Radiation Pressure and Conservation of Momentum

[Samson4]

How do you account for the conservation of momentum for a photon? Specifically, if you have light traveling in a medium where the refractive index is not constant. For example, a graded index multi mode fiber optic.

So here is another diagram to help articulate my question. Inside this graded index fiber, light curves off it's trajectory. If light has momentum, what is the opposite effect of this radial acceleration?

 

[Dale]

In a medium you cannot uniquely separate out the EM momentum and the material momentum. The total momentum of the wave and the medium is conserved.

 

[Samson4]

In a medium you cannot uniquely separate out the EM momentum and the material momentum. The total momentum of the wave and the medium is conserved.

Does that mean the medium(fiber optic), experiences equal and opposite accelerations as the photons?

 

[Dale]

Does that mean the medium(fiber optic), experiences equal and opposite accelerations as the photons?

Yes (equal and opposite changes in momentum), although this is a classical phenomenon so you can just talk about the classical electromagnetic waves and don't need to actually deal with quantized photons.

 

[sophiecentaur]

Radiation pressure doesn't need photons to account for it. There is a force which results from a classical EM wave encountering a medium. Very textbook stuff long before QM came along.

 

[Samson4]

Radiation pressure doesn't need photons to account for it. There is a force which results from a classical EM wave encountering a medium. Very textbook stuff long before QM came along.

I'm intrigued by the momentum em waves exert on the medium. Doesn't this also mean that sunlight curving into the Earth is pushing the medium(atmosphere) in the opposite direction?

 

[Nugatory]

I'm intrigued by the momentum em waves exert on the medium. Doesn't this also mean that sunlight curving into the Earth is pushing the medium(atmosphere) in the opposite direction?

Ever wondered why the tails of comets always point away from the sun?

 

[jbriggs444]

Ever wondered why the tails of comets always point away from the sun?

The standard explanation has little to do with radiation pressure. Similarly, the rotation direction of a Crookes radiometer has little to do with radiation pressure.

 

[Nugatory]

The standard explanation has little to do with radiation pressure

Ah - you're right, there's the solar wind which is an outgoing stream of charged particles. I've always understood that both radiation pressure and solar wind contribute to the formation oif cometary tails, but I've tried looking into the relative contribution of each.

 

[sophiecentaur]

I can only reply "Why not?"
But the actual value of this pressure is what counts. It has visible effects.

 

[sophiecentaur]

the rotation direction of a Crookes radiometer has little to do with radiation pressure.

I know that a standard Crooke's Radiometer works on temperature of the surfaces and local gas pressure. I have always assured students that, if you had a deep enough vacuum, it would go the other way.
Does anyone know of a machine that works 'properly' in the presence of just sunlight? Was I guilty of Teacher BS?

 

[jbriggs444]

I know that a standard Crooke's Radiometer works on temperature of the surfaces and local gas pressure. I have always assured students that, if you had a deep enough vacuum, it would go the other way.
Does anyone know of a machine that works 'properly' in the presence of just sunlight? Was I guilty of Teacher BS?

You are right, of course and taught your students correctly. I was only going after the simple misconception that a comet or a Crookes radiometer is an immediate proof of radiation pressure.

 

[sophiecentaur]

You are right, of course and taught your students correctly. I was only going after the simple misconception that a comet or a Crookes radiometer is an immediate proof of radiation pressure.

But is there a 'proper' one in some museum somewhere? It nags my conscience sometimes. I would never, knowingly lie to students.

 

[Samson4]

I know that a standard Crooke's Radiometer works on temperature of the surfaces and local gas pressure. I have always assured students that, if you had a deep enough vacuum, it would go the other way.
Does anyone know of a machine that works 'properly' in the presence of just sunlight? Was I guilty of Teacher BS?

I can't help you with that but I do have a question.
Why doesn't it take the same amount of energy to stop a photon as it does to create it? A 680 nm photon has 1.8232936424298 ev. It has 9.2058823529411764705882352941176e-28 kg m s of momentum. Or 9.027886617647058e-27 watts or 5.634763867393764823e-8 ev. Why is this the case? If a photon stops, how would it still have energy?

 

[sophiecentaur]

If a photon stops, how would it still have energy?

If it "stops" then it doesn't;t exist, Its energy and momentum will have been transferred elsewhere. It's not like a billiard ball that hits something and then stays there. It has no mass so it can quite happily (for us) disappear.
Edit: What's with the mention of Watts?I don't understand that.

 

[Samson4]

If it "stops" then it doesn't;t exist, Its energy and momentum will have been transferred elsewhere. It's not like a billiard ball that hits something and then stays there. It has no mass so it can quite happily (for us) disappear.
Edit: What's with the mention of Watts?I don't understand that.

Just to convert to ev from watts. I just don't understand why the momentum is .00000003 of the initial energy. If this photon hit a medium with a refraction index of 2, would half of this momentum be transferred to the medium? When it exits this medium, does the medium again experience acceleration opposite of the photon?

 

[sophiecentaur]

Just to convert to ev from watts.

eV is Energy. Watts is Power (= Energy / time). There is no meaningful 'conversion'.

I just don't understand why the momentum is .00000003 of the initial energy.

How can you compare them? They are different quantities and different units. That number you quote is just 1/c.
What you are doing is Numerology, which is not Science. Work in a different Unit system and the two above 'conversions' give different numbers.

 

[Samson4]

eV is Energy. Watts is Power (= Energy / time). There is no meaningful 'conversion'.

How can you compare them? They are different quantities and different units. That number you quote is just 1/c.
What you are doing is Numerology, which is not Science. Work in a different Unit system and the two above 'conversions' give different numbers.

