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Special relativity is the spacetime geometry described by the Minkowksi metric:

$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$

where $c$ is a constant. The Minkowksi metric is the solution to the equations of general relativity when no mass or energy is around to curve spacetime$^1$. All the symmetries you alluded to are encapsulated in the Minkowski metric - indeed all of special relativity is encapsulated in this metric.

Experiment confirms that the Minkowski metric correctly predicts observations i.e. no deviation from it has ever been observed. So our working hypothesis is that the Minkowski metric is the correct description of flat spacetime.

From the metric it's easy to show that $c$ is a velocity and indeed is the maximum possible velocity anything can have. Maxwell's equations also tell us that $c$ is the velocity with which electromagnetic waves propagate. Therefore we conclude that the constant $c$ is the speed of light and therefore that the speed of light is constant.

Any deviation from the predictions of relativity could be evidence that the speed of light isn't constant, and there is no shortage of scientists looking for them. So far no such deviations have been found.

Note that relativity doesn't tell us what the value of $c$ is, only that it is a constant.

To address the specific point in the cited answer:

There are many coordinate systems in which the speed of light is not constant, or even depends on the direction.

For example we can rewrite the Minkowski metric using accelerated coordinates and the result is the Rindler metric:

$$ c^2d\tau^2 = \left(1 + \frac{a}{c^2}x \right)^2 c^2 dt^2 - dx^2 $$

It is very important to emphasise that in this metric $c$ is still a constant, but now it is the local speed of light i.e. the speed any observer will measure if they do a measurement at their location. However if you use the metric to calculate the speed of light as a function of the distance $x$ from the observer you get:

$$ \frac{dx}{dt} = c\,\left(1 + \frac{a}{c^2}x \right) $$

and this speed can be greater or less than $c$ depending on the value of $x$. See my answer to Acceleration and its effect on the speed of light for more on this.

The speed $dx/dt$ is the coordinate velocity of light, and it can differ from $c$ because we have complete freedom to choose our coordinates. However it remains the case that any local measurement of the speed of light by any observer will always return the same value of $c$.

Incidentally, this principle remains true even in curved spacetimes so it is true in general relativity as well as special relativity.

$^1$ strictly speaking the Minkowski metric is only one of several vacuum solutions - the Schwarzschild and Kerr black holes are also vacuum solutions. However it is the only one with zero ADM mass.

Special relativity is the spacetime geometry described by the Minkowksi metric:

$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$

where $c$ is a constant. The Minkowksi metric is the solution to the equations of general relativity when no mass or energy is around to curve spacetime$^1$. All the symmetries you alluded to are encapsulated in the Minkowski metric - indeed all of special relativity is encapsulated in this metric.

Experiment confirms that the Minkowski metric correctly predicts observations i.e. no deviation from it has ever been observed. So our working hypothesis is that the Minkowski metric is the correct description of flat spacetime.

From the metric it's easy to show that $c$ is a velocity and indeed is the maximum possible velocity anything can have. Maxwell's equations also tell us that $c$ is the velocity with which electromagnetic waves propagate. Therefore we conclude that the constant $c$ is the speed of light and therefore that the speed of light is constant.

Any deviation from the predictions of relativity could be evidence that the speed of light isn't constant, and there is no shortage of scientists looking for them. So far no such deviations have been found.

Note that relativity doesn't tell us what the value of $c$ is, only that it is a constant.

To address the specific point in the cited answer:

There are many coordinate systems in which the speed of light is not constant, or even depends on the direction.

For example we can rewrite the Minkowski metric using accelerated coordinates and the result is the Rindler metric:

$$ c^2d\tau^2 = \left(1 + \frac{a}{c^2}x \right)^2 c^2 dt^2 - dx^2 $$

It is very important to emphasise that in this metric $c$ is still a constant, but now it is the local speed of light i.e. the speed any observer will measure if they do a measurement at their location. However if you use the metric to calculate the speed of light as a function of the distance $x$ from the observer you get:

$$ \frac{dx}{dt} = c\,\left(1 + \frac{a}{c^2}x \right) $$

and this speed can be greater or less than $c$ depending on the value of $x$. See my answer to Acceleration and its effect on the speed of light for more on this.

The speed $dx/dt$ is the coordinate velocity of light, and it can differ from $c$ because we have complete freedom to choose our coordinates. However it remains the case that any local measurement of the speed of light by any observer will always return the same value of $c$.

