by **crawler** » Sat Mar 07, 2020 11:13 pm

email from Stephen Crothers to University of Pennsylvania: Regarding the University's propaganda re......

*Where math meets physics.*

https://penntoday.upenn.edu/news/where- ... hvQpwN2WrY

“I think we are ahead of the curve, and I think we’ll stay ahead of the curve.” Pantev

“A physicist comes to us, asks, ‘How do you prove that this is true?’ and we immediately show them it’s false,” says mathematician Ron Donagi.

[Crothers says]...

The evidence says otherwise. Here is a simple counter-example.

Consider Einstein's expanding spherical wave of light (1905). With c = 1 and v = 0.9 the projection of Einstein's spherical wave of light in the x-y plane is a circle with the equation:

x^2 + y^2 = c^2t^2 = t^2

and the Lorentz transformation is (beta = 2.294):

x' = 2.294(x - 0.9t)

t' = 2.294(t - 0.9x)

y' = y

Set t = 1, then

x^2 + y^2 = 1

and the Lorentz transformation is:

x' = 2.294(x - 0.9)

t' = 2.294(1 - 0.9x)

y' = y

Transform the (x,y) points (1,0), (0,1), (-1,0), (0,-1) to get the corresponding (x',y') points and associated times t', thus:

(1,0) gives (x' = 0.229, y' = 0), t' = 0.229

(0,1) gives (x' = -2.065, y' = 1), t' = 2.294

(-1,0) gives (x' = -4.359, y' = 0), t' = 4.359

(0,-1) gives (x' = -2.065, y' = -1), t' = 2.294

The (x',y') points above describe an ellipse, not a circle. Now using the corresponding times t' for each x' confirm that x'^2 + y'^2 = c'^2t'^2 = t'^2 (since c = 1). Thus, the Theorem of Pythagoras is form-invariant under Lorentz transformation, but Einstein's circle is not mapped to a circle, but to an ellipse, hence his spherical wave of light mapped to an ellipsoidal wave of light. So Einstein's argument that x^2+y^2+z^2=c^2t^2 under Lorentz transformation is x'^2+y'^2+z'^2=c^2t'^2 means form-invariance of his spherical wave of light, is false. Therefore his Theory of Relativity is false.

The full analytic proof is here:

Crothers, S.J., Special Relativity and the Lorentz Sphere, Physics Essays, V.33, No.1, p.15, 2020,

http://vixra.org/pdf/1911.0013v2.pdf
Here are two more very simple counter-examples:

Crothers, S.J., Einstein's Pseudotensor - a Meaningless Concoction of Mathematical Symbols,

http://vixra.org/pdf/2001.0499v1.pdf
Crothers, S.J., The Landau-Lifshitz Pseudotensor - Another Meaningless Concoction of Mathematical Symbols,

http://vixra.org/pdf/2001.0531v1.pdf
[u]email from Stephen Crothers to University of Pennsylvania: Regarding the University's propaganda re......

[/u][i][color=#0000FF]Where math meets physics.

https://penntoday.upenn.edu/news/where-math-meets-physics?fbclid=IwAR0BYebB19OpvrHTCMzHdX1YFFhKMPQF9ddniK1Ikhf9bnfoHhvQpwN2WrY

“I think we are ahead of the curve, and I think we’ll stay ahead of the curve.” Pantev

“A physicist comes to us, asks, ‘How do you prove that this is true?’ and we immediately show them it’s false,” says mathematician Ron Donagi.

[/color][/i] [Crothers says]...

The evidence says otherwise. Here is a simple counter-example.

Consider Einstein's expanding spherical wave of light (1905). With c = 1 and v = 0.9 the projection of Einstein's spherical wave of light in the x-y plane is a circle with the equation:

x^2 + y^2 = c^2t^2 = t^2

and the Lorentz transformation is (beta = 2.294):

x' = 2.294(x - 0.9t)

t' = 2.294(t - 0.9x)

y' = y

Set t = 1, then

x^2 + y^2 = 1

and the Lorentz transformation is:

x' = 2.294(x - 0.9)

t' = 2.294(1 - 0.9x)

y' = y

Transform the (x,y) points (1,0), (0,1), (-1,0), (0,-1) to get the corresponding (x',y') points and associated times t', thus:

(1,0) gives (x' = 0.229, y' = 0), t' = 0.229

(0,1) gives (x' = -2.065, y' = 1), t' = 2.294

(-1,0) gives (x' = -4.359, y' = 0), t' = 4.359

(0,-1) gives (x' = -2.065, y' = -1), t' = 2.294

The (x',y') points above describe an ellipse, not a circle. Now using the corresponding times t' for each x' confirm that x'^2 + y'^2 = c'^2t'^2 = t'^2 (since c = 1). Thus, the Theorem of Pythagoras is form-invariant under Lorentz transformation, but Einstein's circle is not mapped to a circle, but to an ellipse, hence his spherical wave of light mapped to an ellipsoidal wave of light. So Einstein's argument that x^2+y^2+z^2=c^2t^2 under Lorentz transformation is x'^2+y'^2+z'^2=c^2t'^2 means form-invariance of his spherical wave of light, is false. Therefore his Theory of Relativity is false.

The full analytic proof is here:

Crothers, S.J., Special Relativity and the Lorentz Sphere, Physics Essays, V.33, No.1, p.15, 2020, http://vixra.org/pdf/1911.0013v2.pdf

Here are two more very simple counter-examples:

Crothers, S.J., Einstein's Pseudotensor - a Meaningless Concoction of Mathematical Symbols, http://vixra.org/pdf/2001.0499v1.pdf

Crothers, S.J., The Landau-Lifshitz Pseudotensor - Another Meaningless Concoction of Mathematical Symbols, http://vixra.org/pdf/2001.0531v1.pdf