@KarimChahine I did not interpret your comments as "harsh or mean", quite the opposite, I consider your statements to have been showing me a great kindness. My question was very poorly phrased and included meta-comments which were not appropriate for the main site
I sincerely apologize for being responsible for creating a situation which spiraled out of control. This was a mistake. I also apologize for creating extra work for the mods
@DakkVader Your point about "There are no three base colours. That's just how a computer displays colours" is well taken. My question revolves around whether or not blue and red photons with opposite polarizations are opposite, and it's extremely difficult to explain why I came to the conclusions I have in my research.
My question directly relates to the mathematics of floating point rounding errors in the implementation of color systems on computers. I am very familiar with photo realistic lighting, which involves 5 different types of control surfaces used in the shader pipeline. The c…
I always thought it was really weird that photo-realistic lighting needs these exact kinds of control surfaces to work properly (its something like diffuse, normal, specular, bump, and one more I can't remember the name of at the moment).
I believe a better understanding of the computational efficiency of photo-realistic lighting might contain important insights into the physics of light.
Note that there is a physical basis for the perception of three base colors: most humans have three different kinds of bright-light-sensitive retinal cells, with different wavelength profiles
Rob, my question is the result of an entire week of non stop work on pure math in extremely difficult parts of complex analysis and three dimensional complex projective geometry
I understand your point about the biology of the human eye, that is biology and not physics. I am interested in the physics of light, and in methods for gaining insights into the nature of light which currently do not exist
I need a result from physics about the computational properties of light for my pure math paper which I wrote
I am struggling enourmously to properly explain my question in a way that makes sense. Does anything I have said address the statement in your previous comment?
So this should imply "white = 1/0", which is not well defined.
Our eyes were built by evolution to be computationally efficient at doing calculations involving light. Consider the theory of special relativity (cont...)
When moving at speeds approaching the speed of light, the "color", i.e the wavelength, changes. This is a result of length contraction. Furthermore, at every point of space, there is a gravitational field, and space is only approximately flat. Therefore, its possible that length contraction can happen for light travelling through the solar system in parts of the gravitational field that we can't currently measure
A better understanding of the nature of light and gravity, should provide insights into the relationship between photons and gravitational fields, imo
My work on General Relativity as it relates to Differential Geometry has led me directly to the RGB way that colors are stored in computers
I am trying to associate the color "white" with the indeterminate form "1/0", which requires 2 functions, $f(z)$, $g(z)$, in order to be well defined. These functions are related (i think(?)) to the covariant and contravariant components of the metric tensor.
but if you are moving at 99% of the speed of light and doing that experiment, and I am standing on Earth watching you do the experiment, we will see different colors of light
Your comments are very interesting and I am considering everything you have said very carefully
I stated "light is infinity colors", to which you replied, "we can use spectroscopy", which I interpreted as meaning "there are a finite number of photons we can count". But my reply was that no, there really are an "infinite" number in the relativistic theory.
You are of course absolute correct to state "No, but we can still use QED to describe the functioning of a spectrometer.", but it would be completely false to claim you can use QED to count the number of photons, because the total number of photons in light of any color is infinite.
(light of any color which can be measured, that is) /END
Aside: there is no way to say with certainty any specific time ordering of events (temporal order) which took place in between starting the experiment and taking the measurement.
You said "So there are two orthogonal ways you might "count" photons"
I claim I have 99% proved the CPT theorem in pure complex analysis
the square of the wave function represents the probability of recording a measurement, and does not contain information about the internal properties of photons which cannot be directly measured
(sorry will AFK for 5 mins to let you finish your thought, please continue)
Now suppose your lamp is drawing one watt of power and turning it into photons
One watt is one joule per second, which is $10^{19}$-ish electron-volts per second
So every second your lamp is emitting a countable number of green photons.
It's big --- but countable.
That's one way that we can talk about "counting" photons. In low-light activities, there are useful photon detectors that are sensitive to single photons.
You put your apparatus in the dark box, turn on the detector, wait a bit, and it tells you "got one! got another one!"
The other way to talk about "counting" photons, the orthogonal way, is to talk about the number different frequencies/wavelengths of photons that you can distinguish.
You seem interested in stating that this number is infinite, which is correct.
But any system you can devise for measuring those wavelengths is going to put them into a finite number of boxes.
How many of those boxes there are is a feature of your spectrometer, not a feature of light itself.
[I am stepping away for a few hours, but I'll watch for pings from this room.]
Rob, thank you for your very thoughtful and insightful comments. You stated "When I think of "counting" photons, I think of detecting a photon with a photomultiplier tube and incrementing a count."
I completely agree with this statement and would like to add a qualification. I consider myself in the Landau family of physicists. This is because my advisor who I had a close professional student/mentor with, and with whom I published multiple papers on applications of bio-physics to experimental nano-technology in organic crystals, was himself from Moscow university and had his office down…
Quoting from Landau, vol 4, Introduction
"The existence of a limiting velocity, however, radically alters the situation... In the relativistic theory therefore, it is impossible to make an arbitrary and accurate measurement of the momentum. An exact measurement (dP -> 0) is only possible in the limit as the duration of the measurement tends to infinity."
"The description of such processes as occurring in the course of time is therefore just as unreal as the classical paths are in non-relativistic quantum mechanics"
I claim there exists a minimum amount of TIME, such that, any interval of TIME which is less than the minimum, is not a physical concept which can be measured by experiment
In conclusion: I disagree with your assertion that the concept of "counting" photons as you describe can be taken in the limit as d(TIME) -> 0, and therefore claim you measurement was using a continuous spectrum in the non-relativistic theory. But I am exclusively interesting in the relativistic quantum theory and the spin of the photon.
