Sign swapping - spacelike intervals

[Svendsen]

Hello guys!

I´ve seen that for spacelike intervals, ie $s^2 < 0$ you´re able to swap the sign of s = x-y = y-x. Why is that?

Thanks!

 

[Svendsen]

Supposedly there exists a continuous transform between x-y and y-x for spacelike intervals, but not for timelike ones. Can anyone show me that?

 

[Svendsen]

Figured it out! The reason is that for spacelike intervals it is possible to choose a reference frame such that the two events x and y occur at the same time. This however is not possible for timelike ones.

 

[Dale]

Supposedly there exists a continuous transform between x-y and y-x for spacelike intervals, but not for timelike ones. Can anyone show me that?

Take the axis which is 45° between x and y. Rotate 180° about that axis. Now you have swapped x and y, and since every rotation about that axis less than 180° is also a valid transform, the transform is continuous.

 

[pmacias]

Hello there!

I can explain this phenomenon using the principles of special relativity. In the special theory of relativity, space and time are intertwined and are considered part of a four-dimensional spacetime. In this spacetime, there are different types of intervals that describe the distance between two events. These intervals can be classified as timelike, spacelike, or lightlike intervals.

Spacelike intervals are those where the distance between two events is greater than the time interval between them. Mathematically, this can be represented as s^2 < 0, where s is the spacelike interval. In other words, the events are separated by a distance that cannot be reached by an object traveling at the speed of light.

Now, for spacelike intervals, it is possible to swap the signs of the coordinates x and y, as you mentioned. This is because in the special theory of relativity, the spacetime coordinates are not absolute. They can be transformed by a mathematical operation known as a Lorentz transformation. This transformation allows us to switch between different reference frames and still maintain the same physical laws.

So, when we swap the signs of the coordinates for a spacelike interval, we are essentially changing the reference frame from which we are measuring the distance between the two events. However, the physical laws governing spacetime remain the same, and thus the interval s remains unchanged.

I hope this explanation helps you understand why we can swap the signs of spacelike intervals. Keep exploring and questioning the laws of the universe!

Best regards,