What is the dimension of the spacetime interval?


by neutrino
Tags: dimension, interval, spacetime
neutrino
neutrino is offline
#1
May7-06, 02:26 AM
P: 2,048
Just what the title says. In the book Spacetime Physics, by Taylor and Wheeler, the time coordinate is measured in metres of light-travel time, but that's just a roundabout way of saying that they are using the second...or am I missing the point.
Phys.Org News Partner Science news on Phys.org
Review: With Galaxy S5, Samsung proves less can be more
Making graphene in your kitchen
Study casts doubt on climate benefit of biofuels from corn residue
neutrino
neutrino is offline
#2
May7-06, 04:59 AM
P: 2,048
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.
George Jones
George Jones is offline
#3
May7-06, 05:50 AM
Mentor
George Jones's Avatar
P: 6,040
Quote Quote by neutrino
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.
Yes. In the first case, everything can be considered to be measured in units of length, e.g., metres, where 1 metre of time is the time taken for light to travel a distance of 1 metre, and, in the second case, everything can be considered to be measured in units of time, e.g., seconds, where 1 second of distance is the distance traveled by light in 1 second of time.

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

neutrino
neutrino is offline
#4
May7-06, 10:26 AM
P: 2,048

What is the dimension of the spacetime interval?


Quote Quote by George Jones
Yes. In the first case, everything can be considered to be measured in units of length, e.g., metres, where 1 metre of time is the time taken for light to travel a distance of 1 metre, and, in the second case, everything can be considered to be measured in units of time, e.g., seconds, where 1 second of distance is the distance traveled by light in 1 second of time.

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.
Yes, I realise that. I'm just wondering why this quantity (dsē), which says something about the unity of space and time does not have a dimension made up of a combination of length and time.
robphy
robphy is offline
#5
May7-06, 07:37 PM
Sci Advisor
HW Helper
PF Gold
robphy's Avatar
P: 4,108
Quote Quote by neutrino
Yes, I realise that. I'm just wondering why this quantity (dsē), which says something about the unity of space and time does not have a dimension made up of a combination of length and time.
The quantity involved in dsē that "unifies" space and time (namely, the speed of light) has the dimensions of "length/time".

Similarly, the quantity that "unifies" momentum and energy has the dimensions of "momentum/energy".
neutrino
neutrino is offline
#6
May8-06, 02:34 AM
P: 2,048
Quote Quote by robphy
The quantity involved in dsē that "unifies" space and time (namely, the speed of light) has the dimensions of "length/time".

Similarly, the quantity that "unifies" momentum and energy has the dimensions of "momentum/energy".
Thanks...now it's all clear.
Ich
Ich is offline
#7
May8-06, 03:54 AM
Sci Advisor
P: 1,883
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?
neutrino
neutrino is offline
#8
May8-06, 08:36 AM
P: 2,048
Quote Quote by Ich
Isnīt "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?
Yes, that's the one. I especially like their spacetime-first approach.
George Jones
George Jones is offline
#9
May8-06, 08:44 AM
Mentor
George Jones's Avatar
P: 6,040
Quote Quote by Ich
Isnīt "Spacetime Physics" ...
This is the book from which I first learned special relativity. Great book.

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
robphy
robphy is offline
#10
May8-06, 09:28 AM
Sci Advisor
HW Helper
PF Gold
robphy's Avatar
P: 4,108
Quote Quote by George Jones
This is the book from which I first learned special relativity. Great book.

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
Here are some useful supplements for Moore's book:
http://www.physics.pomona.edu/facult.../tgerrors.html
http://www.physics.pomona.edu/sixideas/sicpr.html (see "unit R")
Ich
Ich is offline
#11
May8-06, 09:43 AM
Sci Advisor
P: 1,883
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).


Register to reply

Related Discussions
Spacetime interval? Introductory Physics Homework 1
Invariant Spacetime Interval Special & General Relativity 17
spacetime interval of zero Special & General Relativity 15
Simple Question regarding spacetime interval Advanced Physics Homework 2
Spacetime interval formula - what's the d? General Physics 8