Galilean Relativity as Many-Minds Relativity

Many-Minds Relativity MMR explores an alternative to Einstein's special theory of relativity SR. The basic setting in both MMR and SR concerns observations made in different spatial Euclidean coordinate systems moving with constant velocity with respect to each other.

In MMR observers share a common time $t$ (Universal Common Time UTC as in the GPS system), while space coordinates in a system $X^\prime$ with space coordinates $x^\prime$ moving with velocity $v$ respect to a system $X$ with coordinates $x$, are connected by the Galilean transformation

• $x^\prime = x- tv$

stating that the origin of $X^\prime$ moves in $X$ with velocity $v$. 

In SR there is no common time and space-time coordinates are connected by the Lorentz transformation mixing space into time in violation of Newtonian mechanics. SR leads to many strange effects such as "time dilation" and "space contraction" as effects of motion with constant velocity, which are deeply paradoxical. 

The basic assumption of MMR are (see also this post):

1. All observers share a common time set by synchronised cesium clocks according to the SI standard.  
2. The same Maxwell's equations for light propagation is used in all systems. 
3. The length scale in each system is set according to the SI standard with the same speed of light in all systems in compatibility with 2.
4. All observers share the laws of Newtonian mechanics.

A2 as Assumption 2 means that each system carries its own "aether" as the coordinate system used to express Maxwell's equations, in accordance with this post. MMR is a "many-aethers"-theory with as many "aethers" as spatial coordinate systems. A2 means that the speed of light is the same in all systems, by SI standard.

A3 means that the same length scale is used in all systems, by SI standard. 

A1 + A3 means that time and length scale is the same in all systems. There is no time dilation or space contraction in MMR. 

In classical Newtonian/Galilean relativity there is "one-unique-aether", while in MMR there are many  (non-unique) aethers. 

The reason Newtonian/Galilean relativity was replaced by SR was the Michelson-Morley experiment MM, which showed to be in conflict with a "one-unique-aether". On the other hand, the null result of  MM is in harmony with MMR, since each arm in the MM experiment carries its own coordinate system.

MMR is thus a "many-observer"-theory, where different observers use different coordinate systems moving with to respect to each other connected by the Galilean transformation, while they share time and length scale and the same Maxwell's equations expressed the same way in their respective systems.

Recall that SR shares the Lorentz transformation with a "Lorentz unique-aether"-theory, including time dilation and space contraction, with the difference that Lorentz considered these effects to be more illusion than reality. Time dilation and space contraction present a veritable night-mare to science with a wealth of "paradoxes" to handle, and so each possibility of getting out of the trauma must be tried. 

But different observers of MMR may not agree on everything, such as Doppler shifts because Doppler shifts depend on the motion of source and receiver, and the observers are moving with respect to each other. 

To see this consider a (1d) situation where at a specific time $X$ and $X^\prime$ with observers $O$ and $O^\prime$ in their respective coordinate origin overlap, while moving with velocity $w$ with respect to each other.  Consider the perceptions of a signal sent from a source at frequency 1, assuming the speed of light is normalised to 1, moving with velocity $v$ with respect to $X$. The frequency $f$ recorded by $O$ using $X$ will then be 

• $f=\frac{1}{1+v}$

since the source is moving with speed $v$ (to the right say) and the receiver is fixed. On the other hand $X$ would attribute the following frequency to an observation made by $O^\prime$:

• $\bar f =\frac{1-w}{1+v}$ for $X^\prime$, 

because $X$ sees the the receiver of $O^\prime$ moving with speed $w$ (to the left say). But the frequency $f^\prime$ de facto observed by $O^\prime$ will be

• $f^\prime  =\frac{1}{1+v+w}$ 

since $v+w$ is the velocity of the source with respect to a fixed $O^\prime$. Computing we find that 

• $\bar f - f^\prime =-\frac{w^2+vw}{(1+v)(1+v+w)}$,

which is second order in $v$ and $w$ compared to the speed of light = 1. Further aspects are given in  the MMR book.

