Wavelength vs Separating Distance

[Squashed]

What happens, if an emitter** is firing a photon at a receiver**, when the wavelength of the photon is longer than the distance between the emitter and the receiver?

For example if the wavelength is 2 meters and the distance between the emitter and receiver is only 1 meter.

Does the "transaction" have to be completed before the two atoms can be moved apart?

or

If the two atoms are moved apart in the process of the "transaction" then is an additional force required to "stretch" the in-transit wavelength?

** - say both the emitter and receiver are two different atoms

[Ken G]

You are asking a fundamentally quantum mechanical question, and so it has to be phrased in a way that generates a measurable outcome. So what you are asking is, how does the motion of two atoms that are very close together affect the probability that an excitation quantum will pass from one atom to the other? That's a pretty difficult calculation, when they are that close together! And the motion doesn't help much either. It won't "do" anything to the photon if the reaction occurs, but it changes the probabilities.

[Squashed]

You are asking a fundamentally quantum mechanical question, and so it has to be phrased in a way that generates a measurable outcome. So what you are asking is, how does the motion of two atoms that are very close together affect the probability that an excitation quantum will pass from one atom to the other? That's a pretty difficult calculation, when they are that close together! And the motion doesn't help much either. It won't "do" anything to the photon if the reaction occurs, but it changes the probabilities.

Strange things seem to be possible with quantum mechanics which, unless I apply myself to diligent self-study, I will never comprehend.

So I'll tell ya what I was thinking, in a classical sort of way (whether it is truly classical, I don't know).

It seems like a photon is an individual sort of entity and so if we try to rip apart such an entity then it will surely fight back, or resistance will be felt during our ripping efforts.

If that is true then wouldn't this be a mechanism for the always attractive force of gravity - a sort of "photon lock" between particles?

Radio waves have rather long wavelengths in the meter scale as opposed to the nano-meter scale but what if gravity included every wavelength from zero to infinity in length and what if the force of gravity was just the tendency of photons not to be stretched in-transit, or while the transaction was taking place?

If we take two balls with a string attached to both and then we set up a vibration in the string (just by swinging the string like a jump rope) then two effects will be present:

a.) the balls will experience a force that resists the separation of the balls and
b.) the balls will actually be pulled together by the desire of the string to increase the amplitude of the vibration.

So the big question: Would a photon that is simultaneously being transmitted and received by two atoms act similarly to the string between the two balls?

[Ken G]

It seems like a photon is an individual sort of entity and so if we try to rip apart such an entity then it will surely fight back, or resistance will be felt during our ripping efforts.
It's hard to tell without actually doing the calculation. My naive expectation is actually the opposite-- photon transfer while you are separating the atoms should give a "radiation pressure" contribution, making it easier to separate the atoms. Also note that photon wavelengths, unlike rubber bands or strings, correspond to lower energies when they get stretched.

[Squashed]

It's hard to tell without actually doing the calculation. My naive expectation is actually the opposite-- photon transfer while you are separating the atoms should give a "radiation pressure" contribution, making it easier to separate the atoms. Also note that photon wavelengths, unlike rubber bands or strings, correspond to lower energies when they get stretched.

I would have posted this in the ATM section but I know so little about this type of situation that every defense of the idea would just be hand-waving (which is about all I can offer on any topic).

I was thinking about the energy changes with increased (or decreased) wavelength due to stretching but never really thought it all out.

Thanks for your input, though.

[dhd40]

What happens, if an emitter** is firing a photon at a receiver**, when the wavelength of the photon is longer than the distance between the emitter and the receiver?

For example if the wavelength is 2 meters and the distance between the emitter and receiver is only 1 meter.

Does the "transaction" have to be completed before the two atoms can be moved apart?

or

If the two atoms are moved apart in the process of the "transaction" then is an additional force required to "stretch" the in-transit wavelength?

** - say both the emitter and receiver are two different atoms

This seems to be linked to a question which I posted in an other thread, but I never got an answer:
What about an 800 nm femto-second-laser with a 2.5 femto-second impuls? The calculated impuls length would be 750 nm, i.e., less than one wavelength of the photon. What does that mean? Did the electron(s) jump only partially to a lower energy level? Is this allowed/possible at all? Could these photons cause a photoelectric effect? Etc, etc

[Ken G]

What about an 800 nm femto-second-laser with a 2.5 femto-second impuls? The calculated impuls length would be 750 nm, i.e., less than one wavelength of the photon. What does that mean?It means your photon does not have a well defined energy.

Did the electron(s) jump only partially to a lower energy level? In a sense, possibly, though that's not really a quantum mechanically correct statement. The point is, to get such a short beam pulse, you had to do something, either to the atom in transition, or to the photon after it was emitted by the atom. What you had to do would do violence to the normal concept of a photon with a well defined energy, and might also put the atom in a "weird" quantum mechanical state. I'm surprised you can even get much gain in a laser like that-- do such things really exist?

Is this allowed/possible at all? There's probably a significant gain problem.

