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# 物理代写|广义相对论代写General Relativity代考|Special relativity and Coulomb’s law

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## 物理代写|广义相对论代写General Relativity代考|Special relativity and Coulomb’s law

A consequence of this discovery is that it makes no sense to say that a force acts at distance instantaneously: when unqualified, ‘instantaneously’ is meaningless.

This may seem to be in contradiction to Coulomb’s law, which states that two charges $e$ and $e^{\prime}$ at a distance $r$ act on each other with a repulsive force
$$F=\frac{e e^{\prime}}{r^2}$$
[Before reading ahead, try to answer the following: how can this law be compatible with special relativity!]

If Coulomb’s law was a universal law, it would contradict special relativity. But it is not a universal law: it is only valid in the static limit in which the charges do not move or move slowly with respect to one another. In this case, they themselves define the reference system where the law holds.

To see why Coulomb’s law does not have universal validity, consider what happens if we rapidly take away one of the two charges. Does the other one immediately cease to feel the electric force?
The answer is, of course, negative, because information does not travel faster than light: for a time $t=r / c$, the remaining charge keeps feeling the force. During this time, a disturbance of the electromagnetic field travels across the space between the charges at the speed of light, and only when it reaches the second charge does the force on it change. Hence, Coulomb’s law is compatible with special relativity only because it is the static, non-relativistic limit of the interactions carried by a field. This is the observation that motivates general relativity.

## 物理代写|广义相对论代写General Relativity代考|Special relativity and Newton’s law

Let us come to gravity. According to Newton’s law, two masses $m$ and $m^{\prime}$ at a distance $r$ act on each other with the attractive force
$$F=G \frac{m m^{\prime}}{r^2}$$
If this was a universal law, it would contradict special relativity. Indeed: what happens if we rapidly move one of the two masses away from the other? Does the other one instantaneously cease to feel the gravitational force? If special relativity is correct, this cannot be, because information does not travel faster than light: for a time $t=r / c$, the remaining mass keeps feeling the force. During this time, a disturbance of a gravitational field must travel across space at the speed of light, and only when it reaches the second mass will the gravitational force on it change. For this to be possible, there should exist a field describing the degrees of freedom of what travels between one mass and the other.

Therefore, special relativity implies that Newton’s law (1.6) is not a universal law: it is a static, non-relativistic limit, valid only when the masses do not move rapidly with respect to each other. Away from this limit, gravity should be described by a field theory, capable of accounting for the finite speed of propagation of the interaction. General relativity is such a field theory. See Figure 1.2.

## 物理代写|广义相对论代写General Relativity代考|Special relativity and Coulomb’s law

$$F=\frac{e e^{\prime}}{r^2}$$
[在继续阅读之前，试着回答以下问题: 这条定律如何与狭义相对论兼容! ]

## 物理代写|广义相对论代写General Relativity代考|Special relativity and Newton’s law

$$F=G \frac{m m^{\prime}}{r^2}$$

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