# B The relation between photons and waves

1. Nov 14, 2017 at 12:00 PM

### Joao

Hi everyone! Sorry for the bad English!

Please, I learned that a wave is something the photons "surf" on, like, in one electromagnetic wave, can have many photons.

So, is this true? Like, I though that one gamma ray and an infrared photon would ride different waves...

More: the light from the sun is white, after goes to a prism it became the rainbow... Soooo... was the wavelength of the different colors "all together" in the solar light? Or did the prism changed the wavelength to many other kinds of wavelength, corresponding to the other colors?

I'm a little lost here, I guess I cant even make my questions clear! Hehehehehe

Thanks!

2. Nov 14, 2017 at 12:49 PM

### Staff: Mentor

Photons do not surf on EM waves. This is a widespread misconception.

Imagine you have an EM wave hitting a surface. This EM wave will have an intensity that describes how much energy it delivers to any particular area of the surface. Let's say one of these areas is 1 square meter in surface area. Let's also say that our EM wave delivers 1 Joule of energy to this surface per second and that the wavelength of our wave is 1000nm.

If we look closely with the right instruments and experiments, we discover that during any 1 second interval this energy is not being delivered evenly over the surface or over time. Instead we discover that the energy is being delivered in tiny individual "packets" of equal energy, meaning that every time energy is transferred from the EM wave to the surface a fixed amount is transferred all at once to a particular location (so it's not spread out over the surface). This is an incredible discovery! It means that EM waves do not behave like "classical" theory describes it!

Knowing this, we do more experiments with different frequencies and crunch some numbers to discover that the energy in each "packet" is described by the equation $e=\frac{hc}{λ}$, where $h$ is a constant equal to about 6.626×10−34, $c$ is the speed of light, about 3x108m/s, and $λ$ is the wavelength of the wave in meters.

So for our original wave, each "packet" delivers $e=\frac{(6.626*10^{-34})(3*10^8}{10^{-6})} = 2*10^{-19}$ joules worth of energy. Truly a tiny amount. Since our wave transfers 1 joule per second to our surface, there are about 5x10^18 of these packets hitting the surface every second. This is so many packets hitting the surface that most spots only go a short amount of time between absorbing a packet. But if we reduced the energy of our EM wave to very tiny levels, we would find that only one or two packets are absorbed by the entire surface each second. It would be like a Geiger counter where you can pick out each individual click and clack.

If we were to use the wavelength of a gamma ray EM wave and keep the energy of the wave at 1 joule per second, we would get about 1.5x1014 packets per second, or about 33,000 times fewer packets at this shorter wavelength.

Furthermore, once we do more experiments and crunch more numbers, we discover various other odd things about these "packets". They have momentum, spin, and several other properties that are used to describe particles, despite the fact that they aren't like tiny little balls riding on an EM wave. In fact, we can't even say that these packets move in straight lines like a baseball traveling through the air. All we know is that, given some area on a surface and an EM wave, any particular spot in this area has some chance of having one of the packets transfer energy to it every second. What these packets are doing prior to being absorbed is unknown. (If this sounds odd, don't worry. It's very confusing when you first hear about it)

Since the packets have properties similar to other fundamental particles, and because doing so makes it convenient for us to talk about them, we decide to give them the name photons. They are not "surfing" or "riding" an EM wave at all. Without getting too deeply into the philosophical and technical details, they are the EM wave.

That's a bit complicated to explain. The different frequencies all add together to form one wave of varying frequency and the prism splits this wave back into its component waves by sending them in different directions. The adding together of different waves is known as superposition.

3. Nov 15, 2017 at 4:31 AM

### Joao

Thanks a lot! Really! I had a very wrong idea of what a photon was! You really helped me a lot! Your explanation makes a lot of sense! =)

4. Nov 15, 2017 at 6:11 AM

### sophiecentaur

Haha. You are not alone in that. The problem is that they are not 'like' anything. They are what they are and sometimes they are seen to behave like a lot of different things. You can only rely on treating them as something special - except when some well founded explanation shows a photon to behave in a certain way (but only in that particular case).