Many-Minds Relativity

A physical theory of relativity



A theory of relativity is presented, which is physical, in contrast to Einstein’s special theory of relativity, which is non-physical.

The theory of relativity worked out by Mr. Einstein, which is in the domain of natural science, I believe can also be applied to the political field. Both democracy and human rights are relative concepts – and not absolute and general. (Jiang Zemin President of the People’s Republic of China 1993 – 2003, Chairman of the Central Military Commission 1989 – 2004)

Theories of Relativity

This knol connects to the knols:

The End of Physics: No Unified Field Theory

Modern physics is based on quantum mechanics and Einstein´s special/general theory of relativity, which however are incompatible. The search for a unified field theory has been going on ever since Einstein formulated his special theory of relativity  in 1905 and followed up with his general theory of relativity in 1915, however without success. This is today described as “the end of physics” [1][2][3] and thus the incompatibilty of quantum mechanics and relativity theory seems to prevent progress.

Relativity Theory as Root of Trouble

The root of the trouble may be found in Einstein´s theories of relativity. Einstein´s special theory of relativity was first ignored by the scientific community and then dismissed as a non-physical theory belonging to epistemology without significance for the real physical world. Today 100 years later, it is considered to be a corner stone of modern physics, but the initial scepticism and criticism has not been eliminated by reason, only by politics of science and coersion.
We argue below that indeed Einstein´s special relativity is non-physical, and thus of no relevance, and we present an alternative theory of relativity, in a simple model case, which is physical and thus can have relevance.

The Nature of Mathematics

Einstein is famous as an exceptionally brave scientist with an exceptional talent of  drawing far-reaching revolutionary consequences about space and time from almost no assumptions. It is also known that Einstein did not do well in mathematics at school and probably suffered from what today is called dyscalculi. The nature of mathematics is such that everything that can be concluded, is already hiding in the assumptions, just not yet made visible. Without assumptions nothing can be concluded. If the assumptions are non-physical, the conclusions are also non-physical, because physics cannot be brought in on the way by mathematical reasoning from non-physical assumptions. 

Einstein´s Special Theory of Relativity

Einstein´s special theory of relativity formulated in 1905 concerns observations of motion by different observers moving with constant velocity with respect to each other. It is based on the following two assumptions:

  • (E1)  all observers measure the same the speed of light
  • (E2)  there is no aether.

An aether  would be a medium for the propagation of light, which would have the same function as the medium of air for the propagation of sound. The special theory came out from experiments by Michelson and Morley in the late 19th century indicating that 

  • (MM) detecting an aether medium common to all observers is impossible. 

Einstein was led to his special theory in an attempt to handle the apparent contradiction between (E1) and (MM). To see the contradiction, compare with different observers moving through still/motionless air with different velocities, who can agree on the same speed of sound if they only compensate for their velocities with respect to still/motionless air, that is, if they compensate for their different air-winds. 

So Michelson and Morley expected a compensation of the measured speed of light to be necessary depending on the motion of an observer, but could not detect that compensation was necessary.  In other words, they could not detect any aether-wind in the motion of the Earth around the Sun with varying velocity (direction). It seemed that there was no still aether or no fixed vacuum through which light could propagate with a certain velocity. This was the contradiction which had to be resolved. 

Einstein´s solution was radical: remove the aether/vacuum completely from the picture and thus replace (MM) by (E2). If there is no aether, there is no contradiction coming from variable motion through an aether without aether-wind, simply because there is no aether. Clever!?

We shall see below that this is too radical, resulting in a  non-physical special theory, which does not describe any physical reality. We shall see that the special theory is a (trivial) purely mathematical theory without physical interpretation. This was understood by Einstein, who quickly left the special theory (and never returned) and instead raised the bet to his general theory of relativity, which is so difficult that nobody can understand it.

Many-Minds Relativity

There is another less radical resolution, which is to handle (MM) by accepting that different observers

can have different aethers/vacui, which was suggested in 1914 by the British mathematician Ebenezer Cunningham. 

                                                     Many versions of Cunningham.

But it was overshadowed by Einstein´s more radical resolution which took fire in 1919, when the British physicist Eddington proclaimed that the general theory was confirmed by observations at an Eclipse of a very slight bending of light from a distant star around the Sun. And if the general theory was confirmed, also the special theory would be confirmed, right? But the bending was so slight that it was barely notable and there was a risk that expectation influenced the measurement, and Einstein’s relativity is still today waiting for experimental confirmation.

                                                               Many observers.

