# Photon in cartesian space

1. Aug 7, 2011

### Hippasos

Hi all!

Is it possible to derive x-y-z vectors of c in 3d cartesian space?

Is there any way we could then observe the photon (or measure its speed) in parallel with x axis for example?

Thanks.

2. Aug 7, 2011

### Pengwuino

Sure. I'm not sure why you think we can't.

Electromagnetic wave packets are solutions to Maxwell's Equations. So knowing that you can pretty much say "Ok, here's a wave-packet, let's align it with the x-axis".

Also, remember, coordinate axis are abstract concepts. When we see photons, they're flying off wherever the hell they feel like and we could arbitrarily assign an axis so that the photon is propagating along it.

3. Aug 7, 2011

### mikeph

I like that... you could use elliptical coordinates to calculate the electric field between two parallel capacitor plates and get the same answer. The physics is the same regardless of where we put our conceptual axes, the only thing that changes is the difficulty of the mathematics. A photon is a photon in whatever peculiar coordinate system you care to imagine.

4. Aug 7, 2011

### Hippasos

Ok, so in the case of photon we are always measuring the resultant c (coordinates fixed and aligned to the photon no matter howewer the observer assigns his/her coordinates. So obviously one shouldn't think resultant c = sum of all three velocity vector components (axes) in 3d space.

5. Aug 7, 2011

### DrGreg

It's up to you how you choose to align your coordinates. It will be easier if the photon moves parallel to one axis, but in general it will have velocity components of v = (vx, vy, vz) where$$v_x^2 + v_y^2 + v_z^2 = c^2$$And then the equation of motion will be$$\mathbf{r} = \mathbf{r}_0 + \mathbf{v}t$$