336 reputation
212
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location Kolkata,India[91-33-25514464]
age
visits member for 2 years, 10 months
seen Mar 27 '13 at 12:06

Author/Teacher from India. Interested in General Relativity and other areas of physics


Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
Jan
27
revised The Black Hole Problem
rolled back to a previous revision
Jan
27
revised The Particle-Antiparticle Problem in Relation to Special Relativity
rolled back to a previous revision
Jan
27
awarded  Cleanup
Jan
27
revised A Paradox in Special Relativity
rolled back to a previous revision
Jan
27
revised A Paradox in Special Relativity
deleted 2 characters in body
Dec
4
comment Can Parallel Transport always move a Vector Parallel to Itself?
You are not allowed to rotate the tangent planes wrt each other-----they are fixed on the curved surface at the two points concerned.
Dec
4
asked Can Parallel Transport always move a Vector Parallel to Itself?
Dec
4
comment On Parallel Transport
Does "parallel transport" move a vector parallel to itself on a curved surface even in the infinitesimal sense? You may think of two adjacent tangent planes on a curved surface.Is it always possible to have parallel vectors at the points of contact(one vector being preassigned) even if the planes are awkwardly inclined?
Dec
4
comment On Parallel Transport
At the point N'(referring to the original posting)you may consider a second vector tangent to the latitude-line at N'. If it(2nd vector) is parallel transported along the latitude to the point N" on the meridian NB, it is no more a tangent wrt to the latitude at N". The angle this vector makes with the tangent at N" should be equal to the angle which the first vector(moved up from the equator) makes with the meridian at N". This angle is expected to be small
Dec
3
awarded  Quorum
Dec
3
comment On Parallel Transport
Points to Observe:(1)The vector after going through a loop[by parallel transport] rotates by a negligible small angle though the enclosed area is large. You will find this in the example I have referred to in the comment after the question after Lubos Moti's comment.(2)An infinitesimally small area is not sufficient to warrant a flat space-time.The Christoffel symbols are point functions. They have non-zero value for curved spacetime.
Dec
3
comment On Parallel Transport
I am referring to the change between the initial and the final positions of the vector when it goes round a loop on a curved surface(by parallel transport). You may connect the point N'(in the original posting) with some point on the meridian NB by a $small{\;\;}$ curve so that the transported vector on landing on the meridian becomes tangential parallel or nearly tangential to the meridian NB.
Dec
3
comment On Parallel Transport
(in continuation) The above idea is embodied in the non-zero value of the Christoffel tensors in curved space.
Dec
3
comment On Parallel Transport
Let's's consider the vector components $A^\gamma(x^\alpha)$ and $ A^\gamma(x^\alpha+d x^\alpha)$. They have an infinitesimally small separation.This is not indicative of flat space-time over the infinitesimally small spacetime region concerned .Reason:For the purpose of calculating the derivative we have to parallel transport the vector-component $A(x^\alpha +d x^\alpha)$ to the location $x^\alpha$ and this vector definitely changes its orientation wrt to its initial position even though it has moved through an infinitesimally small distance
Dec
2
comment On Parallel Transport
You may consider a small curved line from N' to the meridian NB so that the vector becomes parallel to the meridian NB on reaching it. At A there is no turning all due to the exclusion of a small area.
Dec
2
comment On Parallel Transport
Quoting Ron Maimon:"It ends up in nearly exactly the same direction as it was when you start the parallel transport"---in such a situation if you move back to A the vector does not turn by alpha. It turns by a much smaller amount! On removing the triangle the vector in the initial and the final situation (at A) make a very small angle. If the triangle is there it turns by 90 degrees after looping round
Dec
2
comment On Parallel Transport
Only if you consider a geodesic the an infinitesimally think space round it and parallel to it is nearly flat--the tangent vector propagates parallel to itself
Dec
2
awarded  Caucus