Where does the energy come from?

[Wanda]

TL;DR Summary

Where does the energy emitted come from?

Hello all,
I'm new here … interesting discussions.

My question is: When an electron "jumps" from a higher energy level to a lower one, a photon is emitted. Is it correct to say that it is the electron that emits the photon?

Or when an electron aligns in a magnetic field, a photon is either emitted or not (spin down or spin up). Again: is it correct to say that it is the electron that emits the photon?

(To keep the electron unaligned, energy is needed, and this is the energy that is emitted when it aligns itself. But is it the electron or the field or what that emits the energy?)

An object on top of a mountain is slightly heavier than the same object in the valley. Does this mean that the potential energy is stored in the object itself?

Thanks in advance, Wanda

 

[Vanadium 50]

The electron-nucleus system emits the photon.

 

[berkeman]

Welcome to PF.

An object on top of a mountain is slightly heavier than the same object in the valley. Does this mean that the potential energy is stored in the object itself?

Say what? Can you show a link that says this? Thanks.

 

[Wanda]

Say what? Can you show a link that says this? Thanks.

I remember being told exactly this in school; why I remember it so clearly is because most students didn't get it right. (I imagine that the potential energy when the object is on top of the mountain makes the difference in mass/weight too?)

Anyway, thank you both for your replies.

Why I asked:
Say we prepare a great number of electrons so that they are alltogether in the same state (spin up in regard to a magnetic field). When we now change the direction of the field, the electrons in aligning their spin with the new field either emit a photon (spin down) or don't (spin up). But if I say that the photon/energy is emitted by the electron itself, wouldn't that mean that the electrons are not all in the same state?

The electrons in this experiment (apparently) ARE all in the same state, but how is this compatible with saying that part of the electrons emit a photon and part not?

 

[phinds]

TL;DR Summary: Where does the energy emitted come from?

An object on top of a mountain is slightly heavier than the same object in the valley

I remember being told exactly this in school

Either you remember incorrectly or you were told incorrectly, since this is NOT true but rather is the exact opposite of reality.

 

[Dale]

But if I say that the photon/energy is emitted by the electron itself, wouldn't that mean that the electrons are not all in the same state?

That is correct. In an external magnetic field spin up and spin down are distinct states. This is the operating principle of magnetic resonance imaging, except using protons instead of electrons.

 

[Wanda]

Either you remember incorrectly or you were told incorrectly, since this is NOT true but rather is the exact opposite of reality.

Ok, thank you, maybe I don't remember correctly.

Can anybody tell me if the photon emitted in the spin up/down experiment comes from the electron itself?

 

[Wanda]

That is correct. In an external magnetic field spin up and spin down are distinct states. This is the operating principle of magnetic resonance imaging, except using protons instead of electrons.

Spin up and spin down are distinct states, yes. But at the beginning we prepared the electrons to be all in the same state (spin up with regard to a magnetic field). If we now say that aligning in a new field part of the electrons emit a photon and part not, it sounds to me as if their (prepared) state was not the same for all electrons, as if part of the electrons had this enery "stored" in them and part not, as if this was some "hidden variable" (which is nonsense of course). That's why I have such difficulties to write that it's the electron that emits a photon.

 

[Vanadium 50]

Can anybody tell me if the photon emitted in the spin up/down experiment comes from the electron itself?

The electron-nucleus system emits the photon.

 

[Wanda]

The electron-nucleus system emits the photon.

You mean in the case where an electron jumps from a higher level energy to a lower one in an atom?
In the spin up/spin down experiment there's no such thing as an "electron-nucleus system" (I guess).
Or maybe in this experiment the photon is emitted by the electron-field system?

 

[PeterDonis]

at the beginning we prepared the electrons to be all in the same state (spin up with regard to a magnetic field).

You prepared the electrons to all be spin up with regard to the original magnetic field. When you change the direction of the magnetic field, all of the electrons are now in a superposition of spin-up and spin-down with respect to the new magnetic field. So when you measure their spins along the new magnetic field direction, some will be spin-up and some will be spin-down.

