[QUOTE]
*Originally posted by Whack-a-Mole *
**I don’t see how the possible number of wavelenghts can be truly infinite. we have boundaries on either end.
Hmm. There are boundaries on either side of an hour, for example, yet within an hour are an infinite number of time divisions.
I’ve heard this too, related to how the musical tones cycle through each octave, i.e., infrared is “sort of like” an octave below violet. More of an approximate analogy, really.
Just checking MC Master of Ceremonies are you saying that two photons both with frequency = mu can have different energies? All in the same frame of refference?
My answer would be that color is the amount of excitation of the three color receptors in the human eye ( appologies to those with color blindness, I’m not implying you aren’t human ). The number of distinguishable colors then is the product of all the distinguishable excitation levels of the three different receptors.
Considering that the eye is a complex biological system, you can imagine correctly that the distinguishability of excitation levels for any particular receptor differs from other receptors of the same type within an eye.
Further complicating this, is that the image data from your eyes isn’t processed like a matrix of pixcels where one pixcel doesnot effect the perception of another, instead there is a great deal of crossover between the processing of data from any color receptor in the eye and any other. Also there are aeparate processes detecting edges and movement within an observed image, though not directly having any color value, these processes can effect the observed color through error effects.
(c.f. optical illusions of black and white lines that can create an illusion of color, see http://www.ads-online.on.ca/illusion/directory.html
)
From this you can tell that “color as it relates to light frequency” is not the same as “color as it relates to perception”.
Not really. On paper (mathematically) there is an infinite number of points between any two points but reality has things setup a bit differently. If it didn’t we’d run into Xeno’s Paradox. Loosely stated Xeno’s Paradox postulates that since there is an infinite number of points between any two points no one should be able to get from point A to point B. So, a door could never fully open, a running back could never reach the endzone and so on (they’d always be approaching but never arriving at their destination). Clearly this doesn’t happen.
In physics you have the Planck Length and by extension the Planck Time as the bottom floor for how many times you can slice something up. Planck Time is the time it takes light to traverse the Planck Length. Since nothing can go faster than light the Planck Time is the smallest time slice we can theoretically measure (it’s so tiny we haven’t gotten close). Some of our more scientifically minded folks will probably point out that the Planck limits are not necessarily limits on reality but limits on our ability to measure reality but nonetheless I assumed that this ‘graininess’ in the Universe is what allows us to arrive at our destination and not have an infinite time between breakfast and lunch.
No a photon of a certain frequency can only have one energy, hf (or hν (h*nu) if you prefer), therefore a light wave must have an energy that is an integer mutiple of hf.
This is what I was on about earlier relating to the human eye using subtractive color mixing instead of additive color mixing as we are taught to do in art classes. Basically when a rod or cone (I forget which does which) is triggered in the eye it hampers the reception of color from other nearby receptors (e.g. if a blue is excited in the eye then the nearby red and green receptors are limited in their response). IIRC this has advantages for edge detection but again I am not clear on all the implications of the advantages and disadvantages of this method or why mother nature chose it.
I’m probably getting in over my head - and off topic - but a running back reaches the end zone because time is fluid and not granular. Did I miss the distinction in your explanation?
Dunno…maybe.
The door opening and endzone deal have to do with distance. You had originally asked about time so maybe that is where the confusion arises.
Still, the idea is the same. Xeno’s paradox deals with distance. Between any two points lies an infinite number of points. It should take you an infinitely long time to travel an infinite number of points (which is the paradox).
I think you should be able to say the same thing for time and I was using Xeno’s Paradox as an example. Between any two times lies an infinite number of ‘fractional’ times. Clearly we do not experience infinite time between breakfast and lunch. As a result I am assuming that (back to the OP and wavelengths) you cannot have an infinite number of possible wavelengths between two time slices as reality doesn’t seem to allow for an infinite number of times between two timeslices.
Which was all just a fancy way of me talking out why I think there must be a finite (if very large) number of posssible wavelengths.
No Zeno’s paradox does not need quantization to be solved, it’s a simple infinite series.
