You are here:
Home Jack Sarfatti's Blog Physical Meaning of Gauge Invariance in Gravity and EM-WEAK-STRONG Interactions Part 3

Jack Sarfatti NOW FOR THE REAL PHYSICAL MEANING OF THE LEVI-CIVITA THEOREM THAT THE DIFFERENCE IN TWO LC CONNECTIONS IS A TENSOR

THAT TENSOR IS THE PROPER ACCELERATION OF THE LOCAL NON-INERTIAL FRAME.

On 1/8/2014 9:55 PM, Jacob Sarfatti wrote:

Its physical significance is pretty simple:

The non-tensor inhomogeneous term in the transformation of the Christoffel symbol connection field is the change in proper acceleration of the lnif.

Sent from my iPad

More precisely,

What I meant was that the XdX inhomogeneous term in the GCT gauge transformation LNIF -> LNIF' CANCELS OUT in the computation of the proper acceleration of the LNIF detector, which by definition is a property of its REST FRAME, i.e. the reading of the accelerometer clamped to its center of mass. We are here talking about the local rest frame of the detector not that of the test particle the detector is monitoring.

It's this cancellation of the two equal and opposite XdX terms in the respective rest frames of the detectors that maintains the tensor property of the proper accelerations of the two coincident LNIF/LNIF' connected by GCT X.

GCT X is a an element of the local translational gauge group T4(x).

So in EM we have

A -> A' = A + (hc/e)dS

this keeps

P = mV + (e/c)A gauge invariant.

mV -> mV' = mV + hdS

S = quantum phase of wave function of test particle with inertia m and with charge e.

(e/c)A -> (e/c)A' = (e/c)A - hdS

hdS is the momentum carried by a longitudinally polarized virtual photon that is the CONTACT electrical force in quantum field theory.

dP/dt = 0 is ACTION-REACTION principle between electric charge and coincident EM field.

dP/dt = 0 is the real force law

mdV/dt = eE

since E ~ (1/c)dA/dt

Now for gravity, we focus on the proper acceleration of the detector (a rest frame property of the detector) not the test particle.

The GCT X induces an XdX kinetic acceleration term which is canceled by the equal and opposite XdX term in the LC transformation.

This keeps the tensor property intact for

DV^i(LNIF)/ds = {LNIF}^i00

in every rest frame

i.e.

DV^i'(LNIF')/ds = {LNIF}^i'0'0'

The LC connection in flat spacetime is exactly like the LC connection in curved spacetime.

Flat spacetime is simply an unstable solution of Einstein's field equations.

Mathematically the LC connection has zero self curl in flat spacetime. The self curl of the LC connection is the curvature tensor.

The LC connection is not zero in flat spacetime in non-inertial frames.

The inhomogeneous term is the change in proper acceleration of the frame.

Symbolically X = GCT which physically is the transformation between two COINCIDENT LNIFs each with proper acceleration encoded in their corresponding LCs.

LC --> LC' = XXXLC + XdX

I must have the patience of a saint.

More accurately of a demon!

The proper acceleration of the test particle is the tensor

DV(test particle)/ds = dV(test particle)/ds - LC(LNIF)V(test particle)V(test particle)

The proper acceleration of the LNIF in its rest frame is

DV(LNIF)/ds = dV(LNIF)/ds - LC(LNIF)V(LNIF)V(LNIF)

but in the rest frame, for the 3-vector parts

V(LNIF) = 0

dV(LNIF)/ds = 0

Therefore

DV^i(LNIF)/ds = - LC(LNIF)^i00V^0(LNIF)V^0(LNIF)

V^0 = 1 in the REST FRAME always

therefore,

DV^i(LNIF)/ds = - LC(LNIF)^i00

Under the GCT in the REST FRAME of LNIF'

DV^i'(LNIF)/ds = - LC(LNIF')^i'0'0'V^0'(LNIF')V^0'(LNIF') = - LC(LNIF')^i'0'0'

Because, just like in the U(1) EM gauge transformations

dV(LNIF)/ds -> dV(LNIF')/ds = dV(LNIF)/ds + XdX

Whilst

- LC(LNIF)^i00 -> - LC(LNIF)^i'0'0 - XdX

Therefore the XdX inhomogeneous terms cancel out for the transformation LNIF -> LNIF' when we calculate the proper acceleration change of the center of mass /origin of the LNIF.

Category: MyBlog

Written by Jack Sarfatti

Published on Thursday, 09 January 2014 13:16

- November 2015(1)
- January 2015(1)
- December 2014(1)
- August 2014(2)
- July 2014(2)
- June 2014(2)
- May 2014(1)
- April 2014(6)
- March 2014(6)
- February 2014(1)
- January 2014(3)
- December 2013(5)
- November 2013(8)
- October 2013(13)
- September 2013(8)
- August 2013(12)
- July 2013(3)
- June 2013(32)
- May 2013(3)
- April 2013(6)
- March 2013(6)
- February 2013(15)
- January 2013(5)
- December 2012(15)
- November 2012(15)
- October 2012(18)
- September 2012(12)
- August 2012(15)
- July 2012(30)
- June 2012(13)
- May 2012(18)
- April 2012(12)
- March 2012(28)
- February 2012(15)
- January 2012(25)
- December 2011(29)
- November 2011(30)
- October 2011(39)
- September 2011(22)
- August 2011(41)
- July 2011(42)
- June 2011(24)
- May 2011(13)
- April 2011(13)
- March 2011(15)
- February 2011(17)
- January 2011(31)
- December 2010(19)
- November 2010(22)
- October 2010(31)
- September 2010(41)
- August 2010(30)
- July 2010(27)
- June 2010(12)
- May 2010(20)
- April 2010(19)
- March 2010(27)
- February 2010(34)