Space-Time Velocity: Is It True?

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The discussion centers on the concept of traveling through the four dimensions of spacetime at the constant speed of light, c. It posits that an increase in velocity through spatial dimensions results in a decrease in velocity through time, suggesting that if one were to travel at the speed of light, they would not age because they would not be moving through time. The conversation explores the definition of "travel" in this context and explains how time can be converted into length units using the invariant speed, c, leading to the formulation of spacetime displacement. It highlights that when stationary, only time displacement (aging) is relevant, and this is expressed as cΔt in length units. The discussion concludes with the clarification that from the perspective of someone traveling at the speed of light, time would appear to stop for them, while those at rest would continue to age normally.
strubenuff
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Is it true that we're traveling through the 4 dimensions of space time at the constant, c? This implies that velocity through the spatial dimensions detracts from our velocity through time and vice versa. For example, if I were traveling at the speed of light, I wouldn't be aging because I wouldn't be traveling through time (V=0).
 
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Originally posted by strubenuff
Is it true that we're traveling through the 4 dimensions of space time at the constant, c? This implies that velocity through the spatial dimensions detracts from our velocity through time and vice versa. For example, if I were traveling at the speed of light, I wouldn't be aging because I wouldn't be traveling through time (V=0).

Please define "travel"
 
In converting time to units of length, for use in formuilas and components, we multiply by the invariant speed, c. So many length units per time unit. As a result of that your squared displacement from one event in spacetime to another becomes

c2Δt2 - Δx2- Δy2- Δz2.

If you remain still, your space displacements are all zero, and only your time displacement (aging) is effective. Evidently this is cΔt in length units. This is the origin of the statement that we are moving through time at the speed of light. It is really because we convert time units to length units using c. And we use c because it is the same in all inertial frames of reference.
 
For example, if I were traveling at the speed of light, I wouldn't be aging because I wouldn't be traveling through time (V=0).
Yes, but that will only be true from a perspective that is traveling at c relative to you. From your point of view, your time proceeds normally and it is THEY that do not age.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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