Photon Energy

[martu]

I have never quite understood how or why a photon’s energy is related to the wavelength and thought about it this way:

Picture the photon as a particle with a very small mass that travels in a wave like manner where all the waves have an equal peak-to-peak amplitude and all photons have the same wave speed (c in a vacuum). Though wave speed is fixed (in a medium) the speed perpendicular to travel can vary so that blue photons are oscillating faster than red photons, 1.6 times faster in fact. The faster the photon oscillates the more energy it has and, as amplitude is fixed, the wavelength varies with oscillation speed so that blue photons have a shorter wavelength than red photons.

This amplitude is so small that to us photons travel in a straight line at c.

What observation rules this picture out?

(Ozziemate’s recent threads have made me reread a lot of Feynman’s books recently and I mentioned something in the ‘proof of a photon’ thread that no one commented on so would like some input from the physicists here showing what me what is wrong the picture, thanks in advance)

 

[blutoski]

My limited exploration of quantum mechanics leads me to believe that attempts to model quantum events in classical terms is more likely to lead to frustration than understanding.

Just as an exercise to see if the explanation generalizes, does your analogy work for the wavelength of a thrown baseball?

Oh, and one nitpick (sorry) - I'm not sure why you're assuming that amplitude is fixed. Amplitude variability is important to assigning probability to locality.

Or, are you saying that the amplitude of a single photon is fixed?

 

[Ziggurat]

Picture the photon as a particle with a very small mass

Why? There's no reason or need to assign any mass to photons.

that travels in a wave like manner where all the waves have an equal peak-to-peak amplitude and all photons have the same wave speed (c in a vacuum). Though wave speed is fixed (in a medium) the speed perpendicular to travel can vary so that blue photons are oscillating faster than red photons, 1.6 times faster in fact. The faster the photon oscillates the more energy it has and, as amplitude is fixed, the wavelength varies with oscillation speed so that blue photons have a shorter wavelength than red photons.

This amplitude is so small that to us photons travel in a straight line at c.

Photons do NOT wiggle from side to side in space. The magnetic and electric fields point from side to side, but the field itself is still located along a straight path. Thinking of this in terms of a spatial displacement is wrong. So it's not that photons "appear" to move in a straight line, they do move in a straight line. Waves don't need to involve sideways displacements. In fact, even many physical waves involving displacement of atoms do not involve transverse displacement (for example, sound waves in air).

 

[martu]

My limited exploration of quantum mechanics leads me to believe that attempts to model quantum events in classical terms is more likely to lead to frustration than understanding.

Just as an exercise to see if the explanation generalizes, does your analogy work for the wavelength of a thrown baseball?

Oh, and one nitpick (sorry) - I'm not sure why you're assuming that amplitude is fixed. Amplitude variability is important to assigning probability to locality.

Or, are you saying that the amplitude of a single photon is fixed?

All photons have the same maximum amplitude. Probability of location is defined by the perpendicular oscillation. Too small for us to see.

 

[martu]

Why? There's no reason or need to assign any mass to photons.



Photons do NOT wiggle from side to side in space. The magnetic and electric fields point from side to side, but the field itself is still located along a straight path. Thinking of this in terms of a spatial displacement is wrong. So it's not that photons "appear" to move in a straight line, they do move in a straight line. Waves don't need to involve sideways displacements. In fact, even many physical waves involving displacement of atoms do not involve transverse displacement (for example, sound waves in air).

At any point in time a photon's direction is a straight line defined by velocity in direction of travel and velocity of the oscillation.

 

[Reality Check]

I have never quite understood how or why a photon’s energy is related to the wavelength and thought about it this way:

Picture the photon as a particle with a very small mass that travels in a wave like manner where all the waves have an equal peak-to-peak amplitude and all photons have the same wave speed (c in a vacuum). Though wave speed is fixed (in a medium) the speed perpendicular to travel can vary so that blue photons are oscillating faster than red photons, 1.6 times faster in fact. The faster the photon oscillates the more energy it has and, as amplitude is fixed, the wavelength varies with oscillation speed so that blue photons have a shorter wavelength than red photons.