Cunningham’s resolution may be better, because it is less radical, and suggests a form of physical relativity theory, which we refer to as many-minds relativity [4], based on the following assumptions:

  • (M1)  all observers agree on the same the speed of light
  • (M2)  each observer has his own aether/vaccum in which he does not move.

In Einstein’s special relativity, there is no aether/vacuum, because observers cannot agree on a common aether/vacuum, while in many-minds Relativity different observers are allowed to have different aethers/vacui. To have nothing is not physical, to have something can be physical.

Einstein’s approach resembles the debate climate in Sweden, where an opinion is possible only if it is shared by everybody, which is an extreme form of democracy and can result in no opinion at all.  On the other hand, many-minds relativity resembles the culture in France, where everybody is allowed (expected) to have a different opinion, which does not contradict common agreement to some extent. 

We will below present both Einstein’s non-physical special relativity based on (E1)+(E2), and different forms of physical many-minds relativity based on more precise versions of (M1)+(M2) connecting mathematical theory to physics.

We shall then understand that (M1) really is an agreement to measure length in lightseconds, and thus is simply a definition, and we shall then understand that (E1) is also a definition expressed a little bit differently. If now (E1) is a definition and (E2) a negative statement, then there is no physical content of the special theory, since it is based solely on (E1)+(E2), and thus special relativity is a non-physical theory without physical relevance, which was understood by Einstein, although he kept it for himself.

Propagation of Sound

To understand relativity theory it is useful to recall the basics of propagation of sound through still/motionless air. We know that the speed of sound is about 340 meter/second, and the frequency of audible sound ranges from about 20 periods/second to about 20.000 periods/second.  

Suppose we normalize and in suitable units consider sound of frequency 1 which propagates through still air with a speed of 1. We know that there is a Doppler effect  changing the perceived frequency from 1 to 1/(1 – v)  if the source is approaching an ear at rest in the air with the speed v, and to 1/(1+v) if the sound source is receeding from the ear at speed v. Altogether with the Doppler factor

1/(1 + v)

if we count v negative in approach and positive in recession.

We experience the Doppler effect as drop in pitch of the whistle of a train as the train passes, first approaching and then receeding. The drop in pitch is evidently from 1/(1-v) to 1/(1+v), thus with a factor 
(1-v)/(1+v). If the train is moving with 34 meter/second this amounts to a 20 percent drop in pitch.
The progagation of sound waves in air is mathematically modeled as solution of the wave equation, properly modified according to the air-wind. The wave equation thus takes different forms for different observers moving with respect to each other and with different velocitites with respact to the air.

The SI Standard of Measuring Time and Length

Physics of motion is based on measuring time and length. According to the 1983 SI Standard, time is measured in seconds according to an atomic cesium clock showing Coordinated Universal Time (UTC) with

  • one second equal to 9192631770 cycles of a cesium clock
and length is measured in meters with
  • one meter being the distance traveled by light in 0.000000003335640952 seconds or 9192631770/299792458 cycles of a cesium clock.
This is in particular the standard of the GPS system working so amazingly well. Equivalently, the length standard can be chosen as lightsecond or 299792458 meters. 
With the SI Standard the speed of light is 1 lightsecond/second, and thus all observers following the SI 
Standard possibly moving with respect to each other, will agree on the same speed of light, namely 
1 lightsecond/second:

  • The constancy of the speed of light is an agreement or definition
and not a physical fact which can be verified experimentally. To someone claiming to have measured the speed of light to something different from 1 lightsecond/second,  one would simply say that a mistake has been made. It would be like claiming that measurements indicate that there are 101 centimeters on a meter, which is impossible since by definition 1 meter is 100 centimeters.
The idea of using lightsecond as length standard is not new:  The mathematician Poincare suggested this already in 1897 [5]

  • This hypothesis of Lorentz and Fitz-Gerald (space contraction) will appear most extraordinary at first sight. All that can be said in its favor at the moment is that it is merely the immediate interpretation of Michelson’s experimental result, if we define distances by the time taken by light to traverse them. 

                                        Poincare: Use the 1983 SI length standard of lightsecond!

Often the argument is made that the reason the SI meter standard can be used, is that the speed of light is  constant as a physical fact, but this is not science. It is not allowed in science to view a definition as a physical fact, because a definition can be chosen at will (as long as it is not self-contradictory), while a physical fact cannot. See the discussion of the Michelson-Morley experiment below .

Assumptions of Many-Minds Relativity 

The assumptions of Many-Minds Relativity take the more precise form:

  • (M1) all observers use identical cesium clocks and measure length in lightseconds 
  • (M2) each observer uses Maxwell´s equations in a vacuum to which he is a rest.

