# Einstein unified theory

Sachs' EM field equation is $$\sigma^\mu \partial_\mu \varphi_\alpha(x) = \Upsilon_\alpha(x)$$ where $$\alpha = 1, 2$$ are indices for 2 sub-equations and $$\mu = 0,1,2,3$$ are the dimension indices for time and space respectively

The first two terms are $$\sigma^\mu \partial_\mu = \sigma^0 \partial_v - \sigma \cdot \nabla$$

where

$$\sigma^\mu \partial_\mu = \begin{pmatrix} \partial_0-\partial_3 & -(\partial_1-i \partial_2) \\ -(\partial_1 + i \partial_2) & \partial_0 + \partial_3 \end{pmatrix}$$

$$\varphi_1 = \begin{pmatrix} G_3 \\ G_1 + i G_2 \end{pmatrix}$$

$$\varphi_2 = \begin{pmatrix} G_1 - i G_2 \\ -G_3 \end{pmatrix}$$

where $$G_0 = 0$$ and $$G_k = (H + iE)_k$$ and $$k = 1, 2, 3$$

H and E are the magnetic and electric field vectors

$$\Upsilon_1 = -4\pi i \begin{pmatrix}\rho + j_3 \\ j_1 + i j_2 \end{pmatrix}$$

$$\Upsilon_2 = -4\pi i \begin{pmatrix}j_1 - i j_2 \\ \rho - j_3 \end{pmatrix}$$

Very elegant, but the results I got give only a partial and skewed representation of the Maxwell equations. Here are the spinor equations I came up with where the E and B fields are placed in the quaterion and the operators are placed in the spinor objects (the reverse of Sachs´ formulation):

The field equation is $$\varphi^\alpha \partial_\alpha(x) = \Upsilon(x)$$ where $$\alpha = 1, 2$$ are indices for 2 sub-equations

$$\varphi^1 = \begin{pmatrix} E_3 & E_1 + i E_2 \\ E_1 - iE_2 & -E_3 \end{pmatrix}$$

$$\varphi^2 = \begin{pmatrix} B_3 & B_1 + i B_2 \\ B_1 - iB_2 & -B_3 \end{pmatrix}$$

$$\partial_1 = \begin{pmatrix} i \partial_0 - \partial_3 \\ -\partial_1 + i \partial_2 \end{pmatrix}$$

$$\partial_2 = \begin{pmatrix} -i \partial_0 - \partial_3 \\ -\partial_1 + i \partial_2 \end{pmatrix}$$

$$\Upsilon = 4\pi \begin{pmatrix}\rho + j_3 \\ -\rho - j_1 + i (\rho + j_2) \end{pmatrix}$$

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Thanks, it's right now. I'm using another math typesetting package that's similar to LaTex but just different enough to make the conversion tricky.

PAllen
2019 Award
I myself haven't found anything (of substance) wrong with Sachs' theory, which reveals Einstein to have been the prophet that he was.

The reason the physics community doesn't accept that there is no twin paradox (no differential aging) is, it still hasn't come to terms with relativity (though we're approaching a century!)
Are you saying you don't believe that if two identical clocks start together, then separate and travel differently, and meet later, they will no longer agree? This non-agreement has been demonstrated in numerous ways using atomic clocks. Sachs claimed, verifibaly falsely, that they would agree. (Sach's claim was made before such experiments were reliably carried out).

No problem, I deleted it.

Are you saying you don't believe that if two identical clocks start together, then separate and travel differently, and meet later, they will no longer agree? This non-agreement has been demonstrated in numerous ways using atomic clocks. Sachs claimed, verifibaly falsely, that they would agree. (Sach's claim was made before such experiments were reliably carried out).
Sachs wrote on this again: "On Einstein's Later View of the Twin Paradox," Foundations of Physics, VoL 15, No. 9, 1985. I am not aware of any experiment that has verified non-agreement on re-meeting. For instance, the Hafele-Keating experiment has been analyzed and criticized, in "Hafele and Keating Tests: Did They Prove Anything?" Phys. Essays 13, 616 (2000). But, if you know of any verification, I would like to know.

PAllen
2019 Award
Sachs wrote on this again: "On Einstein's Later View of the Twin Paradox," Foundations of Physics, VoL 15, No. 9, 1985. I am not aware of any experiment that has verified non-agreement on re-meeting. For instance, the Hafele-Keating experiment has been analyzed and criticized, in "Hafele and Keating Tests: Did They Prove Anything?" Phys. Essays 13, 616 (2000). But, if you know of any verification, I would like to know.
Criticisms of Hafele and Keating are spurious, but I need not debate that with you. Here is a quick sample of other more direct tests:

C. Alley, “Proper Time Experiments in Gravitational Fields with Atomic Clocks, Aircraft, and Laser Light Pulses,” in Quantum Optics, Experimental Gravity, and Measurement Theory, eds. Pierre Meystre and Marlan O. Scully, Proceedings Conf. Bad Windsheim 1981, 1983 Plenum Press New York, ISBN 0-306-41354-X, pg 363–427.

