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Author Topic: Do photons (as waves) have fixed amplitude?  (Read 5807 times)

Offline David Cooper

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Do photons (as waves) have fixed amplitude?
« on: 16/08/2014 18:43:12 »
I don't know if a photon officially counts as a photon when it's travelling as a wave, but the shorter the wavelength (frequency of the light/radiation), the higher the energy it carries. However, that would not always apply if the amplitude of the wave could vary. What I'm wondering then it this: is the amplitude fixed in some way relative to the wavelength?


 

Offline jeffreyH

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Re: Do photons (as waves) have fixed amplitude?
« Reply #1 on: 16/08/2014 21:12:08 »
I would assume amplitude to be a variable but only for particles with a varying velocity. It depends upon how the energy is expressed. The energy/frequency relationship of light would not apply to an electron for example. This is only my opinion. Others may disagree.
 

Online evan_au

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Re: Do photons (as waves) have fixed amplitude?
« Reply #2 on: 17/08/2014 03:55:58 »
As I understand it, a changing magnetic field produces an electric field, and a changing electric field produces a magnetic field. This electromagnetic wave propagates through space at the speed of light, as described by Maxwell's equations.

A slowly changing magnetic field produces a smaller electric field, and a slowly changing electric field produces a smaller magnetic field.

By this logic, the amplitude of a single photon would be proportional to its frequency.

When you produce many photons of a single frequency, such as in a laser beam or a radio transmitter, the amplitude is proportional to the number of photons.
« Last Edit: 17/08/2014 04:46:04 by evan_au »
 

Offline jeffreyH

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Re: Do photons (as waves) have fixed amplitude?
« Reply #3 on: 17/08/2014 04:14:36 »
As I understand it, a changing magnetic field produces an electric field, and a changing electric field produces a magnetic field. This electromagnetic wave propagates through space at teh speed of light, as described by Maxwell's equations.

A slowly changing magnetic field produces a smaller electric field, and a slowly changing electric field produces a smaller magnetic field.

By this logic, the amplitude of a single photon would be proportional to its frequency.

When you produce many photons of a single frequency, such as in a laser beam or a radio transmitter, the amplitude is proportional to the number of photons.

I assume you mean frequency modulation representing the amplitude.
 

Online evan_au

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Re: Do photons (as waves) have fixed amplitude?
« Reply #4 on: 17/08/2014 04:50:52 »
The ideal FM (frequency modulation) has a constant transmit power.

Because lower frequencies have less energy per photon than higher frequencies, there would be more photons per second at the lower frequency than at the higher frequencies. This increase in photons exactly cancels the reduced energy per photon, providing a constant transmit power from an FM transmitter.
 

Offline UltimateTheory

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Re: Do photons (as waves) have fixed amplitude?
« Reply #5 on: 17/08/2014 09:30:46 »
When you produce many photons of a single frequency, such as in a laser beam or a radio transmitter, the amplitude is proportional to the number of photons.

Typical laser doesn't produce linearly polarized photons.
 

Offline JP

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Re: Do photons (as waves) have fixed amplitude?
« Reply #6 on: 17/08/2014 13:42:18 »
By this logic, the amplitude of a single photon would be proportional to its frequency.

When you produce many photons of a single frequency, such as in a laser beam or a radio transmitter, the amplitude is proportional to the number of photons.

Yes, exactly!  The classical wave that David Cooper mentioned is not a single photon.  It is a collection of photons whose amplitude is proportional to the expected number of photons, which in turn is proportional to energy deposited on a detector if you were to take a measurement. 

If you were to write out a quantum wavefunction for a single photon, the amplitude would tell you the probability of finding a photon over a region of space.  This is not the same as energy, since you can obviously have a range of anywhere from 0 to 1 probability of finding a photon independently of the photon frequency.  (Though strictly speaking, you can't write out a quantum wavefunction for a single, pure photon, you can do so approximately in many cases).

If you're interested in pursuing the details of how to build a classical wave from individual photons, you want to look up "quantum coherent state."  The math can get ugly, but it describes how to build a classical wave from individual photons.
 

Offline jeffreyH

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Re: Do photons (as waves) have fixed amplitude?
« Reply #7 on: 17/08/2014 14:18:24 »
By this logic, the amplitude of a single photon would be proportional to its frequency.