The observers $O$ and $O^\prime$ will thus share the same time and length scale, but will have different perceptions depending on mutual motion, which can differ up the square of motion speed vs speed of light. With a speed of light of $3\times 10^8$ meter/second the difference would be of size $10^{-6}$ for velocities up to $300$ km/second. In short MMR appears to give a consistent description which can be shared by all observers up to second order accuracy in speeds. For observers on Earth $w$ may be up $1$ km/second and for observers in space up to $10$ km/second, far away from $300$ km/second.

We recall that the addition of two velocities $v$ and $w$ from composite Doppler shift in MMR reads:

• $v+w+vw$,     

  since

• $\frac{1}{1+w}\frac{1}{1+v}=\frac{1}{1+v+w+vw}$.

Altogether, MMR is compatible with the MM null result, and thus offers an alternative to SR which is compatible with Newtonian mechanics and electromagnetics (up to second order in relative light velocity).

The idea of a "many-aethers"-theory can be found in the work by the English mathematician Ebenezer Cunningham, but it was swamped by Einsteins "no-aether"-radicalism.

One can argue that the idea of a "many-aethers"-theory connects post-modern multiculturalism, while Einstein's "no-aether"-theory would correspond to a "no-culture-at-all".

PS1 Lee Smolin writes in Einstein's Lonely Path:

• Special relativity was the result of 10 years of intellectual struggle, yet Einstein had convinced himself it was wrong within two years of publishing it. He rejected his own theory, even before most physicists had come to accept it, for reasons that only he cared about. For another 10 years, as others in the world of physics slowly absorbed special relativity, Einstein pursued a lonely path away from it.

Einstein thus gave up SR in 1907. It is high time for physicists of today to do the same thing.

PS2 The physics community views Einstein with mixed feelings: Sometimes as a God but more often as a crackpot. One may argue that "once champ always champ", or "once crackpot always crackpot". What is your view?

PS3 Of course there is no twin paradox to resolve in MMR, since all twins age at the same rate according to the same clocks, independent of inertial motion. Of course acceleration or gravity forces or temperature, pressure and friction may affect the workings of a mechanical clock and thus clock rate (all clocks are mechanical), but certainly not pure translation with constant velocity, against the core of SR.

What is the Correct Resolution of the Twin Paradox if Any?

In discussions with theoretical physicists I have met the following "resolutions" of the twin paradox of special relativity SR as the paradox/apparent contradiction of different ageing of two twins, one staying at home and the other traveling on a round-trip (showing to be younger at return):

1. The different ageing shown in SR is real physics and can be explained within SR.
2. SR says nothing about the physics of ageing due to round-trip travel and so there is no twin paradox to resolve.
3. The different ageing shown by SR is real but can only be explained by the general theory of relativity.  

Since 1.-3. are contradictory, I have asked a panel of theoretical physicists about the correct resolution, and will report the answers, when received. You are also welcome to submit your own resolution as a contribution to the discussion.

My question is the same as posed in an Open Letter signed by 142 physicists and others directed to the physics community, which received a very vague response. Read and contemplate! You will find clear evidence that there is no commonly accepted resolution, only resolutions which are viewed to be incorrect by parts of the community.

It reminds about the explanation of flight, for which the aerodynamics community only offers a number of different contradictory versions listed on e.g the NASA website as all incorrect, but no explanation claimed to be physically correct. For a physically correct explanation, see The Secret of Flight.

My experience so far (which is the same as that recorded in the Open Letter) is that leading physicists  are not on request willing/able to present a resolution of the twin paradox. What you get is:

• There is no paradox, because SR is free of paradoxes. 
• The paradox was solved very long ago in some way which no longer has any interest. 
• Take a look at what wikipedia says. 
• It can easily be solved within SR by using simple space-time diagrams. 
• A resolution can be found by invoking general relativity, but that is so complicated that details cannot be given. 
• The twin paradox is of interest only to crackpots, not to professional theoretical physicists who have many much more urgent questions to tackle.  

What you don't get is anything claimed to be a correct solution accepted as such by the theoretical physics community. This is more than 100 years after the paradox was formulated.  If you think that what I say cannot be true, try out by asking the question yourself to your physics teacher or college. 

