Time dilation is caused due to

Question

Does time dialtion is caused due to the decrease in temporal velocity of an object

i don't understand temporal velocity clearly

Answer 1

Causes always occur before effects, and “before” indicates an ordering in time. Time dilation is an aspect of time itself, so a cause of time dilation would have to occur before time. And since before is an ordering in time it doesn’t make sense to say that something occurred before time. Therefore the concept of a cause of time dilation is inherently problematic.

However, temporal velocity is clear, as is its relationship to time dilation. So that aspect of the question is answerable. The relationship is just not a cause-effect relationship.

In relativity there are two concepts of time. One is called “proper time”, which is the physical time, $\tau$, measured by a given clock. The other is called “coordinate time”, which is the timelike coordinate, $t$, of a given coordinate system. In an inertial coordinate system they are related to each other by the usual spacetime interval formula $$c^2 d\tau^2=c^2 dt^2 -dx^2 -dy^2-dz^2$$

With that, the temporal velocity is simply defined as $$\frac{d\tau}{dt}$$ and the relationship between temporal velocity and time dilation, $\gamma$, is $$\frac{1}{\gamma}=\frac{d\tau}{dt}$$

A little bit of algebra gives an explicit expression for the temporal velocity in an inertial coordinate system as $$\frac{c^2 d\tau^2}{c^2 dt^2}=\frac{c^2 dt^2}{c^2 dt^2}-\frac{dx^2}{c^2 dt^2}-\frac{dy^2}{c^2 dt^2}-\frac{dz^2}{c^2 dt^2}$$$$\left(\frac{d\tau}{dt}\right)^2=1-\frac{1}{c^2}\left(\frac{dx^2}{dt^2}+\frac{dy^2}{dt^2}+\frac{dz^2}{dt^2}\right)$$$$\frac{d\tau}{dt}=\sqrt{1-\frac{v^2}{c^2}}$$ From this the usual time dilation formula immediately follows $$\gamma=\left(\frac{d\tau}{dt}\right)^{-1}=\left(1-\frac{v^2}{c^2}\right)^{-\frac{1}{2}}$$

Answer 2

Perhaps "temporal velocity" is not an appropriate expression. One of the axioms of relativity is that the speed of light is always the same no matter who measures it. In my opinion, the best intuitive way of understanding how the former axiom implies time dilation is the light clock. Look for a good explanation of the light clock on YouTube and you will understand the time dilation/contraction phenomenon without writing a single formula. For instance https://www.youtube.com/watch?v=Cxqjyl74iu4

Another, in my opinion, more puzzling logical consequence of the constancy of the speed of light is that simultaneity is not absolute. In my view, the impossibility of accepting this logical consequence is the main driving force of the crackpot anti-relativistic movement.

Answer 3

Temporal velocity changes in relation to the speed traveled in space (spatial velocity) so the faster you go the slower time becomes. Temporal velocity can be measured to be different at different different points on the planet Steven hawking did a documentary series called genius which explains it better than i