I was wondering about the wavelength of light; how short can it get? As it gets shorter it gets more powerful, and as it approaches zero wavelength it will approach infinte energy, which is impossible. But is there a limit on the wavelength of light? Could it be shorter than the Planck length? I think that quanta may somehow solve this, but I'm not quite sure how. Does anyone know? How short can light wavelengths be? There must be some limit, else single photons could, in theory, have the power to vaporize planets and other bodies (although that would be quite a short wavelength photon). Is it just that processes in the universe can't produce enough energy to make photons above the energy of hard gamma rays? What do you think (or know?)

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"Too low they build, who build beneath the stars". - Edward Young, 1745

Classically, there is no lower limit to wavelength. Quantumly, who knows? Of course, photons of particularly short wavelength will have a huge amount of energy and are therefore in very short supply.

Classically, there wouldn't be any restriction on the wavelength of electromagnetic radiation, but that may not be the case under quantum theory. After a quick search, it does look like there are those that think it would be impossible to have a photon with a wavelength shorter than the Planck length, since this would be physically meaningless. But it seems an interesting question, and there doen't seem to be much speculation about it.

A photon with a wavelength of the Planck length would have an energy of 12.4 billion Joules, which is the equivalent of about 138 grams of mass, so it's not completely out of the realm of possibility, though that's many orders of magnitude above the normal energy of photons. Any time the most convenient unit for particle energy shifts from eV or MeV to Joules, you know it's large. At really high temperatures (say, very shortly after the Big Bang), there wouldn't be any particular reason why you couldn't get photons with this kind of energy, but these days everything is cool enough that it's just not very likely.

Cosmic rays have been observed with energy above 10^21 eV, which comes out to 160 Joules! Although I believe that these specific observations were of cosmic ray particles, if a single particle can have that kind of energy, there's no reason to believe a photon couldn't have such an energy, and of course a particle has a wavelength, too. That's well below the theoretical limit, but it's about a billion times more energetic than our best accelerators can produce, and about 15 orders of magnitude above typical gamma rays from nuclear interactions.

Didn't Abner Doubleday specify that a baseball would weigh over 142 grams just so pitchers couldn't take advantage of the Heisenberg Uncertainty Principle while pitching?

That's how the curve ball is accomplished- the ball is never actually in one place, but is a probability wave. :P

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"Too low they build, who build beneath the stars". - Edward Young, 1745

I like this part from that page:
I never realized that 1/4 inch converted to 0 centimeters . . .

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SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2010 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

Nice catch.

The page is based on student writings--but the editor should have fielded that. The baseball rules are probably in ounces and inches, for sure, but 9 inches converts to 22.86 cm, which is reasonably close to 23 cm, but surely a baseball of 22.9 cm wouldn't be considered an error. 9 1/4 (how many significant digits are in that?) converts to 23.495 cm. Seems like a toss-up to me. Surely, we would be safe in allowing just another .005 cm here?? and make the upper limit 23.5 cm. I'll run it by 'em and see how soon they change it--I betcha it drives them batty.

Update. I just received an email response from Glenn Elert. He says (to SeanF) "You have a sharper eye than I do."
The date 1999 at the bottom of the page shows its been there for four years (and the counter says 1933273), but now it has been fixed. Says 9 to 9 1/4 inches (22.9 to 23.5 centimeters).

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Do not trust your eyes

One memorable Chemistry workshop had our lecturer explaining quantum mechanics to us by having us calculate our own wavelengths, and pointing out that we're all probably a little blurred around the edges because of the slight possibility that we're not really there. We then had to show why David Seaman couldn't explain away a dodgy save as being caused by diffraction of a ball as it passed between two defenders. Pretty grounding stuff, really.

I'd love to see a 138g photon. Sadly, it would blow my head off when it hit my retina.

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No kidding!!! What do you say at this point?

A laser beam that could generate such photons would be quite a formidable weapon. Imagine a laser in which every photon has the momentum of a baseball. Ouch.

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"Too low they build, who build beneath the stars". - Edward Young, 1745

Actually, you're underestimating the original energy calculation. The energy of such a photon is not equal to the typical kinetic energy of a baseball. It's equal to the rest energy (i.e., the mass) of the baseball. Turn the baseball into energy (if you like, take half a baseball each of matter and anti-matter and put them together), and that's how much energy such a photon would have.* If it hit poor Alex's retina, it wouldn't just blow his head off, it would vaporize the city.

