# Special relativity of a light source moving downstream

• matt_crouch
In summary, the conversation discusses the speed of light through water at rest (Cw) and how it is affected by the speed of water (v) according to one observer. The questions raised are: 1) the speed of light signals in the downstream direction, 2) the speed of light signals in the upstream direction, and 3) what happens to the upstream light signal if v<cw. The concept of relativistic velocity addition is also mentioned.
matt_crouch

## Homework Statement

Let Cw be the speed of light through water at rest. Water is now flowing at speed v parallel to the x-axis according to one observer, and there is also a light source moving with the water at speed v

1) what is the speed at which the light source sends light signals in the downstream direction?
2) what is the speed at which the light source sends light signals in the upstream direction
3) What happens for the upstream light signal, if v<cw?

a. the signal propagates in the positive x direction
b.the signal propagates in the negative x direction
c the signal propagates at zero speed

## The Attempt at a Solution

i don't really know where to start. I was going to use the equation

x=(gamma)(x'-vt')
but since we don't have the time
im not really sure thanks in advance

anyone?

Hint: How do velocities add relativistically?

## 1. What is the principle of special relativity?

The principle of special relativity states that the laws of physics are the same for all observers in uniform motion, regardless of their relative velocities. This means that the laws of physics do not change for objects that are moving at a constant speed.

## 2. How does special relativity apply to a light source moving downstream?

In the special theory of relativity, the speed of light is considered to be constant for all observers, regardless of their relative velocities. This means that the speed of light is the same for a light source moving downstream as it is for a stationary light source.

## 3. What is the concept of time dilation in special relativity?

Time dilation is a phenomenon in special relativity where time appears to pass slower for an object that is moving at high speeds relative to an observer. This means that time is relative and can be different for different observers depending on their relative velocities.

## 4. Can a light source moving downstream exceed the speed of light?

No, according to the principles of special relativity, the speed of light is an absolute maximum speed and cannot be exceeded by any object, including a light source moving downstream. This is because as an object approaches the speed of light, its mass and energy increase infinitely, making it impossible to reach the speed of light.

## 5. How does special relativity impact our understanding of the universe?

Special relativity has had a significant impact on our understanding of the universe, as it has led to the development of new theories and concepts such as time dilation, length contraction, and the equivalence of mass and energy. It has also helped to explain various phenomena, such as the behavior of objects at high speeds and the structure of the universe on a large scale.

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