I want to calculate the minimum energy level of a photon. Obviously E(photon) = c * 1/wavelength so as the wavelength of EM radiation goes to infinity then the energy level goes to zero. But for a photon to exist its energy level can not be zero, so there must be some limit on the absolute length of the wavelength to maintain the existence of the photon. Has this or can this be calculated?
OK, but is there a theoretical minimal energy level for a photon? If there is then there is a theoretical maximal wavelength. With an infinite wavelength there would be infinite zeros after the decimal point. Clearly that energy level would not permit light speed travel, or would it?
Just did a google search and there was a comment on a 30 million kilometer documented wavelength but there was no reference quoted...
Another way of looking at it is to find the lowest electron change in energy state that has been observed to result in a photon emission. That should give us the longest naturally occurring wavelength and a theoretical energy floor for a photon. This has to be known. Does anyone have insight? I need help.
The problem is that you can 'always build a larger antenna' ... I wouldn't be surprised if neutron stars and magnetars gave off frequencies with the wavelength of their radius, given that stars are charged particles moving it is likely that if you could build a receiver for them you would find similar properties just caused by 1 electron that happens to be moving around the star. In this case I use the word antenna to represent any object in which charged particles can move in a cycle. Someone mentioned a detection problem for large wavelength photons : you can always balun an antenna of harmonic size. The signal would be difficult to pick out the further away you are, but you might be able to do it.
While certainly not detectable, if you believe the implications of the mathematics behind the existence of black holes then photons of any and all arbitrarily large wavelengths already exist due to the infinite red-shifting that occurs at the shell of the event horizon.
Also, once you have a super long wavelength photon, you can always get it to Compton scatter off something and lose a bit more energy. Changing reference frame is probably easier though.
No. There is no minimum energy level. Not that you can calculate at least. Like siphra said, you can always build a larger antenna. If you eventually find that ELF electromagnetic waves have a lower bound you have an experimental answer, but not a calculated answer. Have you thought about the upper bound? What's the highest frequency photon you can have? I think it's more interesting than the lower bound.
If you look at the energy used by plankton for bioluminescence you might get an idea as it is necessarily small due to a single celled organism not having much energy to spare. You might get a value in chemical terms, then convert it.
Often wondered that myself, I was thinking recently it would probably be == the mass of some particle, where the particle is probably more stable than the photon. That is to say from E=Mc^2 we get Mc^2 = hc/lambda But I keep just not punching in the numbers to see if there are known photons of higher energy. The particle could even be less stable than a photon come to think of it.
Photons are pretty darn stable it seems to me. Some of the ones you see in the night sky (with a telescope) have been around since how long after the big bang?