Entanglement, entropy and photon energy

[San K]

1. A photon that emerges when an electron jumps one orbital down -- will have a fixed energy
...i.e. the different between the (potential) energy of the orbitals.

However a "free/unbound" photon can have any energy level.

Is that correct?

2. What is the lowest level of energy a "unbound" photon can have?

3. During a process of entanglement say when a photon A strikes a special kind of crystal

we have two photons (in say 1 in a trillion tries) Photon B and Photon C emerge as entangled.

The energy of photon B and C is equal to that of photon A.

Now if we take photon B and have it strike another crystal ...we have photon D and E emerge with half of the energy of Photon B.

4 a ) however Photon D and E would never be entangled with photon C because entanglement between B and C would have broken when B was destroyed (?)

4 b) how long can we keep repeating the process where we are "breaking" a bigger photon into smaller photons...of say half the energy?

is there a lower bound for the energy of the photon?

5. When an electrons jumps one orbital down does it disappear from the higher energy orbital and simultaneously appear at the next lower level orbital

OR

can we actually observe/measure it travelling (in time-space) between orbitals?

6. What is the effect on entropy during the process of entanglement?

 

[Nugatory]

is there a lower bound for the energy of the photon?

Not that we've found. As the wavelength of electromagnetic radiation gets longer and the frequency smaller, the amount of energy in each photon (and you're on shaky ground trying to interpret that as anything more than the amount of energy that will be deposited at a single point when the radiation interacts with something else) gets smaller.

5. When an electrons jumps one orbital down does it disappear from the higher energy orbital and [STRIKE]simultaneously[/STRIKE] appear at the next lower level orbital

OR

can we actually observe/measure it travelling (in time-space) between orbitals?

With the correction above it's the first. Cthuga summed it up nicely in another recent thread:

You start with an atom in the excited state and you end up with a photon getting detected somewhere. You do not know much about what happens in between. Most importantly, usually you cannot figure out a clear cut time when a photon is emitted or things like that.

 

[jfizzix]

1.) yes, though there is uncertainty in the energy of the photon due to uncertainty in the energy levels.

2.) Photons can be created en masse by electromagnets, radio transmitters and the like. Planck's constant times the frequency of a radio wave will give the energy per photon in that radio wave. The lowest radio frequencies I know of would be a few kilohertz, so the smallest known photon energies are probably about 10^-30J, or 10^-10 electron-volts.

4a.) D and E may together be entangled with C because B was entangled with C. The entanglement in this case is due in part to the conservation of energy and momentum, which still applies. The momenta of D and E should add up with C to get nearly the same number, so that they are correlated. If they are also strongly correlated in position, which seems less likely, since D and E do not share a common origin with B, then they would definitely be entangled.

4b.) In the ideal world, there would be no limit, but the ability to break up photons is a function of the peoperties of the crystal. Incidentally, you would need a separate kind of crystal to break C into D and E, than to break A into B and C. Usually these crystals are specially cut and aligned for photons with specific energy and momenta. I don't know precisely what this lower limit would be, though.
'in between state
5.) What we measure is that either the electron is in one orbital, or the other. Since these orbitals are the only states that an electron can be in, the idea of an electron being in an in-between state is a challenge to think about. What one could say is that the electron is in a superposition of two states, and that the details of that superposition govern the probabilities of measuring it in either state, and the electron could be in a 50-50 superposition, where it is equally likely to be measured in either state, but when the measurement is made, the electron is found to be either in one state, or the other.

6.)The entropy of what?
If two particles initially in one pure state interact with each other, they will be in another pure state. The entropy of the both of them put together is zero, and it doesn't change. What does change is the entopy of each particle taken individually. Before the interaction, each particle may be described by their own pure state. Afterword, they cannot, and are described as mixed states, with entropy above zero.

In the process of entanglement, the entropy of the joint system remains the same, and the entropy of the subsystems increases.

 

[San K]

Well answered. Thanks jfizzix and Nugatory and Cthuga.