Note that (M2) means that Maxwells equations take the same form for all observers, in contrast 

to the wave equation for propagation of sound waves, which takes different forms depending on the air-wind.
Many-minds relativity concerns coordination of observations by different observers. If there is just one observer, there is no need for coordination, but if there are several there is. 
Many-minds can take different forms depending on what observations are being made. All observers use identical cesium clocks, which can be synchronized or not synchronized, and  it is natural to distinguish between the following different types of measurements: (i) non-synchronized time + velocity, (ii) synchronized time + length,  (iii) synchronized time + length + velocity.  A more detailed presentation considering these alternatives is given in [4] The GPS system uses (ii).

Specific Assumptions of Many-Minds Relativity

We consider the case (i) in the setting of a one-dimensional space like a long straight line L without any markers, which acts as the universe of an observer X making observations about the motion of an object Y along L:


————-X—-<<<——————————————–<<<<—Y———————————————————————  L
We let X choose one fixed point O on the line L as origin; one can think of X being tied to O and from there being able to make observations. This is like one observer at the Earth making observations of the motion of planets and stars around the Earth. 
We assume that X has a cesium clock and is able to measure the frequency f of light from an object Y moving along L, and we assume that the frequency  f is related to the velocity v of Y relative to X by the above Doppler shift formula

f = 1/(1+v)  or  1+v=1/f  or  v=1/f  - 1,

where the emitted light is assumed to have frequency 1 and propagate with velocity 1.  By measuring the frequency f of incoming light from an object, the velocity v of the object is thus determined. This is how 
velocities of stars with respect our solar system are computed, which means that the light from receeding stars is red-shifted, and from approaching stars is blue-shifted. Observations of far away stars show redshift corresponding to v>1. Far away galaxies appear to race away from us with a speed exceeding the speed of light. 

We observe that in approach v > -1 while in recesssion any v>0 is allowed. Thus Y cannot approach observer X at a speed larger than or equal to the speed of light (=1), but recession at a speed larger than the speed of light is possible, and also observed.
From observations of velocities, distance can be determined by integrating the velocity over time. If the velocity is constant = v, then the distance s traveled over time t is given by  s =  v t.
Consider now two observers X1 tied to an origin O1 and X2 tied to O2 moving with respect to each other and observing the frequencies f1 and f2 of light from Y and computing corresponding velocities v1 =1/f1 -1 and 
v2=1/f2 -1 by the above Doppler shift formula: 

  v1  f1                                                            v2  f2

————-X1—-<<<——————————————————-<<<—-Y—–>>>—————–>>>———–X2—– L
                                                                  v12     f12   
We now assume the following composite Doppler shift formula: 

f12=f1f2  and v12 = 1/f12 – 1 

where the mutual frequency f12  is obtained as the product of two successive Doppler shifts of frequency f1 and f2 and v12 is the mutual velocity between X1 and X2. This  leads to the following formula for composing or adding velocities:

v12 = v1 + v2 + v1v2.

In classical Newtonian mechanics the velocities v1 and v2 would compose as v1+v2, while in many minds velocity they compose as v1+v1+v1v2.  In Einstein´s special relativity velocitites add differently. 
The many-minds composition of velocity is studied in more detail in [4] and it is shown that it is second order consistent in the mutual velocity v12. This means that if X1 uses the formula v1 = v12 – v2 – v12v2 to compute v1 from v12 and -v2, and X2 the corresponding formula  v2=v12 – v1 -v12v1, then they will agree up to a term v12v12. The relative velocity v12 between human observers can only be small with v12v12 very small, while  v1 and v2 can be large and even exceed the speed of light in recession. 

A Relativistic Newton’s 2nd Law

Differentiating the velocity composition v12 = v1 + v2 + v1v2 with v1 constant and v2 a velocity increment satisfying Newton´s second law mdv2/dt = F, where m is the mass of Y and F the force applied to Y, gives  dv12/dt=(1+v1)dv2/dt=(1+v1)F/m so that setting v1=v12=v since v2 is an increment, we obtain the following relativistic Newton’s 2nd Law:


mv dv/dt = F    where  mv   = m/(1  + v)


is relativistic mass corrected with the factor 1/(1+v). We see that in approach the relativistic mass increases and in recession it decreases. We understand that the apparent change of mass depends on the way we measure and compose velocities. In a coordinate system following the body, the apparent mass m does not change, only in a coordinate system not following the body.

What is Relativistic Mass?

