I've heard that the only absolute is the space time interval. That is, Space is not absolute, nor Time, both being relative, but the interval is absolute. I wonder if one of our mathematicians, or scientist could help me understand this concept.
I believe it's similar to the Pythagorean Theorem, that a^2+B^2=C^2?
Thank you for any help.
Pat
Last edited by Profpat; 11-30-2007 at 09:01 PM.
Reason: removed non working URL
Hmmm ... not really sure what your asking Pat. Do you want a concept for how Spacetime curves ... or a full mathamatical answer?
I would have thought that matter is the only absolute?
cool bananas ... greg
__________________ 'Blondie says I must hate all Brunettes. I'll try, but if I can't ... I'll love them both' ... graffiti on Tavern wall, Pompeii, circa AD 70.
The spacetime interval is indeed similar to the pythagorean formula. Suppose we denote the space time interval as ds, then we have , where c is the speed of light, dt is the time between two events in spacetime, and d(x,y,or z) is the distance between two events in the corresponding spatial dimension. Now, if you go searching around a little, you may find it written in different ways: for example you could see , where we have denoted the spatial indices with minus signs, or , where we are implicitly using units that set c=1 (these are called geometric units). This form is used quite a bit in relativity, since it saves time on writing the constants in, and also avoids using too many minus signs!
In fact, it may have been easier for me to introduce this by denoting the spacetime interval as s and then we have , since this doesn't use the "infinitesimal" notation. But basically, for this purpose, you can think of s and ds as both denoting the "distance" between two events in spacetime.
Please feel free to ask any further questions, and I apologise if I've confused you by my poor explanation!
Edit: Oh, and I should probably add, to really answer your question, yes, you are correct about the distance in spacetime being absolute. That is, ds^2 is the same no matter which inertial frame we take measurements in.
__________________ ~neutralino
If you haven't found something strange during the day, it hasn't been much of a day - John A. Wheeler.
Last edited by neutralino; 11-30-2007 at 09:23 PM.
Reason: answering the question!
Thanks I thought I heard that. Would it be similar to say, we have the x axis we'll say thats space, and the y axis that will be time, now the interval which connects the space and time axis is absolute and it can go up the y axis but there will be less on the x axis, and vice versa?
P.S. I liked the 1st link the best.
Last edited by Profpat; 11-30-2007 at 09:43 PM.
Reason: added PS
I've heard that the only absolute is the space time interval. That is, Space is not absolute, nor Time, both being relative, but the interval is absolute. I wonder if one of our mathematicians, or scientist could help me understand this concept.
I believe it's similar to the Pythagorean Theorem, that a^2+B^2=C^2?
Thank you for any help.
Pat
I take it that an absolute is something that doesn't change. In physics it would be called an invariant, or a symmetry. If you're not just thinking of space and time, there are any number of things that don't change in special relativity. Particle energy is invariant. Total electric charge doesn't change. A closed loop stays closed. An overhand knot stays a knot. The word "Pythagorean" still spells "Pythagorean." The inside of a bottle stays on the inside...
I take it that an absolute is something that doesn't change. In physics it would be called an invariant, or a symmetry. If you're not just thinking of space and time, there are any number of things that don't change in special relativity. Particle energy is invariant. Total electric charge doesn't change. A closed loop stays closed. An overhand knot stays a knot. The word "Pythagorean" still spells "Pythagorean." The inside of a bottle stays on the inside...
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