# Speed of light, lasers and mass

Hopefully this isn't a bad question. Light travels at the speed it does and nothing else can travel that fast because things have mass, correct? Or at least correct on an elementary level. And if lasers, which are light as I understand it, have the ability to destroy other things. Doesn't that mean light has energy? But if light has energy shouldn't it have mass? I thought $E = mc^2$ and $E$ is energy, $m$ is mass. 0 mass times speed of light squared would equal zero energy, right? It's probably obvious that I'm no physicist but hopefully its also obvious that I enjoy science and physics.

• The question seems to be caused by confusing invariant/rest mass and relativistic mass. Possible duplicate: physics.stackexchange.com/q/83392/2451 Nov 23, 2013 at 1:30
• 'Speed of ligt' is actually a dated and misleading name for this constant. What we should really be calling it is the speed of massless particles. Nov 23, 2013 at 1:30
• Also, if we were to discover a new interaction that gave photons mass (like the process that gives W bosons their mass) then photons would cease to travel at 'lightspeed'. Nov 23, 2013 at 1:37
• $$m=\frac{E}{c^2}=\frac{ℏω}{c^2}$$ This can be called the mass of a photon. Now, the speed of a photon in vacua is c for all observers and because the relationship of relativistic mass to rest mass for any particle is $$m=\frac{m_0}{\sqrt{1−\frac{v^2}{c^2}}}$$ where $m_0$ is the rest mass and v is the particle's velocity relative to some observer, if there was any non-zero rest mass, the particle's relativistic mass would be ∞, not $\frac{ℏω}{c^2}$, so the rest mass of a photon has to be zero. Read more: physicsforums.com Nov 23, 2013 at 1:42

With the first question you are correct. Any "thing" with nonzero mass cannot achieve light speed. From this equation you can see why

$$m=\frac{m_{0}}{\sqrt{1-\frac{v^2}{c^2}}}$$

where $m_{0}$ is the rest mass of the body (i.e. the mass it has when its speed is zero). As you can see from the equation, when $v=c$, the right hand side will blow up to infinity. And you can't have an infinite mass.

It's true that photons don't have mass, but that doesn't mean they don't have momentum. The relativistic energy momentum relation states that

$$E^{2}=p^{2}c^{2}+m^{2}c^{4}$$

Knowing that the mass of the photon is zero, you get the following relation between the energy and momentum

$$E=pc$$

I will not bore you with more formulas, but the energy and momentum of the photon depend only on its frequency and wavelength in the following way.

$$E=h\nu=\frac{hc}{\lambda}$$

So, the higher the frequency, the higher the energy of light. You can see this when you play with red, green of violet laser. With a violet laser you can light up a matchstick (having a high frequency) but with a red one you cannot because it has a much smaller frequency. You can read more on wiki.

• Fantastic. Thank you. You gave me something to study.
– Kyle
Nov 23, 2013 at 3:25