It is highly debatebale whether or not the Planck lenght is the smallest possible divison esp. when refering to wavelenghths. I mentioned this above but I’ll now illustrate this exactly:
The relativistic Doppler shift is given by the following:
z = Δλ/λ = [(1 + v/c)/(1 - v/c)][sup]1/2[/sup] - 1
Where λ is the original wavelength, Δλ is the change in wavelength due to the Doppler effect, v is the relative velocity of the source and the observer and c is the speed of light in a vacuum.
This can be rearranged into the following:
λ’ = (z + 1)λ
Where λ’ is the observed wavelength (λ + Δλ ) and (z + 1) = [(1 + v/c)/(1 - v/c)][sup]1/2[/sup]
Now consider two beams of light with wavelengths (for an observer sationery to the source) Λ[sub]1[/sub] and Λ[sub]2[/sub] and two observers one sationery to the source and one moving with velocity, v, relative to the source. These two equations can then be derived from the equation above:
λ[sub]1[/sub]’ = (z + 1)λ[sub]1[/sub]
λ[sub]2[/sub]’ = (z + 1) λ[sub]2[/sub]
For the observer sationery to the source the difference between the wavelengths of the beams will be:
dλ = λ[sub]1[/sub] - λ[sub]2[/sub]
For the observer moving with velocity, v, relative to the source the difference between the two wavelengths will be:
dλ’ = λ[sub]1[/sub]’ - λ[sub]2[/sub]’
We can then relate these two differences:
dλ’ = (z+1) dλ
This tells us that the difference between the wavelengths of two beams of lights will be different for different reference frames, therefore in one refernce frame a difference between two wavelengths may be less than or equal to the Planck length yet in another it may be greater.
The Pantone color table list 907 colors. It is supposedky the “world wide standard for the graphic arts industry”.
Thanks to Roches for passing this along in another thread on color.
Well, this is sort of correct - the phenomenon is called ‘lateral inhibition’ but it does not involve the ‘hampering’ of colour reception at the receptor-level.
Some other pointettes: human colour vision essentially operates along (Red - Green) and (Blue - Yellow) colour (hue) dimensions. This is why we can’t generally see ‘blueish-yellows’ or ‘reddish-greens’.
There are various answers to the question ‘how many colours can we see?’; it depends what exactly you mean by ‘see’!
So far as is currently known, it is always possible to find a photon with energy between any two energies. There is an uncertainty relation between energy and time, such that if you want to determine an energy very precisely, you need to spend a long time doing that. But there’s no fundamental limit on how long you can spend making a measurement.
It may be that the Planck scales represent absolute limits of some sort on precision of an energy measurement, but this is utterly unproven, and possibly not internally consistent. In any event, it’s certainly possible to measure energies (or differences in energies) less than the Planck length, since every photon or other subatomic particle we’ve ever observed has had energy many orders of magnitude lower than Planck.
And as covered by no less than Cecil himself, the solution to Zeno’s paradox does not rely on quantization, but only on some notions from calculus.
Yeah, that’s what I was wondering what average number of perceived colors is, and maybe the standard deviation on that.
I also hear that the monitor I’m looking at is able to display more colors than humans can distinguish (16 million). If that’s the case perhaps there are some image files with side-by-side colors that can test how well my meat-based color change detection hardware and firmware work. Anybody know of that? 
-k
If I could summarise:
There are two questions covered in this thread.
Also, colours can appear to be exactly the same and actually be made up of different spectral compositions. Eg pure spectral orange, orange made up of yellow and red or orange made up of green and red. These are called metameric colours.
So we agree that colour is perception, not photons and energies. Yes. Good.
(1)
Now, how many colours can be percieved by humans? It depends on how you measure the granuality of colour perception. Do you compare two very close colours by holding them side-by-side or show them separated in space or time.
It has been shown that humans can distinguish spectral hues (rgbiv) 1-6nm apart, depending on the frequency. We are good at discriminating around the yellow-green area but not very good towards the red end and blue end. This also varies from viewer to viewer and is affected by experience and training.
