WHAT IS THE NATURE OF NATURE : HOMOGENEITY OF SPACE AND TIME

                                          

                            UNIFORMNESS OF SPACE AND TIME

Two people were playing with concave and convex mirror named as Dev and Divya 

Divya , " Don't you think if mirror world were real the there were no uniformness in that universe ??"

Dev, " Such a interesting topic to think on ??.... But"

Divya , " But....What 

Dev , " What does uniformness of space means" 

Divya , " Let me explain"

Dev, " Yes , Go ahead , Mam!!! ."

UNIFORMNESS..........

As the name tells uniformness means being uniform.
For Example - Sugar mixed in water is uniform.
                         A car moving with same speed have uniform motion.
                        A Road with no pits can be called as uniform

But what is the uniformness in space

........SPACE AND UNIFORMNESS

We are going to talk about uniformness of space.

What does it uniformness of space mean ?

It means that two point in free space have no difference. Any experiment performed at both place will have exactly same results.No point is space is special, so the same basic laws of physics should govern all of space.If two electrons repel each other with force of about 4 units on earth then by keeping their distance of separation same and you take it to andromeda galaxy the repulsion will be same.

Let us elaborate it.

Let us two observers A and B.
Now we are going to find the relation between the co-ordinates systems of two observers.
Let us consider observer A is at rest.Then for him  if an object moved from point (0,0) to (2,0) and then from there to (4,0) . Then in both the cases 

Displacement Δx = 2 metres

According to space homogeneity law

Any other observer in another frame of reference will see equal displacement in both the cases.
I  mean to say that space will follow linearity relation between the two frame of reference.

Then we can state that

Δx = kΔx'

                                                  where k is constant
                                                             and Δx ' displacement in the frame of B

As this is a linear relation between space co-ordinates this is also known as

"Linearity of Space and Time"

Could you figure out what will happen when if space will not homogenous??

Let me help you out.

Then there will not be linear variation between the space co-ordinates of two frames of references.
 Let say they follow a relation as

kΔx' = Δx2

Then as object moves from (0,0) to (2,0) in frame A . Then it will move

from (0,0) to (4/k , 0) in other frame B.

While when it will move from there to (4,0) in frame A. Then it will move from  (4/k , 0) to (12/k,0)
in frame of B.


This implies space is function of its position in frame B.This not only changes the displacement but will also change the entire physics.

For Examples -

# 1 meter stick in A frame will change it's length in frame B w.r.t. to its position in A's frame.

It will become 3/k m when put between (2,0) and  (1,0)
and will become 5/k m when put between (3,0) and (2,0).

# Electronic repulsion will also vary in B's frame when entire electronic system will  shift.

# Energy conservation law will be violated in B's frame

Same homogeneity law goes for the time too.

Could you figure out what will happen if time was not homogenous ???



THANK GOD !!! WE ARE NOT LEAVING IN AN MIRROR UNIVERSE.

OTHERWISE WE WILL BECOME FATTER AS MOVE IN PARTICULAR DIRECTION .

THANK YOU GOD !! SPACE AND TIME ARE HOMOGENOUS AND ISOTROPIC{same in all direction}......