 

[PeterDonis]

it sounds to me as if their (prepared) state was not the same for all electrons, as if part of the electrons had this enery "stored" in them and part not

I don't know where you're getting this from. The state of all the electrons before the measurement is the same. The state of all the electrons after the measurement is not, since some are spin-up and some are spin-down--i.e., some have not emitted a photon and some have. Obviously the ones that did emit photons will now have different energy than the ones that didn't. That's because they gave different results from a measurement. I don't see what the problem is.

 

[Wanda]

You prepared the electrons to all be spin up with regard to the original magnetic field. When you change the direction of the magnetic field, all of the electrons are now in a superposition of spin-up and spin-down with respect to the new magnetic field. So when you measure their spins along the new magnetic field direction, some will be spin-up and some will be spin-down.

Yes, this was clear.

I don't know where you're getting this from. The state of all the electrons before the measurement is the same. The state of all the electrons after the measurement is not, since some are spin-up and some are spin-down--i.e., some have not emitted a photon and some have. Obviously the ones that did emit photons will now have different energy than the ones that didn't. That's because they gave different results from a measurement. I don't see what the problem is.

"Obviously the ones that did emit photons will now have different energy than the ones that didn't."
If so, than I have the answer now - didn't think of this possibility. Thank's a lot, seems all clarified now!

 

[Vanadium 50]

These experiments are done with atoms. But even with electrons, energy is a property of the system, not of individual components of the system.

 

[Wanda]

These experiments are done with atoms. But even with electrons, energy is a property of the system, not of individual components of the system.

Yes, rethinking the whole, it doesn't seem correct to me that the electrons that emitted a photon have now different energy than the ones that dindn't.

When a stone falls to the ground, its potential energy transforms in kynetic energy and than in deformation/heat? Think if I ask where the energy of the photon in the spin experiment came from is as if I would ask where the energy for the deformation/heat came from.

(The potential energy was assigned to the stone in view of ist potential for destruction in falling, or mildly for its capacity to do work - that's also the definition of energy. And this potential energy is "released" as heat/deformation in the case of the falling stone and as a photon in the case of an electron aligning its spin.)

So yes, energy is a property of the system.

This was my first doubt:
You can repeat the spin experiment by skipping the magnetic field a second time:
First the prepared electrons have all spin up with regard to the original magnetic filed, after skipping the field by a given angle, the electrons align with this second field, that's they are now all in the same state again (spin up with regard to this field now) and have not different energy. So you can repeat the experiment as if the first one never took place, as the electrons are again all in the same state.

Energy is a property of the system:
Take two space vessels "floating" in space with no acceleration and far away from gravitational fields. Each vessel has (nearly) zero kynetic and zero potential energy. But if they are "alligned for collision", they have now potential energy with respect to each other. When they collide I don't ask where the energy that descructed the vessels came from. It wasn't "stored" in the vessels themselves, nor anywhere else. - It's a property of the system, of the "constellation".

What disturbed me was this photon "coming out from nowhere", but now things become clearer.

Sorry for my long posting, I had to see clearer for myself (think I didn't write nonsense?).

Thank you again, Wanda

 

[PeterDonis]

rethinking the whole, it doesn't seem correct to me that the electrons that emitted a photon have now different energy than the ones that dindn't.

You are wrong here. The electrons that emit photons give some of their energy (or some of the energy of the atom of which they are a part--see below) to the electromagnetic field. The total energy of the electron + field (or atom + field) system stays the same; it just gets redistributed. The field now has more energy, so the electron (or atom) must have less.

Think if I ask where the energy of the photon in the spin experiment came from is as if I would ask where the energy for the deformation/heat came from.

In the actual experiments you are talking about, as @Vanadium 50 has pointed out, the electrons are bound in atoms, so when they emit a photon they transition to a lower energy level in the atom. This is best viewed, as has already been pointed out, as a decrease in the energy of the atom as a whole. None of this affects what I said above.

after skipping the field by a given angle, the electrons align with this second field, that's they are now all in the same state again (spin up with regard to this field now) and have not different energy.

How do you align the electrons with the second magnetic field? Is any energy exchanged in this process?