Then there is also saturation and brightness. You can model a three dimensional space of hue saturation and brightness covering all colours. Some parts of this space will have a high fine granuality of colour discrimination by human perception, some areas especially around the edges of the space will have a course granularity of ‘different colours’. Panamajack cited the CIE chromaticy diagram, which is a 2 dimensional representation of this.
When you multiply out the discrete percieved graduations in hue, saturation and brightness there can be up to 7 million discretly percieved colours.
(2)
How many wavelengths of light are there in the visible spectrum?
This is not the OP, but if we go with Chronos explanation is looks like there could be a continuum of infinite resolution. I hope I havent misinterpreted you Chronos.
You certainly can’t observe for longer than the age of the universe.
The number of modes available for the photons is related to the size of the universe - the mode spacing will be inversely related. So for any frequency range, there will be a finite number of frequencies available.
However, because of the Heisenberg uncertainty principle, the time necessary to distinguish between adjacent modes is longer than the age of the universe, and by a decent measure. Further, because the size and age of the universe are related (expansion rate of c or less) this relationship has always held.
So it would be correct to say both that there are a finite number of frequencies or wavelengths, and, because we cannot possibly distinguish the boundary, that the spectrum is also continuous. That’s sounds contradictory, but hey, that’s quantum mechanics for you. 
Welcome aboard swansont!
Can you explain a bit more, for example WHY is the number of modes for a photon necessarily related to the size of the universe? and what exactly do you mean by the expansion rate of the universe is less than or equal to c? The recession velocity of two objects may be greater than c and H[sub]0[/sub] has different units to c.
sailorbychance I am colorblind also and I do believe the dear doctor is pulling your leg.
I will assume that you are the red/green type, it doesn’t matter anyway. You are missing cones in your eyes. When you see shades of green and brown that are similiar to eachother, your eyes lack the mechanism to realize the color so your brain tries to guess.
If a doctor was able to create a tool to allow you to recognize all color it would not lie between your eye and the color, it would lie between your eye and your brain.
An experiment you can try. (works for me anyway) Take a green crayola and a flashlight and proceed into a dark room. Shine the flashlight on the crayon and you will see green. Change the lighting so you can barely see the crayon and under the right condition you may see brown. Change the lighting to a point directly inbetween the two levels of previous light, and proceed to dilate and undilate your pupils. If done correctly you should notice that you can witness your brain lying to you, right before your eyes (har har) as the color switches from green to brown or maybe red.
I can’t provide you a cite for this because I made it up and it works for me, but it goes with the logic of the disability anyways.
This did prompt me to do some research and I have found a company claiming to offer such a product.
The problem with this is that you could pass the colorblind test by looking through a piece of red celophane. These guys are full of crap.
Sorry about the hijack, I hope I at least eradicated some ignorance =)
If you view the universe as the “box” for a “particle in a box” then all photons modes are standing waves within the box. The lowest mode would have a half-wavelength the size of the universe, the next lowest would have a wavelength equal, and so on. So, some arbitrary mode, n=k would have an adjacent mode of n=k+1, but no mode in between. So the mode density goes as 1/L.
The mode spacing is actually more dense than the 1-D picture I’ve given, because we’re looking at a 3-D problem. The mode density actually goes as 1/L^3
No object will recede with respect to any other with v>c, though even if you want to assume that the universe is expanding at 2c, it doesn’t matter, IIRC. (I worked this out a few months back - going by memory)
The version of Heisenberg’s U.P. you want is delta omega * delta t >1 (h-bar cancels out)
If you let t be the age of the universe, the size is given by ct. You end up with delta t having to be greater than or equal to t in the linear case - it gets even bigger for the 3D case. The c cancels with a term in the mode density equation. (I may have dropped factors of 2 and pi, but really, does it matter if you’re limited to 1/2, 1/4 or 1/8 the age of the universe? Order-of-magnitude-wise, anyway. We aren’t observing for anywhere near that long)
Surely if the wavelength of a phton is dependent on the size of the universe that implies an alarming degree of non-locality, what about a photon between two barriers? Also given that the size of the universe from apparent observations is infinite a photon could still have any wavelength.
No, objects in a co-moving sphere may defintely have recession velocities greater than c, this has been known for a long time.