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this post was submitted on 11 Mar 2024
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I still haven't figured out why
The root of the problem is that you think of momentum as being defined to be the product of something's mass and its velocity, but this is actually only an approximation that just so happens to work extremely well at our everyday scales; the actual definition of momentum is the spatial frequency of the wave function (which is like a special kind of distribution). Thus, because photons can have a spatial frequency, it follows simply that they therefore can have momentum.
Something else that likely contributes to your confusion is that you probably think that where something is and how fast it is going are two completely independent things, but again this is actually only an approximation; in actuality there is only one thing, the wave function, which is essentially overloaded to contain information both about position and momentum. Because you cannot pack two independent pieces of information into a single degree of freedom, it is not possible for position and momentum to be perfectly well defined at the same time, which is where the Heisenberg uncertainty principle comes from.
Why they have momentum or why laser weapons would have recoil?
It would make sense IMHO if it's to create airflow for cooling
There's no reason for that to be a directed force, just suck in air from multiple directions and eject it in multiple directions to cancel out all net forces. Or ramp it up slowly so it isn't so jerky. But even if it's set up in the worst way possible, the forces will be significantly less than shooting a relatively massive bullet.
I'm no psysicist, but I suppose you would create more heat energy, than you'd be able to dissipate anyway
Nah, active air cooling is a thing that computers have been using successfully for decades. It does create more heat overall, but it moves heat away from the parts you don't want to melt.
Even liquid cooling or phase change cooling relies on air cooling eventually, those techs can just move heat quicker to a temporary heat reservoir that is then air cooled. If the cooling on the reservoir is slower than the heating, the cooling system will eventually saturate and fail to continue cooling the heat source faster than the reservoir cooling.
Even liquid nitrogen or dry ice cooling does this, it just dumps that heat earlier when the N2 or CO2 is condensed. And for those, you either have limited cooling time or need to top up the coolant as it evaporates.
Edit: not sure why you were downvoted... Your assumption was wrong but IMO worthy of discussion.
Why they have momentum since they don't have mass
You know that old E=mc² equation? That's actually only the simplified "rest" half of it. The full equation that relativity gives us says E²=m²c⁴+p²c². Meaning if it has energy, it definitely has mass (m), momentum (p), or both.
For a massless particle like a photon, that means E=pc, and its momentum is proportional to its energy and therefore frequency/wavelength.
Weird math bullshit.
But in essence, because they carry energy they must have momentum. It's why they can impart momentum on what they hit, because momentum must be preserved.
https://courses.lumenlearning.com/suny-physics/chapter/29-4-photon-momentum/