I need help /sci/. I'm interested in the energy a photon

>>8630023
You have two different problems here.

1. Wavelength * frequency = c in all frames.

If one changes, the other must adjust so that c is maintained. Otherwise, c would not be constant in all frames which is false.

2. If changing regions causes a change in length or time, by SR you can find exactly what that is and find the corresponding wavelength or frequency. This gives you your new momentum.

Additionally, a change like this could be interpreted as a change in reference frames. This necessarily means a force is involved. The energy difference between the new and old states will be precisely whats put in / taken out by the force.

The question as you ask now is actually nonsense. Momentum doesn't need to be conserved if you're just measuring a system under two different conditions. Is only when those systems/conditions are related that you need to see conservation.

>>8630023
The frequency of the photon tells you its energy--it doesn't change in different regions in space (modulo some "gravitational redshift," but this is, for a technical reason, a moot point). So just assume frequency is constant and describes your photon. Now, as it travels through a medium with index of refraction n, it will have an effective velocity v = c/n and an apparent wavelength' = wavelength / n. Both energy and momentum will be conserved (as they have to be). Notice that for a photon, w = ck (in vac) and so the phase and group velocity are the same. Notice also that the velocity of light is independent of wavelength.

>>8630181
This is completely incorrect, anon. 1) Frequency of light doesn't change to match--it's apparent wavelength does. And apparent velocity of light does change. You're reasoning is true for different photons, where a different f describes a completely different photon.

More importantly, you should go take another look at special relativity. First, changing regions the particle is in has nothing explicit to do with changing reference frame. And a change of reference frames has nothing to do with a force!!!! A force CHANGES the dynamics of a particle--SR says that there is no fundamental difference between a guy moving at a velocity v1 and a guy moving at velocity v2. But a guy who feels a force? Completely different and not at all related to SR reference frames. And note the main assumption that gets you to SR--the velocity of light (in vacuum) is constant, or c. This means there is no rest frame for the photon. Every reference frame observes a photon that is moving at c.

And momentum/energy are always conserved in SR (though not necessarily separately); you just need to work with the combination (i.e. the momentum 4-vector)

>>8630023
I can see why you're confused, and the answers here aren't great (in fact they are wrong, fucking undergrads when will they learn)

When you talk about two differant 'regions' I'm going to assume that you're talking about two regions with differant refractive index. This would produce differant wave-vectors, or k values as you explained. Now the energy of the photon will always be constant, and is dependant on its frequency. When the photon travels through differant meterials, the frequency will always be constant, but the wavelength will change in order to keep the relationship c/n = f*lamda.

Now momentum does have to be conserved when the photon is moving between regions, but as you identified the momentum of the photon does not have to be the same before and after. The resason for this is reflection. The reflected beam also has a momentum, so overall momentum is conserved, even though it has been reduced in the photon. Momentum is also the reason for refraction occuring. In fact, the reason that total internal reflection exists is because this demonstrates the condition in which the momentum is too low for the beam to leave the material.

>>8630490
>>8630356
>>8630376

>Frequency of light doesn't change to match. The frequency of the photon tells you its energy

What if I told you I setup a system where the frequency must change? What then? The solution to the differential equations is an increasing frequency.

Ive tried to find solutions where the wavelength changes, but I've come to the conclusion they don't exist.

>>8630713
>What if I told you I setup a system where the frequency must change? What then?

LIke what? If you are thinking about lasers or OPOs then you start dealing with either atomic changes in the materials or non-linear optical effects. Neither of which are relevant to your question.

When a photon travels into a material with a differant refractive index the wavelength changes but the speed stays the same.

I also hope you relaise that energy and momentum are not the same thing.

>>8630730
this should read

>the wavelength changes but the frequency stays the same.

>>8630730
>When a photon travels into a material with a differant refractive index

the system has a refractive index change in TIME not SPACE. The differential equations only have solutions for changing frequencies.

>>8630794
>the system has a refractive index change in TIME not SPACE. The differential equations only have solutions for changing frequencies.

You're really not giving me enough to go on here. How can it change in time and not space? Is the light stationary? What differential equations have you derrived?

>>8630817
>You're really not giving me enough to go on here. How can it change in time and not space?

The medium properties are a function of time not space. I don't think this is too impossible.

>Is the light stationary?

of course not.

>What differential equations have you derrived?

Im looking at maxwells equations.

>>8630840
So the refreence frame you're using is the refrence frame of the light itself, and not a position? In that case you probably derrived the doppler effect.

What assumptions have you made?

>>8630851
>So the refreence frame you're using is the refrence frame of the light itself,

Im using the lab frame. Im not using anything do do with relativity or anything. Just classical electromagnetics.

>In that case you probably derrived the doppler effect.

The doppler effect requires an emitted photon from an accelerating body. There are non in the system. It's just a photon in a medium where the parameters change to create dispersion. The parameter change is a function of time not space.

>What assumptions have you made?

Just a photon travels in a medium and then the medium parameters change with time.

>>8630863
>Im using the lab frame

So the light is travelling as a function of space, no?

>The doppler effect requires an emitted photon from an accelerating body

If you are using the lab refrence frame then yes.

