Questions about the nature of the electromagnetic spectrum

[sonnybilly]

Hi I had some questions about the nature of the spectrum of electromagnetic radiation, as to whether it is continuous or quantifiable, and whether it is infinite or finite. I haven't been able to find satisfactory answers so far and I'm very interested in the knowledge of this forum.

Can the difference between the frequency (and therefore the energy) of two different waves of electromagnetic radiation be infinitely small?

Can the frequency and energy of electromagnetic waves be measured in natural units of an indivisible quanta?

Are there any upper or lower constraints on the frequency or energy an electromagnetic wave can possess?

Do any of the answers to these questions change for an individual photon?

Thanks for your help.

 

[mgb_phys]

Ok since no experts in QM have replied I will have a go. Ultimately the answer may depend on what model of th euniverse you believe in.

Can the difference between the frequency (and therefore the energy) of two different waves of electromagnetic radiation be infinitely small?

I believe so yes

Can the frequency and energy of electromagnetic waves be measured in natural units of an indivisible quanta?

If the above is true No, although the energy levels in an atom are discrete, the energy states available to a photon would be continuous.

Are there any upper or lower constraints on the frequency or energy an electromagnetic wave can possess?

I suppose the longest wavelength would be the size of the universe and the shortest would depend on the maximum energy available in the universe.
As far as I know there is no widely agreed on law for a maximum temperature or a maximum energy of a photon.

 

[granpa]

depends on whether time and space are continuous or discrete

 

[sonnybilly]

Thanks for your answers. I've got some more questions...

Do Planck Time and Planck Length (and other Quantum Theories) imply a discreet quality to time and space that leads to quantifiable energy and hence a quantifiable frequency of electromagnetic radiation and a discreet EM spectrum?

Does the Planck Length put a limit on the smallest wavelength of EM radiation or Planck Time on the fastest frequency?

Does the Pauli exclusion principle, and its non-application to photons, imply that the energy states of photons can be continuous because they can share the same quantum states? Or is that unrelated?

If the universe is larger than the observable universe, would it be very difficult, or impossible, to put an upper limit on the size of EM wavelengths because we could never observe what it beyond the cosmological horizon and hence measure the size of the entire universe? Could EM wavelengths be longer than the observable universe without any falsifiable theory able to predict an upper limit on their size?

 

[granpa]

also look up 'second quantization'.

 

[granpa]

http://en.wikipedia.org/wiki/Quantum_field_theory#Renormalization

 

[sonnybilly]

Thanks for the link.

The questions arose out of an idea / thought experiment I had, I think I might get further if I state the idea rather than try to understand bits and pieces of classical and quantum theories and how they relate to it.

I'll post it in a new thread titled: "Thought experiment: The 'perfect eye' (and a finite set of colours)"

https://www.physicsforums.com/showthread.php?p=1924946#post1924946