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Author Topic: Quanta and planck's constant/law  (Read 13309 times)

Offline McQueen

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Quanta and planck's constant/law
« Reply #25 on: 10/11/2007 00:07:57 »
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I guess I'm not understanding what is 'quantized' in the assumption of Planck's.  The intensity of the radiation released at a given T and v?  Or is it the energy of the radiation emitted at those frequencies?

Planck’s hypotheses was that the energy of a wave of a given frequency cannot be arbitrary but assumes only discrete values. Within the framework of classical physics it was impossible to explain how an electromagnetic wave can have only discrete values of energy, this is one of the reasons that Maxwell’s theory of Electromagnetic radiation is out of favour. Planck’s work was impeccable, some of the later hypotheses of QM are not.
 

Offline Soul Surfer

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Quanta and planck's constant/law
« Reply #26 on: 10/11/2007 08:25:30 »
I agree sophiecentaur that you should chose your models to match the conditions.  Lightarrow  Fourier analysis is not relevant in this particular case.

This discussion brings me back to a question that I am still looking for a definitive answer to.

Does an individual quantum posses bandwidth? and is this a measurable property of a quantum?  Groups of quanta from specific sources and quantum detection devices can both posses bandwidth ie a quick transition produces a broad band quantum and a high q detector is a narrow band detector and vice versa but does this apply to a single quantum if so  bandwidth as well as energy should be given as a property of a quantum.

McQueen  you are wrong.  All physical theories must be considered as approximations.  Maxwells electromagnetic theory is perfectly adequate for many normal electromagnetic experimentation as is Newtonian gravity  the additional theories of quantum mechanics and relativity are only needed for extreme cases where the accuracy of the theories breaks down.

The breakdown of electromagnetics into quantum mechanics started with experimentation observation and modelling as is being discussed here.  the great genius of Einstein was that the breakdown of Newtonian gravity to relativity  was almost entirely theoretical and would not have been required by practical physics for several more years.


 

lyner

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Quanta and planck's constant/law
« Reply #27 on: 10/11/2007 11:30:00 »
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Planck’s hypotheses was that the  energy  of a wave of a given frequency cannot be arbitrary but assumes only discrete values.
But I think you would agree - and it is the basis of calclus - that , given enough   discrete values and if they are close enough together, you can regard it as a continuum. The discreteness of which Planck is talking is not just limited to the obvious big-steps of the energy levels in a hydrogen atom.
Yes, of course, classical explanations are not sufficient for the full story -we have moved on since late victorian times.

Soulsurfer- your  question about quanta and bandwidth. I think you are really asking about photons and bandwidth. Because a photon has a finite effective lifetime and pulse length, it must have a bandwidth - it s bandwidth relates to the reciprocal of the length of the impulse of energy it carries. It also relates to the  effective Q factor of the oscillation or the time actually taken for the energy transition to occur.
So the 'envelope' of the photon could depend on the process that gave rise to it. I imagine that the high coherence of the light from a laser could imply  a narrower bandwidth.
However, there is probably much more to it than we are getting to in this discussion. The duality thing must come into it - if we are trying to discuss bandwidth then we are, by implication, talking about a wave - which is not the particle aspect of electromagnetism.  Perhaps it's the wrong question to ask?
 

Offline lightarrow

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Quanta and planck's constant/law
« Reply #28 on: 10/11/2007 13:31:32 »
Lightarrow  Fourier analysis is not relevant in this particular case.
Why? You know that it's possible to write every waveform, as short as you like, as an infinite sum of sinusoidal plane waves.
Quote
This discussion brings me back to a question that I am still looking for a definitive answer to.
Does an individual quantum posses bandwidth?
I presume yes, because I know for certain that photons don't have a precise energy, also depending on the specific kind of transition, as sophiecentaur says.
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and is this a measurable property of a quantum?
I don't know the answer; I think it could be done simply, e.g., sending individual photons, all emitted from the same source in the same conditions, through a diffraction grating an collect the resultant pattern in a screen, exactly in the case of "common" light; however the photons cannot be exactly all equal because of an intrinsic statistical inequality.
« Last Edit: 10/11/2007 16:25:16 by lightarrow »
 

Offline lightarrow

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Quanta and planck's constant/law
« Reply #29 on: 10/11/2007 13:34:55 »
However, there is probably much more to it than we are getting to in this discussion. The duality thing must come into it - if we are trying to discuss bandwidth then we are, by implication, talking about a wave - which is not the particle aspect of electromagnetism.  Perhaps it's the wrong question to ask?
Maybe; however you have the interference pattern even sending individual photons; how would you interpret this fact?
 

Offline McQueen

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Quanta and planck's constant/law
« Reply #30 on: 10/11/2007 14:11:51 »
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Because a photon has a finite effective lifetime and pulse length, it must have a bandwidth - it s bandwidth relates to the reciprocal of the length of the impulse of energy it carries.


I am sorry I can’t understand this, a photon is supposed to have an infinite lifetime. That is if it is not absorbed it will maintain its energy,  indefinitely.

