As I understand it, a wave can be described with four characteristics:
Frequency-cycles per second (pitch,color)
amplitude-strength of transmission (loudness,brightness)
polarization-angle of the wavelength
phase-the peaks and valleys of the transmission’s sine wave.
It’s fairly simple to modulate the four characteristics:
With frequency, just add or subtract cycles per second.
Amplitude, increase the power to the transmission.
Polarization, use a polaroid filter to twist the transmission.
Phase, well, it depends where you start from. At the bottom of the valley and go up the slope to the top of the peak, or any point in between.
I figure, these characteristics are continuous in nature.
To quantize these characteristics, we must quantize the measurement parameters.
For Frequency, use Planck Intervals per cycle
for Amplitude, keep adding particles per volume of space per unit of time until the space time continuum is saturated (one particle per cubic Planck Distance per Planck Interval)
I can’t think of a way to quantize Polarity or Phase, do you?
I think you’re mixing up the classical and quantum worlds. Frequency is not quantized, however the energy of a photon associated with a specific frequency is. And it equals the frequency times Planck’s constant.
Quantization was proposed by Max Planck as a solution to the ultraviolet catastrophe in black body radiation. Einstein then used this concept to explain the photoelectric effect. Bohr, Schrodinger and Heisenberg were then able to explain the allowed energy levels in an atom and why the electron in an atom doesn’t spiral into the nucleus due to radiating energy.
Could it be that differences in amplitude and frequency translate into differences in energy, where as differences in phase and polarity do not? On the quantum level, energy is quantized, but not necessarily anything else is.
Is the Energy of an arbitrary photon (I assume we’re talking about photons here) quantized? I’d never heard that. If so, how is it quantized? Is it the same thing that enolancooper was talking about with the Amplitude?
Since photons only manifest themselves when they interact with matter the whole concept of a photon is a very nebulous thing. Between interactions they are nothing more than a probability wave which we commonly call an electromagnetic wave, and the probability of detecting a photon is equal to the magnitude of the electric field vector squared.
But when they do interact with matter their energy must be quantized because atomic orbitals have discrete energy levels.
No. Photons can interact with free electrons, so the energy doesn’t have to be quantized. Also, in Einstein’s photoelectric effect you mentioned earlier, photons above a threshold frequency can all cause electrons to be ejected, with the resulting electron velocity increasing as the frequency increases.
<The sound you hear is Ring kicking himself, because he certainly already knows this.>
Photons are quantized in the sense that you can only have an integral number of them, and so for photons at a particular frequency, the total energy of the collection of photons is quantized.
I was under the impression that any measurable quantity can be quantzed…I assumed this included both polarity and phase, both of which can be functions of degrees of rotation.
Are polarity and phase related to spin…something most definitely quantizable?
Are you talking about a way theoretically to quantize this stuff, or a way that it is quantized? If it’s the latter, then I can tell you that if frequency is quantized, it is definitely not in units of 1/T[sub]P[/sub]. If that were the case, then the smallest possible photon energy would be sqrt(c[sup]5[/sup]×h/G), or about 4.903×10[sup]9[/sup] J.
As I understand it, the quantum wave function is just a function that, when squared, yields the probabilty that a measurement would give a certain discrete value. The measurement is discrete; there is a particle here or not, the spin axis is up or down. But the function itself varies continuously.
If OP is asking how do you quantize the wave function. The answer is “Don’t do that.”
There’s very few quantities that are always unconditionally quantized… Angular momentum and charge are the only ones I can think of offhand. Almost anything can be quantized in the right situation, though. Polarization quantization, for instance, depends on the orientation of your polarizer. If I have a polarizer and pass a beam of photons through it, then every photon will either get through, or it won’t. If it gets through, then its polarization is aligned with the filter. If it doesn’t, then its polarization is 90[sup]o[/sup] off from the polarizer. It doesn’t matter how you turn your polarizer; every photon will be either exactly lined up or exactly unlined up.
I’m not sure how phase quantization would come up, but I wouldn’t be surprised if there’s a situation where it happens.
Don’t go worrying about Planck units, since they only ever get involved when you’re dealing with both gravity and quantum effects.
ZenBeam that is most indubitably correct. However if you will notice I was talking about atomic orbitals which are bound systems and which, I believe most people would associate with matter. (Of course there are also atomic and molecular rotations and oscillations to consider.)
Much to my chagrin, I have no such argument inre the photoelectric effect other than the possible defense that the density of states in the conduction band of a metal is so high that these electrons should not be considered to be part of a bound system. However this is stretching things to the breaking point and I therefore humbly concede.
Given your propensity to be so nasty as to say true things I am very much afraid that I am going to have to stop slap dashing off responses and instead actually give some thought to what I say. Is that a revolting development or what?
You seem to me a bit confused about what quantization means. You can express something in terms of units, e.g. degrees. You’re not quantizing it, you’re just setting a scale.
As has already been mentioned, quantization of waves as it pertains to quantum mechanics comes from the fact that light is made up of massless particles (photons), which can be delocalized and behave like continuous waves, but which are still discrete units. You can’t have 1.4263 photons. You also have the quantization of angular momentum. This doesn’t mean every measurable quantity is necessarily quantized.
So, in general, phase and polarity are not quantized.
Because a photon is a boson and travels at c it can only have two values of m_s - plus one and minus one. So the axis of polarization can only be parallel or antiparallel wrt to the direction of motion.
However circularly polarized light incident on a polarizing filter has a one half probability of being projected into a state of either vertical or horizontal linear polarization. But the actual orientation of the vertical or horizontal polarization is dependent on the measuring device, whereas the orientation of the axis of circular polarization is fixed wrt to direction of motion and therefore independent of any measuring device. This somehow doesn’t seem symmetrical.
Or am I wrong in assuming a photon has a fixed direction of motion? Is this what Feynman is saying in his sum over histories?
Circular polarization is a complex superposition of horizontal and vertical polarization-- Or, if you prefer, linear polarization is a complex superposition of left- and right-circular polarization. If light is truly circularly polarized (as opposed to elliptically polarized), then the amplitudes of horizontal and vertical polarization are equal, so the photon has an equal chance to get through or to not get through. It is a bit surprising, I suppose, that this is all independent of what you choose to call “horizontal” and “vertical”. Do the math and it all works out.
“But the actual orientation of the vertical or horizontal polarization is dependent on the measuring device”
And it wouldn’t be hard to show math if you could do subscripts here.
But nonetheless the quesion still remains:
*"But the actual orientation of the vertical or horizontal
polarization is dependent on the measuring device, whereas the orientation of the axis of circular polarization is fixed wrt to direction of motion and therefore independent of any measuring device. This somehow doesn’t seem symmetrical.
Or am I wrong in assuming a photon has a fixed direction of motion? Is this what Feynman is saying in his sum over
histories? *
A photon’s direction of motion is dependent on your reference frame, but given a reference frame, it’s well-defined. In any given frame, if you measure the component of a photon’s spin in the direction of its motion, you’ll find it’s either +1 or -1, corresponding to left circular polarization or right circular polarization. If you measure the polarization/spin in some other manner (such as with a polaroid filter), then you’re forcing it into some particular state by the act of measurement. Or am I missing entirely what you’re asking here?
By the way, you can do [sup]superscripts[/sup] and [sub]subscripts[/sub] on the board: Use the [****sup] and [****sub] tags.