# How a photon is created?

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1. Jun 10, 2015

### enzan

I hear that the interaction between a photon and an electron is introduced by the local gauge invariance in the quantum field theory. On the other hand, I know that an decelerated electron emits a photon. Are these two saying the same thing? Or how these two are related?

2. Jun 10, 2015

### Demystifier

The latter can be derived from the former, but not the vice versa.

3. Jun 10, 2015

### enzan

Is a photon emission from an atom associated with an electron state transition also derived from the local gauge invariance?

4. Jun 10, 2015

### Demystifier

Yes. The Schrodinger equation, which describes the electron, is also gauge invariant.

5. Jun 10, 2015

### enzan

Does that mean that an electron state transition in an atom is described by a phase transformation of the electron field?
I'm asking this because I understand that the gauge transformation is a phase transformation.

6. Jun 10, 2015

### Demystifier

No. The electron state transition is much more than a phase transformation.

7. Jun 10, 2015

### enzan

What kind of gauge transformation (gauge invariance) is relevant to the electron state transition?

8. Jun 10, 2015

### Staff: Mentor

9. Jun 10, 2015

### enzan

I'm curious about what is the fundamental "principle" of photon emission (creation).
Can I safely say that the gauge invariance (or symmetry) is the one for any case, including a decelerated electron (Bremsstrahlung), Compton scattering, and the electron state transition in an atom?
Thank you.

10. Jun 10, 2015

### Staff: Mentor

Its tied up with the state of a quantum field is a Fock space:
http://en.wikipedia.org/wiki/Fock_space

Basically the question you are asking is not really meaningful in a Quantum Field Theory. A Quantum Field is a superposition of an unknown number of particles. The evolution of the field is basically an evolution of those unknown number of particles.

Symmetries more or less fix the form of a Quantum Field Theory - which is one of the great insights of modern physics. Gauge symmetry (also known as the symmetry of a circle) is the symmetry of EM. In and of itself its not responsible for particle creation, which is a rather subtle concept in QFT.

Thanks
Bill

11. Jun 10, 2015

### enzan

Would it be possible to say something correctly about the fundamental principle of photon emission using words that can be understood by high school students?
For example, can I say that photon emission is always associated with a change of an electron's "state"?
Thank you.

12. Jun 10, 2015

### Staff: Mentor

No it wouldn't. Photons are described by Quantum Field Theory. And everything you have read outside a QFT textbook about it is likely wrong.

For high school students simply have some classes where they watch the master, Feynman, explain it:
http://www.vega.org.uk/video/subseries/8

And outside class read the book:
https://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/0691024170

And if a student asks what is the fundamental principle of photon emission - tell the truth - in the theory of such things - Quantum Field theory - there is no such principle. But its a very advanced theory and understanding how it explains such is beyond what can be explained at their level.

Thanks
Bill

Last edited by a moderator: May 7, 2017
13. Jun 11, 2015

### enzan

I see. Thank you very much!

14. Jun 11, 2015

### Demystifier

Yes, definitiely!

15. Jun 11, 2015

### Demystifier

Theoretically, radiation could exist even without gauge invariance, but then some details of radiation could be somewhat different. For instance, the true radiation has only transversal polarization, while, without gauge invariance, radiation could also have longitudinal polarization.

16. Jun 11, 2015

### enzan

17. Jun 13, 2015

### BillyT

without getting too deep, it is worth while to note, that photons have length. I.e. the more well defined their energy is the more cycles they must contain and the less that can be said about the emission process due to the time energy precision limit of the uncertainty principle. For example, the green line photons from the northern lights are very precise in their energy - have so many cycles they are more than a meter long. And thus even "when" they were emitted is quite uncertain.

I have measured the length of some photons and shown one photon can in a classical sense be far (four feet) from itself! Here is how you do that:

Posting now below a crude "typed" drawing (in two parts):
Extended light source and lens making parallel beams (0nly one shown below) but each part of the source makes a beam at very slightly different angles:

*
*
*
...............................................................()===== This beam enters beam splitter "a" shown below (this part of drawing separated for ease of construction.)
*
*

Ok, that is best I could do. (If I made lens () taller then parts of the light source, represented by some * , would be too far above or below lens.)
Below is one of the slightly divergent beams (only one shown), leaving the lens and going to first 45 degree beam splitter "a" and going straight thru with part (of same photon) going up to hit 45 degree mirror, b, too, which makes it again traveling parallel to the entering beam.
Sorry that these beam splitters and mirrors are not shown actually at 45 degrees - but that is best a "typed drawing" can do.