We are led to the idea that the mass m of a body is defined as m = F/a where F is applied force and a is accelleration,  where the acceleration depends on the coordinate system used to measure the acceleration, which is different if the coordinate system is fixed or moves with the body. In a system moving with the body, a =dv/dt with mass m=F/a, while in a fixed system a = (1+v)dv/dt with apparent mass mv = F/a = m/(1+v). It is possible to view the apparent added mass in approach as a form of energy stored in increasing the frequency of emitted light which is released in recesssion with decreasing frequency, according to a Doppler shift from blue in approach to red in recession.  

An Illuminating Example

Assume Y has mass m = 1  and is accellerated towards X at O with a constant force  F = -1 from rest at a position s(0) > 0 at t = 0.  From Newton’ s 2nd Law  dv/(1+v) = -dt, we find v(t) =  exp(- t) -1, showing that 

0 > v(t) > -1. Further,  s(t) = s(0) +1 – t – exp(-t), showing that independent of initial position s(0), Y will in finite time arrive at O with speed less than 1.  The observer X at O thus will consider the accelleration to decrease, which is interpreted as increasing mass, while an observer following Y will perceive a steady constant accelleration and constant mass.

E=mc2  or  P = mc

Because  for small v we have mv =m/(1+v) ~ m(1 – v) = m + m(-v), one can view the momentum m(-v) with 
v<0 in approach as a contribution to the relativistic mass and thus vice versa view mass as a  potential contribution to momentum. This suggests the following variant of Einstein’s famous E=mc2:

P = mc

where c=1 is the speed of light. Annihilation of mass seems to create momentum and thus energy.
This proof is similar to Einstein´s  proof of E=mc2.

                                                                  P = mc

The Michelson-Morley Experiment Today

Suppose you want to check the Michelson-Morley experiment today.  You would then measure the speed of

light by measuring the time it takes to pass along a straight bar from beginning to end, and you would find that the time is the same independent of the orientation and speed of the bar. What would you conclude today with  the SI standard? That the speed of light is constant? No, because today this is a definition or agreement. You would instead conclude that the length of the bar is independent of its orientation and speed, since you measure length in light-seconds, which would not be surprising. With the present SI standard the Michelson-Morley experiment thus is a triviality, while in Einstein’s hands it caused a scientific revolution.


Einstein’s Special Theory Relativity

The Lorentz Transformation

Einstein´s Special Theory of Relativity is based on (E1) and (E2) supposedly leading to the Lorentz transformation 

                                     x’ = g ( x – vt )  
                              t’ = g ( t – vx )

where g2 = 1/(1-v2) with g  > 0, which connects the coordinates of two coordinate systems (x,t) and (x’ ,t’ )

supposedly moving with respect to each other with velocity v. Note that here -1 < v < 1 so that v > 1 is not allowed. It is assumed that the speed of light c=1.
Here the origin x’ = 0 of the x’-axis moves along the x-axis with speed v, since x’ = 0 is the same as x=vt. We assume that 0<v<1 and understand that x’ = t’ if and only if x = t, which means that an effect propagating in the (x’,t’) system with speed 1 also propagates with speed 1 in the (x.t)-system, which reflects that the speed of light is equal to 1 in both systems (the brown line in the figure).

     The two coordinate systems (x,t) and (x’ ,t’ ) of the Lorentz transformation.

The big problem with Einstein´s special theory of relativity is that it is non-physical, which can be seen from 
the fact that the x’ – axis is not parallel to the x – axis, in contradiction to physical situtation considered, where  X is an observer with an x-axis and X’ and observer with an x’ -axis moving along the x-axis with speed v. 
Einstein picked up the Lorentz transformation form the physicist H. A. Lorentz, who when introducing it
carefully explained that the transformed time t´ – coordinate should not be interpreted as physical time .
What Einstein did was precisely to do that! And to remove the aether completely.
The Lorentz transformation contain effects of length contraction and time dilation, and the question from 
start was if these effects are real physical effects or just mathematical conventions/definitions/agreements.
This was not made clear by Einstein, and nobody else, and has caused the confusion surrounding relativity theory still today, with clocks slowing down and space ships being compressed by motion with constant velocity contrary to all logic. It has gone so far that the lack of logic is used as an argument that the theory is  correct. 

Einstein’s Principle of Relativity

(E2) is alternatively formulated as a principle pf relativity of the form 

  • (E2′) physical laws take the same form in different (non-accellerating) coordinate systems.

