Photons & Waves: A Laymen's Query

[Prannoy Mehta]

Moderator's note: this post follows from the Is light a wave or a particle FAQ

Nothing to add, rather just a query.

1) Do Photons move in a wavelike manner, as given by De Broglie's Equation?
2) If so, will the wavelength obtained over there be different from that of the electromagnetic wave which the photon consists of.

- A Laymen who wants to reason.

Cleared a few of my doubts, thank you for posting an answer to the FAQ.

 

[mfb]

1) Do Photons move in a wavelike manner, as given by De Broglie's Equation?

What does "moving in a wavelike manner" mean? They are not going in curved lines if you imagine something like that.

2) If so, will the wavelength obtained over there be different from that of the electromagnetic wave which the photon consists of.

That question does not make sense.

 

[Prannoy Mehta]

I am sorry for the late reply. mfb and bhooba. I am sorry as I am not very fluent in English.

By Wave like I meant Sinusoidal form.
Do photons move up and down through space as shown in various animations? Thank you for that answer, I always they thought they moved in Sinusoidal manner.

The second question is wrong. As per the first answer. Thank you.

 

[mfb]

No, photons do not move "up and down". They do not even have a well-defined position.

 

[A. Neumaier]

Do Photons move in a wavelike manner, as given by De Broglie's Equation?

Photons do not have a well-defined position, so one cannot describe realistically how they move.

But each photon has a shape, and these shapes take the form of a wave (more precisely of a nonzero solution of the vacuum Maxwell equations). These shapes oscillate, and their frequencies define the color of the photon. Thus, you can have photons of different colors, and in the shape of for example beams or radial waves, etc..

 

[ZapperZ]

Photons do not have a well-defined position, so one cannot describe realistically how they move.

But each photon has a shape, and these shapes take the form of a wave (more precisely of a nonzero solution of the vacuum Maxwell equations). These shapes oscillate, and their frequencies define the color of the photon. Thus, you can have photons of different colors, and in the shape of for example beams or radial waves, etc..

I think this has the risk of someone interpreting it the wrong way. Each photon does not have a "shape", and certainly they don't have the shape of "beams or radial waves". The "nonzero solution" to the Maxwell equation is the classical wave picture of "a lot of photons", not "each photon". And what oscillate are the electric and magnetic field components, to be precise. If this is what people call "shape", then that's fine, but it needs to be explicitly stated, because someone not familiar with physics, such as the OP's layman, has a different concept of what a "shape" is (i.e. a DEFINITE physical boundary of the object in real space).

Zz.

 

[A. Neumaier]

The "nonzero solution" to the Maxwell equation is the classical wave picture of "a lot of photons", not "each photon".

To be completely precise: A photon (even more precisely a pure 1-photon state) is mathematically specified by its wave function, which I called its shape to make it intuitive, and which (in a bounded region, cavity) is an arbitrary normalized solution of the vacuum Maxwell equations. That the shape has a fuzzy boundary is nothing exceptional - the same holds for the shape of a city, a meadow, a cloud, a star, a sun ray, or any material object if its surface is looked at in enough detail.

This picture of shape is the same as that used for simple quantum mechanical systems like a free nonrelativistic particle, which is a point in a Dirac delta state and a fuzzy ball in a radial state. The electron density of a single hydrogen atom in the ground state determines the spherical shape of the atom and its radius, although the boundary is also fuzzy.

A single photon cannot be localized in a point since there are no Dirac delta solutions of the Maxwell equations - but it can be localized in a beam or a spherical wave.

 

[Prannoy Mehta]

I have understood what mfb, ZapperZ and A. Neumaier tried to convey. I guess I should have specific and mentioned photon rather than photons. Though it would take me more time to grasp the concept of photons I believe this would be the answer I needed. Thank you for the answer(s).

