# Wavelengths corresponding to fractions of nanometers?

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• DavidReishi
DavidReishi
In terms of the electromagnetic spectrum, are there wavelengths of light corresponding to fractions of nanometers, for example, 0.5 nm, with their own photon energies? Or are whole nanometers "nature's smallests units" when it comes to the various existing wavelengths of light?

bahamagreen
Soft x-ray wavelengths are on the order of one nanometer, gamma rays may be more than 100 times shorter...

For
frequency f
wavelength λ
photon energy E

where:

Mentor
... and because of the Doppler effect, you can make the wavelength of any electromagnetic radiation arbitrarily small just by moving rapidly enough towards the source.

DavidReishi
So are there wavelengths corresponding to fractions of nanometers, i.e. withouth movement towards or away from the source?

Mentor
Or are whole nanometers "nature's smallests units" when it comes to the various existing wavelengths of light?
Nanometers are a purely human invention, as with most other units. Nature doesn't know or care about them.
So are there wavelengths corresponding to fractions of nanometers
Almost all of them are fractions. (not whole numbers of nanometers)
See hydrogen for example. These numbers are all rounded from more precise values with more decimal places. I'm too lazy to hunt for the more precise values with experimental uncertainties on the NIST web site.

Mentor
So are there wavelengths corresponding to fractions of nanometers, i.e. withouth movement towards or away from the source?
Yes. Check out bahamagreen's post above, and experiment with different values of frequency - you can get any wavelength you please.

Also consider that the meter was originally defined to be one ten-millionth of the distance from the equator to the North pole... It would be beyond bizarre if that totally arbitrary and man-made definition (intelligent eighteenth-century octopi probably would have chosen a power of eight instead of ten) actually happened to be an exact integral multiple of anything else.
Of course we no longer define the meter that way, but the newer definitions are every bit as much human inventions for human convenience.

Homework Helper
Gold Member
... Or are whole nanometers "nature's smallests units" when it comes to the various existing wavelengths of light?
To take another tack, just because some light is said to have a wavelength of 500 nm doesn't mean you *must* use nanometres. You could equally say 500,000 picometres or 0.0000005 metres or 0.00001969 inches or 5000 Angstroms.

DavidReishi
The above responses support what I suspected. But why then do we never hear of people working with 600.25 nm light, or 333.0001 nm light? Or even distinguishing such values as particular wavelengths of the spectrum? Has the development of our instruments regarding light simply not reached that level?

But also, what if we look at the example of the sun? We know that, taking all the wavelengths of its light together, around 100 watts of energy per cm2 reach the surface of the earth. That's a definite amount of energy per cm2 split up between all the various wavelengths of the light. How, then, can there be an infinite variety of different wavelengths of light within that sunlight, each delivering a specific amount of energy? It would seem to imply no definite quantities of energy at all being delivered, just infinite division of energy into arbitrarily smaller and smaller quantities.

DavidReishi
Yes. Check out bahamagreen's post above, and experiment with different values of frequency - you can get any wavelength you please.

I missed what bahamagreen said about gamma rays. But as for the equation, which is the Planck-Einstein relation, of course you can put in any value for the frequency and spit out a wavelength. But you can also put in a whole number for E and spit out a wavelength. But does that mean that light with such a wavelength, e.g. corresponding to a photon energy of exactly 1.000 J, really exists?

Staff Emeritus
The above responses support what I suspected. But why then do we never hear of people working with 600.25 nm light, or 333.0001 nm light?

Before asking why it is true, it is good to check if it is true:

DavidReishi
... and because of the Doppler effect, you can make the wavelength of any electromagnetic radiation arbitrarily small just by moving rapidly enough towards the source.

