Nature of Light
This is partly a response to Nat's Facebook post.
The quote:"The only way to stay stationary in the fourth dimension is to move at the speed of light through the three spatial dimensions. Ergo the fourth dimension is expanding at the rate of c relative to the three spatial dimensions." -= Elliott McGucken
This quote is garbage - why - the reason is if your are a massless particle moving at the speed of light, you are not stationary in the time dimension - you are stationary in space-time.
For simplicity, let's assume your in flat space-time. The space-time interval is defined as
(Δs)2 = -c2(Δt)2 + (Δx)2
where x stands for all three spatial dimensions. No matter what coordinate system you transform into, the space-time Δs interval is the same. For objects moving less than the speed of light, (Δs)2 is defined as negative. An associated concept, is proper time, which is defined as
(Δτ)2 = -(Δs)2 = c2(Δt)2 - (Δx)2
Proper time is also the elapsed time for an object in its rest frame (where (Δx)2 = 0 ) .
For a particle moving at the speed of light, let's assume a photon, the space-time interval is zero, such that
0 = -c2(Δt)2 + (Δx)2
which means in its own rest frame, (Δt)2 and (Δx)2 are zero, and the concept of "elapsed time" doesn't exist. So the statement that you are stationary in the 4th dimension is bull, you can consider the particle to be stationary in space-time, if you define that as the space-time interval is zero.
If we observe the photon in our reference frame (t' and x') we know that (Δs)2 = 0, as it is invariant to coordinate transformations, so
0 = -c2(Δt')2 + (Δx')2
which we can rewrite as
(Δx')2 / (Δt')2 = c2 -> Δx' / Δt' = c
thus a particle with space-time interval zero moves at speed c (= the speed of light).
In both SR and GR you do a lot of coordinate transformations, and thus you cannot treat space and time separately. Time is treated the same as the spatial dimensions with the exception that it is assumed one can only move forward in time. A statement such as "the fourth dimension is expanding at the rate of c relative to the three spatial dimensions" will end up leading to paradoxes.
The quote:"The only way to stay stationary in the fourth dimension is to move at the speed of light through the three spatial dimensions. Ergo the fourth dimension is expanding at the rate of c relative to the three spatial dimensions." -= Elliott McGucken
This quote is garbage - why - the reason is if your are a massless particle moving at the speed of light, you are not stationary in the time dimension - you are stationary in space-time.
For simplicity, let's assume your in flat space-time. The space-time interval is defined as
(Δs)2 = -c2(Δt)2 + (Δx)2
where x stands for all three spatial dimensions. No matter what coordinate system you transform into, the space-time Δs interval is the same. For objects moving less than the speed of light, (Δs)2 is defined as negative. An associated concept, is proper time, which is defined as
(Δτ)2 = -(Δs)2 = c2(Δt)2 - (Δx)2
Proper time is also the elapsed time for an object in its rest frame (where (Δx)2 = 0 ) .
For a particle moving at the speed of light, let's assume a photon, the space-time interval is zero, such that
0 = -c2(Δt)2 + (Δx)2
which means in its own rest frame, (Δt)2 and (Δx)2 are zero, and the concept of "elapsed time" doesn't exist. So the statement that you are stationary in the 4th dimension is bull, you can consider the particle to be stationary in space-time, if you define that as the space-time interval is zero.
If we observe the photon in our reference frame (t' and x') we know that (Δs)2 = 0, as it is invariant to coordinate transformations, so
0 = -c2(Δt')2 + (Δx')2
which we can rewrite as
(Δx')2 / (Δt')2 = c2 -> Δx' / Δt' = c
thus a particle with space-time interval zero moves at speed c (= the speed of light).
In both SR and GR you do a lot of coordinate transformations, and thus you cannot treat space and time separately. Time is treated the same as the spatial dimensions with the exception that it is assumed one can only move forward in time. A statement such as "the fourth dimension is expanding at the rate of c relative to the three spatial dimensions" will end up leading to paradoxes.