Can we observe the motion of a photon in cartesian space?

In summary, photons have no inherent spatial direction. They can be measured in any arbitrary coordinate system and their resultant velocity will be the same.
  • #1
Hippasos
75
0
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.
 
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  • #2
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
Pengwuino said:
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.

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
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
Hippasos said:
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.
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[tex]
v_x^2 + v_y^2 + v_z^2 = c^2
[/tex]And then the equation of motion will be[tex]
\mathbf{r} = \mathbf{r}_0 + \mathbf{v}t
[/tex]
 

1. What is a photon in cartesian space?

A photon in cartesian space refers to a particle of light that exists in three-dimensional cartesian coordinates. It is a fundamental unit of electromagnetic radiation and has properties of both a particle and a wave.

2. How is a photon represented in cartesian space?

A photon is represented in cartesian space as a point in a three-dimensional coordinate system, with its position determined by its x, y, and z coordinates. Its direction of travel is represented by a vector pointing in the direction of its motion.

3. What is the relationship between a photon's wavelength and its position in cartesian space?

A photon's wavelength is inversely proportional to its position in cartesian space. This means that as the photon moves further away from its source, its wavelength will increase.

4. Can a photon exist in multiple positions in cartesian space simultaneously?

According to the principles of quantum mechanics, a photon can exist in multiple positions in cartesian space simultaneously. This is known as the wave-particle duality of light, where a photon can exhibit both particle-like and wave-like behavior.

5. How does a photon interact with matter in cartesian space?

A photon can interact with matter in cartesian space through a variety of processes, including absorption, reflection, and scattering. The type of interaction depends on the properties of the material and the wavelength of the photon.

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