The special theory of relativity is the generalization of Gallilian in-variance.
What Galilian invariance says is that, if the frame of observer is not at rest, the location or coordinates of the event observed will differ with actual coordinates by the difference between the velocities of the observer and observed event.
You can consider frame as a container in which events occurs. For Example: If two trains are moving parallel with same velocity, any observer in either of the train will be unable to determine whether his or other train is moving or not without looking at the ground.
Now what special theory of relativity puts is that there is no absolute reference frame, to put it simply there is nothing which is at rest. When things are moving we assume that land is the reference frame, but earth is also moving, solar system is also moving, milky way.. also moving. So there is nothing that is can be used as a frame of reference for all of the events.
Second special theory of relativity puts that speed of light remains same to all observers irrespective of the velocity of source of light.
So this is what we can use to calculate the event in different moving frames.
To understand the theorem let us suppose two frames having the respective velocity of v in x direction. The first frame is K and second frame is K'. The coordinates of any event in K are x, y,z,t. Here x ,t, z are the space dimensions and t is time dimension. Similarly the coordinates of any event in K' are given by the variables x', y', z', t' .
What Galilian invariance says is that, if the frame of observer is not at rest, the location or coordinates of the event observed will differ with actual coordinates by the difference between the velocities of the observer and observed event.
You can consider frame as a container in which events occurs. For Example: If two trains are moving parallel with same velocity, any observer in either of the train will be unable to determine whether his or other train is moving or not without looking at the ground.
Now what special theory of relativity puts is that there is no absolute reference frame, to put it simply there is nothing which is at rest. When things are moving we assume that land is the reference frame, but earth is also moving, solar system is also moving, milky way.. also moving. So there is nothing that is can be used as a frame of reference for all of the events.
Second special theory of relativity puts that speed of light remains same to all observers irrespective of the velocity of source of light.
So this is what we can use to calculate the event in different moving frames.
To understand the theorem let us suppose two frames having the respective velocity of v in x direction. The first frame is K and second frame is K'. The coordinates of any event in K are x, y,z,t. Here x ,t, z are the space dimensions and t is time dimension. Similarly the coordinates of any event in K' are given by the variables x', y', z', t' .
Now given the values of coordinates of an event occurred in K what will be the values of x', y', z', t' for that event. This will be :
y' = y
z' = z
These equations are known as Lorentz Transformation. If you place the value of speed of light as infinite you will find the Galilean Transform.
x' = x - vt
y' = y
z' = z
t' = t
Galilean Transform means in very simple terms that the information of the event happening in K frame does not take any time to reach frame K', while it takes some time.
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