 

[ZapperZ]

To be completely precise: A photon (even more precisely a pure 1-photon state) is mathematically specified by its wave function, which I called its shape to make it intuitive, and which (in a bounded region, cavity) is an arbitrary normalized solution of the vacuum Maxwell equations. That the shape has a fuzzy boundary is nothing exceptional - the same holds for the shape of a city, a meadow, a cloud, a star, a sun ray, or any material object if its surface is looked at in enough detail.

This picture of shape is the same as that used for simple quantum mechanical systems like a free nonrelativistic particle, which is a point in a Dirac delta state and a fuzzy ball in a radial state. The electron density of a single hydrogen atom in the ground state determines the spherical shape of the atom and its radius, although the boundary is also fuzzy.

A single photon cannot be localized in a point since there are no Dirac delta solutions of the Maxwell equations - but it can be localized in a beam or a spherical wave.

You are mixing up the spread in its POSITION and the SIZE of the object itself! I'm not arguing about the various probability density of the location. I'm arguing that when we talk about "size", we are defining a definite shape and volume of the object, NOT the spread it its position!

A ping-pong ball has a volume (if you include the empty inside as part of the ball). It has a spherical shape. Yet, it's location, when it is stationary, is defined by the position of its center of mass. An electron is a point object. It's location may be defined to within the HUP, but that is its location. It's probability density may be spread out, signifying where it can be found at some instant, but its VOLUME is still zero, i.e. it has no or undefined shape!

A photon has no size and shape. It may have a range of position, and we may use some properties such as its wavelength to define some characteristics length, but there has been no physics that defines the same and volume of a single photon.

Zz.

 

[drphysica]

Photons travel as waves and particles due to wave particle duality and it also applies to electrons and all bosons and fermions i.e. all particles. The only difference between photon an electron is its energy relations for electron particle energy relates to its mass is E^2=(mp)^2+(mc^2)^2 and for photon E = hf where f ~ is frequency and h is Plank Constant 6.62607004 × 10-34 m2 kg / s Thus you can calculate energy of your AM frequency favorite radio buy just plugging in a number between 535 to 1700 kHz into equations and getting the energy of your photon. Remember photons don't have mass and electrons and other particles do.

 

[ZapperZ]

Photons travel as waves and particles due to wave particle duality and it also applies to electrons and all bosons and fermions i.e. all particles.

We have had bad consequences when people state this. So you should explain yourself.

What exactly do you mean when you say "photons travel as waves and particles"? Start by what you mean by "photons travel as waves"? Note that laymen will likely think that these "photons" are going through space bouncing up and down like the water waves they are familiar with. If you don't believe me, browse through many posts on this forum, and you'll come across such a misunderstanding. All this because they have a picture of what a "wave" is, and someone simply and callously wrote something similar to what you've written.

We ALL need to be careful in looking at what we write. What you write, and what you MEAN, may not translate exactly to what the other person understands! This is especially true if you use similar terms and words, but having different meaning when applied to the context of physics. If you do not spend the effort to clarify and elaborate, and if you do not anticipate the misunderstanding, then you will be perpetuating the mistake!

Zz.

 

[Prannoy Mehta]

Okay, I guess I have messed it up again. Anyhow, the reason I found it reasonable because I read this. (It is the text we are referring now) Please go to Page 19 or Pg. 432. There is a big blue box regarding LASERS in that the third paragraph has the lines below. (Please see the figure also)

www.ncert.nic.in/ncerts/l/leph204.pdf

These are the lines I am trying to refer to.

" The wavelength of each packet is almost the same. Also, the average length of the packet of waves is much larger. This means that there is better
phase correlation over a longer duration of time. This results in reducing the divergence of a laser beam substantially."

As per what you have mentioned it has no size and shape. (By Shape we refer to the oscillating electric and magnetic fields.) What does length stand for here? The length of the packet seemed more reasonable if the conclusion I came up to earlier was true.

