Contradiction between the show Cosmos and what someone here told me?

[phinds]

I wonder if it is not a matter of difference between "why" and "how". We can describe the process ("how"), but do we know "why" it happens?

If we can in fact fully describe the process then the timeline of event should show which is cause and which is effect (or, more properly, which COULD be cause and effect, since we have to be careful of the logical fallacy "post hoc, ergo propter hoc"). CAN we in fact fully describe the process?

 

[bluemoonKY]

@DrDu, I'm curious about this as well. You seem to be implying that the drop in energy state is an effect and electron emission is a cause. Do we really know that for sure?

Phinds, on your second sentence, you mean photon emission is a cause.

 

[Ygggdrasil]

We know from stimulated emission that if we "tickle" the excited state with certain frequencies of light (close to the resonant frequency of system), we can cause the system to emit a photon. For some transitions (e.g. nuclear spin flips in NMR spectroscopy) where there is almost no spontaneous emission, this causal relationship is very clear as we see emission only when we tickle the system with a photon.

In the case of spontaneous emission, we know that quantum vacuum fluctuations cause an excited state system to drop back down to the ground state. How do we know this? If we calculate how often the quantum vacuum fluctuations should tickle our excited state and cause the emission of a photon, we see that the calculated rate of emission matches observations from experiments.

 

[bluemoonKY]

In the case of spontaneous emission, we know that quantum vacuum fluctuations cause an excited state system to drop back down to the ground state. How do we know this? If we calculate how often the quantum vacuum fluctuations should tickle our excited state and cause the emission of a photon, we see that the calculated rate of emission matches the theoretical prediction.

What does quantum vacuum fluctuations mean? When you say "We know that quantum vacuum fluctuations caused an excited state system to drop back down to the ground state", do "excited state system" mean an electron with a bumped up energy level?

Ygggdrasil, unless I am misunderstanding you or DrDu, you two seem to have contradictory answers. It appears to me that one of you might be right and the other wrong, or you might both be wrong, but you cannot both be correct.

 

[Ygggdrasil]

I'd have to point you to someone with a much better understanding of QED than me. For example:
https://profmattstrassler.com/artic...basics/quantum-fluctuations-and-their-energy/

 

[bluemoonKY]

For what it's worth, I'm going to write a transcript of the part of the Hiding in the Light episode of the tv show Cosmos in which Neil deGrasse Tyson says that nobody knows why electrons drop in energy levels. At about 34:50 into the episode Tyson says the following: "The force that holds an electron in orbit has nothing to do with gravity. It's a force of electrical attraction. The electron dances a wavy ring around the central nucleus of a hydrogen atom and makes quantum leaps from orbit to orbit, up or down. The larger the orbit, the greater the energy of an electron. An electron has to get energy to leap to a larger orbit, and it has to lose energy to jump back down. Every upward leap is caused by an atom absorbing a light wave, but we have no idea what causes the downward leaps. What we do know is that such leaps always produce a light wave whose color matches the energy difference between the orbitals."

 

[phinds]

Phinds, on your second sentence, you mean photon emission is a cause.

Yeah, you would think I could keep electrons and protons separated, but no, not me

ARRRGGGHHH. PHOTONS, dammit !

 

[IsometricPion]

I think it may be a little misleading to say that photon emission causes a change in energy level or vice versa. In order to give the state of the whole system one must say in what state the electron field is and in what state the photon field is. The state is only allowed to change in certain ways, one of these is for the electron to go to a lower energy level and the number of photons to increase by one.

If the question is: why does the system change state?, then the answer is that there is an uncertainty relation between the uncertainty in the state of the system (the number of photons and the state of the electron) and the uncertainty in the energy.

More technically, the number operators for the photon field and the electron field do not commute with the Hamiltonian. This means that if the system starts off in one state, it may not remain in that state (in the sense that there will a non-zero probability of measuring the system to be in a different allowable state at a later time).

 

[bluemoonKY]

More technically, the number operators for the photon field and the electron field do not commute with the Hamiltonian.

What does "the Hamiltonian" mean?

 

[Borek]

What does "the Hamiltonian" mean?

Wikipedia, therefore not necessarily reliable: https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)

 

[DrDu]

Ygggdrasil, unless I am misunderstanding you or DrDu, you two seem to have contradictory answers. It appears to me that one of you might be right and the other wrong, or you might both be wrong, but you cannot both be correct.