>medium parameters change with time.

What parameters? Refractive index?

>>8630870
>So the light is travelling as a function of space, no?

Yes. The photon travels in space and time.

>>medium parameters change with time.
>What parameters? Refractive index?

Refractive index or permittivity or permeability.

>>8630990
Well then just refractive index then, seeings as its a function of those.

The freunecy will remain unchanged as the refractive index is increased, however the light is slowed down. So if you're getting a result that gives a change in frequency then you're doing something wrong.

>>8630376
You are the one that seems to be mistaken.

For example, moving towards a signal at relativistic speeds causes a doppler effect. The light waves become shorter. Since lambda*f = c, shorter wavelength means frequency MUST change.

In SR, reference frames have constant velocity. Changing frames means chaging velocity. Changing velocity implies acceleration. Non zero acceleration means there is a force acting.

Please don't put me down when you have no idea what you're talking about

>>8631033
>The freunecy will remain unchanged as the refractive index is increased, however the light is slowed down. So if you're getting a result that gives a change in frequency then you're doing something wrong.

fxx = ftt/c^2 + a*t*f/c^2

This is the form of differential equation you get when the material parameters are changing. a is a constant that makes the units work.

Give me a solution where the frequency is constant then. The x and t represent partial derivitives .

>>8631051
Its been a long time since I solved maxwells equations, I don't tihnk I have the mental energy to have a go.

All I'm trying to do is tell you what you should be getting. And if you're getting a result that says that the frequency changes, then either your math is wrong, your assumptions are wrong or you're using c as the refrence plane.

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>>8631085

Check for yourself. I cannot use the monochromatic wave assumption. My work is posted

>>8631091
You know that the relative permittivity is a function of frequency right?

>>8631137
>You know that the relative permittivity is a function of frequency right?

What function? In my system it is a linear function of time.

Here is some simplification. Find a monochromatic solution.

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>>8631148
Lost the picture

>>8631137
>You know that the relative permittivity is a function of frequency right

Let me try to make it a little more clear. I know the effective permittivity a monochromatic wave sees in a material is different for different frequencies of radiation. What if I took the dielectric and put it in an oven or freezer, or if it is a gas and I change the pressure? I'm not changing these things in space but in time. these are real physical systems. I'm interested in the real solutions.

As far as I can tell the physics tells me a monochromatic wave cannot exist in any of the systems I mentioned.

>>8631036
You're completely fucking retarded. Changing reference frames via a boost is NOT A FUCKING ACCELERATION. That would make it non-inertial. It would then have different dynamics and certainly couldn't be an equivalent reference frame (violating relativity). And I didn't say that frequency never changes for a photon--I said it's not the thing that changes "to match" when it goes to a different region (meaning area of different refractive index). You should learn to fucking read before you recite whatever high school physics you remember hearing.

>>8631036
And also as I said, the speed of light is not effectively constant in a medium (due to scattering reducing it's mean free path). So no, shorter wavelengths do not mean frequency must change. Seriously, the fucking intro to physics for bio majors undergrads know this shit.

>>8631036
And notice the original post describes a photon moving from one region of SPACE to another. That's why I'm talking about refractive index. Your point on the doppler effect is not relevant to what he is asking about.

>>8631213
>>8631221
I assume the medium is constant across the regions of space considered. So good job trying to put words in my mouth and say what I didn't say is untrue.

If I am in some frame u with velocity v relative to something else, and then change frames to u' with velocity v', then some sort of acceleration occurred. I never said the new frame was non inertial or had any forces at all.

You might get away with this shitty strawman stuff with other people, but not here.

How about you argue my premise and conclusion instead of claiming I'm arguing something that I'm not. K thx.

>>8631238
anon. Go read fucking special relativity. There is a HUGE fucking difference between what happens when you compare two equivalent observers at the same point (x,t) who have different velocities (which are just boosted reference frames), but they will see something in general COMPLETELY different for another observer at (x,t) who had some velocity shift due to acceleration (which would have to be an instantaneous shift for it to be a transformation at the same point (x,t)). You could quickly figure this out from the most basic SR problem, the twin paradox, and by viewing the instantaneous change in the planes of simultaneity of the accelerating twin. You completely misunderstand the entire concept of SR. Literally completely.

And you said in your point 2 "if changing REGIONS...a change like ths could be interpreted as a change of reference frames" which is completely fucking idiotic. Lorentz transformations are local transformations of SO(3, 1), meaning they are completely local transformations. SR doesn't tell you how to "transform" from one point of space to another. To do that, you need the concept of a geodesic, which is an actual path and NOT a transformation. And, like I said, I was responding to the actual post which asked about changing regions. That's why I said your nonsense about f changing to compensate wavelength was retarded.

>>8631238
tl;dr Changing reference frames from u to u' is for the sake of locally comparing two observers at the same point (x,t) with different velocities, NOT a way for YOU to change YOUR velocity w.r.t. the same stationary observer.

And OP, you have to decide if you're treating light classically or not. Do you want to go the wavepacket route?

>>8631198
>What if I took the dielectric and put it in an oven or freezer, or if it is a gas and I change the pressure?