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McQueen  you are wrong.  All physical theories must be considered as approximations.  Maxwells electromagnetic theory is perfectly adequate for many normal electromagnetic experimentation as is Newtonian gravity  the additional theories of quantum mechanics and relativity are only needed for extreme cases where the accuracy of the theories breaks down.

That is just the point a model is appropriate providing it is an honest one. Take the treatment of EM by Quantum Mechanics for instance, forget about quantization, what about the second quantization and the third and the fourth and after each of these, normalization takes place where infinities are reduced to zero. This is still OK except for the claim that the theory has an accuracy of 10^^12 !! Under these circumstances where could quantum mechanics possibly be needed?

Again, Maxwell’s theory even though it might work, does not satisfy the fact that EM is quantized, therefore it is not an acceptable theory. Why was P.Drude’s explanation of electrical conduction dropped ? It was dropped because it didn’t correspond to new facts that came to light. Note that Drude’s theory did work quite well to a certain extent. But it was still wrong in the end.
 

Offline lightarrow

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Quanta and planck's constant/law
« Reply #31 on: 10/11/2007 16:30:25 »
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Because a photon has a finite effective lifetime and pulse length, it must have a bandwidth - it s bandwidth relates to the reciprocal of the length of the impulse of energy it carries.
I am sorry I can’t understand this, a photon is supposed to have an infinite lifetime. That is if it is not absorbed it will maintain its energy,  indefinitely.

He meant to say that the interval of time during which the photon is generated is finite, so the "train of EM waves" (if a photon is a "train of EM waves) has a finite lenght, and this means it cannot have a unique frequency (it can be seen through Fourier transform).
 

lyner

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Quanta and planck's constant/law
« Reply #32 on: 10/11/2007 16:35:29 »
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Why? You know that it's possible to write every waveform, as short as you like, as an infinite sum of sinusoidal plane waves.
You should be more accurate if you want to get it right.
Fourier ANALYSIS  takes a repeating waveform and replaces it as an infinite series of harmonically related sinusoids. 
The Fourier TRANSFORM  can be carried out on any function.  The FT of a sinewave  (in the time domain)which has been modulated by a pulse (i.e. a burst of sinewave) has a peak (in the frequency domain)  at the 'carrier frequency' and, potentially, a continuum of sidebands (sinusoids of infinite duration) which stretch out on either side. The shorter the pulse in time , the more the spread of the sidebands in frequency.

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you have the interference pattern even sending individual photons; how would you interpret this fact?
The two slit interference pattern would give a density pattern, corresponding to the probability of a particle / photon hitting  a particular bit of the screen. That is the same pattern as the wave interference approach would give. (As the probability density function of the electron around the atom relates to the wave function.)*
The detailed pattern, seen on the screen (i.e. the actual spacing of the half power points, for instance) would depend on the range of frequencies (bandwidth) of the light / population of photons. It would be interesting if someone had compared the detailed interference patterns from different sources. Ah, yes, of course there would be spectral spreading due to Pauli exclusion - as with high pressure sodium lamps.
No two photons would be of the same frequency - even in a low pressure gas .- Also, because of Heisenberg uncertainty,  you could not be sure of the precise frequency of any photon.
As for the lifetime of a photon McQueen, - it can be as long as you like - but, once you have measured it, it is ended. It starts life 'sometime', when an atom (or system of atoms) changes energy level and it ends when it has interacted with another system. (Yes, Lightarrow -I have  just read your post)

*You get the same thing with electrons interfering as they pass through a thin carbon sheet.
« Last Edit: 10/11/2007 18:03:23 by sophiecentaur »
 

Offline lightarrow

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Quanta and planck's constant/law
« Reply #33 on: 11/11/2007 17:58:02 »
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Why? You know that it's possible to write every waveform, as short as you like, as an infinite sum of sinusoidal plane waves.
You should be more accurate if you want to get it right.
Fourier ANALYSIS  takes a repeating waveform and replaces it as an infinite series of harmonically related sinusoids. 
The Fourier TRANSFORM  can be carried out on any function.  The FT of a sinewave  (in the time domain)which has been modulated by a pulse (i.e. a burst of sinewave) has a peak (in the frequency domain)  at the 'carrier frequency' and, potentially, a continuum of sidebands (sinusoids of infinite duration) which stretch out on either side. The shorter the pulse in time , the more the spread of the sidebands in frequency.
Exactly, and any arbitrarily short function of time f(t) (in the sense that it's ≠ 0 in an arbitrarily short time interval) can be written as an infinite sum of pure sinusoids, that is an integral, where the function inside the integral is the FT of f(t):

f(t) = (1/Sqrt(2π))∫F(ω)eiωt

F(ω) = (1/Sqrt(2π))∫f(t)e-iωtdt

and the integrals are from -∞ to +∞.
 

lyner

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Quanta and planck's constant/law
« Reply #34 on: 11/11/2007 18:15:17 »
Sure thing boss.
 

Offline lightarrow

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Quanta and planck's constant/law
« Reply #35 on: 11/11/2007 18:19:43 »
 

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Quanta and planck's constant/law
« Reply #35 on: 11/11/2007 18:19:43 »

 

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