Can A point reference frame detect the nature of Wave?

[dkv]

For classical physics this problem is not new. How many points are needed to define a reference frame? One or two or three or few ?

Suppose a point p lies in space. A wave reaches to it.

A point can interact with only a point. A point can be vector i.e it can give the direction of wave but can the point find out the radius of curvature of the Wave ?

In order to determine the Radius of Curvature it must be able to solve the second order differential equation.

[Erasmus00]

For classical physics this problem is not new. How many points are needed to define a reference frame? One or two or three or few ?

Suppose a point p lies in space. A wave reaches to it.

 

This is a ridiculous question- you can't have a point reference frame. A reference frame is a coordinate system, not a coordinate.

-Will

[dkv]

I agree that a point is not coordinate system but reference frames are real. They have properties like relative velocity , relative distance , relative time and acceleration.. My question is how many points are necessary to define a reference frame ? Does it really exist ? Or it exists in a mathematical space ?

When two point masses move relative to each other then how do we define the reference frame ?

[dkv]

In order to define a reference frame the physical entity must be capable of carrying a clock , must have at three points on it to ascertain the radius of curvature of a wave.

With distance the magnitude of Field Vectors decreases or increases... but I think not only the magnitude but the direction also changes.

 

For example if a ball of mass m is kept at an infinite distance from mass M then the ball simply doesnt know about the existence of M... As the distance between m and M reduces it gains vector and magnitude which is not as precise as given by the Newtons formula.. only at a small distance it becomes possible to define the forumla F=GMm/r^2 .. At large distances the magnitude and directions vary.

 

Why this should happen?

Because the radius of curvature of field becomes directionless at large distance...

And the magnitude falls exponentially.

Why the field should become directionless ?

Becuase there is a residual gravitational field which has been omnipresent since the time of big bang.

Evidence ?

Universe is filled with Neutrinos just like the CMB.

 

Therefore with distance the Gravitational interactions do not remain vectorial.

[Boerseun]

A "point" is a perfectly valid reference frame - in 1-dimensional space. A wave, however, lives in 3-dimensional space, and is therefore invisible in 1-d space. It's like trying to visualise a 4-dimensional hypercube using 3-dimensional imagery. :shrug:

[dkv]

This is serious problem in GR which tries to define the Equivalence Principle.

Inspite of the new interpretation I remain unconvinced because it fails to define the frame of reference.

[Erasmus00]

This is serious problem in GR which tries to define the Equivalence Principle.

Inspite of the new interpretation I remain unconvinced because it fails to define the frame of reference.

 

The "gravity is indistinguishable from acceleration" equivalence principle is nicely intuitive, but isn't mathematically rigorous.

 

First, GR is all about describing things in a coordinate free geometric way- we avoid using coordinate systems wherever possible and stick to objects independent of a frame of reference.

 

Hence, we need to recast the equivalence principle in terms of geometric objects, in this case the Riemann curvature tensor. The more "mathy" way of stating the equivalence principle is that the Riemann tensor is locally flat. i.e. in the limit that the size of the patch of space we are considering tends to 0, the curvature also tends to 0.

-Will

[dkv]

What is a reference frame ?

[Erasmus00]

What is a reference frame ?

 

A system of coordinates covering some non-trivial region of spacetime. Also, I showed you how to recast the equivalence principle in a manner that doesn't require reference frames at all.

-Will