# How is it possible photons have no mass but have energy?

I know my question is so simple to ask but I'm new in this subject.

I'm studying energy systems engineering in university and I took physics and advanced physics but I never truly understand how photons have no mass but they're carrying energy. How is it possible ?

I thought photons are some kind of pure energy but I saw NASA made solar sails to create propulsion, how can you create propulsion without exhaust mass ? (Momentum equation collisions)

Also how can we "create" photons ? Like you can convert something into something else but creating must be impossible.

I read about double slit experiment and it confused me even more and it gets more and more complicated the deeper I go.

I'm sorry if my lack of knowledge or English making my question hard to understand & read

• Wow that was rude, at least you can write what's wrong with question instead of just downgrade it. – Mordecai Oct 30 '19 at 13:33
• you have perhaps the worst typo I have ever seen. Please fix it. (Maybe it was the cause for -1?). – JEB Oct 30 '19 at 13:36
• You're still not specifying what's wrong, is it grammar or I can't explain myself properly ? There is a big difference between a destructive criticism and constrictive criticism. – Mordecai Oct 30 '19 at 13:44
• The following videos might help you: science asylum, sixty symbols – user238497 Oct 30 '19 at 14:11
• Here is the video that will enlighten: youtube.com/watch?v=2Vq5-dRYp-c . It's not grammar. – JEB Oct 30 '19 at 14:18

It's a matter of classical mechanics & relativistic mechanics.

In classical mechanics, momentum ($$p$$) is proportional to the mass and the velocity of an object ($$p=mv$$) and kinetic energy is $$E_k=\frac{1}{2}mv^2$$. Thus you might think photon has no momentum and energy since mass is zero.

However, according to the relativistic theory, all these formula is changed. The mass of an object with certain velocity is increased by a factor of $$\frac{1}{\sqrt{1-\frac{v^2}{c^2 }}}$$. Since the velocity of speed of just what we call 'speed of light' ($$c$$), this factor becomes infinity and we can guess the momentum of photon might be a finite quantitiy. $$(0\times\infty$$)

More precisely, what Einstein found is $$E^2 =m_0^2 c^4 +p^2 c^2$$ where $$E$$ is the energy, $$m_0$$ is rest mass, $$p$$ is momentum.

$$m_0$$ of photon is $$0$$, so $$E=pc$$ for photon. Energy of photon is $$E=h\nu$$ where $$h$$ is planck constant and $$\nu$$ is the frequency of photon. Automatically the momentum of photon is $$p=E/c=h\nu/c$$.

• Thank you for answer. I always thought the equation was E=mc2 but in my school they didn't include p2c2 part, that clarify most of my confusion. So it's possible to have momentum without mass. But what happen if photons collide a object ? Collision equation says energy divide by mass so do photon transfer all his energy into object and simply disappear ? Also I wonder something, we can convert mass into energy so can we convert energy into mass ? – Mordecai Oct 30 '19 at 14:05
• If photon collide with other object, it can be absorbed or be scattered. Whatever happens, total energy and momentum have to be conserved. If 1eV of photon is absorbed by an object with 100eV of energy, its energy will be 101eV. And yes, we can convert energy into mass. That's what happens inside particle collider. Particles which are almost accelerated to the speed of light have very big energy thus their collisions can produce many new particles. – Jaesung Kim Oct 30 '19 at 15:10

It all started with Einstein photoelectric effect explanation. If you have light of frequency v, you can receive energy nhv, where n is integer. There comes the concepts of photon in which we say light composed of particles called photons of energy hv, thats why we can receive energy nhv from light where n is always integer. We can say photons are Quantum of electromagnetic energy. Photons always travels with speed of light. Rest mass is zero means it cannot exist at rest. We should not talk about mass of the photons. Only its energy and momentum are well defined. (Compton effect confirms photon have momentum).

Two kind of things can happen with photons. If an atom makes transition from higher energy to lower energy, in the process, atoms energy will be decreased and photon will be created (emitted). An atom from lower energy state, can 'absorb' photon and go to higher energy. In that process, photon will vanish, we say atom absorbed it.

We can use probabilistic interpretations to explain double slit experiment with particles. So, even if we treat light as photons, we can explain double slit experiment. I tried this in these videos: At the end of this video: https://youtu.be/I77WbGqKM4U

At 31:00 in : https://youtu.be/fpEg9a-YsXU