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# 物理代写|广义相对论代写General Relativity代考|PHY-568 Relativistic Units

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## 物理代写|广义相对论代写General Relativity代考|Relativistic Units

Relativistic Units. Because the speed of light $c$ is frame-independent, we can connect space and time units in a frame-independent way. The nearly universal convention in general relativity is to express both distance and time in units of meters (rather than in seconds), where we define a meter of time to be the time it takes light to travel a meter of distance. Since light travels $299,792,458 \mathrm{~m}$ in $1 \mathrm{~s}$ (by definition of the SI meter), a meter of time is $1 / 299,792,458 \mathrm{~s}=3.34 \mathrm{~ns}$.

Light moves at a speed of $1 \mathrm{~m} / \mathrm{m}=1$ by definition in this unit system, so all other velocities are expressed as unitless fractions of the speed of light. This implies that mass $m$, momentum (which must have the same units as $m v$ ), and energy (which must have the same units as $\frac{1}{2} m v^2$ ) all have the same units. For macroscopic objects, I will use the SI kilogram as the common unit for these quantities, but for microscopic objects (molecules and smaller), I will use the electron volt (eV).

Let us call the unit system where time and distance are measured in meters and mass, momentum, and energy are measured in kilograms the GR (General Relativistic) unit system. See box $2.2$ for conversion factors between SI and GR units.

## 物理代写|广义相对论代写General Relativity代考|Clock Synchronization

Clock Synchronization. If the time coordinates assigned by the clocks in a reference frame of the type shown in figure $2.1$ are to have any coherent meaning, the clocks must be synchronized. Since the speed of light $c=1 \mathrm{~m} / \mathrm{m}=1$ must have the same value in all IRFs (as argued a few paragraphs back), these clocks will be synchronized if and only if an observer concludes that the speed of a light flash traveling between any pair of clocks is 1. This means that if a master clock emits a light flash at time $t$, a clock a distance $d$ from the master will be correctly synchronized with it if it reads time $t+d$ when a signal passes. This provides a straightforward method for synchronizing the clocks in an inertial frame.
(Note that this method does not work in NIRFs, so we will have to use a different approach to assigning events coherent time coordinates in general relativity.)

## 物理代写|广义相对论代写广义相对论代考|时钟同步

(注意这个方法在nirf中不起作用，所以我们将不得不使用不同的方法来分配广义相对论中的事件相干时间坐标。

## MATLAB代写

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