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This is yet another question concerning lasers as employed by sorcerers in a particular fantasy setting, but this one pertains to the momentum that photons possess and whether it's possible to generate light that imparts a higher proportion of its energy to an object in the form of momentum, rather than say an increase in temperature. Particularly, I'm concerned with something I read on Physics Stack Exchange:

And here we have it: photons have 'mass' inversely proportional to their wavelength!

This post is more detailed and is worth reading, but relying on the sentence above, have I completely misunderstood the author by concluding that in order to increase the "momentum imparting" aspect of light, we need light with increasingly shorter wavelengths? In other words, does light with a short wavelength cause less heating, or will that aspect remain constant?

I would like to repeat the question: Is it possible to create light that imparts a greater proportion of its energy as momentum rather than heat?

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    $\begingroup$ Momentum is momentum and energy is energy and the two are not the same. You cannot impart not even a tiny little bit of energy as momentum, because the two physical quantities do not have the same dimensionality. $\endgroup$
    – AlexP
    Apr 4, 2019 at 16:52
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    $\begingroup$ @Jasper: Angular momentum is $M \cdot L^2 \cdot T^{-1}$, for example kg·m²/(s·rad). Energy is $M \cdot L^2 \cdot T^{-2}$, for example kg·m²/s². Not dimensionally equivalent. Fun factoid: in languages such as French, Italian, Romanian or Russian, linear momentum and angular momentum are named with dissimilar words, usually something like impulse or quantity of motion vs. kinetic moment or moment of impulse. $\endgroup$
    – AlexP
    Apr 4, 2019 at 22:31
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    $\begingroup$ AlexP --- Oops. Thank you. Torque has the same units as energy. $\endgroup$
    – Jasper
    Apr 4, 2019 at 23:03

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No. The momentum of a photon is in direct proportion to its energy. A shorter wavelength of light has both more energy and more momentum in equal proportions.

If you want to maximize imparted momentum while minimizing heating, you need to change not the light, but what it is hitting. A perfect blackbody will absorb all of the momentum of a beam of light, and all of the energy as heat. A perfect mirror, on the other hand, will absorb no energy and experience no heating, but will absorb double the momentum.

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    $\begingroup$ Good, concise answer. As an added note, it's possible to measure the force exerted by light if you have a sensitive enough setup. See this video for an example of the type of setup you need. It's maybe also worth noting that decreasing the wavelength isn't the only way to increase the energy you're imparting in a given unit of time (the power), you can also increase the number of photons. In general: $E_{tot} = \hbar \omega N_{\gamma}$ for some pulse of given duration. $\endgroup$
    – realityChemist
    Apr 4, 2019 at 14:22
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    $\begingroup$ @Hearth- the energy does change direction. If it is in one direction then there is a change in net momentum. If it randomly changes the motion of part(icle)s then the momentum is heat (net zero). $\endgroup$
    – amI
    Apr 4, 2019 at 17:04
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    $\begingroup$ @Hearth If the mirror moves away from the light, then yes. However, it is entirely possible for light to exert a force, and thus transfer momentum, while doing no work and thus transferring no energy. If the mirror is moving towards the light source, it will actually do work on the light, and thus lose energy. $\endgroup$
    – Logan R. Kearsley
    Apr 4, 2019 at 19:20
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    $\begingroup$ @aml Energy doesn't have any direction, or more accurately , the energy component of an energy-momentum 4 vector is orthogonal to all of the momentum components. $\endgroup$
    – Aron
    Apr 4, 2019 at 19:27
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    $\begingroup$ It will do no work in the reference frame of the object being hit, but from an observer on Earth, or orbiting in space (or wherever you consider "stationary") the photon should be redshifted to compensate for the kinetic energy imparted to the object. (Or blueshifted to compensate for the kinetic energy taken from the object, if it's slowing down) $\endgroup$
    – user253751
    Apr 4, 2019 at 23:15
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As Logan has pointed out. "Light" has some very concrete and specific properties to it.

However. Since we are in World Building and you tagged "magic", I think straying away from the Standard Model would be allowed.

First, a bit of history about the Standard Model. It is filled with "particles" which we have very concrete properties and numbers and mathematical formulae for (plus field equations).

However, in the beginning, these properties weren't known, the formulae and maths was not invented. Even particles weren't a concept. We figured them out from the shadows that they cast into our cave.

Each new effect we gave a new name to; like "Light", "Magnetism", "Heat", "Energy", "Strangeness", "Charmness", "Topness", "Bottomness", "Anti-Red Quantum ChromoDynamics-ness".

Quite simply your world can have all the different effects you want and those effects can be explained away with a new set of fields/particles/equations.

TLDR: Invent a new magical particle called "Qi", make your sorcerers fire "Qi" based "beams" that radiate cherenkov radiation when fired in the atmosphere when they cast the Haduken spell.

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  • $\begingroup$ That certainly helps, not that I was ever going to go into an explanation of the mechanics. I simply wanted to know if it was possible to explain in our universe. $\endgroup$
    – Red Robin
    Apr 4, 2019 at 16:40
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Here's a short answer:

Reading your question literally, No. Energy and Momentum are completely different.

On the other hand, if you are actually talking about acceleration/velocity:

Sure! its called Gamma Radiation.

Before you get mad at me for uttering heresy, here is a logical proof using elementary physics:

  • All radiation is a form of light.

  • Acceleration is the result of the energy from something which is already accelerated being transferred to it, sort of like how a billiards ball moves after it is hit by a cue ball.

  • The reason why gamma radiation is so damaging is that it is extremely good at transferring the energy of its acceleration to anything it hits, such as cells or DNA. This causes what it hits to either (a) accelerate (move), or (b) store the energy by becoming an ion. Either way, the effect is extremely damaging.

Therefore, Gamma radiation is a form of light which is significantly better at imparting acceleration than visible light is.

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