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I have been told that photons can not be blue shifted to the point where they become black holes, although a photon with a Planck scale wavelength would also have a relativistic mass equal to a black hole with a Schwarzschild radius on the scale of its wavelength. (Imagine a photon stuck in a loop around its own relativistic mass).

So my question now is, what are the limits of relativistic mass or momentum that a single photon could have?

Also, by extension, how short a wavelength could it have? If the wavelength gets to the Planck scale does it become a particle, or matter?

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  • $\begingroup$ related: physics.stackexchange.com/q/3436 $\endgroup$ – Ben Crowell Aug 20 at 3:17
  • $\begingroup$ You may get a different answer if you ask about too very blue photons getting close. $\endgroup$ – safesphere Aug 20 at 4:57
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    $\begingroup$ A photon is by its definition a partile and has mass zero. en.wikipedia.org/wiki/… There is no relativistic mass for a single photon, no matter what its wavelength. $\endgroup$ – anna v Aug 20 at 5:52
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In modern terminology, mass means invariant mass. See Why is there a controversy on whether mass increases with speed? . The mass of a photon is zero. So to make this question more intelligible based on modern usage, a better title would be "Greatest energy possible for a single photon."

I have been told that photons can not be blue shifted to the point where they become black holes

This is true because the criterion for being a black hole (light can't escape to infinity) is observer-independent. It doesn't mean that there's a limit on how much of a blueshift you can have. There is no such limit. Although it is true for a collapsing star, in its rest frame, that $r/m \lesssim G/c^2$ is a criterion for being a black hole, this is not true in other frames of reference. It would make sense in terms of Newtonian mechanics if the criterion was $r/m \lesssim G/c^2$, but general relativity is different because in GR the source of gravity isn't mass, it's the stress-energy tensor.

Also, by extension, how short a wavelength could it have.

We don't have a theory of quantum gravity, so we don't know for sure how to interpret the Planck length. However, it probably shouldn't be interpreted as a minimum length scale. That would violate Lorentz invariance.

If the wavelength gets to the Plank scale does it become a particle, or matter?

A photon is both a wave and a particle regardless of its wavelength. Modern physicists don't really use the term "matter" much, but to the extent that they do, they mean fermions. A photon is a boson regardless of its wavelength.

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  • $\begingroup$ So can a photon have an energy density greater than a black hole? Also, if it did, could it be bent around its own center of mass? $\endgroup$ – Joseph Hirsch Aug 20 at 0:12
  • $\begingroup$ Pions aren't matter? $\endgroup$ – Danny Aug 20 at 0:57
  • $\begingroup$ @JosephHirsch: So can a photon have an energy density greater than a black hole? As stated in my answer, density (or rather $m/r$) is not a general criterion for a black hole to exist. See the question linked to from my comment on your question. $\endgroup$ – Ben Crowell Aug 20 at 3:17
  • $\begingroup$ "Modern physicists don't really use the term "matter" much, but to the extent that they do, they mean fermions." Not really. To a relativist, matter is simply anything that contributes to the energy-momentum tensor. To a cosmologist, matter is anything that obeys the non-relativist equation of state. To a condensed matter physicist, a Bose-Einstein condensate is most definately a state of matter. $\endgroup$ – mmeent Aug 20 at 6:20

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