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According to Einstein and Brian Greene, does it logically follow that the photon remains stationary in the fourth dimension?
In An Elegant Universe, Brian Greene writes:
“Einstein found that precisely this idea—the sharing of motion between different dimensions—underlies all of the remarkable physics of special relativity, so long as we realize that not only can spatial dimensions share an object’s motion, but the time dimension can share this motion as well. In fact, in the majority of circumstances, most of an object’s motion is through time, not space. Let’s see what this means.” Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49
Brian Greene and Albert Einstein also state that there is one and only one velocity for all entities through the four dimensions--the velocity of light or c.
A photon travels at c through the three spatial dimensions. All of its velocity is directed through the three spatial dimensions. Thus Brian and Einstein are stating that a photon must be stationary in the fourth dimension. For if the photon had any velocity component in the the fourth dimension, its velocity would be different from c, which is not the case.
On the other hand, if an object is stationary in the three spatial dimensions, it must be moving at c through the fourth dimension.
We can summarize this as:
Axiom: All entities have one velocity through the four dimensions--c. (Einstein & Brian Greene).
Axiom: The velocity of light (photons) is c through the three spatial dimensions. (Einstein)
Theorem: The photon remains stationary in the fourth dimension, as all of its velocity c is through the three spatial dimensions.
Does this logic make sense?
Also, do you prefer using the word "Axiom" or "Postulate"?
An Axiom or a Postulate is a Truth.
A Theorem is that which follows logically from Axioms.