Can photons exist on top of each other or do they have to travel side by side?
If they travel side by side does that mean the maximum density for light would be 1 photon/planck²?
If they can travel on top of each other then would it be possible to have enough photons intersect at a single point such that the energy density is high enough to cause a black hole?
I’ve seen the equations somewhere that showed that 1 photon per planck was suffient distance between photons to stop a black hole from forming, but am unable to find it again… can someone please help me with this?
It depends what you mean by “saturated”. Interstellar space is filled with the photons from the microwave background radiation. But it’s not saturated in the sense of “can’t put in any more”.
Photons are bosons, so they can coexist in the space-time.
Yes! But realistically, matter has a much higher energy-density than photons. Thus it is easier to create a black hole with matter.
This will be a function of the photon’s energy (or frequency). Hypothetically, one could create a single photon with high enough energy (and therefore an extremely small wavelength) that it by itself would have sufficeint energy density to collapse into black hole.
True; if I recall correctly, the number density from the CMB is on the order of 400 photons per cubic centimeter. If you put that in “natural” units (per cubic Planck length) then it’s a tiny number indeed!
Also, there is no magic density at which matter will collapse into a black hole. It depends on the size. Even regular water will form a black hole if it’s large enough (galaxy-sized does it, I believe).
Well seeing as though no one here knew it or was willing to help with this proof I’ll try to put it together, please let me know if I make a mistake.
Equation for effective mass of light m = h f/c²
Schwarzschild Radius Rs = 2MG/c²
Frequency to wavelength equation f=c/λ
Constants used: Planck length (1.6 x 10^ˉ35m)
Light travels at 299,792,458ms in a vacuum.
Universal Gravitation Constant (6.67 x 10^ˉ11 N m²/kg²)
Planck’s constant (6.626 x 10^ˉ34)
The highest frequency of light possible (would have a wavelength of 1 planck length) is equal to 1.8737028625 x 10^43 hz
So the largest effective mass of light would be 1.3813723092393 x 10^ˉ7 kg.
m = h (c/λ)/c^2 then we plug this into the SR equation…
Rs = 2(h (c/λ)/c²)G/c²
now I think that becomes
Rs = 2h (c/λ) G
but I’ll put the whole lot into my calculator just incase.
Ok… so the Rs for the largest effective mass of light is 2.0503366257263 x10^ˉ34m. And seeing as though the smallest wavelength possible (1.6 x 10^ˉ35m) is smaller than that length it appears that my calculations show that you CAN create a single photon with enough energy to become a black hole!!!
Andy, because I didn’t think I could do the equation, but as it turns out I think I can, just waiting for someone to come along and tell me I forgot to carry a 1… :S
These photon black holes are gonna be TINY… so they will evaporate within 10^ˉ17 seconds giving off hawking radiation. Now I’ll try to make a bigger photon black hole, one that lasts long enough for us to see (or not see as it maybe be ;))…
There were no objections to that so I assume I can use equations with more than one photon intersecting each other to create more than enough mass in one spot.
Now I can’t use photons that are already black holes (I’ll name them Illuvatar photons)… the smallest frequency Illuvatar photon would be…
Planck Length = 2(h (c/λ/c²)G/c²
ok… Now I have to work backwards to find what the frequency will be.
The smallest Illuvatar photon has an effective mass of 1.07796723 x 10^ˉ8 kg, and its frequency would be 4.87724789896762 x 10^33 hz.
So to have the photons move into place without evaporating they’d have to be just below the smallest Illuvatar photons mass.
How does one go about making high frequency photons, what is the highest frequency scientists can make on a large scale?
Actually, you can’t create a black hole with a single photon. The frequency (and hence, energy) of a photon is dependent on the frame of reference in which you look at it, so for any photon, there are some frames of reference where it has an insanely high energy, and some frames of reference where it has an arbitrarily low energy.
With two photons, the situation is different. As long as they’re not travelling exactly parallel to each other, there is a limit to how low you can get the energy by shifting to different referrence frames: Try to reduce the energy of one below that, and you’ll end up increasing the other by a larger amount. It is, then, possible to form a black hole, of any initial mass, from two (or more) photons. In actual practice, this would require more energy than we have access to. However, this situation is often studied in theoretical models, since it’s (relatively) easy to understand.
While a photon with a wavelength of 1 Planck Length would be quite impressive, I don’t think that there’s any reason to think that’s the limit for photons. As Chronos said, you can always pick a frame a reference to give you an arbitrary wavelength for your photon.
Of course, this doesn’t change your proof in the slightest, but I thought I’d point it out.
Chronos, how does that work? Can you show me some mathematical proofs please. I couldn’t googlize any of the proof I developed, so I certainly couldn’t find why it wouldn’t work.
Achernar, a planck is the smallest unit of length, if you had a photon with a wavelength smaller than a planck then it wouldn’t exist.
I thought I developed something new. Please show me with proofs why it doesn’t work.
A black hole is a global phenomenon. In other words observers cannot disagree as to whether a BH exists. If it exists, it exists for all observers, and vice versa.
Since the universe is scale dependent the Planck length doesn’t come into play in our macro world, so there is theoretically no upper or lower bounds on the energy of a photon. Doppler shift can always be used to make the frequency of a photon, in some frame, as small or as large as you like.
Since the energy of a photon is frame dependent it cannot create a global phenomenon, and it therefore cannot create a black hole. Although two anti parallel photons, as Chronos said, could.
Ring, has anyone ever observed (with a radio telescope) a droppler shift into frequencies as high as the ones I used to make Illuvatar photons. Or is that also a theory?
Okay, Illuvatar, thanks! I won’t ask you for any more cites, because I know you’re in a hurry, but I guess I was looking for something from someone a little more authoritative than an undergrad. Anyway, I don’t understand how that can be, since any time interval can be Lorentz-shifted arbitrarily small. Can’t it?
Achernar, I have to bumb this thread up while I wait for some mathematical proof to show that I can’t make Illuvatar photons, here’s a few other google results:
Planck length is a fundamental unit. It is atomic. You cannot divide a quantum particle into a space smaller than 1 planck length.
I’m happy that you agree that it’s possible to create Illuvatar photons with two massive anti parallel photons. But I see no reason why it can’t be done with 1. Can someone please show, with proofs, why individual Illuvatar photons cannot exist?
I thought I developed something new. Please show me with proofs why it doesn’t work.