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Photons are real, physical objects.

The fourth dimension is a real, physical entity.

Therefore, photons must have a relationship with the fourth dimension. They must have some velocity relative to it.

What is the velocity of the photon through the fourth dimension x4?

Do you agree with the following:

  1. Maxwell/Einstein teach that light has the velocity c through the three spatial dimensions.

  2. Relativity teaches us that the velocity of every object is c through the four-dimensional spacetime manifold.

  3. If a photon has a velocity other than zero relative to the fourth dimension, then either #1 or #2 above would no longer be true.

  4. As #1 and #2 must always be true, a photon must remain stationary relative to the fourth dimension.

  5. As a photon is stationary relative to the fourth dimension, it tracks and traces x4's movement. The fourth dimension is moving at c relative to the three spatial dimensions. Remarkably, this is exactly what Einstein/Minkowski taught with x4=ict which means dx4/dt=ic -- the fourth dimension is moving at c relative to the three spatial dimensions.

Einstein's GR taught us that dimensions could bend, curve, and move and so does dx4/dt=ic.

Does the above logic make sense to you?

What, in your opinion, is the velocity of the photon through the fourth dimension x4?

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closed as unclear what you're asking by CuriousOne, WillO, sammy gerbil, knzhou, rob Jul 19 '16 at 18:14

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Well, I'm not going to tell you my opinion, because that would be irrelevant to the actual science. But, what I can do is assess your premises and conclusions.

What you should note first, and I'm unsure if you know this or not already, is that the four dimensions of spacetime are the three spatial dimensions and time. We can define a velocity through the spatial dimensions easily, but there isn't any particular way of defining a velocity through time, except by relating it to some other reference frame's progression in time. That said, let me assess your 5 premises:

  1. This is true. Locally, light moves at $c$, although not in all three perpendicular directions at once.

  2. I'm not sure where you got this from. Relativity certainly doesn't teach us this. I notice you mentioned $ict$ at some point. Perhaps this led you to believe that relativity says things move at $c$, but really, the $c$ is in the equation simply to ensure unit agreement between space and time. And don't pay attention to the $i$, that's a common teaching mistake.

  3. Even assuming #2 was correct, I'm still not sure how you would make this particular leap in logic. It doesn't follow at all. There's no reason to believe that photons have to be stationary in time. In fact, since they move at $c$ in all reference frames, photons have no rest frames themselves in which to judge their experience of time.

  4. This is a conclusion from #3. Since #3 is incorrect, this statement is immaterial.

  5. Again, this is not quite true. $ict$ is wrong. The opposite sign of the temporal dimension comes from the historical implementation/significance of the term, not from any imaginary time component. And the $c$ factor does not mean things travel at $c$ through time, just that $ct$ is the max anything could travel in time $t$.

From this, it should be clear that the "velocity" of light through time is a meaningless statement. There's nothing to compare here. Light has no reference frame and there is no alternative temporal dimension to measure it against for a velocity.

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