Is there a smallest wavetrain corresponding with photons?

[fxdung]

Is there a smalless wave packet of EM wave corresponding with photons?I read on Internet saying that EM wave consist of many random wavetrains.(Although it seems to me that this wavetrain can be divided into two parts example in double slit Young experiment)

 

[PeterDonis]

I read on Internet

Where? Please give a specific reference.

 

[fxdung]

It is Web: Light bends by Itself

 

[berkeman]

It is Web: Light bends by Itself

LOL. Please post the link. Do you know how to copy/paste a URL from your browser to here?

 

[fxdung]

Here is the link:https://www.sciencemag.org/news/2012/04/light-bends-itself
It says: Light is a jumble of waves

 

[PeterDonis]

It says: Light is a jumble of waves

Of all the sentences to focus on in that article, that one is probably the least helpful. The rest of the article is basically describing a scenario in which the light is not a "jumble" of waves, but a carefully controlled configuration of waves.

In any case, I'm not sure how this relates to the question you ask in the OP.

 

[fxdung]

In the point of view of this, light in mediun is superposition of wave incident and wave emission by atoms of medium. But I do not understand why light in medium has velocity smaller than that in vacuum base on quantum mechanics point of view?

 

[fxdung]

I only occasionaly saw the article, and happen saw the "jumple of waves" and the question appear

 

[PeterDonis]

light in mediun is superposition of wave incident and wave emission by atoms of medium.

This is one way of looking at it, yes, but I don't see how you are getting this from the article you reference. The phenomenon discussed there does not require the light to be traveling in a medium and has nothing to do with any difference between the way light travels in a medium and the way it travels in vacuum.

I do not understand why light in medium has velocity smaller than that in vacuum base on quantum mechanics point of view?

This is a valid question, but it has nothing to do with anything said in this thread thus far, including the question you asked in the OP of the thread. So which question do you want to discuss?

 

[fxdung]

All these questions appear in my head at the same time,so I would like to understand all of them

 

[sysprog]

But I do not understand why light in medium has velocity smaller than that in vacuum base on quantum mechanics point of view?

The standard explanation for why $c$ in a medium is slower than in a vacuum doesn't require quantum theory $-$ in a vacuum there is nothing for the light to collide with, while in a medium, there are atoms.

 

[PeterDonis]

All these questions appear in my head at the same time,so I would like to understand all of them

Well, the question you asked in the OP...

Is there a smalless wave packet of EM wave corresponding with photons?

...doesn't really make sense. A wave packet doesn't really have a "size". What do you mean by "smallest wave packet"?

Also, what do you mean by "corresponding with photons"? We're in the QM forum here, so photons are "wave packets" (but quite possibly not the kind you're imagining, since I suspect you're imagining classical wave packets of electric and magnetic fields, which is not what photons are).

 

[fxdung]

The smalless wave means the weakest wave( the weakest intensity)

 

[PeterDonis]

The smalless wave means the weakest wave( the weakest intensity)

There is no lower limit to wave intensity, either in classical or quantum physics.

 

[fxdung]

Photon is wave packet, and this packet has not lower limit in intensity?

 

[PeterDonis]

Photon is wave packet, and this packet has not lower limit in intensity?

Basically, yes. But please note the caveat about what photons are and are not in the last part of my post #12.

 

[Lord Jestocost]

Photon is wave packet, ...

The photon is not a wave packet. To yield a wave packet, one needs a superposition of traveling waves with an appropriate distribution of various frequencies. The less spread out spatially, the more spread in frequencies required to make it. http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/wpack.html#c1

Quantization of electromagnetic radiation means that the field energy can only be changed by integer numbers of „energy portions“ (called photons) of amount $h\nu$, where $\nu$ is light frequency and $h$ Planck's constant.

 

[PeterDonis]

The photon is not a wave packet.

It can be viewed as one, although it is true that that view is limited. What a photon is not is a wave packet of classical electric and magnetic field waves.

Quantization of electromagnetic radiation means that the field energy can only be changed by integer numbers of „energy portions“ (called photons) of amount $h \nu$, where $\nu$ is light frequency and $h$ Planck's constant.

No, this is not correct. Our understanding of quantum electrodynamics has come a long way since Planck's original hypothesis.

 

[fxdung]

Why the light collides with atoms in medium make it slower?

 

[Lord Jestocost]

When light travels through a medium like, for example, a glass plate, it appears to slow down. The apparent "slower speed" is the result of the superposition of two radiative electric fields:
The incoming light, traveling at speed c, and the light re-radiated by the atoms in the medium (oscillating charges driven by the incoming light) in the forward direction, traveling at speed c, too.
The superposition shifts the phase of the radiation in the air downstream of the glass plate in the same way that would occur if the light were to go slower than c in the glass plate. If one wants to understand the essential aspects of the phenomena, I recommend to read chapter 31 “The Origin of the Refractive Index” in “The Feynman Lectures on Physics, Volume I". (http://www.feynmanlectures.caltech.edu/I_31.html).

 

[PeterDonis]

The apparent "slower speed" is the result of the superposition of two radiative electric fields...

The explanation you give is a classical explanation, not a quantum explanation. We are in the quantum physics forum.

 

[PeterDonis]

Why the light collides with atoms in medium make it slower?

Because the presence of the atoms changes the probability amplitude for photons to travel at various speeds due to the interaction between the atoms and the photons. In vacuum, the probability amplitude peaks at speed $c$. In the presence of atoms, it peaks at some lower speed (exactly which speed depends on the specific atoms involved and what kind of state they are in).

 

[Nugatory]

We may have conflated two pretty much unrelated issues, one classical and one quantum, in this thread. The initial post asks about a "wavetrain corresponding to a photon" which is a QED question, but much of the discussion has been driven by this article which is all about classical light waves. It might be most illuminating (yes, I did that on purpose!) to juxtapose the two descriptions of the "light bending by itself" phenomenon.