Somehow I don't think that's true. It's the same as saying that photon energy changes according to the movement of someone observing the light. No way. Are you only saying it because the Planck-Einstein relation involves frequency and hence speed? The Planck-Einstein relation isn't connected to speed in reality, since in the equation speed is a constant. Photon energy is inversely related to wavelength plain and simple.

pixel
But also, what if we look at the example of the sun? We know that, taking all the wavelengths of its light together, around 100 watts of energy per cm2 reach the surface of the earth. That's a definite amount of energy per cm2 split up between all the various wavelengths of the light. How, then, can there be an infinite variety of different wavelengths of light within that sunlight, each delivering a specific amount of energy? It would seem to imply no definite quantities of energy at all being delivered, just infinite division of energy into arbitrarily smaller and smaller quantities.

By the same token, if I put a brick on a table its weight is divided up between all the "infinite number" of locations on the table. So you can ask how there can be an "infinite variety" of locations each experiencing a specific amount of the weight, implying no definite amount of weight on the table.

We never deal with a totally exact wavelength as any measuring device has a finite resolution. So the energy from the sun is divided into a finite number of resolution elements, Δλ, with a finite amount of energy in each.

Mentor
Somehow I don't think that's true. It's the same as saying that photon energy changes according to the movement of someone observing the light. No way.

It's true. Although energy is conserved, it is not frame-independent - different observers moving at different speeds will find different values for the total energy of a system. Energy conservation means that the energy they find will not change, not that they will find the same value for the energy. (As an aside, momentum and angular momentum work the same way).

An example from classical mechanics that should make this clear: A bullet weighing .01 kg and moving at 1000 meters per second strikes an elephant weighing 1000 kilograms. We usually analyze this situation from a frame in which the hunter and the unfortunate elephant are at rest and the bullet is moving, so the energy of the bullet-elephant system, by ##E_k=(mv^2)/2##, will be ##.5\times.01\times{1000}\times{1000}## Joules. However, we could just as easily consider the situation from the point of view of the bullet: it is at rest, while a 1000 kg elephant is moving rapidly towards it. Now there are ##.5\times{1000}\times{1000}\times{1000}## Joules in the bullet-elephant system.

Different observers finding different amounts of energy in the same electromagnetic radiation is the same thing.
(I notice that you said "photon" above, and in this case you could think of the photon as being analogous to the bullet... But be aware that this model will fail dismally if more than one frequency/wavelength is involved).

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Staff Emeritus
Homework Helper
The above responses support what I suspected. But why then do we never hear of people working with 600.25 nm light, or 333.0001 nm light? Or even distinguishing such values as particular wavelengths of the spectrum? Has the development of our instruments regarding light simply not reached that level?
There is a finite degree of precision associated not only with all measurements, but also all measuring instruments, be they mechanical or whatever.
But also, what if we look at the example of the sun? We know that, taking all the wavelengths of its light together, around 100 watts of energy per cm2 reach the surface of the earth. That's a definite amount of energy per cm2 split up between all the various wavelengths of the light. How, then, can there be an infinite variety of different wavelengths of light within that sunlight, each delivering a specific amount of energy? It would seem to imply no definite quantities of energy at all being delivered, just infinite division of energy into arbitrarily smaller and smaller quantities.
You have to be careful throwing around terms like "infinite variety of different wavelengths" and such.

A lot of things happen to sunlight on its journey from the sun to the surface of the earth. The fact is, not all of the energy which leaves the sun reaches the ground on earth. Along the way, solar radiation can be blocked by dust, either in space or in the atmosphere, or absorbed by things like the ozone layer, which is why we don't get irradiated with fatal doses of X-rays or gamma radiation coming from the sun or solar flares.

https://en.wikipedia.org/wiki/Sunlight

The atmosphere of the Earth allows visible light frequencies to pass thru undisturbed and a few frequencies of EM radiation which lie beyond the visible spectrum (such as ultraviolet light).

DavidReishi
It's true. Although energy is conserved, it is not frame-independent - different observers moving at different speeds will find different values for the total energy of a system. Energy conservation means that the energy they find will not change, not that they will find the same value for the energy. (As an aside, momentum and angular momentum work the same way).