When you produce many photons of a single frequency, such as in a laser beam or a radio transmitter, the amplitude is proportional to the number of photons.

Yes, exactly!  The classical wave that David Cooper mentioned is not a single photon.  It is a collection of photons whose amplitude is proportional to the expected number of photons, which in turn is proportional to energy deposited on a detector if you were to take a measurement. 

If you were to write out a quantum wavefunction for a single photon, the amplitude would tell you the probability of finding a photon over a region of space.  This is not the same as energy, since you can obviously have a range of anywhere from 0 to 1 probability of finding a photon independently of the photon frequency.  (Though strictly speaking, you can't write out a quantum wavefunction for a single, pure photon, you can do so approximately in many cases).

If you're interested in pursuing the details of how to build a classical wave from individual photons, you want to look up "quantum coherent state."  The math can get ugly, but it describes how to build a classical wave from individual photons.

That is actually the most informative and helpful post I have seen in a long time. Thanks JP.
 

Offline David Cooper

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Re: Do photons (as waves) have fixed amplitude?
« Reply #8 on: 17/08/2014 18:56:18 »
Thanks for those highly informative replies - you've answered my planned follow-up question too which would have been about how photons collectively generate high amplitude waves.
 

Offline PmbPhy

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Re: Do photons (as waves) have fixed amplitude?
« Reply #9 on: 17/08/2014 22:46:59 »
I don't know if a photon officially counts as a photon when it's travelling as a wave, but the shorter the wavelength (frequency of the light/radiation), the higher the energy it carries. However, that would not always apply if the amplitude of the wave could vary. What I'm wondering then it this: is the amplitude fixed in some way relative to the wavelength?
It's always been my understanding that a photon doesn't have an amplitude. I just e-mailed David Griffiths to find out for you.
 

Offline David Cooper

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Re: Do photons (as waves) have fixed amplitude?
« Reply #10 on: 18/08/2014 18:10:36 »
I don't know if a photon officially counts as a photon when it's travelling as a wave, but the shorter the wavelength (frequency of the light/radiation), the higher the energy it carries. However, that would not always apply if the amplitude of the wave could vary. What I'm wondering then it this: is the amplitude fixed in some way relative to the wavelength?
It's always been my understanding that a photon doesn't have an amplitude. I just e-mailed David Griffiths to find out for you.

Thanks - different explanations from different people tend to be pitched at different levels, and that helps to clarify things for a wider range of readers and to strengthen their understanding of things. I'm still a long way from even half an understanding of this (though I have found out what I initially wanted to know), so I look forward to hearing his reply. I've always imagined individual photons travelling along as waves with wavelength and amplitude because that's how they're typically drawn in diagrams, but it didn't seem to fit when I was thinking about high powered radio signals with a large amplitude - I started to wonder if photons merged together in some way to combine their small amplitudes into larger ones. It seems that, in a way, they do, but at the same time they can't, because they don't have amplitudes to combine. So, the thing that was wrong in my model of reality has now gone, but I haven't yet replaced it with a fully clear picture of what replaces it.
 

Offline alancalverd

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Re: Do photons (as waves) have fixed amplitude?
« Reply #11 on: 19/08/2014 08:05:40 »
You are not alone!

The problem is that you can't impose a classical macroscopic model on quantum reality: electromagnetic radiation behaves as it does, regardless of your model. The best we can achieve mathematically is two approximations to what actually happens, neither of which is a complete description.

Whether you think of an elephant as a bulky herbivore or an intelligent manipulator, doesn't fully describe it, but if you want to keep one as a working animal, you need both approximations. 
« Last Edit: 19/08/2014 08:07:34 by alancalverd »
 

Offline jeffreyH

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Re: Do photons (as waves) have fixed amplitude?
« Reply #12 on: 19/08/2014 20:54:12 »
You are not alone!

The problem is that you can't impose a classical macroscopic model on quantum reality: electromagnetic radiation behaves as it does, regardless of your model. The best we can achieve mathematically is two approximations to what actually happens, neither of which is a complete description.

Whether you think of an elephant as a bulky herbivore or an intelligent manipulator, doesn't fully describe it, but if you want to keep one as a working animal, you need both approximations.

Of course if you try to describe it classically then you are describing it as deterministic. Which it most certainly isn't.
 

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Re: Do photons (as waves) have fixed amplitude?
« Reply #12 on: 19/08/2014 20:54:12 »

 

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