Please let me know if this answers your previous comment about "counting" photons. /END
Question. You said "And a "white" spectrum is one that has a particular shape, roughly corresponding to the spectrum emitted by the Sun." Does this refer to black body radiation?
Regarding spectrum: yes, what humans perceive as "white light" is based on the blackbody-ish spectrum emitted by the Sun and other hot sources.
Regarding counting photons: I think you are trying to tell me that Landau would have said a photomultiplier tube, or a photon-triggered Geiger counter, doesn't count photons or isn't relativistic? I don't think that's correct.
I was not trying to tell you "Landau would have said a photomultiplier tube". I can only speak for myself, and have absolutely no idea what Landau would have said.
I was trying to provide some information regarding my personal identity and credibility and qualifications to be able to ask questions at this level of complexity
Let me try to explain it another way
Let E be an experiment of "counting photons" according to the well defined experimental procedure, and let t be the amount of time under which the experiment takes place
then I claim time has been divided into three completely disconnected components 1) the time before E 2) the time during E 3) the time after E
given that there is an inherit experimental uncertainty in how long t actually was (i.e. how many decimal places did you use for t?), then its clear that by increasing the amount of time the experiment is done, we will detect a different number of photons than if we use an amount of time which is so small that 0 photons arrive
What I am saying (not Landau) is: what is the global state of the quantum electromagnetic field during that time interval under which 0 photons were counted?
I could have done an experiment on the other side of the room, but I choose to do it where it was. That would have meant I solved a boundary value PDE for the geometry of my lab, and was in a different part of the solution of that PDE which is the solution of maxwells equations in a material medium (air).
So I don't know what it means to talk about the electromagnetic field when d(time) is so small that 0 photons were counted (by chance).
If you run an experiment for a time t and detect 0 photons, all that tells you is that the rate of photons is probably less than ~1/t. I don't see how this would imply that there must be an infinite number of photons.
@MattCalhoun The energy of individual photons is always subject to uncertainty, but the total number of photons over a given energy threshold is fairly well-defined.
Re the experimental uncertainty in the duration of an experiment changing the detected number of photons: we model this using “Poisson statistics.”
Suppose you detect 300 uncorrelated photons during a ten-hour experiment. You might find it convenient to divide the time into 600 little bins (“minutes”). You can treat each little bin as an independent experiment, and the average number of photons you’d detect in each minute is 0.5. But you can’t detect half a photon. The Poisson distribution tells you how many intervals to expect to have no events, how many to expect to have one event, how many to expect to have two events, and so on.
These distributions are not sensitive to rounding errors in the size of the bins.
Rob, good call on Poisson distribution, I want to make sure I really understand what you are saying before replying further along those lines.
Chris, you said "I don't see how this would imply that there must be an infinite number of photons." which I find to be completely wrong.
Let me know if we are on the same page or not: In the relativistic theory of quantum mechanics, there is no such physical concept as a field which contains a finite number of photons. Therefore the number of photons in a quantum EM field in infinite.
Aha, Rob, you said "You might find it convenient to divide the time into 600 little bins (“minutes”). You can treat each little bin as an independent experiment, and the average number of photons you’d detect in each minute is 0.5"
I do not understand this procedure which you described as "divide time".
Question: when I "divide time", do I have to worry about temporal ordering of events or not?
@MattCalhoun Photons are perturbations of the vacuum state. The vacuum state, by definition, contains 0 photons. In any other state, assuming you're only considering photons above a given energy threshold (~1.8 electronvolts for the human eye) then the total number of photons within a finite volume is always finite. Because if it's infinite, then the energy is also infinite.
When you see white light, you are certainly seeing a finite number of photons. Because if you were seeing an infinite number of photons, your eye would be absorbing an infinite quantity of energy. Which would be blinding, to say the least.
There are some situations where the “photon number operator” doesn’t commute with the Hamiltonian, and so there is some quantum-mechanical uncertainty in the number of photons a system contains. (I’m pretty sure that lasers and other coherent light sources fall into this category.) However, “infinity” is not an allowed number of photons for such states.
Rob, I don't think that is how it works in QED, correct me if I am wrong, but I thought you needed to compute an integral which contains all possible ways a given event could happen regardless of temporal ordering. en.wikipedia.org/wiki/Path_integral_formulation
Chris, I find your statement very confusing. When you said "the total number of photons within a finite volume is always finite", you seem to be claiming it's possible to have a quantum field with a finite number of particles, furthermore, you strangely seemed to claim my eye is capable of "seeing photons". I cannot see photons because my eyes cannot detect individual photons. Do you mind if I ask, how familiar with relativistic quantum mechanics are you?
Chris, you also said "Because if it's infinite, then the energy is also infinite". There is no such physical concept as "infinite energy". What does infinite energy mean to you?
Finally, Rob, you make a nice observation about the commutation properties of creation and annihilation operators with the Hamiltonian. I need to think more carefully about what you are saying because that seems interesting!
Of course infinite energy is non-physical. That's my point. If you have infinite photons, each of which has energy bounded from below with some finite value, then you have infinite energy. The latter is non-physical, so too much be the former.
Discussion on question by Matt Calhou…
Discussion on question by Matt Calhou…