The only way out in this hopeless situation is to opt for the "no paradox" version insisting that SR is logically consistent and as such free of paradoxes and beyond reach for physical paradoxes. But this would mean that SR is not a theory about some physics, which can (appear to) be paradoxical or be false, only a mathematical theory identical to the Lorentz coordinate transformation. The effect of such a step would be far-reaching, since modern physics is based on SR, and if SR is empty of physics that would make a lot of modern physics empty as well. So this way out is not possible...

PS If you repeat your question, because you don't get any reasonable answer, then you are met with anger and frustration, which is understandable if not very pleasant, or simply silence. 

Galilean Special Relativity as a Many-Aethers Theory

Einstein's special theory of relativity SR is based on the following postulates:

1. Laws of physics take the same form in all inertial systems.
2. The speed of light is the same in all inertial systems.

An inertial system is a Euclidean coordinate system in space together with a time coordinate and different inertial systems (with the same spatial orientation) are moving with constant velocity with respect to each other.  

Consider the following realisation of 1+2: Assume

• Inertial systems are connected by a Galilean transformation. 
• Newtonian mechanics.
• Maxwell's equations for electromagnetics in each inertial system.

Newtonian mechanics is Galilean invariant and thus satisfies 1. Assuming that identical Maxwell's equations are used in all inertial systems makes 1 true by definition, and then also 2.

Using formally identical Maxwell's equations in all inertial systems can be viewed as a "many-aethers"-theory with each Euclidean coordinate system representing an "aether" for propagation of light. The speed of light will then be the same in all systems. Compare with this post.

This is the set-up in Many-Minds Relativity as a "many-aethers"-theory. It should be compared with Einstein's "no-aether" SR, where Galilean transformation is replaced by Lorentz transformation. 

A Galilean transformation connects the space coordinates $x$ and $x^\prime$ of two inertial system moving with velocity $v$ with respect to each other by the simple transformation 

• $x^\prime = x-tv$

where $t$ is a time coordinate shared by both systems. A Galilean transformation has a direct simple realisation as a translation  with constant velocity, as the simplest possible motion. 

A Lorentz transformation mixes space coordinates with time and has no physical realisation. Even more disturbing: Newtonian mechanics is not Lorentz invariant and thus has to be given up in SR. Einstein paid his tribute in his "Newton, forgive me!"

How could then Einstein end up with his SR based on Lorentz transformation with all its mysteries and sacking of Newton, starting from the same basic postulates 1+2  as we saw could as well be satisfied by Galilean transformation without mystery and with Newton intact? 

The answer is hidden in Einstein's derivation of the Lorentz transformation from 1 + 2, which starts with light pulses initiated in two different inertial systems. By identifying the two light pulses to be one and the same taking different expressions in the two systems, Einstein then derived the Lorentz transformation. But the identification is unphysical in the sense that initialisation as coexistence at an initial time of a wave form in space necessarily takes different forms in different systems when space is mixed into time. It means that the identification of the pulses cannot be made and so Einstein's derivation of the Lorentz transformation from 1+2 is incorrect from physical point of view.

In his derivation of the Lorentz transformation Einstein relied on the concept of event  as something of unknown nature which has no extension in space, which can be labeled with a single space coordinate $x$ and time coordinate $t$. This made it possible for Einstein to view the launch of the  light pulses as one and the same event with different labels in the different systems and from that derive a connection between the labels in the form of Lorentz transformation.

An event labeled by $(x,t)$ carries unclear physics and can lead to misunderstanding of physics. The notion of particle as something without spatial extension but still physical presence, also can lead to misunderstanding.

Sum up: Einstein's SR is a "no-aether"-theory with strange physics in conflict with Newtonian mechanics. Many-Minds Relativity is a natural "many-aethers"-theory in harmony with Newtonian mechanics and electromagnetics.

PS To see the difference between one-pulse and two-pulse physics, consider two intertial systems which coincide at the light pulse launch. In the Galilean setting the launch physics will be the same in both systems which effectively means launch of two pulses with different translation speeds in two different "aethers", while in the Lorentzian setting they will be the same which is unphysical.