Incidentally, this principle remains true even in curved spacetimes so it is true in general relativity as well as special relativity.

$^1$ strictly speaking the Minkowski metric is only one of several vacuum solutions - the Schwarzschild and Kerr black holes are also vacuum solutions. However it is the only one with zero ADM mass.

Special relativity is the spacetime geometry described by the Minkowksi metric:

$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$

where $c$ is a constant. The Minkowksi metric is the solution to the equations of general relativity when no mass or energy is around to curve spacetime$^1$. All the symmetries you alluded to are encapsulated in the Minkowski metric - indeed all of special relativity is encapsulated in this metric.

Experiment confirms that the Minkowski metric correctly predicts observations i.e. no deviation from it has ever been observed. So our working hypothesis is that the Minkowski metric is the correct description of flat spacetime.

From the metric it's easy to show that $c$ is a velocity and indeed is the maximum possible velocity anything can have. Maxwell's equations also tell us that $c$ is the velocity with which electromagnetic waves propagate. Therefore we conclude that the constant $c$ is the speed of light and therefore that the speed of light is constant.

Any deviation from the predictions of relativity could be evidence that the speed of light isn't constant, and there is no shortage of scientists looking for them. So far no such deviations have been found.

Note that relativity doesn't tell us what the value of $c$ is, only that it is a constant.

To address the specific point in the cited answer:

There are many coordinate systems in which the speed of light is not constant, or even depends on the direction.

For example we can rewrite the Minkowski metric using accelerated coordinates and the result is the Rindler metric:

$$ c^2d\tau^2 = \left(1 + \frac{a}{c^2}x \right) c^2 dt^2 - dx^2 $$

It is very important to emphasise that in this metric $c$ is still a constant, but now it is the local speed of light i.e. the speed any observer will measure if they do a measurement at their location. However if you use the metric to calculate the speed of light as a function of the distance $x$ from the observer you get:

$$ \frac{dx}{dt} = c\,\sqrt{1 + \frac{a}{c^2}x } $$

and this speed can be greater or less than $c$ depending on the value of $x$. See my answer to Acceleration and its effect on the speed of light for more on this.

The speed $dx/dt$ is the coordinate velocity of light, and it can differ from $c$ because we have complete freedom to choose our coordinates. However it remains the case that any local measurement of the speed of light by any observer will always return the same value of $c$.

Incidentally, this principle remains true even in curved spacetimes so it is true in general relativity as well as special relativity.

$^1$ strictly speaking the Minkowski metric is only one of several vacuum solutions - the Schwarzschild and Kerr black holes are also vacuum solutions. However it is the only one with zero ADM mass.

Special relativity is the spacetime geometry described by the Minkowksi metric:

$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$

where $c$ is a constant. The Minkowksi metric is the solution to the equations of general relativity when no mass or energy is around to curve spacetime$^1$. All the symmetries you alluded to are encapsulated in the Minkowski metric - indeed all of special relativity is encapsulated in this metric.

Experiment confirms that the Minkowski metric correctly predicts observations i.e. no deviation from it has ever been observed. So our working hypothesis is that the Minkowski metric is the correct description of flat spacetime.

From the metric it's easy to show that $c$ is a velocity and indeed is the maximum possible velocity anything can have. Maxwell's equations also tell us that $c$ is the velocity with which electromagnetic waves propagate. Therefore we conclude that the constant $c$ is the speed of light and therefore that the speed of light is constant.

Any deviation from the predictions of relativity could be evidence that the speed of light isn't constant, and there is no shortage of scientists looking for them. So far no such deviations have been found.

Note that relativity doesn't tell us what the value of $c$ is, only that it is a constant.

To address the specific point in the cited answer:

There are many coordinate systems in which the speed of light is not constant, or even depends on the direction.

For example we can rewrite the Minkowski metric using accelerated coordinates and the result is the Rindler metric:

$$ c^2d\tau^2 = \left(1 + \frac{a}{c^2}x \right)^2 c^2 dt^2 - dx^2 $$

It is very important to emphasise that in this metric $c$ is still a constant, but now it is the local speed of light i.e. the speed any observer will measure if they do a measurement at their location. However if you use the metric to calculate the speed of light as a function of the distance $x$ from the observer you get:

$$ \frac{dx}{dt} = c\,\left(1 + \frac{a}{c^2}x \right) $$

and this speed can be greater or less than $c$ depending on the value of $x$. See my answer to Acceleration and its effect on the speed of light for more on this.

