Are photons really massless?

they are massless because they travel at the speed of light, which means all of their rest mass is converted into energy.

Kek.

Sort of related but how did physicists discover photons? My professor said they saw that the light would knock electrons off metal and that led them to suspect light particles were responsible but couldn't the electric field portion of the light waves cause the electrons to move? Thanks

around three bits

I'm half way serious though. Does the math not work out at all if the energy gets converted to mass?

Photons don't exist. A photon is the process between detection and absorption, and we do not know what happens inbetween, other than what Maxwell equations suggest us.

You're missing about half the explanation.

You're right that light causes electrons to pop off metals when you shine it on them, that's because the energy from the light goes into the electrons, allowing them to escape the surface. In the EM wave view of light this should work for any wavelength. As long as light keeps shining, more energy should go in so eventually there should be enough to pop an electron off, right? Well, it turns out that below certain wavelengths no electrons were emitted at all. This doesn't work with pure EM waves but it does work if you consider light to come in discrete packets with energy proportional to frequency [math]E=hf[/math] which are absorbed separately.

If a packet of light with too low a frequency hits the metal, that amount of energy will never be enough to excite an electron from the surface. If a packet with a high enough frequency hits it then it excites as usual.

>Using a calculator to prove its wrong
The answer is fairly obvious

What your professor was describing is called the photoelectric effect, it was bit of problem back in the day, and the solution was what won Einstein his Nobel. Physicists knew that it couldn't be showing light was a wave because, as the theory went, if you had a high intensity light then it should liberate more electrons, that wasn't observed. What was observed was that even low intensity light could remove electrons. This implied that photons have to be discrete particles, a bit like them undergoing a collision of some sort.

It wasn't the fact that it worked for different intensities that was weird, it was the fact that there was a cutoff frequency.

>if you had a high intensity light then it should liberate more electrons, that wasn't observed
It certainly should, because you're hitting it with more photons per unit time, it only wasn't observed below the threshold frequency.

>What was observed was that even low intensity light could remove electrons.
This still makes sense with the EM wave model.

But if they have no rest mass their energy zero by e=mc^2? I'm a physics brainlet is there something I'm not getting

>pair production

That's the formula for energy at rest, photons are never at rest so you need the bigger formula:
[eqn]
E^2=p^2c^2+m^2c^4
[/eqn]This describes moving objects. The p is relativistic momentum, which is not necessarily zero if your rest mass is zero.

Do people consider that our math is sometimes lying to us since the most things we theorize about are not possible to actually see/touch/measure?

>most things we theorize about are not possible to actually see/touch/measure?
idk where you're getting this idea from. Aside from extremely theoretical stuff like String Theory, the only reason we take any theories of physics seriously is because they make measurable predictions that we can verify.

>Being a retard
wolframalpha.com/input/?i=3987^12+4365^12 = 4472^12

yeah, it's this one. wikimedia.org/api/rest_v1/media/math/render/svg/7c87a47e0d2db63818810cb62589181abd473285

I told my professor they are massless, he pulled the whole "continuous symmetry theory" on me, he said that they are massless for now until future scientists make a discovery that will surely prove us wrong.

>photons are never at rest
Not him, but what exactly is meant by this? Like, if one was to theoretically make a photon stay at rest, would it just cease to exist? Or would is simply be unobservable? Or is it simply impossible, because for it to be observed some form of energy transfer would have to occur, exciting it and thus making it no longer at rest?

There is no frame(an observer) where photons will be at rest. The fundamental postulate of special relativity is that in ALL frames photons move at velocity c. This fact lets us define an invariant 'length' between different observers by s^2=x^2+y^2+z^2-c^2*t^2. Called the interval. If one observer computes this then another computes it in their frame s^2 will be the same. This fact leads to all the weird relativistic effects. Refer to Schutz-general relativity chapter 1-2 for more on this.

The math is there to explain things we can test and measure. From our mathematical models we can sometimes modify them to obtain predictions on phenomena. Many fundamental particles discovered in the past decade were theorized long before we had measured them due solely to the math.

One example is from E^2=m^2*c^4+p^2*c^2 you get a positive and negative energy. Both are solutions since when you square E and -E you get E^2. But what does negative energy mean? Maybe it's some kind of anti-particle. But there's no way something like that could exist right?

your professor is the ultimate brainlet who is either saying he doesn't understand the basic representation theory of the Lorentz group or that local Lorentz invariance is violated which in principle is not impossible but highly unlikely considering current experimental limits andn hardly theoretically motivated at all.

The only thing you need to know about photons is that they're on a spectrum

Massless but they have energy which is equivalent to mass.