Modern Physics in Free Fall Crisis

Modern physicists in joint free fall under quantum supergravity.

There are many witnesses of a modern physics in serious crisis. The process started at the turn to 20th century modernity with Einstein's special theory of relativity and Planck's derivation of the law of blackbody radiation based on statistics of energy quanta opening to quantum mechanics.

Evidence of the crisis can be seen in the 2019 Special Breakthrough Prize in Fundamental Physics to a 1970 speculation about supergravity, which has resisted 50 years of experimental verification, see also Where are we now?. The Breakthrough website motivates the Prize to supergravity as follows:

• In the four decades since its development, supergravity has had a powerful influence on theoretical physics. It showed that supersymmetry was capable of accounting for all the phenomena we see in the real world, including gravity. It represented a completion of the current understanding of particle physics – a rigorous mathematical answer to the question, “What theories of nature are compatible with the principles of both quantum mechanics and special relativity?” And it provided a foundation for the attempt – still ongoing – to build a full theory of quantum gravity that describes space and time at a fundamental level.

We see that the 2019 Breakthrough Prize concerns precisely the question discussed in this sequence of posts: How to reconcile the principles of quantum mechanics and special relativity? But the 1970 answer in the form of supersymmetry appears to have few proponents today outside the Prize committee as a (failed) "attempt". It is not impossible that the 2020 Fundamental Physics Prize will go to the discovery that special relativity is not fundamental physics, and thus that there is no contradiction with quantum mechanics.   

The shift to modernity was a break-off from classical physics as science of "what is" (ontology) into a modern physics as science of "what we can say" (epistemology) as expressed by Niels Bohr, in which a material world going around even without any (human) observer was replaced by a mist of statistics of (human) observation.

In the new view of modern physics causality/determinism was given up, under much agony because that had been the basic principle of physics since Aristotle, while the monumentality of the sacrifice added to its thrill.  But a sacrifice carries a cost and the cost is now showing up in the form of a modern physics in free fall without any thinkable connection to experiments as string theory in 11 dimensions and multiversa statistics of all possibilities.

What is then the effect of a physics in free fall? Is it helpful to humanity? What was the basic reason that forced Einstein and Bohr followed by generations of modern physicists, to give up causality and rationality?

Einstein was led to special relativity in an effort to handle the lack of physicality of a vacuum or "aether" as a medium for propagation of electromagnetic waves/light. It appeared in experiments like that by Michelson-Morley as if there was not just one single "aether", but many different as if each source/receiver system in motion would "drag" its own aether along. Einstein however could not handle the diversity of many aethers (put forward by e.g. Ebenezer Cunningham) and so took the radical step of declaring that there is no aether at all, in particular not many aethers causing confusing. In modern psycho-physiological terms it could be described as a syndrome of not being able to handle the many sometimes conflicting perspectives of life.

In any case the "no-aether" idea led Einstein into the his special relativity where all observers are compelled to share the same mathematical formulas under a banner of Lorentz invariance, however  without being able to agree on anything else of importance such as simultaneity, time and space. The scientific world met Einstein's special relativity with a yawn as epistemology without physics, which made Einstein turn to his general theory of relativity, which as a consequence of efforts to reconcile England and Germany after World War I in the hands of Eddington, took off in the media and then was turned into a pillar of modern physics.

The trouble was that this pillar was incompatible with the other pillar of modern physics, namely quantum mechanics founded on Schrödinger's equation, which resisted to Lorentz invariance. Modern physics has carried this incompatibility for 100 years as a basic trauma on which much of the present crisis can be blamed, with supergravity as failed attempt to reconcile quantum mechanics with gravitation. The rest of the blame can go to the use of statistics as a collapse of causality/determinism, which was forced from the multi-dimensional form of Schrödinger's equation.

Modern physicists bear witness of the crisis, but I have met little interest in possible ways to take off instead of falling down, by questioning Lorentz invariance and the necessity of a statistical approach to the physics of an atom. But the crisis goes on and maybe some day, discussion will be possible.

The similarity with a climate science dominated by one gospel of alarm is obvious. More precisely, the corruption of climate science today is made possible by the fact that modern physicists have retreated from the world.