The speed $dx/dt$ is the coordinate velocity of light, and it can differ from $c$ because we have complete freedom to choose our coordinates. However it remains the case that any local measurement of the speed of light by any observer will always return the same value of $c$.

Incidentally, this principle remains true even in curved spacetimes so it is true in general relativity as well as special relativity.

$^1$ strictly speaking the Minkowski metric is only one of several vacuum solutions - the Schwarzschild and Kerr black holes are also vacuum solutions. However it is the only one with zero ADM mass.

Special relativity is the spacetime geometry described by the Minkowksi metric:

$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$

where $c$ is a constant. The Minkowksi metric is the solution to the equations of general relativity when no mass or energy is around to curve spacetime$^1$. All the symmetries you alluded to are encapsulated in the Minkowski metric - indeed all of special relativity is encapsulated in this metric.

Experiment confirms that the Minkowski metric correctly predicts observations i.e. no deviation from it has ever been observed. So our working hypothesis is that the Minkowski metric is the correct description of flat spacetime.

From the metric it's easy to show that $c$ is a velocity and indeed is the maximum possible velocity anything can have. Maxwell's equations also tell us that $c$ is the velocity with which electromagnetic waves propagate. Therefore we conclude that the constant $c$ is the speed of light and therefore that the speed of light is constant.

Any deviation from the predictions of relativity could be evidence that the speed of light isn't constant, and there is no shortage of scientists looking for them. So far no such deviations have been found.

Note that relativity doesn't tell us what the value of $c$ is, only that it is a constant.

$^1$ strictly speaking the Minkowski metric is only one of several vacuum solutions - the Schwarzschild and Kerr black holes are also vacuum solutions. However it is the only one with zero ADM mass.

Special relativity is the spacetime geometry described by the Minkowksi metric:

$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$

where $c$ is a constant. The Minkowksi metric is the solution to the equations of general relativity when no mass or energy is around to curve spacetime$^1$. All the symmetries you alluded to are encapsulated in the Minkowski metric - indeed all of special relativity is encapsulated in this metric.

Experiment confirms that the Minkowski metric correctly predicts observations i.e. no deviation from it has ever been observed. So our working hypothesis is that the Minkowski metric is the correct description of flat spacetime.

From the metric it's easy to show that $c$ is a velocity and indeed is the maximum possible velocity anything can have. Maxwell's equations also tell us that $c$ is the velocity with which electromagnetic waves propagate. Therefore we conclude that the constant $c$ is the speed of light and therefore that the speed of light is constant.

Any deviation from the predictions of relativity could be evidence that the speed of light isn't constant, and there is no shortage of scientists looking for them. So far no such deviations have been found.

Note that relativity doesn't tell us what the value of $c$ is, only that it is a constant.

To address the specific point in the cited answer:

There are many coordinate systems in which the speed of light is not constant, or even depends on the direction.

For example we can rewrite the Minkowski metric using accelerated coordinates and the result is the Rindler metric:

$$ c^2d\tau^2 = \left(1 + \frac{a}{c^2}x \right) c^2 dt^2 - dx^2 $$

It is very important to emphasise that in this metric $c$ is still a constant, but now it is the local speed of light i.e. the speed any observer will measure if they do a measurement at their location. However if you use the metric to calculate the speed of light as a function of the distance $x$ from the observer you get:

$$ \frac{dx}{dt} = c\,\sqrt{1 + \frac{a}{c^2}x } $$

and this speed can be greater or less than $c$ depending on the value of $x$. See my answer to Acceleration and its effect on the speed of light for more on this.

The speed $dx/dt$ is the coordinate velocity of light, and it can differ from $c$ because we have complete freedom to choose our coordinates. However it remains the case that any local measurement of the speed of light by any observer will always return the same value of $c$.

Incidentally, this principle remains true even in curved spacetimes so it is true in general relativity as well as special relativity.

$^1$ strictly speaking the Minkowski metric is only one of several vacuum solutions - the Schwarzschild and Kerr black holes are also vacuum solutions. However it is the only one with zero ADM mass.