# Thread: The Space-Time interval.

1. I have begun to familiarise myself with the notion that x,y,z,t coordinates in one Frame of Reference can be "paired" with primed equivalents in a second ,relatively moving Frame of Reference.

In the second FoR Space intervals and also Time intervals are different (proportionally) from those as measured in the first FoR.

I have also recently learned (I hope) that when "events" are measured in these terms then intervals between "events" can be calculated according to

t2x2y2z2=t2x2y2
z2

where it appears to me that the (measurement of) the SpaceTime interval is
independent of the FoR.

In other words if a sequence of events takes place in a second FoR ,the measurement (and possibly description) of these events is equally accurate no matter where you happen to be in the universe or at what speed (or acceleration-I think I saw that too) you are moving wrt the events.

Have I correctly understood this situation?
If so is this an important finding? Has it had practical consequences (is it used in research for example?)

Could the SpaceTime interval be considered to play a role a bit like a Rosetta stone between moving or accelerating FoR s?

2.

3. Have I correctly understood this situation?
Yes, you have. The space-time interval is invariant, i.e. it is the same for all observers.

If so is this an important finding? Has it had practical consequences (is it used in research for example?)
It is the basis of the theory of special relativity - the group of operations which leaves this space-time interval invariant is just precisely the Lorentz group, the elements of which are the Lorentz transformations.

Could the SpaceTime interval be considered to play a role a bit like a Rosetta stone between moving or accelerating FoR s?
It could. It the common basis on which all observers in space-time agree.

4. thanks.That is reassuring. I am glad there is something on which all observers can agree. It makes the subject seem little more grounded.

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