B Planck Length: Upper Limit on Photon Frequency & Momentum

[negativzero]

TL;DR Summary

Assuming that a wavelength shorter than the Planck length is not allowed, does that mean that photons can only carry so much momentum and no more?

Is it known how much momentum a photon possesses if it's wavelength is at the Planck length, and what happens if it's momentum is somehow increased from that?

 

[phinds]

Summary: Assuming that a wavelength shorter than the Planck length is not allowed...

Very bad assumption. Nature doesn't care about the Plank length any more than it cares about the foot or the meter.

 

[Ibix]

Is it known how much momentum a photon possesses if it's wavelength is at the Planck length

Yes. The momentum is $h/\lambda$, where $\lambda$ is the Plank length.

what happens if it's momentum is somehow increased from that?

Nothing special, as far as we know. The Planck units are expected to be the scale on which quantum gravity effects become apparent. As far as I'm aware this is simply because there's no other natural scale for such effects to start kicking in. We don't know what quantum gravity will look like yet, but we have no reason to expect the Planck units to be some kind of hard cutoff on the notion of length or momentum or whatever.

 

[pervect]

Summary: Assuming that a wavelength shorter than the Planck length is not allowed, does that mean that photons can only carry so much momentum and no more?

Is it known how much momentum a photon possesses if it's wavelength is at the Planck length, and what happens if it's momentum is somehow increased from that?

It'd be better to assume that physics at the energy scale involved are not well understood, than to assume that photons with that energy are "not allowed".

Certainly we can assign a number to the energy and momentum of a photon whose wavelength is the Planck length.

 

[negativzero]

Thank you. I hope I'm not transgressing to ask if this means the constant is a mensuration issue not a physical constant or limit of any kind?

 

[Nugatory]

Thank you. I hope I'm not transgressing to ask if this means the constant is a mensuration issue not a physical constant or limit of any kind?

Yes. (That's "yes that's what it means" not "yes you're transgressing" - you aren't).
This question comes so often that we have an Insights article about it: https://www.physicsforums.com/insights/hand-wavy-discussion-planck-length/

 

[Heikki Tuuri]

Let us assume that Special Relativity is a correct theory of nature. Suppose that a static observer points a red laser beam at you. You start moving to the direction of the laser.

The Doppler effect makes you to measure the frequency of the light higher than the static observer. Furthermore, if you move at a relativistic speed, the static observer sees your clock run slower than his clock. That makes the frequency you measure even higher.

You may measure the frequency of normal visible light as so high that in your frame, the wavelength is less than the Planck length.

A photon of light always in some frame looks like having more than the Planck mass worth of energy. That does not mean that it collapses into a black hole. However, if an observer who is static in the fast frame collides with the photon, suddenly 1.2 * 10^28 eV of energy is freed, and a collapse into a black hole might happen.

 

[negativzero]

"You may measure the frequency of normal visible light as so high that in your frame, the wavelength is less than the Planck length. "
Thank you for that. Hypothetical frames of reference. I can't think of any hypothetical frames of reference that would apply, rushing in toward the point-like observer. But I'm not good at interpreting what the math means to physical reality. For instance, the mere fact that someone can imagine a different set of rules that create a different universe doesn't mean to me that such a universe would necessarily exist. Yet some math is famously accurate at describing reality. However, taking what you suggest to heart, I'm trying to imagine a universe where every photon has the momentum of a super black hole relative to infinite frames of reference. I infer that you somehow dismiss your picture of a cosmology wherein every photon measured from infinite onrushing frames is black hole. Is it too speculative to ask why not? I look forward to any reply.