An example from classical mechanics that should make this clear: A bullet weighing .01 kg and moving at 1000 meters per second strikes an elephant weighing 1000 kilograms. We usually analyze this situation from a frame in which the hunter and the unfortunate elephant are at rest and the bullet is moving, so the energy of the bullet-elephant system, by ##E_k=(mv^2)/2##, will be ##.5\times.01\times{1000}\times{1000}## Joules. However, we could just as easily consider the situation from the point of view of the bullet: it is at rest, while a 1000 kg elephant is moving rapidly towards it. Now there are ##.5\times{1000}\times{1000}\times{1000}## Joules in the bullet-elephant system.

Different observers finding different amounts of energy in the same electromagnetic radiation is the same thing.
(I notice that you said "photon" above, and in this case you could think of the photon as being analogous to the bullet... But be aware that this model will fail dismally if more than one frequency/wavelength is involved).

Are you sure this isn't the idea of just a small sect of physics? Honestly, it doesn't sound plausible. That we can turn pretty visible light, which has already been emitted from a source, into deadly gamma rays based purely on how fast we move in relation to it?

Even though you didn't answer either way, I suspect that this notion is a theory derived purely from the Planck-Einstein relation. If that's the case, then I think the conclusion is being drawn from it incorrectly.

Staff Emeritus
Homework Helper
Are you sure this isn't the idea of just a small sect of physics? Honestly, it doesn't sound plausible. That we can turn pretty visible light, which has already been emitted from a source, into deadly gamma rays based purely on how fast we move in relation to it?
Light which we observe from distant celestial objects is shifted either to the blue or red ends of the spectrum. We surmise this shift tells us how fast these objects are moving relative to the earth.

https://en.wikipedia.org/wiki/Redshift

Mentor
Are you sure this isn't the idea of just a small sect of physics?
Yes, quite sure.
Even though you didn't answer either way, I suspect that this notion is a theory derived purely from the Planck-Einstein relation. If that's the case, then I think the conclusion is being drawn from it incorrectly.
It is altogether unrelated to that equation, and indeed to the entire concept of photons; instead it's a fairly straightforward calculation from the behavior of classical electromagnetic waves.

Suppose that I am at rest and light waves with a frequency of 500 THz (orangish, comfortably in the visible spectrum) are passing me from left to right. I will see a crest come by, and then .002 picoseconds later I'll see another crest, and so on. Because the crests are moving at the speed of light, I easily calculate that they are separated by about 600 nanometers; that's the wavelength.

But suppose that you are moving from right to left, "upstream" against the light while I'm watching you. I see one of the crests reach you while the next one is 600 nm away from you... But because you are moving towards it, you meet that next crest partway and it doesn't have to travel the full 600 nm to reach you. Thus, it doesn't take the whole .002 picoseconds for the next crest to get to you - the time between successive crests hitting you is less than the time between successive crests reaching me. That means you're getting a different and higher frequency than I am.

This effect has been observed many times and with many different frequencies, from radio to visible, on experiments on earth.

If your speed is large enough, there will be some relativistic subtleties here. These don't change the overall picture but you'll need them to properly calculate, for example, how fast you need to moving relative to me to increase the number of crests reaching you per second by a factor of 10,000. That factor of 10,000 will be enough to mean that what I'm experiencing as orangish light is hitting you as hard gamma radiation.

Googling for "relativistic Doppler effect" will find much more information as well as more rigorous derivations.

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Mentor
This thread was temporarily closed to remove a number of unnecessarily argumentative posts. Warnings have been issued to the offenders and the thread is open again.

Everyone is reminded that Physics Forums is here to help people with the current understanding of the science. It is not for entertaining challenges to mainstream physics.

sophiecentaur
DavidReishi
It is altogether unrelated to that equation, and indeed to the entire concept of photons; instead it's a fairly straightforward calculation from the behavior of classical electromagnetic waves.