This is the kind of system I'm talking about. I've done experiments with a similar system wth a monocramatic wave, except I was changing the refractive index by changing the systems pressure. I can assure you that the measurable frequency does not change.

By doing this you are basically gradually slowing the light down. Which is what got me thinking about the doppler effect, because thata the only way I can see the freuency chaning.

> I'm not changing these things in space but in time
But in a real system, the light propagates through space as time passes. When I did that experiment the light still had to physically pass through the material.

>>8631288
Not sure you can assume a separable form. I'd try something of the form exp[i (-k*x + wt)] while noting that k will not be constant in x.

Actually OP, I think you should just be more careful here. It's not obvious to me how you so simply transform from one region of space to another. If I were you, I wouldn't just call things like permittivity or permeability your time-dep values; in a new region, E and B will in general be different. If you want an answer that explicitly conserves energy and momentum, you're going to have to do this as (most simply) a plane wave of light traveling in say, n=1 incident on a surface of n2=something else.

>>8631288
>t I was changing the refractive index by changing the systems pressure. I can assure you that the measurable frequency does not change.

Do you have more details on your setup and results or is there a paper or publication I can be referred to.

Maxwell's equations do not support this.

>>8631259
Lorenz transformation has a space time dependency. If you are talking about simultaneity, then you must address this. It's literally the entire point of sr. I'm not sure why you even bring this up at all.

I think you're assuming op was talking about light in one medium changing to another. Op made no mention of this at all which is why it's weird for you to assume so.

I was arguing that generally, if region a has frame o and region b has frame o' that the frequencies observed will be different, which is true. I literally said nothing more than that.

As far as changing frames goes, I understand SR doesn't describe what hapens if you do. I never claimed any predictions of what would happen. It was a stramwan by you.

What I did say is that if the same person was in frame o then moved to o' and measured in that frame, they would get two different results which is also true. Comparing those two results would show that a force had been present. Which is true because the observer experienced forces to change frames.

All of this is perfectly valid within sr and nothing weird happens

>>8631350
Not trying to sound patronising, but this is so basic that there isn't a publication I can think of to refrence. The experiment I did was part of my MSc course.

I have a feeling thats whats happened is that you've incorrectly treated the system as space-invariant and are observing the doppler effect due to the fact you're not taking into account the increasing/decreasing optical path.

>>8631350

I was thinking about this.

Assuming your chamber is 1 meter long
Assuming regular pumping speeds
Assuming a normal speed of light

The photon would have cross the chamber in nanoseconds, there is no way you significantly changed the pressure in a chamber in nanosecond. What resolution frequency detector did you have?

>>8631369
>Not trying to sound patronising, but this is so basic that there isn't a publication I can think of to refrence.

What was the goal of the experiment?

>>8631373
To observe the light slowing down as the refractive index changed.

Look, you said yourself you were confused by your results. A quick google search will tell you that when light experiances a change in refractive index, its freuquency does not change.

>>8631402
>To observe the light slowing down as the refractive index changed.

It seems you observed group delays from different photons. I'm interested in the refractive index changing significantly while the photon is traveling through the chamber.

>Look, you said yourself you were confused by your results. A quick google search will tell you that when light experiances a change in refractive index, its freuquency does not change

But I've studied Maxwell's equations and come to the conclusion Google must be wrong, or Maxwell's equation. Look at my derivation and tell me where I am wrong.

>>8631410
>It seems you observed group delays from different photons.

This doesn't make sense. Group veolicity does not refer to single photons. I'm perfectly aware what I observed.

>refractive index changing significantly while the photon is traveling through the chamber.

How is this any differant from just passing the light through an interface between two materials?

You'll have to find the mistake in the derriation on your own, kid.

>>8631436
>This doesn't make sense. Group veolicity does not refer to single photons. I'm perfectly aware what I observed.

Did you observe the refractive index change in the time it took the photon to travel the length of the chamber?

>>refractive index changing significantly while the photon is traveling through the chamber.

What kind of pump did you use to significantly chmage the pressure in a nano second?

>How is this any differant from just passing the light through an interface between two materials?

Because in my system the change is a function of time not space.

>You'll have to find the mistake in the derriation on your own, kid.

I actually did lol

>>8631450
>I actually did lol
Do tell. I mean it'll be totally over my head but I'm sure others are similarly gripped by this soap opera here.

>>8631575
>Do tell. I mean it'll be totally over my head but I'm sure others are similarly gripped by this soap opera here.

What I meant was "I actually laughed out loud at this comment."

My derivations are sound.

>>8631581
>sound derivations
>results inconsistent with modern physics

K lol

>>8631612
>>sound derivations
>>results inconsistent with modern physics

But what law am I breaking? It's just one of those those things people say that the frequency never changes of EM radiation.

Show me the law that's being broken. I know it's uncommon for refractive index to change abruptly with time, and it is common for it to change abruptly with space so it seems to defy common logic.

>>8631366
Lol ok I'm done. I think it's hilarious that the obvious undergrads on this site want to continually debate shit they don't understand rather than trying to listen to what people are telling them. Congratulations on convince yourself that you mastered special relativity after your first undergrad course in it.