4a.) D and E may together be entangled with C because B was entangled with C. The entanglement in this case is due in part to the conservation of energy and momentum, which still applies. The momenta of D and E should add up with C to get nearly the same number, so that they are correlated. If they are also strongly correlated in position, which seems less likely, since D and E do not share a common origin with B, then they would definitely be entangled.

.

Energy and momentum...entanglement...just some clarification.

The momentum can be converted into energy...via the below equation:E^{2}=(pc)^{2}+(m_{0}c^{2})^{2}\,

So when we say...momentum entangled and energy entangled...are we referring to two different entanglements?

the momentum entanglement I can understand, where is the "other/separate" energy entanglement coming from?

Not that we've found. As the wavelength of electromagnetic radiation gets longer and the frequency smaller, the amount of energy in each photon (and you're on shaky ground trying to interpret that as anything more than the amount of energy that will be deposited at a single point when the radiation interacts with something else) gets smaller.

and yet the photon's speed will always remain the same...(in all frames of reference)...no matter what it's energy

 

[jfizzix]

In the context of ordinary quantum mechanics, we would say they are entangled in both energy and momentum. In the contest of relativistic quantum mechanics, we could say they are entangled in "four-momentum", though I must admit, I know little of full-blown quantum field theory, and can only claim to be competent in ordinary quantum mechanics.

The speed of light is a fundamental constant, and one way of seeing wave particle duality comes right out of applying relativity to the wavefunction:

Say you had a particle of energy E at rest with respect to you, which is Planck's constant times its frequency. The wave function we may say oscillates uniformly at this frequency in time. If we looked at this wavefunction from a moving reference frame, relativity tells us that what was simultaneous at rest, is no longer so in motion. Because of this, at different locations in space, we would see the wavefunction at different times. Instead of oscillating uniformly, its oscillation at different locations would have a time lag, proportional to its distance away from you. Because of this, if a wavefunction has a frequency proportional to its relativistic energy, it must have a reciprocal wavelength proportional to its relativistic momentum. De Broglie won his Nobel prize for this among other insights.

 

[San K]

Well summarized jfizzix and interesting information

So De Broglie believed in a "real" wave. Is that yet to be proved/discovered?...in reality...

Say you had a particle of energy E at rest with respect to you, which is Planck's constant times its frequency. The wave function we may say oscillates uniformly at this frequency in time. If we looked at this wavefunction from a moving reference frame, relativity tells us that what was simultaneous at rest, is no longer so in motion. Because of this, at different locations in space, we would see the wavefunction at different times. Instead of oscillating uniformly, its oscillation at different locations would have a time lag, proportional to its distance away from you. Because of this, if a wavefunction has a frequency proportional to its relativistic energy, it must have a reciprocal wavelength proportional to its relativistic momentum. De Broglie won his Nobel prize for this among other insights.

 

[jfizzix]

The only things we can prove in physics are mathematical theories (which is more math than physics). The extent to which the theories accurately represent reality is only borne out by experiment. In quantum physics, no one disagrees on the details of a calculation; there is no controversy as to the likelihood of measuring the energy of a hydrogen atom to be "x" electron volts. However, there is still ongoing debate as to the fundamental interpretation of the mathematical theories of quantum mechanics. Until experiments can be devised which can tell one interpretation from another, we won't know for certain if there is a "real wave". To be fair, most scientists (I expect) are content in the knowledge that the math works, and don't worry too much about the underlying philosophy. I like thinking about these things, but I have no conclusions about the matter either.

 

[San K]

The only things we can prove in physics are mathematical theories (which is more math than physics). The extent to which the theories accurately represent reality is only borne out by experiment. In quantum physics, no one disagrees on the details of a calculation; there is no controversy as to the likelihood of measuring the energy of a hydrogen atom to be "x" electron volts. However, there is still ongoing debate as to the fundamental interpretation of the mathematical theories of quantum mechanics. Until experiments can be devised which can tell one interpretation from another, we won't know for certain if there is a "real wave". To be fair, most scientists (I expect) are content in the knowledge that the math works, and don't worry too much about the underlying philosophy. I like thinking about these things, but I have no conclusions about the matter either.

agreed jfizzix