How can it be altogether unrelated to the Planck-Einstein relation when that's precisely what it's derived from?

Suppose that I am at rest and light waves with a frequency of 500 THz (orangish, comfortably in the visible spectrum) are passing me from left to right. I will see a crest come by, and then .002 picoseconds later I'll see another crest, and so on. Because the crests are moving at the speed of light, I easily calculate that they are separated by about 600 nanometers; that's the wavelength.

But suppose that you are moving from right to left, "upstream" against the light while I'm watching you. I see one of the crests reach you while the next one is 600 nm away from you... But because you are moving towards it, you meet that next crest partway and it doesn't have to travel the full 600 nm to reach you. Thus, it doesn't take the whole .002 picoseconds for the next crest to get to you - the time between successive crests hitting you is less than the time between successive crests reaching me. That means you're getting a different and higher frequency than I am.

This effect has been observed many times and with many different frequencies, from radio to visible, on experiments on earth.

What you're speaking about above is simply the fact that the wavelengths of the light will be hitting a person or object at a faster or slower rate than if that person or object is still. What isn't established, however, is that wavelengths hitting a person or object at different rates actually changes the wavelengths of the light.

As for Doppler-Redshift, don't forget that while the Doppler effect is accepted as causing it, it's the only example of the effect known, and the explanation (the movement of the objects) is unable to be verified since it's observed only with celestial bodies very far away.

Staff Emeritus
2022 Award
What you're speaking about above is simply the fact that the wavelengths of the light will be hitting a person or object at a faster or slower rate than if that person or object is still. What isn't established, however, is that wavelengths hitting a person or object at different rates actually changes the wavelengths of the light.

From the point of view of the person with respect to the coordinate system, both the frequency and the wavelength are certainly changed. This is an extremely well understood phenomenon.

As for Doppler-Redshift, don't forget that while the Doppler effect is accepted as causing it, it's the only example of the effect known, and the explanation (the movement of the objects) is unable to be verified since it's observed only with celestial bodies very far away.

That is incorrect. This is verified every single day by police officers using radar guns, aircraft radars, various optical and other E&M experiments, and more.

davenn
DavidReishi
That is incorrect. This is verified every single day by police officers using radar guns, aircraft radars, various optical and other E&M experiments, and more.

From what I could gather, Doppler technology meaures the frequency of the light, i.e. wavelengths per unit of time, not any difference in the wavelength itself. So those devices aren't examples of how the changes in frequency changes the wavelength of the light.

Staff Emeritus
2022 Award
From what I could gather, Doppler technology meaures the frequency of the light, not any difference in wavelength. So those devices aren't examples of how the changes in frequency change the wavelength of light.

Yes they are. Frequency and wavelength are inversely proportional to each other, so a change in one is necessarily a change in the other. (With some caveats regarding the wave moving between different mediums. But our medium stays the same in these examples, so those caveats don't apply.)

DavidReishi
Frequency and wavelength are inversely proportional to each other...

Right, when comparing light of different wavelengths at the same speed!

Staff Emeritus
2022 Award
Right, when comparing light of different wavelengths!

Nope. It also applies to the same wave when seen by observers moving at different speeds with respect to the coordinate system in use.

DavidReishi
Nope. It also applies to the same wave when seen by observers moving at different speeds with respect to the coordinate system in use.

You just got finished telling me that Doppler technology is proof that changes in frequency change the wavelength. Then I tell you that Doppler technology measures the frequency only. And then you tell me that everyone knows that changes in frequency change the wavelength.

Mentor
How can it be altogether unrelated to the Planck-Einstein relation when that's precisely what it's derived from?
It's not. It's derived from classical E&M in which light is electromagnetic waves and the rate at which energy is transferred by the waves depends on the intensity, which is a function of the amplitude and the frequency. All this was well-known physics worked out decades before the Planck-Einstein relationship was dreamed of.