I looked at it from a different angle this morning. Since I know that the photon has 1.8233 ev of energy. I took an electron and calculated its velocity in vacuum after accelerating across 1.8233 volts. Then I found the momentum it would have. The answer was 7.2977e -25 newt m/s. I converted this to kg m/s, 7.444153e-26.

So a photon has 2 orders of magnitude less momentum for the same energy as an electron. I am unsure of the math though.

 

[Samson4]

Looks like it was actually 7.246e-25 kg m/s so it is 3 orders of magnitude more than a photon of the same energy.

Does them seem correct or atleast a feasible method to compare the two?

 

[jbriggs444]

Looks like it was actually 7.246e-25 kg m/s so it is 3 orders of magnitude more than a photon of the same energy.

Does them seem correct or atleast a feasible method to compare the two?

You were challenged on a conversion between energy units and power units. You responded with a way to start with the energy of an electron and end with its corresponding momentum. No, that does not give you a conversion factor between power and energy.

It does not even give you a conversion factor between energy and momentum. The conversion is not linear. Momentum does not scale linearly with energy except in the high energy limit.

 

[Samson4]

You were challenged on a conversion between energy units and power units. You responded with a way to start with the energy of an electron and end with its corresponding momentum. No, that does not give you a conversion factor between power and energy.

It does not even give you a conversion factor between energy and momentum. The conversion is not linear. Momentum does not scale linearly with energy except in the high energy limit.

But an electron of 1.8233 ev of energy has 3 orders of magnitude more momentum than a photon of the same energy. I can't look at it this way? How do I approach this problem?

 

[jbriggs444]

But an electron of 1.8233 ev of energy has 3 orders of magnitude more momentum than a photon of the same energy. I can't look at it this way? How do I approach this problem?

What problem are you trying to solve?

Edit: My teachers said in school that a problem properly defined is halfway to being solved. Boy, were they right!

 

[Samson4]

I want to compare the momentum for a given energy( 1.8233 ev or 680 nm photon) between an electron and photon.

 

[sophiecentaur]

Ok. You have the formulae. So . . .

 

[Samson4]

Ok. You have the formulae. So . . .

I thought I did it right. Was my answer in post 19, correct.

 

[ProfChuck]

In a medium you cannot uniquely separate out the EM momentum and the material momentum. The total momentum of the wave and the medium is conserved.

This suggests that radiation pressure acts as a force that tends to expand the system. Is it possible that radiation pressure is at least a component of dark energy and cosmological expansion?

 

[Dale]

Is it possible that radiation pressure is at least a component of dark energy and cosmological expansion?

It is certainly part of cosmological expansion, but it is light not dark.

 

[ProfChuck]

Ha ha, yes. Photon pressure between galaxies will introduce a force that will tend to drive them apart. This must be included in the expansion model as part of the dark energy question. As I understand it a dark energy candidate is thought to be positive space-time curvature as described by deSitter. It would be interesting to compare photon pressure force with gravitation at intergalactic distances to see if it alters the cosmological constant.

 

[Dale]

This must be included in the expansion model as part of the dark energy question.

No, it must be included in the model as part of the normal energy. It is not dark energy and it has nothing whatsoever to do with dark energy. It is literally light energy.

I don't know how I can be more clear. It is already in the model, it is not dark energy.

 

[ProfChuck]

Thanks. You answered my question. "It is already in the model." I know that photon pressured is not "dark energy" but it does exert an expansion force. I worked as an astronomer at Cal Tech for a number of years and I see difficulties in separating the effects of photon pressure from "dark energy". Deep sky surveys suggest that the rate of expansion is not constant but there are models where photon pressure or "dark energy" or both can account for this. To my mind the issue is the underlying nature of "dark energy", is it positive ST curvature or something more mundane?

 

[Dale]

I see difficulties in separating the effects of photon pressure from "dark energy"

Dark energy isn't an effect, it is a source. We measure the effects, we calculate the required energy, we measure the ordinary energy (including EM), the difference is dark energy. The light is in the ordinary energy category, not the dark energy category, by definition.

Do you understand that EM radiation is light and that light is not dark?

 

[ProfChuck]

WRT "Do you understand that EM radiation is light and that light is not dark" Of course I do. You are correct in that the bookkeeping shows that when all known forces are taken into account there is still a deficiency that we chose to call "Dark Energy". So, assuming dark energy is real what is the underlying mechanism? Is it an "ordinary" Newtonian force that we have not included in the model or is it something more exotic? Back in the 70's part of my thesis was "Apparent non Newtonian factors in galactic rotation models." It was clear that undetected forces, probably caused by unseen matter, were influencing the rotational dynamics of many if not all galaxies. Sb type or Barred spirals are examples of this. In my mind the question "what is it?" remains very much an open issue. Is it matter that is so cold that ordinary detection methods are ineffective or is it something more interesting like non baryonic matter? One way it's just inadequate instrumentation the other is it "new physics". I think a similar question applies to dark energy. Are we dealing with something more or less ordinary that has evaded detection or is it something more exciting?

 

[anorlunda]

what is the underlying mechanism?

We don't know.

 

[Dale]

WRT "Do you understand that EM radiation is light and that light is not dark" Of course I do.

Then it seems strange to keep asking if this has anything to do with dark energy.

In my mind the question "what is it?" remains very much an open issue.

Certainly.

 

[Samson4]

I thought I had a grasp on this and now I'm not so sure. A photon's momentum is a function of its energy, but it is not proportional to the velocity, which is always c.
That brought up a question about light slowing down in a medium. Since the energy doesn't change, does this mean the momentum doesn't either?