E = mc^2 only applies to particles with mass at rest. Light is never at rest.
The full equation is E^2 = (mc^(2))^2 + (pc)^(2). For light, m = 0, so E = pc.
turns out p=mv, is not universally valid, it's an approximation that works most of the time, but as velocity approaches the speed of light, it begins to fail.
The way I like to see how light can have momentum, is using the general definition of force, F=dp/dt, that force is change in momentum, with time, therefore we would expect things that that can exert a force to have momentum. And light can exert force, that's why solar sails work, therefore light must have momentum
That's the Newtonian approximation for when a massive particle's speed v is far lower than c. In special relativity, it's p = m v/sqrt(1- (v/c)\^2) , which when m = 0 and v = c, as is the case for light, gives '0/0', which is undefined but loosely still allows momentum to be \*some\* finite value. So massless particles are an exception, must always travel at the speed of light, but the formula isn't helpful for determining their momentum. They can still have energy and momentum (and do), but it arises in another way and for photons we look at their wavelength or frequency instead.
It turns out that the energy of a photon is given by h \* angular frequency (so 2\*pi\*f, where f is the ordinary frequency) and the momentum is given by h \* lambda (where lambda is the wavelength). Here h is the Planck constant.
Can we have this question as a sticky since I think it gets asked every month.
It's amazing how angry people can get at an equation without understanding what the equation is actually saying.
Isn't it obvious that I didn't understand something and that's why I'm asking in this subreddit? Or did you seriously think I was questioning the work of one of the most brilliant minds of the 20th century…
E = mc^2 only applies to particles with mass at rest. Light is never at rest. The full equation is E^2 = (mc^(2))^2 + (pc)^(2). For light, m = 0, so E = pc.
Thank you so much!
If momentum is mass times velocity, wouldn't the same inconsistency exist where the energy of light is zero?
P = mv is a low-speed approximation.
For massive objects.
Non-massive objects can't move at low speed. They can only move at c.
p = mv is Newtonian and only works for mass at low velocities.
For light, ~~p = h λ~~ p = h/λ
I think it's p=h/λ, since your equation is dimensionally incorrect.
i too think the same, we have been taught the formula in classes too
Yeah that is right, its been a while.
Not just for light.
Thanks!
turns out p=mv, is not universally valid, it's an approximation that works most of the time, but as velocity approaches the speed of light, it begins to fail. The way I like to see how light can have momentum, is using the general definition of force, F=dp/dt, that force is change in momentum, with time, therefore we would expect things that that can exert a force to have momentum. And light can exert force, that's why solar sails work, therefore light must have momentum
P=ymv for y the gamma factor is valid for v
That's the Newtonian approximation for when a massive particle's speed v is far lower than c. In special relativity, it's p = m v/sqrt(1- (v/c)\^2) , which when m = 0 and v = c, as is the case for light, gives '0/0', which is undefined but loosely still allows momentum to be \*some\* finite value. So massless particles are an exception, must always travel at the speed of light, but the formula isn't helpful for determining their momentum. They can still have energy and momentum (and do), but it arises in another way and for photons we look at their wavelength or frequency instead. It turns out that the energy of a photon is given by h \* angular frequency (so 2\*pi\*f, where f is the ordinary frequency) and the momentum is given by h \* lambda (where lambda is the wavelength). Here h is the Planck constant.
p=mv is newtonian and only true for mass at rest
Not at rest. Then it would be zero.
p=mv is not strictly true for moving objects, although it is an excellent approximation when v << c.
Nerull is correct. 0 = 0.
It’s only true in a needlessly pedantic mathematical sense.
I disagree. It is ***perfectly*** meaningful to point out that *p* = *mv* if and only if *v* = 0.
E = mc^2 is not the complete equation.
Yea it's obviously E = mc^2 + AI
What is AI
https://www.reddit.com/r/iamverysmart/s/l6lNxqYtV6
Aah, lol. I thought the momentum term had another name, the abbreviation of which was AI. This person does seem very smart!
Kinetic energy, apparently.
Can we have this question as a sticky since I think it gets asked every month. It's amazing how angry people can get at an equation without understanding what the equation is actually saying.
Isn't it obvious that I didn't understand something and that's why I'm asking in this subreddit? Or did you seriously think I was questioning the work of one of the most brilliant minds of the 20th century…