Could these photons cause a photoelectric effect? Yes, because their energy is not well determined, it could be high or low. It's all a question of how it alters the probabilities of various things happening, like photoelectric effects. Good questions though.

[dhd40]

It means your photon does not have a well defined energy. (SNIP)
I'm surprised you can even get much gain in a laser like that-- do such things really exist?


Ken, thanks for your response.
Actually, I don´t know whether femto-second-lasers exist whose impuls duration (calculated as an ´impuls length´) is shorter than the wavelength of their emitted light. That´s why I asked ´is this allowed at all´. My intuition tells me that it´s not allowed, i.e., such lasers are impossible to work. But, of course, femto-second-lasers do exist, as we all know
Dieter

[Ken G]

The basic function of the laser requires a sharp resonance, so if you wanted a pulse shorter than the period, you couldn't do it by affecting the atoms themselves. You'd have to have a closer laser cavity to build up the desired amplitude, and then open and close a "shutter" in the box, very quickly. I think you could get a short pulse that way, but at the cost of the coherence of the laser. Thus you could never get much power out of such a laser, because laser power sensitively relies on lots of constructive interference at the target. That's my sense anyway, I might ask a laser expert to clarify this interesting question.

[dhd40]

The basic function of the laser requires a sharp resonance, so if you wanted a pulse shorter than the period, you couldn't do it by affecting the atoms themselves. You'd have to have a closer laser cavity to build up the desired amplitude, and then open and close a "shutter" in the box, very quickly. I think you could get a short pulse that way, but at the cost of the coherence of the laser. Thus you could never get much power out of such a laser, because laser power sensitively relies on lots of constructive interference at the target. That's my sense anyway, I might ask a laser expert to clarify this interesting question.

That sounds perfectly reasonable, confirming my intuition. I actually asked a German laser expert but didn´t get any response. If you succeed, please let me know the answer.

[swansont]

Not an expert (though getting to know such devices is likely in my future), but I know that femtosecond lasers use either gratings or chirped mirrors to compress the pulses. It's not all done with the lasing transition, and you also have to fight the natural spreading of the pulse from normal dispersion. (the gratings or mirrors performing anomalous dispersion)

However, you really can't say that such a laser has a particular single wavelength. If you look at it in the frequency domain, a single pulse will have a spectrum that is the Fourier transform of the envelope function of the pulse and it will be centered at the optical frequency of the carrier, i.e. a short pulse has a large spectrum. A series of pulses will have individual frequencies in that spectrum, separated by the repitition rate.

A paper I have read on this is, pertaining to generating the comb of frequencies, is: Cundiff and Ye, REVIEWS OF MODERN PHYSICS, Vol 75, Jan 2003 p. 325

So Ken G's answer of not having a well-defined energy is correct, though that is applied to an ensemble of photons. I'm not sure if you can consider a single photon to be a pulse.

[Ken G]

So Ken G's answer of not having a well-defined energy is correct, though that is applied to an ensemble of photons. I'm not sure if you can consider a single photon to be a pulse.

I think that's actually a pretty deep question into what a "photon" really is. If one views a photon as a quantum of excitation of the electromagnetic field using an energy operator, then it has to be an energy eigenstate-- that is, it has to have a definite energy. But if one is viewing a photon as whatever happens to an individual quantum of excitation of an atom, then it has a wave function that can be a pulse and not have a definite energy. I'm using the latter meaning, though I agree that there is some need for clarification there. I think you are right that it would be the more generally used terminology to say that the atomic excitation quantum couples into a superposition of photon modes and each photon has a definite energy, but you just don't know which photon you are going to get. So in that sense, the photon you are going to get does not have a known energy until you measure it. Did it already have that energy, or did you give it that energy with your measurement? That's the sticky issue, I would tend to say the latter here. All of this is connected to the ultra-subtle concept of "quantum entanglement".

[dhd40]

(SNIP)
However, you really can't say that such a laser has a particular single wavelength. If you look at it in the frequency domain, a single pulse will have a spectrum that is the Fourier transform of the envelope function of the pulse and it will be centered at the optical frequency of the carrier, i.e. a short pulse has a large spectrum.

That´s astonishing for me. I´m familiar with Fourier transform. I would have expected only one peak in the frequency domain.


A series of pulses will have individual frequencies in that spectrum, separated by the repitition rate.

Again, I´m surprised. I would have expected all pulses to have the same frequency


A paper I have read on this is, pertaining to generating the comb of frequencies, is: Cundiff and Ye, REVIEWS OF MODERN PHYSICS, Vol 75, Jan 2003 p. 325

Thanks for the link, I will have a look at this. Hopefully, I will better understand the topic after having read it

[dhd40]

I think that's actually a pretty deep question into what a "photon" really is.

Absolutely true from my layman´s point of view.


(SNIP) All of this is connected to the ultra-subtle concept of "quantum entanglement".

Yes, and the photon itself is an ultra-subtle concept. It´s one of the most fascinating concepts of modern physics, almost more fascinating than big bang theory.