What would happen if you had a photon that was blueshifted enough to have a wavelength below the Planck length?


I’ve read that there’s no limit on how close to the speed of light you can travel, and by doing so, photons will blueshift to infinity. So eventually you would be traveling so fast, that photons would have a wavelength of 1 Planck length. What happens if you speed up more? Can wavelength go below the Planck length, or would something else happen?

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4 Answers

Anonymous 0 Comments

We cannot measure anything below the Planck length.

Planck length is not a limitation of physical reality, but on our ability to observe, measure, and predict physical reality.

So the true answer is we have no idea.

Anonymous 0 Comments

The energy of a photon rises as the wavelength decreases, so when the wavelength of a photon hits 1 Planck length there is so much energy all packed into such a small space that it just turns into a black hole.

Anonymous 0 Comments

Things would get weird

How weird and what exactly would happen? We’ve got no idea though it’d almost certainly split into an electron and positron longgg before it got to Planck length

That’s really what the Planck units tell you. They’re not the smallest possible unit, they’re just smaller than our physics can handle. Any interactions at that scale would be dominated by quantum gravity but we don’t have a good model for quantum soo it’s not really predictable

Things actually get weird well before the Planck length, that’s more a “here there *definitely* be dragons” level than a hard threshold

Anonymous 0 Comments

We do not know.

I’m basing this answer off of [this thread](https://physics.stackexchange.com/questions/273888/can-a-photon-have-a-wavelength-less-than-the-planck-length) which goes through this in more detail.

Classical relativity (both special and general) say that while observers may disagree on the relative locations of events in spacetime, they will always agree on the nature of those events. You can’t see a particle as both a photon in one reference frame and a black hole and another. So classical relativity says that you will simply see the photon’s wavelength become smaller than a Planck length.

However, we have no good quantum theory for what would happen when a photon has such a small wavelength which is also consistent with general relativity, since they *do* apparently predict that such a localized particle would become a black hole. Someone has to be wrong. Perhaps relativity is wrong – there are various ways it could be wrong that are consistent with present observations. Perhaps both are wrong and a unified theory would resolve this in some other way.

This is generally true for any claims about the Planck length/time. If anyone makes specific predictions about what we can or cannot do at the Planck scale they are overstepping our current knowledge. It’s just a length that pops out of certain naïve calculations that include both general relativity and quantum mechanics.