Unravelling Metrics of Spacetime

  • Context: Graduate 
  • Thread starter Thread starter alejandrito29
  • Start date Start date
  • Tags Tags
    Spacetime
Click For Summary

Discussion Overview

The discussion revolves around the interpretation of time units in a spacetime metric expressed as ds²=f(t)(-dt²+dx²+dy²+dz²). Participants explore the dimensional consistency of time with spatial dimensions and the implications of different unit systems.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions the unit of time t in the given metric, asking if it is measured in seconds or "meters of time."
  • Another participant asserts that for dimensional consistency, the unit of time must match the units of spatial dimensions (dx, dy, dz).
  • A follow-up response reiterates that if spatial dimensions are in meters, then time t would also be in "meters of time."
  • One participant references a geometrized unit system to support their point about time units.
  • Another participant elaborates that a "meter of time" can be defined as the time it takes for light to travel one meter, equating it to (1/299792458) seconds, and suggests that spatial dimensions could also be measured in light-seconds, making dt in seconds.
  • It is noted that a factor of c² should be included before dt² to convert time into distance units, but in relativistic units where c=1, this factor is omitted.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of time units in relation to spatial dimensions, with no consensus reached on the terminology or implications of "meters of time."

Contextual Notes

The discussion highlights the dependence on unit definitions and the implications of using different unit systems, but does not resolve the underlying assumptions or mathematical steps involved.

alejandrito29
Messages
148
Reaction score
0
In a space time with metrics :
[tex]ds^2=f(t)(-dt^2+dx^2+dy^2+dz^2)[/tex]

which is the unit that measures time t?

second?, meter of time?
 
Physics news on Phys.org
For dimensional consistency it would have to be the same units that dx, dy, and dz are measured in.
 
DaleSpam said:
For dimensional consistency it would have to be the same units that dx, dy, and dz are measured in.

then , if dx,dy and dz are in meters, then t is in meters of time?
 
alejandrito29 said:
then , if dx,dy and dz are in meters, then t is in meters of time?
A "metre of time" is the time it takes for light to travel one metre, i.e. (1/299792458) seconds.

Or you could measure dx, dy and dz in light-seconds and then dt is in seconds.
 
to be explicit, a c^2 should appear before dt^2 to explicitly convert time into units of distance. But, in relativistic units c=1 so we just omit the c and it's understood.
 

Similar threads

Graduate Spacetime interval in Galilean relativity
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Minimal property of Spacelike geodesics in GR/curved spacetime?
  • · Replies 76 ·
3
Replies
76
Views
4K
High School Sign of Expansion Scalar in Expanding FLRW Universe
  • · Replies 35 ·
2
Replies
35
Views
4K
Graduate Solving Geodesics with Metric $$ds^2$$
  • · Replies 10 ·
Replies
10
Views
3K
High School How to Add Metres & Seconds for Equal ds2: Einstein's Theory
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad On the physical meaning of Minkowski's spacetime model
  • · Replies 40 ·
2
Replies
40
Views
3K
Undergrad Einstein Definition of Simultaneity for Langevin Observers
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Characterizing GR Traj in Minkowski Space
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad A question about static spacetime in GR
  • · Replies 10 ·
Replies
10
Views
2K
Graduate B and A in Curved Space Time: Does \nabla \times A =B?
  • · Replies 3 ·
Replies
3
Views
2K