*Of course, particle-antiparticle annihilation always produces two photons travelling in opposite directions to conserve momentum. So I suppose you'd really need a baseball-antibaseball collision that somehow channels all the energy released into two such photons.

Maybe you'd just need the right bat. I'm thinking the Ted Williams model.

Would E = MC^2 be the appropriate equation?

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"Too low they build, who build beneath the stars". - Edward Young, 1745

Somebody's numbers are off here.

If the energy of the Planck-length photon is 12.4 billion Joules (12.4x10^9 J), then its mass equivalent should be that divided by c^2, or 1.38x10^-7 kg. That's .000138 grams, not 138g.

That being said, it's still a lot of energy. One kiloton is considered to be 4.18x10^12 J, so your photon is the equivalent of some three tons of TNT.

Hmmm, let me see, what if the "12.4 billion" is in English billions (10^12 rather than 10^9)? Then the energy equivalent scales up three orders of magnitude and you get a 3 kiloton photon - still smaller than Hiroshima, but not too shabby for a single photon.

So basically if you had a laser of those, you'd basically have the Death Star's planet destroying ray on steroids.

Okay, I just recomputed the energy of a Planck-length-wavelength photon from first principles, and it does work out to be 12.4x10^9.

So, dividing that by c^2 gives an equivalent energy of .000000138kg, or 138 micrograms, not 138g. More like a pharmaceutical dosage than a baseball. And it's a mere 3 ton explosive yield.

I guess I don't want a Planck flashlight, though... too much kick when you turn it on.

Added later: Dang it, I originally used a km value for the Planck length instead of meters. The numbers above should be right now. To make the math explicit, the Planck length is around 1.6x10^-35m. Taking this as a wavelength and converting to frequency using c = (lambda)(nu), you get nu = c/lambda, or (3x10^8 )/(1.6x10-35). To get the equivalent energy, use E = (h)(nu), or Planck's constant times the frequency. The result is our old friend 12.4x10^9 J. But to get the mass-equivalent, divide that by 9x10^16 = .000000138kg, or .000138g, or 138 micrograms.

Also, (12.4x10^9)/(4.18x10^12) = .003kilotons = 3 tons TNT equivalent.

Either that or an incomparable starship thruster. (Stay out of my wake, folks!)

Imagine a star that gave off such photons. Ouch. 3 tons of high explosive from every individual photon,. That might be more dangerous to look at than the sun.

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"Too low they build, who build beneath the stars". - Edward Young, 1745

Rats, you're right. I made my kilometer-meter mistake with the speed of light; just not paying enough attention. But it's such a shame to lose the nice baseball image. What's six orders of magnitude among friends?

How far away would it have to be before the Hubble redshift made it safe to look at?

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Everything I need to know I learned through Googling.

It seems like that would depend on your definition of "safe." If the energy of an individual photon weren't the equivalent of 3 tons of high explosive, but still the equivalent of a fastball, is it safe?

This thread made me wonder; is there is an upper limit to the wavelength of light? As the wavelength approaches infinity, the energy should approach zero, but in practice it seems like the wavelength couldn't be larger than the size of the universe (as an upper bound), and I have no idea what might generate something with such a low frequency.

Now I'm reminded of why I love science.

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No kidding!!! What do you say at this point?

Well, if the universe were static and had reflecting boundaries (as a poster seemed to assume in a different thread recently), you could get standing waves (cavity resonance). But it might be a little hard to build the antenna to receive them. Hmmm, a quarter of a wavelength of 13.7 billion LY works out to... a pretty big dipole.

I guess you'd have to hope it wasn't very luminous. 8)

You'd have to hope that you couldn't see it, period. Spontaneous Human Combustion?

Unless you had sunglasses and really, really, really good sunblock. :P

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"Too low they build, who build beneath the stars". - Edward Young, 1745

Hmm, interesting...

At what rate would the Sun be producing these 3-ton photons (that's three tons of TNT explosive equivalent energy, not three tons of mass-equivalent energy [yikes!]) if all its radiation were in such a form? And what would you call such an object? In one sense it would be just as "luminous" as the Sun (same total energy flux), but it another it would be vastly "dimmer" (putting out far fewer photons per second). It would also be considerably less safe to live near.

I wonder if there's any imaginable process short of the Big Bang itself that could produce such photons... If there's no such naturally-occurring process, could a sufficiently-advanced technology produce them?

If a photon is shorter than 1/2 the Compton wavelength of the electron, whenever it hits anything it transforms itself into mass. It stops its travel at c and becomes an electron and a positron. This a sorta practical limit to the size of a photon.