[katieHaylor (OP)]

Ken says:

After reading about Planck and the Ultraviolet Catastrophe I wondered if it implied that there is a maximum electromagnetic (EM) frequency and conversely a minimum EM frequency? I think this is the same as asking if there is a minimum and maximum wavelength for Electro-Magnetic Radiation?


What do you think?

[timey]

: Best answer at Stack Exchange
There is no maximum or minimum wavelength, any wavelength can be transformed into another one with the right choice of reference frame. A possible exception to this is if quantum gravity breaks Lorentz symmetry, and then there will be some minimum Planck-scale wavelength.

This answer was so concise I just had to copy and paste it across...

[jeffreyH]

Ok so let's think about the maximum wavelength. That implies an infinite length. That equates to a frequency of zero or maybe undefined. Let's think about a minimum wavelength. It can't be zero because of zero point energy. This all implies some limit on the range.

[evan_au]

Some extreme limits (rather loose):
- A photon can't have a wavelength greater than the size of the universe
- A single photon can't have an energy greater than the energy of the universe

It is thought that in the high energy environment of the early universe, all 4 fundamental forces would have been unified, so it is questionable whether a photon as such would be "a photon" as we know it.

[timey]

What about looking at the fact that any wavelength can be transformed into another one with the right choice of reference frame?

Which choice of reference frame would result in equating a wavelength the size of the universe?
Which choice of reference frame would result in equating a photon with the same amount of energy as the universe?

[jeffreyH]

God's frame of reference?

[timey]

Huh?

Can I just check with you - in the statement "any wavelength can be transformed into another one with the right choice of reference frame", what do you think is meant by "the right choice of reference frame'?

[chiralSPO]

Huh?

Can I just check with you - in the statement "any wavelength can be transformed into another one with the right choice of reference frame", what do you think is meant by "the right choice of reference frame'?

My interpretation was this: Imagine a beam of monochromatic light (EM radiation) of Frequency F₀ when observed by a someone at rest with respect to the source. If our observer approaches the source at velocity (0 < v < c), the observed frequency will be higher with greater velocity, and arbitrarily high as v approaches c. Similarly, if the observe moves away from the source, the observed frequency will decrease to arbitrarily low values as v approaches c.

This is only one way to change the reference frame. One can also imagine different gravitational potentials etc.

[timey]

Ah yes... very good.  But lets simplify the matter and use GR time dilated clocks situated at rest with respect to the gravity field in different gravity potentials.  We measure a clock that is in the higher gravity potential it has one wavelength.  To change the wavelength of the clock we have just measured we can move the clock we are measuring to a different gravity potential, or leave the clock that we are measuring in the same location and simply move our own position in the gravity potential.

Just saw your edit, posting anyway.

[timey]

So you can see that things can be quite interesting (in a loose kind of way) where I have asked this question:

Which choice of reference frame would result in equating a wavelength the size of the universe?
Which choice of reference frame would result in equating a photon with the same amount of energy as the universe?

If we transpose the question as regarding the wavelength of a clock:
Then a wavelength the size of the universe would be 1 tick of the clock.
And the minutely short wavelength that would be associated with the incredibly high frequency that would result from all the energy in the universe, would result in clock ticks that are so close together there would be no telling them apart.

One might draw this scenario as a graph like this:

*                       *
_____________

Where the 2 dots represent 1 tick of the long wavelength clock, and the line represents, crikes don't ask me how many, ticks of the short wavelength clock.

Where am I going with this?  Well fact is that you could only measure each of these reference frames as being those wavelength from the other.
If I make the graph look like this:

