Born to Do Math 177 – Photon Energy: No Top, Asymptote Bottom
Author(s): Scott Douglas Jacobsen and Rick Rosner
Publication (Outlet/Website): Born To Do Math
Publication Date (yyyy/mm/dd): 2020/07/15
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Rick Rosner: You just asked, “What’s the lowest possible wavelength for a photon?” I think you could probably set up some electron-scattering apparatus that would have a range of energies for emitted photons. I am talking out of my ass. It would be arbitrarily close to zero. I think there’s no limit on the least energy that a photon could have. But it might be tough to set up an apparatus that reliably produces super low energy photons, but maybe not. The lowest energy commonly found photons without setting up a special apparatus are the photons close to the Big Bang, the Cosmic Microwave Background (CMB). These are photons that have travelled across the universe since the universe was 300,000 years old. So, they’ve lost all but 1/10,000th of their energy. They’ve got a temperature of 2.7 degrees above Absolute Zero. They are really weak.
Scott Douglas Jacobsen: Let’s take a step back, so, this is an impossible experiment in reality, in terms of it actually happening. The one mentioned earlier with a pipe, vertical, shoot a photon through the top. It splits through a perpendicular pathway going one way and the other way. So, this is a question about what is possible and impossible. In terms of light, what can you not do with them (photons)?
Rosner: You can’t divide them.
Jacobsen: So, they are functionally indivisible.
Rosner: You can’t add energy to them. Unless, the energy is due to the shape of space. In other words, a photon travelling down a gravitational well will gain some energy. But it is not like you can inject a photon with energy. It’s not like you can bounce energy off a photon. Maybe, I’m wrong. You definitely can’t turn one photon into two. There might be a way to scatter a photon that would change its energy. But I kind of don’t think so. You can have a pair of photons spontaneously appear and shoot off in opposite directions. It doesn’t happen very often at all. But you could do that. I don’t know what you’re going after with two photons shooting off in either direction.
Jacobsen: I was making an incorrect assumption of a probability goo entering the pipe and then becoming definite as photons.
Rosner: It is not like a photon is one thing until it is observed and then it is another thing. There are equations describing photons. They describe them as both particle and wave. You can design experiments that will show a more wavelike nature to the photons. You can have experiments showing the photons as particles. But you are not changing the nature of the photons. They are what they are. For a photon to be detected, I would have to read up on how you detect a photon without absorbing the photon. But obviously, there are ways to do that.
Jacobsen: What would be an approximate number of active photons traversing the observable universe?
Rosner: I would guess the mass of all the photons out there would be within an order of magnitude of 2 or 3 or 5 or 10 of the combined mass of all the non-photon particles. I don’t know how neutrinos fit into that. I would guess that one way to get not too far off to the number of photons out there would be to take the mass of all the particles that have mass and come up with some kind of average energy of a photon; that you’d find out in the universe and divide the mass of all the massive particles by the average energy of a photon. That would give a rough idea. Or you could Google it. Someone has done that calculation out there. Let’s say it is 10^95th or 10^100th photons out there.
Jacobsen: If we take the 10^95th to the 10^100th range, and if we take those two numbers as a post in a range, somewhere in the goal posts there. There is going to be a photon that could get warped around galaxy after galaxy after galaxy without hitting anything. So, if IC is right, and if the universe is cycling, and if that happens to something of a single data point for billions upon billions of years, then it’s…
Rosner: There are a gazillion photons that haven’t hit anything; that have wrapped around stuff and warped around space. They have travelled across space without hitting anything. The CMB photons, I don’t know how many there are. Those are photons from when the universe became transparent to photons. They are constantly hitting us. Also, there are ones constantly hitting us.
Jacobsen: How long can those photons travel without their energy completely lost?
Rosner: Basically, forever.
Jacobsen: Is it lost to an asymptote across the curvature of space-time? In some sense, it seems like a convergence of having a finite amount of energy, but they have an infinite capacity to not be nullified to non-existence through the traversing of space-time.
Rosner: Yes, they lose energy. There is some equation. The simplest would be of the universe at which they were emitted over the current age of the universe. It is probably not that simple. That is one stab at it. So, you take 300,000 over 13,800,000,000. You get 1/46,000 of their energy is left. That’s probably too simple. It seems too straightforward, but it is something like that. Their wavelength keeps getting stretched out as they traverse the universe. You can look at the universe as if it is expanding. The expansion stretches out the wavelength of the photon, then the less energy it has. Maybe, it is that simple.
Jacobsen: Is there an upper limit to the amount of energy a photon can contain?
Rosner: Something has to happen that releases energy to release a photon. When atomic nuclei fuse, when two lighter nuclei fuse into a heavier nucleus, that, generally, changes the total atomic number of the combined nuclei. You could have two deuterium atoms. Anyway, if the atomic number changes, then you have two neutrinos or anti-neutrinos emitted. When nuclei fuse, you have a huge amount of energy released. It is a huge x-ray spectrum photon being emitted. If nothing else is being emitted, say two deuterium nuclei, one proton plus one neutron, they can fuse to form one new helium nucleus. If no other particles are emitted, that may be a possible interaction. All of the energy created in that fusion will be shot off by a super high-energy x-ray photon. You have to set up some kind of system where the energy created or released in a system is emitted in the form of a photon.
Theoretically, if stuff fell into a black hole, it would be super accelerated. But then, you have horizon problems. But theoretically, there is no upper limit. You just have to have some process that would release energy. I know how you do it! You take the most massive particle that you can find, single particle, and then you take its anti-particle and then smash them together. They are obliterated and then they release two photons shooting in opposite directions. There are hugely massive particles that you can create, or that you can find in the universe. The Higgs boson is the most massive particle every created. It has the mass of 500 or 1,000 protons. If you can create a Higgs and an anti-Higgs, if there is such a thing, and if you could smash them together, they would obliterate each other. They would be 1,000 more energetic then x-ray photons. That’s impossible to do with current technology. They barely manage to create a Higgs for probably one trillionth of a second. So, yes, you can make arbitrarily energy photons.
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