E=mc2 and Large Red Shift in Many-Minds Relativity

The Galaxy GN-z11 is seen to recede at 11 times the speed of light with large redshift.

Many-Minds Relativity MR presents and alternative to Einstein's Special Theory of Relativity SR, which gives new light to Einstein's $E=mc^2$ as a fundamental postulate of modern physics as well as an explanation of large red shifts observed in receding galaxies. 

Many-Minds Relativity leads to a modified version of Newton's second law of the form 

• $F=\frac{m}{1+v}\dot v$     (MR1)

where $F$ is force, $m$ is (inertial/gravitational) mass, $v$ is the velocity of a body approaching ($v<0$) or receding ($v>0$) as observed by an observer $O$ equipped with a standard clock measuring time $t$ while sitting still at the origin of a Euclidean coordinate system, with speed of light normalised to 1 and $\dot v=\frac{dv}{dt}$. 

This gives an apparent increase of mass in approach making $v>-1$ and an apparent decrease of mass in recession allowing $v$ to increase without limit from a constant force $F$.

 

A rocket with mass $m=1$ launched by O at time $t=0$ supplied with constant propulsion force $F=1$ would thus with time be seen by O to recede with the velocity $v(t)=t\exp(t)$ as solution to (MR1) thus  with seemingly exponentially increasing velocity and corresponding arbitrarily large Doppler shift.  This connects to the observed large red shift of far away galaxies increasing with distance. 

We recall the velocities in MR are computed from Doppler shifts and that (MR1) is the result of composite Doppler shifts. 

We compare with Einstein's relativistic version of Newton's 2nd Law of the form

• $F=\frac{m}{\sqrt{1-v^2}}\dot v$   (SR1)

with an apparent increase of mass in both approach and recession, seemingly in contradiction to recession velocities larger than the speed of light.

Let us now make a connection between MR and Einstein's $E=mc^2$. Using that $\frac{m}{1+v} = 1-v$ with error scaling with $v^2$, we can reformulate (MR) into

• $F=(m - P)\dot v$

where $P=-mv$ as momentum can be seen as a change of mass $P=\Delta m$, which without normalisation to $c=1$ reads 

• $Pc = \Delta mc^2$.       (MR2) 

as an apparent relation between momentum $P$ and mass change $\Delta m$. This relation closely connects to the following (SR) version of Einstein's $E=mc^2$ viewed to be a more "relativistically correct" version: 

• $E^2 =(pc)^2 + m^2c^4$.   (SR2)

We see that (MR2) is contained in (SR2). 

We understand that (MR2) to O can be seen as a connection of momentum to change of mass in the same spirit as Einstein's $E=mc^2$ connects energy to change of mass, but that this is a consequence of the system of observation used by O. There is no sufficient reason for O to believe that the mass of the body under observation effectively changes in accordance with momentum (or energy). 

To explain the change of mass in (MR2) and (SR2) to the scientific community, $O$ as a smart observer can say that this is no real change of mass only an apparent change or illusion. In addition $O$ can give an explanation of the observed large red shifts in recession for which no convincing explanation is given in standard cosmology. 

The highest-confirmed spectroscopic redshift of a galaxy is that of GN-z11, with a redshift of $\frac{v}{c} = 11.1$ that is with a velocity $11.1$ times the speed of light, see image above.

As concerns apparent dependence of mass on energy, which is not real, we can compare with the apparent shrinking of the size of an object when viewed at distance. Only a person equipped with magical thinking would conceive this as a real shrinking of physical size.

The longer the distance to the tree, the smaller the view angle and apparent size on the retina: