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What is the dimension of the spacetime interval? 
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#1
May706, 02:26 AM

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Just what the title says. In the book Spacetime Physics, by Taylor and Wheeler, the time coordinate is measured in metres of lighttravel time, but that's just a roundabout way of saying that they are using the second...or am I missing the point.



#2
May706, 04:59 AM

P: 2,047

Ok...it took me sometime to realise that [itex]ds^2 = c^2dt^2  dx^2  dy^2  dz^2[/itex] that has the dimensions of length . But now another question came up...why length? Isn't spacetime a a union of space and time. Even if we divide the whole expression by [itex]c^2[/itex], we get a dimension of time only.



#3
May706, 05:50 AM

Mentor
P: 6,232

Most relativity books use the former, but I have seen the latter used. In cosmology the latter is often used, i.e., (light)years and years. Regards, George 


#4
May706, 10:26 AM

P: 2,047

What is the dimension of the spacetime interval?



#5
May706, 07:37 PM

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PF Gold
P: 4,119

Similarly, the quantity that "unifies" momentum and energy has the dimensions of "momentum/energy". 


#6
May806, 02:34 AM

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#7
May806, 03:54 AM

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P: 1,892

Isn´t "Spacetime Physics" exactly the book where they start with the example of length in northern direction has different units than lenght eastwards, despite both describe the same thing?



#8
May806, 08:36 AM

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#9
May806, 08:44 AM

Mentor
P: 6,232

I recommend also "A Traveler's Guide to Spacetime: An Introduction to Special Relativity, which is the book from which I lifted the accelerometer that I used in the "A falling object" thread. Regards, George 


#10
May806, 09:28 AM

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http://www.physics.pomona.edu/facult.../tgerrors.html http://www.physics.pomona.edu/sixideas/sicpr.html (see "unit R") 


#11
May806, 09:43 AM

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P: 1,892

Yes, the book is a good one (maybe pete would disagree see #20 and #22).
And their point is: c is simply an arbitrary conversion factor from time units to length units. "meter" and "second" are two units where you need only one. Comparable with inches and meters. Two units for the same thing. The difference between time and space is then not the units, but the metric (1 1 1 1 instead of 1 1 1 1). 


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