<p>First, imagine that you're in an inertial reference frame. We can think of this as a sort of lattice throughout space, with a synchronized clock at each lattice point in space. Now imagine two events, $A$ and $B$, which occur at space-time coordinates $(t_A, x_A, y_A, z_A)$ and $(t_B, x_B, y_B, z_B)$. The reference frame has (again, synchronized) clocks at $(x_A, y_A, z_A)$ and $(x_B, y_B, z_B)$. The <a href="https://en.wikipedia.org/wiki/Coordinate_time" rel="nofollow"><em>coordinate time</em></a> $\Delta t_{AB}$ is the difference in time measured by the clock at $B$ and the clock at $A$, so that $\Delta t_{AB}=t_B-t_A$. If $\Delta t_{AB}=0$, the events are <em>simultaneous</em> in that reference frame. However, an observer in a different inertial frame (say, in one with a boost $\vec{\beta}$ in the $x$-direction) might measure a different $\Delta t_{AB}$. This means that coordinate time is <em>frame-dependent</em> - it depends on the reference frame you're in.</p>

<p><a href="https://en.wikipedia.org/wiki/Proper_time" rel="nofollow"><em>Proper time</em></a> is sometimes called "wristwatch time". Now, there's a single clock, and it measures the time between two events $A$ and $B$ on a single worldline. This proper time $\tau_{AB}$ does <em>not</em> depend on your reference frame, but it does depend on the path you take from $A$ to $B$ - that is, it's <em>path-dependent</em>.</p>

<p>One way to think of the difference is that coordinate time tells you something about one reference frame relative to another (because it's frame-dependent), while proper time tells you something about the worldline of the observer (because it's path dependent).</p>

CC BY-SA 3.0
2016-09-06T17:37:44.033Z
2016-09-06T18:34:20.047Z
2016-09-06T18:34:20.047Z
HDE 226868
<p>The meaning of the $t$ which appears in space-time intervals or metrics in general relativity. I concluded that $t$ was just a mathematical thing which allows us to label the "space-time manifold" and only proper time τ had a physical meaning too. On Wikipedia I also found that the coordinate time is not a time that could be measured by a clock located at the place that nominally defines the reference frame. What does it really mean?</p>

CC BY-SA 3.0
2016-09-06T14:45:26.667Z
I think your question could be helped by being a bit more clear about what you're asking and providing links to sources.
zephyr
<space-time><coordinate><time-dilation>
What does the coordinate of time really mean?
Darth Ewok
# What does the coordinate of time really mean?

(Asked by: username_0 on 2016-09-06)

The meaning of the $t$ which appears in space-time intervals or metrics in general relativity. I concluded that $t$ was just a mathematical thing which allows us to label the "space-time manifold" and only proper time τ had a physical meaning too. On Wikipedia I also found that the coordinate time is not a time that could be measured by a clock located at the place that nominally defines the reference frame. What does it really mean?

**Tags:** space-time, coordinate, time-dilation
> **Comments:**
> **username_1**: I think your question could be helped by being a bit more clear about what you're asking and providing links to sources.  

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## 1 answers

### Answer by username_2 on 2016-09-06. Score: 2

First, imagine that you're in an inertial reference frame. We can think of this as a sort of lattice throughout space, with a synchronized clock at each lattice point in space. Now imagine two events, $A$ and $B$, which occur at space-time coordinates $(t\_A, x\_A, y\_A, z\_A)$ and $(t\_B, x\_B, y\_B, z\_B)$. The reference frame has (again, synchronized) clocks at $(x\_A, y\_A, z\_A)$ and $(x\_B, y\_B, z\_B)$. The [*coordinate time*](https://en.wikipedia.org/wiki/Coordinate_time) $\Delta t\_{AB}$ is the difference in time measured by the clock at $B$ and the clock at $A$, so that $\Delta t\_{AB}=t\_B-t\_A$. If $\Delta t\_{AB}=0$, the events are *simultaneous* in that reference frame. However, an observer in a different inertial frame (say, in one with a boost $\vec{\beta}$ in the $x$-direction) might measure a different $\Delta t\_{AB}$. This means that coordinate time is *frame-dependent* - it depends on the reference frame you're in.

[*Proper time*](https://en.wikipedia.org/wiki/Proper_time) is sometimes called "wristwatch time". Now, there's a single clock, and it measures the time between two events $A$ and $B$ on a single worldline. This proper time $\tau\_{AB}$ does *not* depend on your reference frame, but it does depend on the path you take from $A$ to $B$ - that is, it's *path-dependent*.

One way to think of the difference is that coordinate time tells you something about one reference frame relative to another (because it's frame-dependent), while proper time tells you something about the worldline of the observer (because it's path dependent).


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