This amplitude is so small that to us photons travel in a straight line at c.

What observation rules this picture out?

(Ozziemate’s recent threads have made me reread a lot of Feynman’s books recently and I mentioned something in the ‘proof of a photon’ thread that no one commented on so would like some input from the physicists here showing what me what is wrong the picture, thanks in advance)

The observation that photons have no mass?

But perhaps you can give us a list of predictions from your picture?

 

[Ziggurat]

At any point in time a photon's direction is a straight line defined by velocity in direction of travel and velocity of the oscillation.

"Velocity of oscillation" is meaningless for a photon. Velocity is distance/time. But what's oscillating is the field. It's got a frequency to that oscillation, but it's not a displacement, so you CANNOT assign it a velocity. It has a field strength/time, which one might be tempted to label as a velocity, but 1) it has the wrong units, 2) it adds when multiple photons are present, and 3) even for a single photon it depends on normalization requirements (ie, how spread out the photon is spatially - and no, that's NOT the same thing as the photon wavelength), not just frequency.

Edit to add: there are only two velocities which ever make sense for light: a group velocity and a phase velocity. In a vacuum, they are identical, and they are in the direction of propagation.

 

[Vorpal]

Photons are pointlike. A photon's energy and momentum are related through E = pc as required by relativity, and the wavelength is connected to the uncertainty of the photon's position. The frequency of a photon is not really in terms of anything it itself is "doing" (although it does measure energy), but rather the frequency of its probability amplitude. If you want a (relatively) intuitive picture, look up Feynman's "arrows" in both his book "QED" and some video lectures available online.

 

[Acleron]

Photons are pointlike. A photon's energy and momentum are related through E = pc as required by relativity, and the wavelength is connected to the uncertainty of the photon's position. The frequency of a photon is not really in terms of anything it itself is "doing" (although it does measure energy), but rather the frequency of its probability amplitude. If you want a (relatively) intuitive picture, look up Feynman's "arrows" in both his book "QED" and some video lectures available online.

Good. A very clear description. But may I ask a question which has perplexed me for some time? A light sail works by the photon imparting momentum to the sail. My question is this: What measurable physical property of the photon changes after losing momentum to the sail?

 

[Scazon]

Its frequency. E=hf where f is the frequency and h is the size of the Planck. On hitting the sail, it is reflected, and imparts some of its energy to the sail, and goes off at a different angle with a redder face.

 

[Acleron]

Its frequency. E=hf where f is the frequency and h is the size of the Planck. On hitting the sail, it is reflected, and imparts some of its energy to the sail, and goes off at a different angle with a redder face.

Ah, I think I see what I was getting wrong. I was thinking that light reflected from a light sail would be the same as from a bathroom mirror. Thanks for that.

 

[martu]

The observation that photons have no mass?

But perhaps you can give us a list of predictions from your picture?

What observation that photons have no mass? We have observed a limit but that is all.

Here are a couple:

We wouldn't be able to predict exactly where a photon is due to the oscillation until we observed it.
The equations for energy of a photon would include a constant related to the amplitude.

As both of these phenomena are related to the amplitude it should be the same constant that defines both the Uncertainty and the Energy. Planck’s constant.

 

[martu]

"Velocity of oscillation" is meaningless for a photon. Velocity is distance/time. But what's oscillating is the field. It's got a frequency to that oscillation, but it's not a displacement, so you CANNOT assign it a velocity. It has a field strength/time, which one might be tempted to label as a velocity, but 1) it has the wrong units, 2) it adds when multiple photons are present, and 3) even for a single photon it depends on normalization requirements (ie, how spread out the photon is spatially - and no, that's NOT the same thing as the photon wavelength), not just frequency.

Edit to add: there are only two velocities which ever make sense for light: a group velocity and a phase velocity. In a vacuum, they are identical, and they are in the direction of propagation.

How can something have a frequency that isn’t due to displacement? If it isn’t displacement what is it? The only other thing I can think of is a change in size\mass.

 

[martu]

Its frequency. E=hf where f is the frequency and h is the size of the Planck. On hitting the sail, it is reflected, and imparts some of its energy to the sail, and goes off at a different angle with a redder face.