 

[fxdung]

But Special Relativity says massless particle has velocity is c. Then in medium photon has slower velocity, so photon must have "effective mass'' in medium?

 

[hutchphd]

I don't think that is a useful concept. More useful is to concentrate on the "dispersion relation" which relates frequency (energy) to wavenumber (~momentum). This is a very useful concept and can become interesting in solids. In free space of course it is simply $\omega=ck$

 

[vanhees71]

The explanation you give is a classical explanation, not a quantum explanation. We are in the quantum physics forum.

Well, concerning photons you are better off with a classical calculation in this case, because the "motion of a photon" through matter is also best described by the Maxwell equations for the field operators. As long as linear-response theory is justified the only formal difference between the classical theory and QFT is that the fields are operator valued (using the Heisenberg picture). The medium can be described classically simply by a (in general) complex index of refraction $n(\omega)$, as in classical electrodynamics too. The expecation values for the em. field thus follow the classical Maxwell equations within this approximation.

 

[Lord Jestocost]

Why the light collides with atoms in medium make it slower?

When light travels through a medium like, for example, a glass plate, it appears to slow down. The apparent "slower speed" is the result of the superposition of two radiative electric fields:
The incoming light, traveling at speed c, and the light re-radiated by the atoms in the medium (oscillating charges driven by the incoming light) in the forward direction, traveling at speed c, too.
The superposition shifts the phase of the radiation in the air downstream of the glass plate in the same way that would occur if the light were to go slower than c in the glass plate. If one wants to understand the essential aspects of the phenomena, I recommend to read chapter 31 “The Origin of the Refractive Index” in “The Feynman Lectures on Physics, Volume I". (http://www.feynmanlectures.caltech.edu/I_31.html).

The explanation you give is a classical explanation, not a quantum explanation. We are in the quantum physics forum.

No problem! On Bruce Sherwood’s homepage (https://brucesherwood.net/) you find the article “Refraction and the speed of light” dealing with this question. Let me quote some passages:

"Blau and Halfpap posed the question in the American Journal of Physics of how to interpret refraction (Snell's law; index of refraction) and the (apparent) slower speed of light in glass in terms of quantum mechanics. The following response by Bruce Sherwood was published in the American Journal of Physics 64, 840-842 (1996).

Answer to Question #21. ["Snell's law in quantum mechanics," Steve Blau and Brad Halfpap, Am. J. Phys. 63(7), 583 (1995)]

The question of how to interpret Snell's law and the index of refraction from the point of view of photons and quantum mechanics can usefully be recast as a question of how to interpret these concepts from a microscopic point of view, whether quantum-mechanical or (semi-)classical. Feynman has an excellent microscopic analysis of the index of refraction in his Chapter 31 on 'The Origin of the Refractive Index.' ...

... The original question asked about Snell's law from the point of view of photons. The main issue isn't really photons, but microscopic versus macroscopic analyses. The passage to quantum mechanics introduces still more mathematical complexity but doesn't change the main point. The reflected and refracted light consists of the (quantum) interference of incoming photons with photons re-emitted by atoms in the glass. The fundamental speed of light is unaffected."

 

[PeterDonis]

concerning photons you are better off with a classical calculation in this case

There is no such thing as "photons" in classical electrodynamics. So this makes no sense to me.

 

[vanhees71]

Classical electrodynamics of course is the classical limit of quantum electrodynamics. What I wanted to say with the quoted statement is that, if you want to use classical analogies to understand photons you are closer when you think in terms of elctromagnetic waves than as if photons were massless particles. The reason is that in very many practical cases you come pretty far with linear-response theory, where the expectation values of the quantized em. field follow the Maxwell equations, i.e., the field operators just obey the Maxwell equations (in the Heisenberg picture).

It's also clear that single-photon states or Fock states are as "quantum" as you can get. So there the classical picture is most misleading.

On the other hand, particularly in GR, often a "naive photon picture" is used. E.g., when calculating the famous bending of light beams at the Sun (Einstein's breakthrough when it was confirmed in 1919 by Eddington et al), one just calculates the null-geodesics arguing with "photons" as if they were massless test particles. Of course, in this case you don't deal with photons but with classical electromagnetic waves, but the "naive photon picture" works, because the eikonal approximation ("geometric optics") is a good approximation, and the corresponding eikonal equation is analogous to the Hamilton-Jacobi equation for a massless particle.

 

[PeterDonis]

if you want to use classical analogies to understand photons

I don't think you can use classical analogies to understand photons in cases where the term "photon" is actually appropriate (such as, as you mention, Fock states). At best you can use classical analogies to deal with cases where the term "photon" is being misused to describe something that really doesn't involve any quantum aspects of the EM field at all, as in the two examples you give--cases where expectation values of the quantum EM field look like a classical EM field; and cases where light can be treated as "massless test particles" (or, as MTW sometimes describes it, very short pulses of laser light), whose spacetime description can be well approximated as a single null worldline.

 

[vanhees71]

Of course, I agree. The problem is that even in textbooks often "photons" are used in hand-waving arguments, particularly in GR textbooks, where what is in fact meant is the eikonal approximation of Maxwell's equations in "curved spacetime". Of course that's a tremendous shortcut in calculations.

What's always wrong with this "naive photon picture" is the assumption that "photons" were localized massless particles. So if you envoke the "naive photon picture" you are always better off when thinking in terms of em. waves than in terms of massless point particles.

Field quantization, is of course, not only needed when you deal with Fock states. E.g., you need it also for thermal radiation. It's not by chance that the entire discovery of quantum theory historically came from Planck's discovery how to theoretically describe thermal (black-body) radiation!