It is

Thanks! I still don't know anything about lensing but it is nice to not get it confused with redshift deflection.

Yawyaw. I would like to ask you how works the de Broglie oscillation in the quaternion theory?.
There is a repulsive energy according to Pauli exclusion principle and gravitational attractive warping of the space. That way the matter interacts repulsive and attractive.

Are you saying that the quaternion and the four-vectors formulations are equivalent?
If so, that was my point, and you refute you claim that "The mathematics was compromised to satisfy physics dogma".


I am still waiting for you to show us that imaginary part in the space-time interval...

__________________
papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

Quaternions and 4-vectors NOT the same, see 1.,2.,3.

see point 3. for imaginary: point p and p^2 for 4-vector -(ct) + x^2 + y^2 + z^2

I am not familiar with de Broglie oscillations. I looked it up and here is a link that may help.

http://www.calphysics.org/mass.html

My work relates Planck's Constant h to the fine structure constant thru z, the free space impedance. z=W/C =375 Ohms and h=WC where W= 500 atto Webers (volt second) and C=4/3 E-18 (atto) Coulombs. The Ether Vacuum has quantum and magnetic charges, C and W. h=zC^2.

The Fine Structure Constant alpha=1/2 (e/C)^2/n . This may help.

What is "redshift deflection"?

What we have been talking about is the deflection of a photon as it passes by the Sun.

Is it your claim that gravity is described by a classical Newtonian potential?

Does that potential propagate with infinite velocity, or at some other speed?

Off Topic.

My undergraduate physical chemisty professor used to include a bonus question on the final exam to reduce the failure rate or to entertain himself.

He'd post a picture and ask: Who is this?

It was J. Willard Gibbs, the inventor of Physical Chemistry.

__________________
Olsen the moderator.

Thanks for the comment. A nice diversion. Gibbs was a great physicist and educator, with many contributions. I looked him up after your post.

I claim that Gravity is described by a classical quaternion energy E= -mu/R + mcv. This energy is quaternion containing the classical Newtonian potential(real) energy and the vector energy of motion mcv. The Quaternion second derivative is the wave equation. The first derivative is X=(d/dR + Del)= (d/cdt + Del). The second derivative is the square of the first derivative:
X^2 = ((d^2/c^2dt^2 - Del^2) + 2d/dR Del) The wave equation for Gravity is a quaternion and consists of a real part and a vector part: a real longitudinal wave equation and a vector Transverse wave equation. The

X^2E= ((d^2/c^2dt^2 - Del^2)(-mu/R) -2mcd/dR Del.v) + ((d^2/c^2dt^2 - Del^2)mcv + 2d/dR(mcDelxv + Del(-mu/R))

x^2E = ((d^2/c^2dt^2 - Del^2)(-mu/R) + 2mcvcos(g)/R^2) + ((d^2/c^2dt^2 - Del^2)mcv + 2mv(csin(g)/R^2 + v r/R3))

Here you see the Quaternion wave equations, a real longitudinal wave and the vector transverse wave. At the equilibrium condition, 0=XE, the waves are simplified.

X^2E = -(d^2/c^2dt^2 + Del^2)(-mu/R + mcv).

What is "R"?

I never said they are.

But you said: "It appears that for Relativity Theory, the 4-vector is a QUATERNION... "
So I asked whether - according to you - the formulation of Relativity in terms of quaternions is equivalent to the formulation in terms of four-vectors.

Of course, you are utterly wrong when you finish the sentence with "and not the Minkowski 4-vector elsewhere", since the "Einstein" space-time interval you quoted is at the basis of the definition of Minkowskian vector-space.


No, you claimed that there is an imaginary in this space-time interval: I = x^2 + y^2 + z^2 - (ct)^2.
So, where is it? I see only squares of real numbers.

__________________
papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

Ah. The joy of metrics (or pseudo-metrics...)

No, x² + y² + z² - (ct)² can be written as x² + y² + z² + (ict)².
Not that I'm advocating the replacement of vectors with quaternions, or anything.

__________________
"All your bias are belong to us." Ara Pacis
"A witty saying proves nothing." Voltaire

SR is frequently taught in that fashion, but I think that the forcing of SR onto a Euclidean geometry, via the use of i, masks the underlying geometry of Minkowski spacetime. The use of a metric (or pseudo-metric) tensor allows you to move forward in a more natural fashion, and is pretty much essential when working with GR. Mind you, that is a personal opinion.

"So I asked whether - according to you - the formulation of Relativity in terms of quaternions is equivalent to the formulation in terms of four-vectors."

See my new ATM post on Quaternion Relativity!

Please can you tell me what "R" is in

"R" is the separation distance between m and M, in the gravitational Real or Potential energy E= mu/R=mGM/R.