[/quote]As for Doppler-Redshift, don't forget that while the Doppler effect is accepted as causing it, it's the only example of the effect known, and the explanation (the movement of the objects) is unable to be verified since it's observed only with celestial bodies very far away.[/QUOTE]
You have the logic backwards. Doppler and redshift are routinely observed in earthbound experiments with objects moving around under our noses, so we know light works that way, Because we know light works that way, we use it to measure the velocities of distant objects. (We also have independent confirmation from observations of supernova ejecta. This is known to be moving away from the star in different directions but at the same speed, so the stuff on the far side is known to be moving away from us and the stuff on the near side is known to be moving towards us. This provides pretty good evidence that the Doppler effect out there is the same as in our labs and on earth).

What you're speaking about above is simply the fact that the wavelengths of the light will be hitting a person or object at a faster or slower rate than if that person or object is still. What isn't established, however, is that wavelengths hitting a person or object at different rates actually changes the wavelengths of the light.
What makes gamma radiation gamma radiation is that a crest arrives about once every ##10^{18}## seconds or thereabouts. That arrival rate is what determines the interaction between the radiation and the matter it strikes. The wavelength is the speed of a crest divided by the frequency with which crests arrive - there's no way the light can have a wavelength independent of its frequency, and the frequency is inherently frame-dependent.

You might consider the Doppler example above, but try describing it as if I am moving and you are at rest.

Staff Emeritus
2022 Award
You just got finished telling me that Doppler technology is proof that changes in frequency change the wavelength. Then I tell you that Doppler technology measures the frequency only. And then you tell me that everyone knows that changes in frequency change the wavelength.

No, I said that the effect is verified all the time, which was in reply to your statement that doppler-redshift cannot be verified to be caused by motion.

The proof that changes in either frequency or wavelength necessarily change the other is found in the details of the equations governing waves.

Edit: My apologies, I missed one of my own posts when re-reading the thread earlier. I did indeed imply exactly what you said I did. You are correct in that radar devices measure the frequency, not the wavelength. However, the part about frequency and wavelength being inversely proportional to each other is correct. This relationship can easily be verified with several experiments, including the double slit experiment and all radio and microwave antennas, among others many, many other things. Diffraction and interference of waves require that the two properties be related to each other in this manner, otherwise we wouldn't observe diffraction and interference as working the way they do. Essentially all of optics, radio/wireless communication, and even electrical power distribution are built off of the fundamental properties of waves. They work. And they work well. If that isn't enough evidence for the accuracy of these laws, I don't know what would convince you.

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Gold Member
You just got finished telling me that Doppler technology is proof that changes in frequency change the wavelength. Then I tell you that Doppler technology measures the frequency only. And then you tell me that everyone knows that changes in frequency change the wavelength.

These days they measure frequency directly. Many older instruments measured the frequency of light in this range (UHF/MW) indirectly using a so-called wavemeter (still used in teaching labs), which do indeed measure the frequency by keeping track of where the crests of the wave are; i.e. it measures the wavelength.
This was presumably how old Doppler radars worked.

Drakkith
Gold Member
As for Doppler-Redshift, don't forget that while the Doppler effect is accepted as causing it, it's the only example of the effect known, and the explanation (the movement of the objects) is unable to be verified since it's observed only with celestial bodies very far away.
That's a sweeping statement. Have you never heard of Doppler Radar, which tells you the speed of an object by the doppler shift of a reflected radar pulse?
Have you not heard of the Doppler Broadening of the spectrum of light from hot gases, due to the velocity distribution of the atoms?
Doppler is alive and well on the Earth's surface. Local magistrates issue speeding fines on the basis of it.
If you are concerned about the difference between the frequency effect and the wavelength effect, just consider that optical spectroscopy uses a diffraction grating . . . . . . . . .

Drakkith