Can anyone explain the relationship between t²-x² in relativity theory?

[Merkur]

Hallo!

At the beginning of my first thread I'd like to introduce myself

I'm Alexander and I live in Bavaria ... because of this my English sometimes is really bad ... But I hope you all can understand me...
And my hobbies are: Basketball, Latin (or in general: languages), Uncycling ...
If somebody of you needs help with Latin - or German, of course - I will perhaps be able to help him/her


But let's talk about my problem:

I'm reading a book about the relativity theory (Sorry ... I don't know what's the correct English word - in German it's "Relativitätstheorie" ) . The author says that everything (i.e. the time and the space) is distorted only to keep difference t²-x² constant. But I don't understand why ...
The book says that t = g-faktor and things like that ...
I don't understand this.

I would be very very very very very ... grateful for help and I hope that you have understood the sense of my question at least (because of my mistakes of course )


Thank you and good night ...

 

[Merkur]

Thank you very much for your explanations ...


Now I understand ... So I must imagine of a "ball", whose middle is the origin. And the term t²-x² is actual "accidental".

But you can find a very nice derivation of it in Schutz's book A First Course in General Relativity, if you know some matrix algebra.

Thank you for this clou ... but I think I begin with German books ... ... and I must learn the basics of maths and physics in the beginning, I think (I've been learning since 2 years physics at school, so we haven't even been tractating the terminus "energy" )

By the way: What's matrix algebra? (I know ...Sometimes I'm asking dumb questions ... )

 

[quartodeciman]

Your book sounds bad. Nothing is "distorted" in relativity theory. Everything preserves the unvarying value of lightspeed just as light would travel through space uninterrupted.

I think it is a mistake for an elementary book to teach relativity theory without the letter 'c' for lightspeed. Physicists like it set to value '1' for computational purposes, but they already understand what it means. When 'c' is set to value 1 (light-seconds per second), then one is apt to forget that there is a speed and to assume space² and time² are being combined. The second term of the expression is really a space term, (ct)², which is the square of the product of a speed and a time, and that yields a space term squared. My second objection is that complex computations with 'c' set to 1 leave the responsibility of reinserting the actual value wherever needed at the end of the computation. This requires much experience.

Sind Sie Münchener?

 

[Merkur]

Originally posted by quartodeciman
Your book sounds bad. Nothing is "distorted" in relativity theory. Everything preserves the unvarying value of lightspeed just as light would travel through space uninterrupted.

O.K. ... you mustn't listen to each words of mine because I don't know how to express all those things in English ... but I hope I will get better ...

Sind Sie Münchener? [/B]

No ... When you open the Atlas, you will find the village I live in there, where the Danube crosses the Bavarian frontier (near Passau)

Ciao!