 

[Wanda]

In the actual experiments you are talking about, as @Vanadium 50 has pointed out, the electrons are bound in atoms, so when they emit a photon they transition to a lower energy level in the atom. This is best viewed, as has already been pointed out, as a decrease in the energy of the atom as a whole. None of this affects what I said above.

I never heard that this experiment is carried out with entire atoms; I read a lot about it and saw many videos, and NOT ONCE I heard about entire atoms, just electrons in a magnetic field. I don't want to say I don't believe you. I also didn't try to figure out the technical aspects, how a great number of electrons can be kept in a magnetic field. Would this be technically possible? (as all electrons have negative charge). Also in the double slit experiment you always hear of just electrons being shot through the slits, and here I think it's really only electrons? (although the experiment was carried out with atoms too and even with molecules).

How do you align the electrons with the second magnetic field? Is any energy exchanged in this process?

Good question, I don't know. As part of the electrons emit a photon I would say yes. It's the potential energy that would be needed to keep the electrons with spin down. Correct?

Last question: you say the electrons/atoms that emitted a photon are now at a lower energy level than those that didn't. But to repeat the experiment you need all electrons to be in the same state: so does this mean only with regard to their spin, and their energy level would be an other state and doesn't matter for this experiment?

@Sorry, Vanadium 50 J

And thank you, Wanda

 

[PeroK]

I never heard that this experiment is carried out with entire atoms; I read a lot about it and saw many videos, and NOT ONCE I heard about entire atoms, just electrons in a magnetic field.

If we are talking about the Stern-Gerlach experiment, then that was done with silver atoms.

it can't work with electrons, because the Lorentz force acting on the electron charge would dominate the force caused by the electron spin. You can read about it here,and perhaps reassess the sources you have been relying on:

https://en.m.wikipedia.org/wiki/Stern–Gerlach_experiment

 

[PeterDonis]

I read a lot about it and saw many videos, and NOT ONCE I heard about entire atoms, just electrons in a magnetic field.

Please give specific quotes from specific references that make you think this. Vague statements about "read a lot" and "many videos" are not a good basis for discussion.

 

[PeterDonis]

this experiment

So far in this thread it is not clear exactly which experiment you want to talk about. All we have are vague statements like:

When an electron "jumps" from a higher energy level to a lower one

when an electron aligns in a magnetic field

Both of these, if we try to pin them down to actual experiments that have actually been done, will involve electrons in atoms (in fact the first statement makes no sense for electrons not bound in atoms or similar bound states; and the second, as @Dale has pointed out, looks like a description of an MRI, which involves bound states as well).

At this point I think you need to give us a specific scenario with specific references so we know exactly what you want to talk about. Otherwise we are likely to be talking past each other and that doesn't help anyone.

 

[vanhees71]

Ok, thank you, maybe I don't remember correctly.

Can anybody tell me if the photon emitted in the spin up/down experiment comes from the electron itself?

As was stressed already before, the photon comes from the bound state as a whole. The most simple "gedanken experiment" is to put an atom in one its excited "energy eigenstates". Now these eigenstates by definition only refer to the part of the Hamiltonian describing the nucleus + electrons bound together by the Coulomb forces between the nucleus and the electrons and among the electrons.

In addition all these charged particles couple to the quantized electromagnetic radiation field, which shows quantum fluctuations. This additional interaction can be described by perturbation theory, and indeed there's a certain probability that the excited atom emits a photon, going to a lower-energetic state. This energy is then the energy of the emitted photon. Since the bound-state energy eigenstates of the atom have discrete eigenvalues, the corresponding energy differences are also discrete and make up the line spectrum of the atom.

The above described spontaneous-emission process is the most simple proof for the necessity of quantizing also the electromagnetic field and not only the charged particles.

 

[Dale]

Of importance for MRI is that the energy of the perturbation depends on the molecule. Protons in a water molecule have an energy change that is about 3.5 ppm greater than the energy change of protons in a fat molecule in the transition between spin up and spin down. So, not only is the energy dependent on the bound state of the molecule, that fact is clinically useful and is therefore experimentally verified many thousands of times each day.