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First, how is the invariant interval useful? How can it help us understand things around us in the universe?

Second, I know that they changed time into space or better say SPACETIME in order to measure the invariant interval, but how did they already conclude from the special theory of relativity that the universe is made of spacetime and not space and time?

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The spacetime interval invariance property allows us to, for example, compare the rate of time passing for two observers moving at relative velocities to each other. Although no observer in the universe is at complete rest, the interval is a benchmark for comparison of the physical effects of differences in velocity, or indeed location. Say one observer is close to the event horizon of a black hole, the interval can be used to compare the observations and physical properties measured by another observer, located far from the black hole.

The development of the theory of special relativity forced Einstein, and us, to abandon the notion of an absolute 3 D space or (1 D) absolute time, and instead combine them into a 4 D mathematical framework.

Please check I have the following details right, using almost any relativity book, as I am writing this from memory:)

Initially Einstein had no reason to doubt the conventional wisdom that time would pass at the same rate no matter how fast you traveled at ALL points in the universe, When he realized, helped by his famous thought experiments, that Maxwell's equations implied that the speed of light is the same for all observers, then, in order to preserve invariance, some assumption had to give, and that assumption was the idea that time was absolute (invariant). It was impossible to reconcile the measurements of two observers moving at different velocities without using the mathematics of 4 D spacetime, which combine time and space measurements using Lorentz transformation equations, rather than Galilean transformations.

The best non technical book I have read on this part of Einstein's career is "Einstein's Mistakes" by Hans Ohanian.

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  • $\begingroup$ I like the answer for my first question, but please i need more explained answer for the second $\endgroup$ – Omar Ali May 20 '16 at 3:45
  • $\begingroup$ My remark above regarding location, and black holes, is based more on the general theory of relatively, rather than the special theory. Have a look through wikipedia:en.m.wikipedia.org/wiki/Special_relativity $\endgroup$ – user108787 May 20 '16 at 8:04
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Invariants are useful, in general, because they represent something that all observers can agree upon. Relativity showed us that the concept of time-intervals, spatial-distances, and even sequences of events can be drastically different from different observers. So how can one observer 'relate' to another? I.e. how could I, standing still, figure out what my friend on a relativistic spaceship would observe? I can figure it out using the invariant interval.

Let's imagine an analogy in which an american and a european are tell each other how tall they are via mail. The american says she is 6' tall, and the european says he is 1.8 meters tall. They have no idea how they compare, because they're different units. They need some sort of invariant to relate the two. Luckily, they're sending mail to eachother, so each describes the size of the envelope (8 3/4" and 22.2cm) and now they know how to convert.

The situation is more complicated in relativity, where even the length of a fixed object isn't necessarily invariant. We need to know the full space-time interval of the letter, but once we measure that, now we can translate between reference frames.

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