Space/Time Interval

[Profpat]

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

[Graybeard]

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

[neutralino]

The spacetime interval is indeed similar to the pythagorean formula. Suppose we denote the space time interval as ds, then we have [imath]ds^2=-c^2dt^2+dx^2+dy^2+dz^2[/imath], 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 [imath]ds^2=c^2dt^2-dx^2-dy^2-dz^2[/imath], where we have denoted the spatial indices with minus signs, or [imath]ds^2=-dt^2+dx^2+dy^2+dz^2[/imath], 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!

Here are a few links that may help:
http://www.cavendishscience.org/bks/rel/spactime.htm
http://www.physics.fsu.edu/users/Pro...y/Interval.htm
http://scienceworld.wolfram.com/phys...eInterval.html

In fact, it may have been easier for me to introduce this by denoting the spacetime interval as s and then we have [imath]s^2=-c^2t^2+x^2+y^2+z^2[/imath], 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.

[Profpat]

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.

[Profpat]

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

Thanks for the response Greg, but Neutralino hit the topic right on.

I don't think matter ( mass ) is an absolute, however, in that it can expand or contract depending on the velocity.

I would think the speed of light may also be an absolute and therefore perhaps the photon, would be also.

Best to you,

Pat

[Yeltsin]

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...

[Profpat]

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...

Thanks for your input Yeltsin, I appreciate that.

Best,

Pat

[greenbug]

I don’t know if I agree with that. I would say that its on the right path, however..

A measurement is only absolute in its frame of reference. That’s to say if the perspective changes, then so does the measurement.

Lets say you were measuring a second in an area of space A, however the second your measuring is in an area of space B. A^2 + B^2 = C^2… The over all difference would be C, however you would have to do this with every measurement of a second you were to take.. This would leave C different for every case, as the difference of a second wouldn’t be absolute, even if we were to assume space was absolute.

The addition of c^2 (the speed of light) would suggest time is stopped for every instance. However even if time were stopped it could not make up for the difference there currently is. So considering that C is the difference between the two events, you could then use difference to describe an “absolute” measurement between those two events. However like I said every C would be different between any given two sets, and so wouldn’t be an absolute over all.

So...

That is, ds^2 is the same no matter which inertial frame we take measurements in.

Would be wrong to assume.. unless you were only measuring that same set..

[greenbug]

Never mind.. There is a right tool for everything and for some reason my mind is always trying to expand that.. Some things are just sufficient. The spacetime interval works for the reasons its intended..