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Author Topic: Light quanta, wavelengths and energy.  (Read 2530 times)

Offline Aethelstan

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Light quanta, wavelengths and energy.
« on: 13/12/2013 17:37:08 »
Hi, I am just reading about how Plancks use of light quanta for convenience, and then Einsteins proof that they existed gave birth to quantum mechanics. It's interesting to me how the discrete packets carry different amounts of energy based on frequency, but it left me gasping for more. Are photons all the same physical size, and therefore carry the energy within each peak? Do they differ in size and each carry the same number of waves, and the energy is in the frequency itself? Is there a minimum and maximum frequency within the EM spectrum?

Thanks for taking the time to read this, hopefully they are not daft questions :)


 

Offline JP

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Re: Light quanta, wavelengths and energy.
« Reply #1 on: 13/12/2013 18:00:19 »
This gets at one of the fundamental oddities of quantum mechanics.  How do you define the size of something that behaves as both a wave and a particle? 

Take an electron, for example, which is much less weird than a photon.  We know it's a particle and that if we shoot it at a detector, it will hit the detector at a given point.  Ok, maybe this point has some area to it--we can't measure an infinitesimally small point, but we can measure that the electron strikes the detector at a very small point. 

At the same time, we can fire the electron at a screen designed to block electrons and punch 2 tiny holes in it.  The distance between these holes is further apart than the electron size we measured at our detector, yet somehow the electron manages to pass through both holes at once on its way to our detector.  Even odder, we can somehow spread an electron over macroscopic distances even though our detector measurement shows it to be microscopic in size!

This is part of the weirdness of quantum mechanics.  In our large scale world, things tend to behave EITHER like a particle or like a wave.  But on a tiny scale, things somehow behave like both!

As to photons, when they're traveling between points, we can't give them a size in a rigorous way.  A single photon is technically infinite in size as its traveling.  When its detected it is (at least in our models) infinitesimally small in size--it literally does strike at a single point.  (Of course, we can't measure this for certain, but we keep looking for a smallest size and haven't found one yet.)  The defining property of a photon is not what its wave looks like or how its particle-ness behaves, but rather what Einstein and Planck discovered: that light comes in packets and a photon is somehow, one packet.  The fact that it appears to be infinite when traveling and infinitesimal when striking a detector come from the physical requirements of bundling energy into a precise packet.

To go a bit deeper, you're probably heard of the Heisenberg uncertainty principle.  A photon has a precise energy and a precise direction of propagation by definition.  The uncertainty principle says that if it has a precise energy, its wave must be spread out over all time.  It also says that if it has a precise direction of propagation, it must be spread out over all space.  This is why it's infinite while traveling. 
 

Offline Pmb

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Re: Light quanta, wavelengths and energy.
« Reply #2 on: 14/12/2013 02:00:45 »
Quote from: Aethelstan
Hi, I am just reading about how Plancks use of light quanta for convenience, and then Einsteins proof that they existed gave birth to quantum mechanics.
To be precise, Planck was attempting to explain blackbody radiation (bbr) distribution function u(L) (where L = wavelength). In 1900 Max Planck announced that by making certain assumptions he could he could derive a function u(L) that fit the bbr.

Planck first found an empirical function that fit the data. Then he searched for a way to modify the calculation so as to fit the empirical formula. To accomplish this he imagined a black body to be composed for harmonic oscillators that could absorb and emit radiation only in discrete wavelengths. This is a quantum hypothesis; the first one of I have my history of physics right. The radiation being emitted from these oscillators were thus quantized. So it wasnít for convenience that Planck proposed these quanta. It was because it was the only way he could find to be able to describe bbr. These quanta would later become to known as photons.

In 1905 Einstein hypothesized that light was quantized so that he could describe the photoelectric effect.  Thus Einstein never proved that these quanta existed. He simply hypothesized them. Itís only when experiment after experiment and many other ways are found which imply their existence is run and confirmed do we become convinced that such things are real and actually exist.

Quote from: Aethelstan
It's interesting to me how the discrete packets carry different amounts of energy based on frequency, but it left me gasping for more. Are photons all the same physical size, and therefore carry the energy within each peak?
Photons donít have size since theyíre point particles. They simply have different properties that depend on the photonís energy. But regardless of the energy of a photon they are all still point particles.