Anyhow, just another curiosity question. As Zapper Z earlier mentioned,

" The "nonzero solution" to the Maxwell equation is the classical wave picture of "a lot of photons", not "each photon". "

So for each photon, it can be zero?

Also, the picture I requested you to see, (In the lasers box.)

What is the thing which is depicted as a wave? Is it the motion of a photon through space or is it with respect time.

 

[Prannoy Mehta]

The only difference between photon an electron is its energy relations for electron particle energy relates to its mass is E^2=(mp)^2+(mc^2)^2 and for photon E = hf where f ~ is frequency and h is Plank Constant 6.62607004 × 10-34 m2 kg / s

I don't think it is mp. I think pc was intended.

 

[drphysica]

We have had bad consequences when people state this. So you should explain yourself.

What exactly do you mean when you say "photons travel as waves and particles"? Start by what you mean by "photons travel as waves"? Note that laymen will likely think that these "photons" are going through space bouncing up and down like the water waves they are familiar with. If you don't believe me, browse through many posts on this forum, and you'll come across such a misunderstanding. All this because they have a picture of what a "wave" is, and someone simply and callously wrote something similar to what you've written.

We ALL need to be careful in looking at what we write. What you write, and what you MEAN, may not translate exactly to what the other person understands! This is especially true if you use similar terms and words, but having different meaning when applied to the context of physics. If you do not spend the effort to clarify and elaborate, and if you do not anticipate the misunderstanding, then you will be perpetuating the mistake!

Zz.

I have no idea what you talking about! I simply state the fact that photons are waves and particles and it also applies to any other particles. Now if you don't agree with that you shouldn't be in physics forums. If you want to talk philosophy you should be at philosophy forums. This place needs to be cleaned up a bit.

 

[drphysica]

I don't think it is mp. I think pc was intended.

Yes you right I made a mistake there.

 

[blue_leaf77]

I must acknowledge that the physics community is divided into (at least) two groups with regard to how they picture the word "photon" in their mind. Physicists working closer towards the experimental side or theoriticians in the scope of applied physics (note that I'm not by any means referring to anyone involved in this thread, this is just evident) tend to depict photons as the grains making up light. The other groups, the genuine theoretical physicists (when I call "genuine", I don't mean to disregard the other types of theoretical physicists), i.e. those which go down the path of physics rigor, will frown upon hearing that photons are ball-like entities. The correct view of photons are that depicted by the second group. In spite of this, I would refrain from blaming the first group for their simplified view of photons because to them, that is the most convenient way of explaining the phenomena they are dealing with, phenomena in which the correct view of photon are not urgent to be incorporated. For example, in the field of diffraction imaging, many people will probably say something like "photons being scattered" or "photons hitting the camera pixel chip", such wording will easily be interpreted as photons having dynamics in space. While that kind of depiction is not justified in the quantum theory of light, the correct one will not get them anywhere either, because most of the times diffraction physicists are working with high intensity light, in which the classical nature heavily overshadows the quantum one.

So, @Prannoy Mehta, to layman like you which is probably not yet certain to which group of the two physicists I talk about above you are going to, photon is better to be regarded as a quantum object, not "worldly" object. One photon is described by the so-called Fock state, which is basically the same state as you encounter in quantum harmonic oscillator. One photon state is written as $|n=1\rangle$, two photons state as $|n=2\rangle$ and so on. This is what ZapperZ was trying to tell you. It obeys the same quantum properties as the harmonic oscillator eigenstate, e.g. if you apply raising operator to $|n=2\rangle$ photon state, you will get $|n=3\rangle$ photon state.

" The wavelength of each packet is almost the same. Also, the average length of the packet of waves is much larger. This means that there is better
phase correlation over a longer duration of time. This results in reducing the divergence of a laser beam substantially."

That passage does not talk about the quantum nature of light, instead it tries to explain the difference between laser light and light bulb in terms of classical electrodynamics. What the author refers to when he gave an example of a crowd walking in the same direction vs soldiers marching synchronously is the phase relationship at any point in the light beam, again, the phase, not the photons.