The last sequence of posts give arguments that Lorentz invariance has no role to play in physics.
In Real Quantum Mechanics a variant of Schrödinger's equation free of statistics as a system in 3 space dimensions, is presented.

Comments from physicists are welcome. Is any form of discussion possible? Or is the crisis permanent?

PS In many respects modern physics appears as a game of poker, where the physicist player all the time can raise the bet and avoid being called by the public/tax payer. This is what Einstein did, when confronted with questioning of the special theory of relativity, by turning to general relativity, which when questioned was further raised to cosmology. Or when Schrödinger's equations for atoms was confronted with Lorentz invariance and the bet was lifted to Dirac's equation, not for atoms but only for one free electron, and then further to quantum field theory with a universe of infinities, which was handled by "renormalisation" and so on to string theory in 11 dimensions, which cannot be called because it is very far beyond both experimental conformation and refutation.

The Seduction and Spell of the Lorentz Transformation

Modern physics is based on the idea of Lorentz invariance as the basic postulate of Einstein's special theory of relativity:

• Laws of physics are invariant under the Lorentz transformation between different inertial systems, that is, laws of physics are Lorentz invariant.  

Recall that the Lorentz transformation connecting two inertial space-time coordinate systems $(x,t)$ and $(x^\prime ,t^\prime )$ for two observers moving with velocity $v$ with respect to each other, reads:

• $x^\prime =\gamma (x - vt)$, $t^\prime =\gamma (t - vx)$,
• $x =\gamma (x^\prime + vt^\prime )$, $t =\gamma (t^\prime + vx^\prime )$,

where $\gamma = \frac{1}{\sqrt{1-v^2}}$ assuming the speed of light is 1 and $\vert v\vert \lt 1$. We see that the space coordinate $x$ and time coordinate $t$ appear in symmetric form with a an apparent similarity between space and time, which Lorentz viewed to be a formality without physics, but Einstein took as a basis of modern physics with space mixed into time.

Which laws of physics are then formally Lorentz invariant? By the chain law, we have

• $\frac{\partial}{\partial x}=\gamma (\frac{\partial}{\partial x^\prime}-v\frac{\partial}{\partial t^\prime})$,
• $\frac{\partial}{\partial t}=\gamma (\frac{\partial}{\partial t^\prime}-v\frac{\partial}{\partial x^\prime})$,

and so 

• $\frac{\partial}{\partial t}-\frac{\partial}{\partial x}=\gamma (1+v)(\frac{\partial}{\partial t^\prime}-\frac{\partial}{\partial x^\prime})$,
• $\frac{\partial}{\partial t}+\frac{\partial}{\partial x}=\gamma (1-v)(\frac{\partial}{\partial t^\prime}+\frac{\partial}{\partial x^\prime})$,
• $\frac{\partial^2}{\partial t^2} - \frac{\partial^2}{\partial x^2}=(\frac{\partial}{\partial t}-\frac{\partial}{\partial x})(\frac{\partial}{\partial t}+\frac{\partial}{\partial x})$
• $=\gamma^2(1-v^2)(\frac{\partial}{\partial t^\prime}-\frac{\partial}{\partial x^\prime})(\frac{\partial}{\partial t^\prime}+\frac{\partial}{\partial x^\prime})=\frac{\partial^2}{\partial t^{\prime 2}} - \frac{\partial^2}{\partial x^{\prime 2}}$.

We see that the second order wave equation

• $\frac{\partial^2u}{\partial t^2} - \frac{\partial^2u}{\partial x^2}=0$, 

is Lorentz formally invariant, in the sense of reading exactly the same in the $(x^\prime ,t^\prime )$ system.  On the other hand, for the first order wave equation:

• $\frac{\partial u}{\partial t} - \frac{\partial u}{\partial x}=0$,

the multiplicative factor $\gamma (1+v)$ appears, and so only a form of restricted formal Lorentz invariance is in place.

The second order wave equation describes waves in an elastic string with clear material spatial presence or coexistence, as well as plane electromagnetic waves in a vacuum without material spatial presence.  

