreversible in some sense - but not in time - the renormalization process can be considered a coarse graining in the space of theories, and so is irreversible in "theory space". However, by defining renormalization as an approximation to some quantum theory that is well-defined, such as QED on a lattice, the theory itself should be exactly unitary in time (until an observation is made).

Last edited: Mar 14, 2015
20. Mar 14, 2015

### TrickyDicky

Well, that's the trick. That the final picture is cleaned up doesn't mean all the steps were unitary, and that's what I meant by "the complete picture". Yes, one ends up cancelling the divergences term by term, but in taming these divergences one introduces a non-unitary deformation procedure(regularization) and even though one gets rid of the regulator dependence by taking the limit where it vanishes, it is still true it had to be introduced in the first place in order to get finite results from the calculations.
But that is not possible as of today.