This principle is vaguely formulated since “take the same form” is ambigous, and therefore can be interpreted in different ways, e.g. that all observers use the same Maxwell´s equations independent of motion with constant velocity, which is (M2). But requiring that all physical laws should behave like Maxwell’s equations, that take the same mathematical form in different coordinate system,  is non-sensical. It is also a truism that the physical meaning of a physical law is independent of the coordinate system used. This is the same as saying that the meaning of a sentence is independent of the language used to express it. Thus (E2′) is either non-sensical or a truism without physical content.

Einstein’s Equivalence Principle

Defining mass m = F/a indicates that there is only one mass, the inertial mass, with the inertial mass by

definition being equal to the gravitational mass, since gravitational mass is defined by gravitational acceleration. This means that Einstein´s principle of equivalence of inertial and gravitational mass is nothing but a definition, another indication that Einstein´s special relativity is non-physical. 

Einstein’s Special Relativity is Non-Physical

The fact that Einstein’s special theory is not a physical theory, just a simple mathematical coordinate transformation without physical interpretation, can be understood from the fact that the basic assumptions (E1) and (E2)-(E2′) contain no physics. This has also been expressed by many prominent scientists over the years:
  • Length contraction and time dilation are ways of regarding things and do not correspond to physical reality. (Born)

  • A transformation of the time was necessary. So I introduced the conception of a local time which is different for all systems of reference which are in motion relative to each other. But I never thought that this had anything to do with real time. This real time for me was still represented by the old classical notion of an absolute time, which is independent of any reference to special frames of coordinates. There existed for me only this true time. I considered my time transformation only as a heuristic working hypothesis. (Lorentz) 

  • Poincare never spells out how he interpretes the primed coordinates in the Lorentz transformation….and like Lorentz believes in local time…. (Sartori)

  • The question whether the Lorentz contraction does or does not exist is confusing. It does not really exist in so far as it does not exist for an observer who moves (with the rod); it really exists, however, in the sense that it can as a matter of principle be demonstrated by a resting observer. (Einstein)

  • ... the general theory of relativity. The name is repellent. Relativity? I have never been able to understand what the word means in this connection. I used to think that this was my fault, some flaw of my intelligence, but it is now apparent that nobody ever understood it, probably not even Einstein himself. (Synge)


  • Thus we can sum up: general relativity can not be physical, and physical relativity is not general. (Fock)
  • Many people probably felt relieved when told that the true nature of the world could not be understood except by Einstein and a few other geniuses who were able to think in four dimensions. They had tried to understand science, but now it was evident that science was something to believe in, not something which should be understood. (Hannes Alfven, Swedish Nobel Laurate in physics)
  • Time and space are modes in which we think and not conditions in which we live. (Einstein) 
  • In 1905 Einstein recognized that Lorentz contractions and local time were not mathematical devices and physical illusions but involved the very concepts of space and time. (Born) 

  • It is hardly possible to illustrate Einstein’s kinematics by means of models. (Born) 

  • It is certainly remarkable that these relativity concepts, also those concerning time, have found such rapid acceptance. (Lorentz)
All these quotations give evidence that Einstein´s special relativity is non-physical, and only is a mathematical construct without significance in physics.

How Smart was Einstein Really?

There are many stories and cartoons joking with the stupidity of Einstein as the smartest physicist ever, who could not understand much, in particular not relativity theory:

  • In 1931 Charlie Chaplin invited Einstein, who was visiting Hollywood, to a private screening of his new film City Lights. As the two men drove into town together, passersby waved and cheered. Chaplin turned to his guest and explained: “The people are applauding you because none of them understands you, and applauding me because everybody understands me.”
  • Scientific American once ran a competition offering several thousand dollars for the best explanation of Einstein’s general theory of relativity in three thousand words. “I am the only one in my entire circle of friends who is not entering,” Einstein ruefully remarked. “I don’t  believe I could do it”.

Can Anybody Understand Relativity?

Apparently, Einstein did not understand relativity theory, and it appears to be difficult to find physicists claiming understanding. 
The physicist Brian Greene expresses a general sentiment in [6]:
  • The relativity of space and time is a startling conclusion. I have known about it for more than 25 years, but even so, whenever I quitely sit and think it through, I am amazed.
  • It is not the depth of mathematics that makes Einstein’s special relativity challenging. It is the degree to which the ideas are foreign and apparently inconsistent with our everyday experience.

We understand that physicists do not understand relativity, but the mere fact of not understanding is taken as evidence that the theory is correct. If you could understand the theory you would understand that it is pseudo-science without significance to physics, but since you cannot understand the theory, you can only accept it as  a profound truth beyond human understanding and rationality.