The idea of Einstein (picked up from Lorentz) was that since the wave equation takes the same form in all inertial systems connected by the Lorentz transformation (more or less), all inertial systems are equally valid (with in particular the same speed of wave propagation/light), which Einstein declared to be the essence of the new physics of the special theory of relativity. This was the seduction of Lorentz invariance which promised to solve the mystery on an "aether" medium for the propagation of electromagnetic waves in vacuum without material presence.   

For both wave equations we see the space coordinate $x$ and time coordinate $t$ appearing in symmetric form, which opens up to some invariance with respect to the Lorentz transformation with similar symmetry.

But the formal symmetry in space and time in the wave equations does not say that space and time have the same nature and can be mixed into each other. In the wave equations there is a clear distinction between space and time which is expressed in the initial condition complementing the wave equation in a mathematical description of a wave $u(x,t)$, which takes the form  

• $u(x,0)=u_0(x)$ for all $x$, 

for the first order equation (with also an initial condition for $\frac{\partial u}{\partial t}$ in the second order case), where $t=0$ is an initial time and $u_0(x)$ an initial wave form with extension in space. With the initial condition a clear distinction between space and time is made. This is physics which is very obvious for the elastic string but also relevant for electromagnetic waves. The initial wave form shows spatial coexistence at different points $x$ for some common initial time $t=0$. 

And now comes the catch showing that the Lorentz transformation is not compatible with physics, even if the wave equation is formally (more or less) Lorentz invariant: The initial condition is not invariant under Lorentz transformation, because $(x,0)$ translates into

• $(x^\prime ,t^\prime ) =\gamma (x, -vx)$, 

which does not have the form of an initial condition for $t^\prime =0$. The physics of coexistence expressed in the $(x,t)$-coordinates through the initial condition for $t=0$ does not carry over to physics of coexistence of an initial condition for $t^\prime =0$. This means that the physics expressed in the different inertial systems is different. The whole idea of relativity of expressing the same physics in different inertial systems thus collapses.

The formal symmetry of the space and time coordinates in the two forms of the wave equation misled a confused Einstein to believe that space and time could be mixed, because Einstein did not properly understand the physical meaning of the mathematics of the wave equations. The sad fact is that generations of physicists have followed in the footsteps of Einstein with a mantra of Lorentz invariance as a necessary requirement of a law of physics.

A traveling wave is a solution $u(x,t)$ of either of the above wave equations of the form 

• $u(x,t)=f(x+t)$, 

where $f(\cdot )$ is a function of one variable. For example $f(y)=\sin(y)$ with 

• $u(x,t)=\sin(x+t)$. 

The initial condition for $t=0$ would then have the form $u_0(x)=\sin (x)$ as a wave in space, while an observer sitting at $x=0$ would experience a wave in time of the form $\sin(t)$, but the observer would have no reason to mix the wave in space with the wave in time just because the mathematics looks the same. To do that as Einstein did, shows that the mathematics is misunderstood.

The second order (but not the first order) equation also has standing wave solution of the form

• $u(x,t)=sin(t)sin(x)=\sin(\gamma (t^\prime +vx^\prime))\sin(\gamma (x^\prime +vt^\prime ))$,

with seemingly stationary spatial character in $(x,t)$-coordinates, but visibly not so in $(x^\prime ,t^\prime )$ coordinates. A standing wave solution is not Lorentz invariant. A standing wave for the observer using $(x,t)$-coordinates is not a standing wave for the observer using $(x^\prime ,t^\prime )$, of course not since the observers are moving with respect to each other.

In general the equations of mathematical physics do not show the symmetry of space and time of wave equations and thus do not show any Lorentz invariance at all. The physics is the same for all observers but its mathematical description varies between moving observers, as soon as the physics has some spatial presence, which is the nature of physics.  Only Maxwell's equations for vacuum can show formal Lorentz invariance, but not in the presence of charges and not with respect to initial conditions. The equations of physics are not Lorentz invariant. Not Maxwell with charges, not Schrödinger, not MHD, not Navier, not Navier-Stokes, not anything.