They flew atomic clocks in airplanes that remained localized over Chesapeake Bay, and also which flew to Greenland and back.

Bailey et al., “Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” Nature 268 (July 28, 1977) pg 301. Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).

They stored muons in a storage ring and measured their lifetime. When combined with measurements of the muon lifetime at rest this becomes a highly relativistic twin scenario (v ~0.9994 c), for which the stored muons are the traveling twin and return to a given point in the lab every few microseconds. Muon lifetime at rest: Meyer et al., Physical Review 132, pg 2693; Balandin et al., JETP 40, pg 811 (1974); Bardin et al., Physics Letters 137B, pg 135 (1984)

Note, especially: flying to Greenland and back makes it literally a twin test. The muons are also literally a twin test: you compare slow muon with muon in orbit, they meet once per orbit.

I would have to say that if you believe differential aging is false, that is a fringe belief. I do not believe that PhilDSP disbelieves differential aging.

There are options to investigate perceived differential aging as a dynamic effect of EM interaction, specifically due to retarded propagation rather than a necessary space-time symmetry condition. Jefimenko has done so and shows that the effect can vary depending on the particular situation and construction of the device being used as a clock. I haven't looked at that in detail so I'm not willing to venture an opinion yet.

PAllen
2019 Award
There are options to investigate perceived differential aging as a dynamic effect of EM interaction, specifically due to retarded propagation rather than a necessary space-time symmetry condition. Jefimenko has done so and shows that the effect can vary depending on the particular situation and construction of the device being used as a clock. I haven't looked at that in detail so I'm not willing to venture an opinion yet.
To go this route, you would need to consider electroweak interaction (or just weak, as an approximation) for the muon case. I figure only QED is needed for atomic clocks. Classical EM would be inapplicable to either of these clocks. Then, if you really think that two different types of clocks brought on twin like spacetime will end up with clock type dependent differences, that is a specific testable prediction of violation of SR. I suspect that 99+% of physicists would be willing to take a large bet against such a violation, but it would be an interesting experiment.

Criticisms of Hafele and Keating are spurious, but I need not debate that with you. Here is a quick sample of other more direct tests:

C. Alley, “Proper Time Experiments in Gravitational Fields with Atomic Clocks, Aircraft, and Laser Light Pulses,” in Quantum Optics, Experimental Gravity, and Measurement Theory, eds. Pierre Meystre and Marlan O. Scully, Proceedings Conf. Bad Windsheim 1981, 1983 Plenum Press New York, ISBN 0-306-41354-X, pg 363–427.

They flew atomic clocks in airplanes that remained localized over Chesapeake Bay, and also which flew to Greenland and back.

Bailey et al., “Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” Nature 268 (July 28, 1977) pg 301. Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).

They stored muons in a storage ring and measured their lifetime. When combined with measurements of the muon lifetime at rest this becomes a highly relativistic twin scenario (v ~0.9994 c), for which the stored muons are the traveling twin and return to a given point in the lab every few microseconds. Muon lifetime at rest: Meyer et al., Physical Review 132, pg 2693; Balandin et al., JETP 40, pg 811 (1974); Bardin et al., Physics Letters 137B, pg 135 (1984)

Note, especially: flying to Greenland and back makes it literally a twin test. The muons are also literally a twin test: you compare slow muon with muon in orbit, they meet once per orbit.

I would have to say that if you believe differential aging is false, that is a fringe belief. I do not believe that PhilDSP disbelieves differential aging.

Let me address your last remark first: the beauty of physics -- the reason I took it up -- is that physics is that which is, regardless of consensus. Copernicus was "fringe" for awhile, too!

I appreciate your pointing me to these other sources. Still, if one takes the time to understand relativity in its entirety, one will see that, time and space, by definition, being merely measures that enable the laws of physics to be expressed covariantly in all reference frames -- not absolute in themselves -- then anything based on the "twin paradox" must be false!

What tends to be glossed over -- and I see this time and again -- is that any measure, be it time, space, or other, is valid only in relation to some reference frame; it is never an absolute in itself! This has become so accepted (even if misunderstood) that the General Conference on Weights and Measures has come to define a meter to be the distance that light in "vacuum" travels during 1⁄299 792 458 of a second. Thereby, if the value of the time measure changes relative to a reference frame, then the value of the length measure relative to the same reference frame must change accordingly.

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