If force is equal to mass times the rate of acceleration, yet

>>8389086
Energy and momentum.

>>8389086
Massless photons don't really work without SRT.

>>8389086
>If force is equal to mass times the rate of acceleration
It's not.

>>8389536
It is, Photons' mass doesn't change

Of course zither don't accelerate, but hey-ho

>>8389086

My understanding is that a solar sail is powered by the reactions of the photons hitting it, not by the momentum of said photons (since they have none, as they lack mass and don't accelerate)

>>8390613
it's dp/dt you turd.

>>8390613
In relativity, force is not equal to mass times acceleration, but we do have:
[math]f = \frac{d\textbf{p}}{dt}}[/math]
The point being that momentum in relativity is now [math] \textbf{p} = m \gamma \textbf{v}[/math] for a massive particle, or [math] \textbf{p} = \textbf{k} [/math], where [math]\textbf{k}[/math] is the wave vector.

>>8390633
> not defining mass as inertial mass

>>8390633
[math]f = \frac {d\textbf{p}} {dt}[/math]

>>8390635
What are you even talking about? Is there any other kind of mass in special relativity?

>>8389086
>rate of acceleration
wat

>>8389086
I thought solar wind contained lots of other particles that had mass.

>>8389086
Because force isn't actually equal to mass times acceleration. Newton thought it was; Einstein revised it. You probably should have figured this out from the fact that photons have no mass, but can exert a force - it's much simpler than what you came up with.

F = dp/dt, the change in momentum with respect to time. In Newtonian physics, momentum p = mv, and dv/dt = a, so for constant mass this is equivalent to F = ma.

In relativity, however, momentum is not the same thing, and so dp/dt is not equal to ma anymore. Because mass and energy are equivalent, massless objects with energy can also have momentum. E=mc^2, which you may have seen, is a special-case (massive, not moving) simplification of the full mass-energy-momentum relation E^2 = (mc^2)^2 + (pc)^2. For massless objects, like photons, this simplifies to E = pc, and so p = E/c.

So, if you're shining a laser of frequency f Hz and power dE/dt = P Watts on something that absorbs photons, that beam will have d(E/c)/dt = dp/dt = P/c Newtons of force associated with it, which by Newton's Third Law will both push the laser and whatever you're shining it on away from each other.

Since c is pretty huge, though, the thrust is tiny unless P is enormous, which is why flashlights don't go rocketing around.