.........................................................d
..........................b/======/======.....This is the path of "self- rejoined" photon to the screen thru another lense one focal length from it.
............................||..........................||
............................||..........................||
............................||..........................||
............................||..........................||
()===== / ======/c
Lens.....................a

Optically an "extended source" with lens one focal lengh from it followed by a second lense one focal length from the screen, just images the source (up side down) on the screen. Inserting these beam splitters and mirrors does not change that. It only make it possible for slightly differing path "split photons" to arrive at the screen where they would have but now they "want" to get back in phase with them selves, and do so as best a they can. Leaving dark lines where if they can not become "particles" there as they would not exist there since their waves are 180 degrees out of phase with themselves there. Note almost all the time photons can be thought of as waves, but if detected / absorbed they "die as particles" in one spot - not spread out over miles as they can be when waves.

Note that the length of paths: abd and acd, are the same. I.e. when the separate SINGLE photo get back together with itself, after being at times in its flight it 4 feet from itself, it arrives at the screen, unified, at the same time, but some of the many slightly divergent beams arriving there are "out of phase" with themselves and cancel (make dark interference lines) on the screen. The diverse in angle beams following paths abd & acd are exactly the same length ONLY for paths with pairs of equal angle degree corners. (parallelograms or rectangles.)

I will not go into details, but it is well known that photons ONLY interfere with themselves (and proven by using such low intensity sources that most of the time not even one exist - long exposure film, still has an interference pattern on the developed film, etc.) This is why one only needs monochromatic light, but not coherent light, source to produce interference patterns.

Now here is what you do to measure the length of a photon: You rotate beam splitter a very slightly counter clockwise, so that the path ab passes to the left of mirror at b, but pull mirror b back to still be hit by that now tilted beam. You of course must also rotate mirror b slightly clockwise, so the beam leaving it follows the old path to beam splitter d again. Now the corner turned at b is not 90 degrees. Perhaps this adds 5 cm of extra length to path abd.

What one sees on the screen is that there is a little light where there was none. I. e. the interference pattern on the screen is a little "washed out." This slight twisting of a & b is increased and then the pattern is more washed out. I kept repeating this until with ~30 cm extra path length for abd, the screen was with uniform illumination.

Crudely speaking this implies that none of the part of the photon going via path abd had yet arrived at the screen before the full length of the part of the same photon going by path acd had already disappeared into the screen. I.e. my spectral line source was making photons that were about 30cm long.

PS I have Ph. D. in physics and would be more active here, but my first post about time were removed as like this one I told things most do not know. Hope you get to read this one before it is removed.

Last edited: Jun 13, 2015
18. Jun 13, 2015

### vanhees71

Well, there are very interesting cases, where we observe photons, where no electrons are involved, like pion annihilation in a hot hadron gas or quark-gluon processes in the QGP (both created in heavy-ion collisions at various collision energies ranging from GSI (HADES experiment) via RHIC (STAR and PHENIX experiments; now also at a variety of beam energies up to top Au+Au collisions at $\sqrt{s}=200 A \text{GeV}$ to the LHC. For a theory perspective, see my lectures for graduate students:

http://fias.uni-frankfurt.de/~hees/hqm-lectweek14/index.html

For a shorter version for the Quark-Matter 2014 Student Day, see

http://fias.uni-frankfurt.de/~hees/publ/qm14-lect.pdf

19. Jun 14, 2015

### Staff: Mentor

I thought it was an excellent post. I don't think it will be removed.

Thanks
Bill

20. Jun 14, 2015

### yoron

Interesting, as well as confusing (for me that is:), description BillyT. How do you think of it? As some practical limitation of a 'field concept', considering a 'particle', if I now would be so rude as to lend from Bhobba's " A Quantum Field is a superposition of an unknown number of particles. The evolution of the field is basically an evolution of those unknown number of particles."? Or, how would you prefer to describe it otherwise?

[Mentor's note - edited to remove text quoted from a removed post]

Last edited by a moderator: Jun 14, 2015