*                      *
~~~~~~~~~~~
____________

Where the wavy line in-between is a longer wavelength that is causing the clock there to tick slower than the short wavelength clock, and we are now measuring from the clock ticking at this wavelength, then this will alter our measurements of the first two clocks.

[timey]

The above suggests (in a loose kind of way) that it clearly is quite pertinent to the measurement as to the choice of tick rate one is using to measure with... For instance the age of the universe in relation to it's size.

But it is also quite interesting to think (in these loose terms) about the physics of these reference frames from which it would be possible to measure these hypothetical extremes.

In relation to the wavelength of a clock, the wavelength the size of the universe would occur in the lowest possible gravity potential, and the shortest wavelength would occur in the highest possible gravity potential...
However, let's now transpose the consideration back to the remit of EM radiation, and what we now find is that the longest wavelength will occur in the highest possible gravity potential, and the shortest wavelength in the lowest possible gravity potential.

Can anyone tell me about the factors that must therefore differ within the gravitational shift equation for a clock, and the gravitational shift equation for EM radiation?

[alancalverd]

Some extreme limits (rather loose):
- A photon can't have a wavelength greater than the size of the universe

Not true. You can in principle generate a radio wave of any frequency greater than zero, so however large the dimenson d of the universe may be, you can envisage a photon of such minute energy E = hf that c/f > d.

But
 

- A single photon can't have an energy greater than the energy of the universe

is obviously true.

[timey]

I'm not quite sure it can be so clear cut as all that Alan.  It depends on whether the distance in which the universe exists is finite or infinite doesn't it? If it is finite then the hypothetical longest wavelength can only be as long as the distance within which the universe exists.
And, as the quote in post 1 states:

Best answer at Stack Exchange
There is no maximum or minimum wavelength, any wavelength can be transformed into another one with the right choice of reference frame. A possible exception to this is if quantum gravity breaks Lorentz symmetry, and then there will be some minimum Planck-scale wavelength.

...Doesn't the choice of reference frame affect the measurement of any length wavelength?
Also, isn't there a minimum energy?

[timey]

:Jerzy Michał Pawlak, PhD in High Energy Physics (experimental)
there is actually a lower limit for the photon energy, and it comes from the uncertainty principle. In another formulation it states, that the product of energy and time uncertainty is of the order of Planck constant. To produce a low energy photon you therefore need more time, than to produce a higher energy one. Another way to see it is thinking about frequency - you can't really say you produced a wave, unless you wait for a time in the order of the period of this wave. So, the minimal photon energy is of the order of E=ℏ/T, where T is the age of the universe.

Which was what I was saying (in not such a concise form) in post 9...

So - going back to post 10:

In relation to the wavelength of a clock, (edit: electron transitions) the wavelength the size of the universe would occur in the lowest possible gravity potential, and the shortest wavelength would occur in the highest possible gravity potential...
However, let's now transpose the consideration back to the remit of EM radiation, (edit: photons) and what we now find is that the longest wavelength will occur in the highest possible gravity potential, and the shortest wavelength in the lowest possible gravity potential.

Can anyone tell me about the factors that must therefore differ within the gravitational shift equation for a clock, and the gravitational shift equation for EM radiation?

For instance - Are the gravitational shifts of electron transitions of the same magnitude as the gravitational shifts of photons when subject to the same differences in gravity potential?

[timey]

In relation to the wavelength of a clock, (edit: electron transitions) the wavelength the size of the universe would occur in the lowest possible gravity potential, and the shortest wavelength would occur in the highest possible gravity potential...
However, let's now transpose the consideration back to the remit of EM radiation, (edit: photons) and what we now find is that the longest wavelength will occur in the highest possible gravity potential, and the shortest wavelength in the lowest possible gravity potential.

Can anyone tell me about the factors that must therefore differ within the gravitational shift equation for a clock, and the gravitational shift equation for EM radiation?

For instance - Are the gravitational shifts of electron transitions of the same magnitude as the gravitational shifts of photons when subject to the same differences in gravity potential?

Bump...

Surely someone here at this forum can answer the question?

[alancalverd]

There is no requirement for electromagnetic waves to be "complete" within a universe.

Fix one end of a string to a rock, then lift the free end and lower it. The string describes half a wavelength. The length of an open organ pipe is half the wavelength of its fundamental frequency. So whether the universe is closed or open, you can generate an electromagnetic wave of any frequency and thus any wavelength within it, even if you can't measure the wavelength because it is bigger than the observable universe.

[timey]

Yes - I can appreciate the truth in what you are saying Alan.

Is there any chance that you could answer the question I posed?
I am (have been for a long time) interested in understanding if a clock that shifts to a higher frequency in a higher gravity potential compared to a lower gravity potential (within the mathematical framework of GR) is shifting to the same magnitude as a photon shifts to a lower frequency when moving from the same lower potential to the same higher potential (within the mathematical framework of GR)...

[timey]

There is no requirement for electromagnetic waves to be "complete" within a universe.

On reflection, Jeff's mention of zero point energy returns to the consideration.  Isn't this a limiting factor?

[PmbPhy]

My interpretation was this: Imagine a beam of monochromatic light (EM radiation) of Frequency F₀ when observed by a someone at rest with respect to the source. If our observer approaches the source at velocity (0 < v < c), the observed frequency will be higher with greater velocity, and arbitrarily high as v approaches c. Similarly, if the observe moves away from the source, the observed frequency will decrease to arbitrarily low values as v approaches c.

This is only one way to change the reference frame. One can also imagine different gravitational potentials etc.

So beautifully put it almost brought a tear to me eye!    I simply could not have said it better myself. In fact when I saw this thread I was going to say almost the exact same thing, just phrased differently. But you phrased it better than I would have.

BTW - How to I do a "Thank you" for a post? I can't see a link to do it with.

[jeffreyH]

Ok so let's think about the maximum wavelength. That implies an infinite length. That equates to a frequency of zero or maybe undefined. Let's think about a minimum wavelength. It can't be zero because of zero point energy. This all implies some limit on the range.

Well spot the stupid mistake. Zero point energy relates to an infinite wavelength. A wavelength approaching zero is also approaching infinite energy. And no one spotted THAT?