The net result is that the notion of Lorentz invariance has only a purely formal mathematical meaning and carries no real physics. If the spell of Lorentz invariance can be broken, then many possibilities  to progress seem to open up. But this is not something physicist like to hear. They will cling to Lorentz invariance no matter the cost and lack of reason. It is a spell.

Getting out of the spell means understanding that Leibniz distinction between space and time is valid also for modern physics:

• space = order of coexistence.
• time = order of succession.

But the spell has such strong grip on the minds of modern physicist that not even a basic discussion is possible.

Why so Difficult to Discuss Special Relativity with Physicists?

I fooled you. 

The attempted discussion with Swedish media physicist Ulf Danielson illustrates the difficulties met when trying to discuss aspects of the special theory of relativity SR with physicists, who must defend SR by all means to keep their academic jobs. The difficulties arise because, in a tradition mastered by Einstein, it is never clear what the premises are. In particular, there are several forms of SR:

• SR = consequences of the two postulates of SR. (1. Laws of physics must take the same form in all inertial systems. 2. Measurements of the speed of light must give the same result in all inertial systems).
• SR+ = SR + some physics.
• SR++ = SR+ + some more physics.

The postulates of SR have the form of stipulations without concrete physical content and the Lorentz transformation derived from the postulates is a coordinate transformation between inertial systems, which as such has no concrete physical content. Postulate 1 says that laws of physics must take the same form in all inertial systems, that is they must be Lorentz invariant. SR is thus empty of real physics as a specific coordinate transformation, which has no truth value as being the result of stipulations without concrete physics. Einstein's used the term Postulate to signify that SR is based on stipulations without truth value and not propositions about physics, which may be true or false. Since Postulates 1 and 2 are not contradictory, a physicist can argue that SR is not contradictory.

On the other hand, one can argue that Postulates 2  is a consequence of Postulate 1 and as such redundant, but not contradictory. 

SR+ = SR + Maxwell's equation for electromagnetic waves in a vacuum can be argued to be correct physics because Maxwell's equations for vacuum describe physics and are Lorentz invariant. But SR does not add anything to such a picture and can then as well be discarded.

SR+ with physics in the form of clocks and traveling symmetric twins with unsymmetric ageing leads to a paradox, which is "resolved" by adding some more physics like one twin staying at rest at home and the other traveling undergoing acceleration and retardation into a S++ with unsymmetric ageing seemingly without paradox. 

In this way SR+ can be just anything and as such can be twisted to fit with observations with the message that SR+ has experimental support including the postulates of SR, which in fact are stipulations beyond experimental verification. By adding some physics some experimental support can be constructed, but the role of SR itself is then unclear since the support concerns the added physics.

A physicist can thus ague that SR in basic form contains no contradiction, and in suitable SR+ form has experimental support. The message is that SR is a theory without contradiction, which has massive experimental support. It could not be better. With this message the physicist can keep his job.

But there is one form of SR+ which shows to be incompatible with experiments, and that is SR+ = SR+gravitation, which was the dream Einstein had to abandon as soon as SR was confronted with the reality of gravitational forces. A desperate Einstein tried to save his scientific life by cooking up a form of SR including gravitation, by effectively reducing to SR without gravitation by sweeping gravitational forces/acceleration away into geometry, named general relativity. Einstein thus gave up the basic stipulation of SR of Lorentz invariance to keep his job. The question is why today physicists have to in public confess to the sermon of Lorentz invariance to keep their jobs: When laws of gravitation are not Lorentz invariant. When Schrödinger's equation of quantum mechanics is not Lorentz invariant. When the equations describing the mechanics of solids and fluids are not Lorentz invariant. When Maxwell's equations with charges are not Lorentz invariant. Why cling to Lorentz invariance when doing so misses the whole cake? 

Summary: SR + Maxwell in vacuum is fine, but here SR has no role since Maxwell in vacuum carries itself. SR + gravitation does not work. The net result is that SR can be put into the wastebin of thought experiments without physics, and when that is done a step forward can be taken. Too long has physics been forced into a straitjacket of Lorentz invariance invented by the young ambitious Einstein from which the mature Einstein managed to escape but not his followers. 