Quote from: Aethelstan
Do they differ in size and each carry the same number of waves, and the energy is in the frequency itself?
They do not differ in size. Itís not meaningful to say that a particular photon carries a number of waves. The wave phenomena only manifest itself when there are a large number of them present or a large number of identical experiments are executed and later compared.

Quote from: Aethelstan
Is there a minimum and maximum frequency within the EM spectrum?
No.
 

Offline Pmb

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Re: Light quanta, wavelengths and energy.
« Reply #3 on: 14/12/2013 02:08:56 »
Quote from: JP
The distance between these holes is further apart than the electron size we measured at our detector, yet somehow the electron manages to pass through both holes at once on its way to our detector.
I bet Feynman rolled over in his grave when you wrote ďthe electron manages to pass through both holes at onceĒ! :D  Quantum mechanics never allows us to say such things and we certainly canít measure it.

Quote from: JP
Even odder, we can somehow spread an electron over macroscopic distances even though our detector measurement shows it to be microscopic in size!
The electron never gets spread out. The only thing that gets spread out is the electronís wave function.

Quote from: JP
This is part of the weirdness of quantum mechanics.  In our large scale world, things tend to behave EITHER like a particle or like a wave.  But on a tiny scale, things somehow behave like both!
They behave either as a particle or a wave, but never both a particle and a wave at the same time.

Quote from: JP
As to photons, when they're traveling between points, we can't give them a size in a rigorous way.  A single photon is technically infinite in size as its traveling.
And Feynman roles over a second time when he saw you write that.  Lol! :)   A single photon always behaves as a particle.
 

Offline JP

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Re: Light quanta, wavelengths and energy.
« Reply #4 on: 14/12/2013 03:55:50 »
Ah, poor Feynman.  He must be uncomfortable with all the rolling you're imposing upon him!

I don't have the time to argue over interpretations of quantum mechanics, so I'll provide this link and a brief commentary:  http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

It's sufficient for the layperson to know that physics doesn't deal with absolute reality--it deals with predicting the results of measurements.  So far as that goes, the only way to predict the outcome of firing an electron at two slits (provided we don't know which slit it went through) is to use mathematics that states some entity is passing through both slits at once and that when it arrives at the detector, it is detected at (to our most precise measurements) a single point.  There is no mechanism we know of that would have an entity pass through only one slit and produce the results that we see in experiments so clearly something passes through both slits.

So on one end, we fire an electron. On the other end we detect an electron.  In the middle something goes through both slits.  We can call that something an electron, an electron wavefunction, a pilot wave.  We can say we branch into infinitely many multiverses corresponding to different measurements to explain this.  We can say that the world is quantum all the way down and there is no divide between particle and wavefunction, but a continuum. We can't distinguish between these cases using experiments, so they're all viable.  As far as simplicity goes, if we have an electron on one end and an electron on the other end, it should probably be an electron in the middle and any extraneous unmeasurable things are a bit wasteful.  (Occam was thinking of rolling over in his grave, but he was afraid of disturbing Feynman!)  But I'm not going to spend time arguing that one explanation is right.
 

Offline Pmb

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Re: Light quanta, wavelengths and energy.
« Reply #5 on: 14/12/2013 05:15:18 »
Quote from: JP
It's sufficient for the layperson to know that physics doesn't deal with absolute reality--it deals with predicting the results of measurements.  So far as that goes, the only way to predict the outcome of firing an electron at two slits (provided we don't know which slit it went through) is to use mathematics that states some entity is passing through both slits at once and that when it arrives at the detector, it is detected at (to our most precise measurements) a single point.
The particle does no such thing. Itís the wave that does that. Quantum mechanics does not allow anything to be said unless a measurement is made and no measurement detects a particle at two places at the same time. Quantum mechanics does not allow you to tell what its doing when you're not observing it.

Regarding the link you posted - please show me where in it that it speaks of such an interepretation. Thanks.
« Last Edit: 14/12/2013 05:29:22 by Pmb »
 

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Re: Light quanta, wavelengths and energy.
« Reply #5 on: 14/12/2013 05:15:18 »

 

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