I have no idea what you talking about! I simply state the fact that photons are waves and particles and it also applies to any other particles. Now if you don't agree with that you shouldn't be in physics forums. If you want to talk philosophy you should be at philosophy forums. This place needs to be cleaned up a bit.

ZapperZ didn't try to refute your answer, your answer is not wrong in the loose sense. He asked you to elaborate on what you said that photons travel in space, because this has the potential of misleading the OP given his limited theoretical knowledge of photons. Probably, had this thread been in general physics section, you may not get such response.

 

[Prannoy Mehta]

So, @Prannoy Mehta, to layman like you which is probably not yet certain to which group of the two physicists I talk about above you are going to, photon is better to be regarded as a quantum object, not "worldly" object. One photon is described by the so-called Fock state, which is basically the same state as you encounter in quantum harmonic oscillator. One photon state is written as $|n=1\rangle$, two photons state as $|n=2\rangle$ and so on. This is what ZapperZ was trying to tell you. It obeys the same quantum properties as the harmonic oscillator eigenstate, e.g. if you apply raising operator to $|n=2\rangle$ photon state, you will get $|n=3\rangle$ photon state.

This is not the first time you have replied to my questions, so I will take a blind word for that one (The different group of physicists). The fact that photons are not 'worldly' makes it very counter intuitive (Can't blame them. Can we? ). We generally like the relate to things to what we see every day. We do not get to play/ do the major experiments we have just read about them. Though Zapper Z did state that imagination without knowledge is dangerous. We still tend to test it out every day it helps us deepen our understanding regarding the subject.

Anyhow, back to the topic. What do you mean by 'Fock state'? What does the length of a packet mean? Could you please answer the question added earlier on what the image depicts. That is one of the main questions from the beginning of this forum.

PS: I have a very small idea of what those Quantum Harmonic Oscillators are. For now, I will just assume they are energy. If it is not enough for answering my queries. I think it would be better I keep this question aside and come back to it when I have a better understanding of light.

Thank you

 

[ZapperZ]

I have no idea what you talking about! I simply state the fact that photons are waves and particles and it also applies to any other particles. Now if you don't agree with that you shouldn't be in physics forums. If you want to talk philosophy you should be at philosophy forums. This place needs to be cleaned up a bit.

I shouldn't be in physics forums? How long have you been here again?

Note that I asked you to ELABORATE on what you mean by "photons are waves" and not just to leave it at that! I painstakingly explained why this can easily mislead a lot of people who do not understand the physics. Photons are not "waves", and certainly not in the conventional, physical sense. Tell that to someone off the street, and the picture that the person will get is a bunch of objects bouncing up and down as it moves through space. This is not even true for electrons, etc... etc!

This isn't philosophy. It is a plea to pay attention to what you say, because often times, especially on here, what you mean is not what they understand!

Understand?!

Zz.

 

[blue_leaf77]

This is not the first time you have replied to my questions, so I will take a blind word for that one (The different group of physicists).

I come from the first group, probably all of my laboratory colleagues will tend to depict photons as ball-like entities. But as I have also taken quantum optics course, I realize that photons are actually not as simple as it would have been if it really were like particles in the classical sense.
Fock state is the number state a photon can have, it is therefore the eigenstate of the number operator $a^\dagger a$. More on this :http://www.qms.uni-rostock.de/filea...heel/Quantenoptik/Quantenoptik-Vorlesung3.pdf.

 

[A. Neumaier]

A photon has no size and shape. It may have a range of position

This is not true. Since there is no position operator for the photon, one cannot speak of a photon of having a range of positions (or a probability distribution of being in some small region of space) - this is impossible for conceptual reasons.

But a single photon has an energy density, which very well describes its shape. This is evident in the design and analysis of experiments that create single photons on demand. See my lecture Classical and quantum field aspects of light.