1 = v^2 + t^2? and look at spacetime as velocity as x axis, time as y axis.

[darkhorror]

I am not so sure how to explain this. But when looking at sqrt( 1 - v^2/c^2 ) for time dilation. It seems to follow that you may be able to think about it as 1 = v^2 + t^2 if look at v as fraction of c, and t as the amount a clock will be dilated.

Then you could think about it in your frame of reference that all objects are moving at 1 through spacetime. If the velocity of an object gets larger then that just means that the t gets smaller.

 

[ghwellsjr]

You explained it very well. The equation you derived is for the reciprocal of gamma, the time dilation factor. It plots as a circle. See this post:
https://www.physicsforums.com/showpost.php?p=3158481&postcount=6

 

[HotBuffet]

I think it's more like sqrt(x^2 + y^2 + z^2 + t^2) = 1
4 dimensional law of pythagoras, using space and time.

next step is using this to understand / work out a twin paradox :)

 

[jedishrfu]

that should be a - t^2 right?

 

[elfmotat]

I think it's more like sqrt(x^2 + y^2 + z^2 + t^2) = 1
4 dimensional law of pythagoras, using space and time.

next step is using this to understand / work out a twin paradox :)

Do you mean s²=-t²+x²+y²+z² ? The OP wasn't talking about the interval. He was talking about the relationship between time dilation and velocity.