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

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Discussion Overview

The discussion revolves around the possibility of deriving x-y-z vectors for the speed of light (c) in three-dimensional Cartesian space and whether it is feasible to observe or measure the motion of a photon along a specific axis, such as the x-axis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the feasibility of deriving x-y-z vectors for the speed of light and measuring a photon's motion along a specific axis.
  • Another participant asserts that electromagnetic wave packets, as solutions to Maxwell's Equations, can be aligned with an axis, suggesting that coordinate axes are abstract concepts.
  • A further contribution emphasizes that photons can be assigned to any coordinate system, and the physics remains unchanged despite the mathematical complexity that may arise from different coordinate choices.
  • One participant clarifies that the resultant speed of light should not be thought of as the sum of its velocity components in three-dimensional space, but rather as a fixed measure aligned with the chosen coordinates.
  • Another participant reiterates that the velocity components of a photon can be expressed in terms of its components along the x, y, and z axes, maintaining the relationship that the sum of the squares of these components equals c squared.

Areas of Agreement / Disagreement

Participants express differing views on the nature of coordinate systems and the measurement of a photon's motion, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

There are unresolved assumptions regarding the interpretation of coordinate systems and the implications of measuring a photon's motion in different frames of reference.

Hippasos
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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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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.
 
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.
 
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.
 
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<br /> v_x^2 + v_y^2 + v_z^2 = c^2<br />And then the equation of motion will be<br /> \mathbf{r} = \mathbf{r}_0 + \mathbf{v}t<br />
 

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