Indeed which can be explained by the photon having mass to give it a momentum and variable perpendicular velocity which is affected by the sail. If it slows down the wavelength gets longer and hence a ‘redder face’. h defines the amplitude and mass which is equal for all photons.

Another question related to the OP is how a photon can have momentum if it doesn’t have mass?

 

[Vorpal]

How can something have a frequency that isn’t due to displacement? If it isn’t displacement what is it? The only other thing I can think of is a change in size\mass.

The frequency is related to the oscillation of the position wavefunction rather than the photon itself. If you've read Feynman, as you claimed to have done in the OP, you should have a clearer picture of the probability amplitude and its frequency.

Indeed which can be explained by the photon having mass to give it a momentum and variable perpendicular velocity which is affected by the sail.

Uh... sure, but why would it need mass to give it momentum?

Another question related to the OP is how a photon can have momentum if it doesn’t have mass?

Because the stage is that of spacetime, where the conserved quantity is the momentum four-vector. Its time component gives the energy of the particle and the spatial components the ordinary three-momentum. In ordinary Euclidean space, the length of vectors is given by the distance formula: sqrt[x²+y²+z²]. But in spacetime, four-vectors may be nonzero but still have zero length due to a curious signature of the Minkowski distance formula: sqrt[t²-(x²+y²+z²)]. The four-momentum is actually proportional to the particle four-velocity, and the length is the mass of the particle, or in ordinary units mc² = sqrt[E² - (pc)²].

 

[Dancing David]

Oh, mighty sages, thank you for this discussion, I am glad to see that there are answers to these questions.

 

[Ziggurat]

How can something have a frequency that isn’t due to displacement? If it isn’t displacement what is it? The only other thing I can think of is a change in size\mass.

Easily. I already told you: the field is changing with time in a periodic manner. This is an oscillating field, so it has a frequency of how fast the field is changing, but it is not a displacement. You keep trying to picture the photon in terms of a massive particle rather than a field, but that's not what it is.

 

[Ziggurat]

h defines the amplitude and mass which is equal for all photons.

Another question related to the OP is how a photon can have momentum if it doesn’t have mass?

Some people talk about photons having "relativistic mass", which is nonzero but is NOT constant for all photons. But relativistic mass is redundant with energy, and it's a pointless concept which isn't used anymore. Rest mass (or invariant mass) is the only mass one ever needs to use, and it's zero for photons. As previously indicated, relativity allows for non-zero momentum even for massless particles. The equation given above is usually written as E²=m²c⁴+p²c². Putting in a zero for m still gives you p=E/c.

 

[The Man]

Ah, I think I see what I was getting wrong. I was thinking that light reflected from a light sail would be the same as from a bathroom mirror. Thanks for that.

Refection of the photons results in transferring twice the momentum to the sail as absorption see radiation pressure.

 

[martu]

The frequency is related to the oscillation of the position wavefunction rather than the photon itself. If you've read Feynman, as you claimed to have done in the OP, you should have a clearer picture of the probability amplitude and its frequency.

I didn’t say I fully understood it....

Feynam describes phenomena then the maths that can predict behaviour to certain probabilities. It doesn’t rule out a particle travelling like a wave.

Uh... sure, but why would it need mass to give it momentum?

Because p = mv. Or to put it another way how can something have momentum if it doesn’t have mass?

Because the stage is that of spacetime, where the conserved quantity is the momentum four-vector. Its time component gives the energy of the particle and the spatial components the ordinary three-momentum. In ordinary Euclidean space, the length of vectors is given by the distance formula: sqrt[x²+y²+z²]. But in spacetime, four-vectors may be nonzero but still have zero length due to a curious signature of the Minkowski distance formula: sqrt[t²-(x²+y²+z²)]. The four-momentum is actually proportional to the particle four-velocity, and the length is the mass of the particle, or in ordinary units mc² = sqrt[E² - (pc)²].

Yes I just about follow that Six Not So Easy Pieces was a joy to read again. How exactly does this rule out a particle travelling along a wave?