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Space-Time Intervals

MasturDbtor
Posts: 45
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7/20/2014 2:59:45 AM
Posted: 2 years ago
http://www.physics.fsu.edu...

There are quite a few gaps in their explanations.

For one thing they say

What about the proper time of observers who are moving relative to the coordinate system? How do we compute their proper times? Let's start with the formula for the space-time interval

(a) ds2 = -(cdt)2 + dl2

And then say:

After a little bit of algebra we get
dt = |ds2|1/2/c = dt[1 - (v/c)2]1/2.

The following
dt = |ds2|1/2/c

is the expression for the proper time difference not only for observers at rest in the coordinate system but for all observers, however they move,

provided that they move only along time-like world-lines.

How did they get from one equation to the next? What is the "little bit of algebra?"
Floid
Posts: 751
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7/22/2014 9:04:09 AM
Posted: 2 years ago
At 7/20/2014 2:59:45 AM, MasturDbtor wrote:
http://www.physics.fsu.edu...

There are quite a few gaps in their explanations.

For one thing they say

What about the proper time of observers who are moving relative to the coordinate system? How do we compute their proper times? Let's start with the formula for the space-time interval

(a) ds2 = -(cdt)2 + dl2

And then say:

After a little bit of algebra we get
dt = |ds2|1/2/c = dt[1 - (v/c)2]1/2.

The following
dt = |ds2|1/2/c

is the expression for the proper time difference not only for observers at rest in the coordinate system but for all observers, however they move,

provided that they move only along time-like world-lines.

How did they get from one equation to the next? What is the "little bit of algebra?"

I guess it would be called "isolation of variables" or something. You pick the variable you want to solve for and perform operations to isolate it on one side of the equation. So if that variable is multiplied by something you divide both sides by it, if it is squared you take the square root of both sides, etc.
MasturDbtor
Posts: 45
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7/23/2014 12:33:03 AM
Posted: 2 years ago
That still doesn't answer much of anything. For one thing the page does not say anything about why they suddenly use "Delta tau".

This is one of those "did not specify terms" thing. I get math, I'd understand this fine if the terms were actually specified but they leave a number of terms unspecified.

Is "delta tau" about time? And how so?
Floid
Posts: 751
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7/23/2014 7:21:56 AM
Posted: 2 years ago
At 7/23/2014 12:33:03 AM, MasturDbtor wrote:
That still doesn't answer much of anything. For one thing the page does not say anything about why they suddenly use "Delta tau".

This is one of those "did not specify terms" thing. I get math, I'd understand this fine if the terms were actually specified but they leave a number of terms unspecified.

Is "delta tau" about time? And how so?

Besides the fact that dt (difference in time), dl (difference in distance), c (speed of light) are common notations in science and engineering it looks to me like they explicitly define every term:

" the distance between two points in space, dl"
"The space-time interval ds"
"dt is the difference between the time labels at the two nearby events. "
MasturDbtor
Posts: 45
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7/23/2014 5:10:04 PM
Posted: 2 years ago
OK I just noticed that when I copied and pasted it turned tau into a regular t.

And I also noticed that it explains "delta-tau" at the bottom of the page below the equation that starts with delta-tau.