is there an infinite spectrum of colour (emr spectrum if you like)? or is there a finite number of frequencies in the emr spectrum?

Boris said:

is there an infinite spectrum of colour (emr spectrum if you like)?

More like this one

Only our eyes aren’t sensitive enough to differentiate.

i was wondering about photons and quanta etc and the h in planck constants and if there was a limit to how far down you can divide the energy. and stuff.

Depends on how you define colour.

If the universe is infinite, then the wavelength (momentum) can be arbitrarily precise. If the universe is compact, then the precision is limited to the standing waves over the entire universe. However, this is the theoretical maximum precision as the precision of a real pulse of electromagnetic radiation will be limited by the size of the pulse (as well as its shape).

is this related to HUP? from another forum they were talking about this sort of thing in a HUP thread. and fourier transforms.

http://www.thescienceforum.com/physics/33502-heisenberg-uncertainty-principle.html

It is worth pointing out that no waveform can have compact support in both time and frequency domains.

Boris said:

is this related to HUP? from another forum they were talking about this sort of thing in a HUP thread. and fourier transforms.

http://www.thescienceforum.com/physics/33502-heisenberg-uncertainty-principle.html

The HUP is not a specifically quantum mechanical phenomenon. It applies to all types of waveforms due to the mathematical nature of Fourier transforms. There is an uncertainty between time and frequency as well as position and wavenumber that is not to do specifically with quantum mechanics. The HUP of quantum mechanics is ultimately due this, but involves the Planck constant only because of the relation between frequency and energy and the relation between wavenumber and momentum. Thus, the quantum mechanical HUP is between position and momentum, whereas the universally applicable mathematical uncertainty is between position and wavenumber.

KJW said:

It is worth pointing out that no waveform can have compact support in both time and frequency domains.

However, the HUP is expressed in terms of the standard deviation, which may be finite in both domains. It is an inequality because the product of the two standard deviations depends on the particular waveform, but is minimal (the equality) for a Gaussian waveform, which is Gaussian in both domains. Note that although the Gaussian function has finite standard deviation, it does not have compact support (thus, the Gaussian waveform has compact support in neither domain).

Boris said:

i was wondering about photons and quanta etc and the h in planck constants and if there was a limit to how far down you can divide the energy. and stuff.

If you have light of frequency f, then the energy in each photon is given by
E = hf
So a bunch of that light must have energy that’s a multiple of hf.

OTOH, no light source can emit light of an exactly precise frequency, there will always be a spread of frequencies. A simple model of light emission tells us that a particular electron transition should cause light of a fixed frequency to be emitted. However, a more realistic model tells us to expect a range of frequencies because the atoms that are emitting the light are not static, they have some kinetic energy and their random motion causes a Doppler shift in the light that they emit. And of course, any photon detector is also prone to Doppler shifting for the same reason.

Also, in any measurement of a quantum process there will always be a spread in the measurements obtained. And as KJW mentioned, it’s not mathematically possible
to get an exact frequency value of a wave unless you have an infinite number of wave cycles to measure, or you assume that all the cycles are exactly identical.

There are probably other causes for the spread of frequencies, but I can’t think of them at the moment. :)

It’s fairly likely that there is a maximum frequency, which corresponds to a photon having an energy equal to the Planck energy. That amount of energy packed into a single particle is enormous, and it may be impossible for any process less energetic than the Big Bang to create particles with anywhere near that energy.

Frequency can probably be any real number greater than 0 and less than that maximum. OTOH, if spacetime is not continuous, then the possible wavelengths / frequencies will also be quantized. But such questions cannot be answered without a theory of Quantum Gravity.

> But such questions cannot be answered without a theory of Quantum Gravity.

Well come on then.

drums fingers on desk

I’m waiting, here.

sibeen said:

> But such questions cannot be answered without a theory of Quantum Gravity.

Well come on then.

drums fingers on desk

I’m waiting, here.

Sorry, that’s above my paygrade. :)

I admit that it does feel like a bit of a copout to end an answer with the QG disclaimer, especially when the question doesn’t appear to involve extreme conditions like black holes or the Big Bang. But our theories about the fine structure of spacetime are only tentative without a working Quantum Gravity theory.

thank you KJW and PM2Ring, between you i now have a better understanding.

once again it is limited by those wacky quantum effects.

PM 2Ring said:

It’s fairly likely that there is a maximum frequency, which corresponds to a photon having an energy equal to the Planck energy. That amount of energy packed into a single particle is enormous, and it may be impossible for any process less energetic than the Big Bang to create particles with anywhere near that energy.

Frequency can probably be any real number greater than 0 and less than that maximum.

I needs to be said that as a consequence of Lorentz invariance (special relativity), there is no upper limit to the frequency of electromagnetic radiation. It is sometimes said that at some very high frequency, the concentration of energy is so high that a blackhole would form. However, this is false (due to Lorentz invariance). One need only consider an observer travelling arbitrarily close to the speed of light towards a light-source, and the resulting Doppler blueshift.

KJW said:

PM 2Ring said:

It’s fairly likely that there is a maximum frequency, which corresponds to a photon having an energy equal to the Planck energy. That amount of energy packed into a single particle is enormous, and it may be impossible for any process less energetic than the Big Bang to create particles with anywhere near that energy.

Frequency can probably be any real number greater than 0 and less than that maximum.

I needs to be said that as a consequence of Lorentz invariance (special relativity), there is no upper limit to the frequency of electromagnetic radiation. It is sometimes said that at some very high frequency, the concentration of energy is so high that a blackhole would form. However, this is false (due to Lorentz invariance). One need only consider an observer travelling arbitrarily close to the speed of light towards a light-source, and the resulting Doppler blueshift.

Well, I did say fairly likely. :)

And in my defence, I did recently say
“if photons did gravitationally interact with each other, by choosing a sufficiently fast frame heading towards a light source we could blue-shift any beam of light to gravitationally collapse into a black hole. But if a bunch of stuff is a black hole in one frame it ought to be a black hole in all frames (eventually). And clearly, your typical bunch of photons is not generally observed to be in a black hole state. :)”
in this thread: http://forums.xkcd.com/viewtopic.php?p=3286964