Why do you think so? Ygggdrasil, like me, told you that vacuum fluctuations of the electromagnetic field are responsible for the transition.
An important point, which already has been made repeatedly in this thread is that the change of orbital and the emission of a photon are not independent events and not one is causing the other.
This weekend I thought how to explain spontaneous emission somewhat better. But as a proviso I have to say that if you really are seeking a precise in depth explanation, you have to learn the mathematical apparatus.
So, the transition probability, whether classical or quantum mechanical, depends on the coupling of the dipole moment $d=e r$ with e electric charge and r the position vector, to the electric field E.
More precisely, the transition probability per unit of time is proportional to $d^2 E^2$. Now considering the spontaneous emission, d is an operator and we have to equate it between the initial excited and final ground state orbital. As an order of magnitude, $d\approx e a$ where a is the Bohr's radius of the hydrogen orbit. $E^2 \propto h f (n+1/2)$ where h is Planck's constant, f is frequency and n is the number of photons. The interesting point here is that the square of the field amplitude is non-vanishing even if there are no photons (n=0). This is the vacuum fluctuation Ygggdrasil has mentioned.
In QED, E is the momentum density of the electromagnetic field, just like p is the momentum of the electron. Now like the momentum squared $p^2$ does not vanish for a hydrogen atom even in it's ground state, the momentum density does not vanish for an electromagnetic field even in the vacuum, but takes the value $hf/2$.

 

[Ygggdrasil]

When you say "We know that quantum vacuum fluctuations caused an excited state system to drop back down to the ground state", do "excited state system" mean an electron with a bumped up energy level?

By excited state system, I mean an atom or molecule with an electron that has been bumped up an energy level.

Ygggdrasil, unless I am misunderstanding you or DrDu, you two seem to have contradictory answers. It appears to me that one of you might be right and the other wrong, or you might both be wrong, but you cannot both be correct.

I agree with Dr Du's explanations. We've probably used different terminologies to discuss the same process in a very informal way (me) vs a more rigiorous approach (Dr. Du), but we are talking about the same thing.

 

[phinds]

... the change of orbital and the emission of a photon are not independent events and not one is causing the other.

Unexpected (for me for sure and I think for BluemoonKY as well) but good to know. Thanks for that explanation.

 

[Cecil Tomlinson]

You are all in agreement that the movement of an electron from one energy level to another within an atom is associated with the absorption or emission of photons. No argument there. You are also in agreement that the movement of an electron to a higher energy level has a cause, which is the absorption of a photon (by the atom, actually, not the electron; the energy level belongs to the atom; the electron is merely the traveling messenger). What is in question is what triggers the movement of an electron back to a lower energy level that happens to be vacant. Does it have a cause? Or is it a totally random, spontaneous occurrence? The answer is: Of course it has a cause. The stability of the electron at the higher energy level depends on the threshold energy required to knock it back out of the higher energy level, which is a much smaller amount of energy than it took to put it there. That actually requires another photon. That other photon can come from something as simple as the thermal collision of this atom with another, but it always has a cause. Identifying that cause is more difficult than identifying the original high energy photon. It could be considered to be a random occurrence.

 

[ensign_nemo]

Historically, it was a big surprise to discover that electrons in the ground state do not lose energy and drop into the nucleus of an atom.

The classical electrodynamic model of a moving charge would have the charge radiate energy and eventually lose all of its energy.

Electrons in the ground state do not seem to do this, and that's a subtle but important difference between classical electrodynamics and quantum electrodynamics.

That is probably what was referred to in the show, albeit indirectly: the loss of energy is always at certain frequencies that correspond to leaps from one energy level to the next. It's "quantized" - only some energies are legal, and there is a base level or "ground state".

I found a neat set of answers to this question here:

https://www.researchgate.net/post/Why_dont_electrons_emit_radiations_in_stationary_orbits_while_revolving_around_the_nucleus

 

[IsometricPion]

What does "the Hamiltonian" mean?

A Hamiltonian is the name people give to a "function" (technically a functional or an operator) that takes in the fields or positions and momenta of the things in a system and returns the energy associated with those fields or positions and momenta.

The stability of the electron at the higher energy level depends on the threshold energy required to knock it back out of the higher energy level

Please give some reference or explanation about this threshold, I have never heard of it for spontaneous emission. As far as I know, there is no such threshold. Even if the only things in the universe initially were the electromagnetic field (with zero photon number) and a hydrogen atom in an excited state, the excited state would eventually decay and emit a photon.