Why the Speed of Light Can Be Independent of Translation of Source-Receiver

To see that it is most natural that the speed of light between a source and receiver is independent of translation with constant velocity of both source and receiver, as if the "aether" was moving along with the same velocity, consider the following mechanical analog: 

Connect a source to a receiver by waves carried by a stretched rope with the source at one end and the receiver at the other end, and assume that the whole system source-rope-receiver is subject to a translation with constant velocity. We would then make the observation that the speed of propagation of the waves from source to receiver through the rope would be independent of the translation. 

This is because the rope as the medium for wave propagation moves along with the source/receiver. The analog would be an "aether" as an immaterial medium for propagation of light waves, which moves along with the source/receiver. The idea is that the light source and receiver establishes a connection like a rope which is moving along with the source/receiver.  This would be compatible with the null result of the Michelson-Morely experiment.

There is thus no common background aether, but a multitude of aethers connecting and moving along with a multitude of sources/receivers.  The immaterial quality of aethers would then allow a multitude without conflict. This is the idea of Many-Minds Relativity. Think of that.

PS If the source and receiver move with respect to each other they could still share a common aether (connected to either source or receiver) with still  he same speed of light, while light frequencies would be subject to Doppler effects. 

Special Theory of Relativity Incompatible with Gravitation

Sorry to say, but I had to abandon my most beautiful special theory of relativity SR because it could not be combined with laws of gravitation. The demand of Lorentz invariance of course was not compatible with the presence of matter in space.
I thus turned to the general theory of relativity giving up Lorentz invariance for covariance, and never returned to SR. 

From its start in the 1905 article On the Electrodynamics of Moving Bodies, Einstein connected his special theory of relativity SR to Maxwell's equations for electromagnetic waves. From the two Postulates of SR (1. Relativity Postulate and 2. Constancy of speed of light). Einstein derived the Lorentz transformation connecting coordinates in different inertial systems moving with constant velocity with respect to each other. The catch was that Maxwell's equations in vacuum showed to take the same form in all coordinate systems connected by the Lorentz transformation and thus showed to be Lorentz invariant as required by the Relativity Postulate.

Einstein then tried to extend SR with its requirement of Lorentz invariance to gravitation, but failed and so Einstein abandoned SR for his general theory of relativity. The situation is the same today:

• SR cannot be extended to include gravitation. 
• Laws of gravitation are not Lorentz invariant.

This is shown in e.g. Relativistic Theories of Gravitation by Withrow and Murdoch giving a survey of attempts to extend SR to gravitation,  all failing because of incompatibility with observations. The trauma of modern physics can thus be captured as follows:

• Newton's mechanics is Galilean invariant but not Lorentz invariant.
• Maxwell's equations are not Galilean invariant, but Lorentz invariant (in a restricted sense).
• SR is incompatible with mechanics including quantum mechanics.

The trauma is a result of insisting on the Relativity Postulate asking a "law of physics" to have the same formal expression in all inertial systems connected by the Lorentz transformation, that is to require Lorentz invariance. 

What then to do? 

1. Allow the trauma to continue to paralyse modern physics? 
2. Give up Lorentz invariance as a necessity to impose on laws of physics?  

I suggest 2. This means that SR is given up because it is incompatible with in particular laws of gravitation. Laws of gravitation cannot be Lorentz invariant if they are going to match observations. This was what Einstein understood when turning to his general theory of relativity. If a theory does not fit with experiments, like SR with gravitation, then it has to be given up.

What then would be the effect of giving up SR? Nothing! It is illustrated by the fact that GPS system works because SR is not included, not because SR is included.

What then about the null result of Michelson-Morley experiment, as the main motivation for asking for Lorentz invariance? Is it possible to explain the null-result without invoking Lorentz invariance? Of course, as will be shown in an upcoming post.

The reason Maxwell's equations in vacuum can be viewed to be formally Lorentz invariant, that is take the same in all inertial frames, is that the vacuum has no material presence in space. As soon as you introduce material presence in space in the form of charges or matter, the idea of Lorentz invariance collapses because necessarily the spatial motion of the inertial system vs the charges/matter must come in. Since SR is incompatible with any form of material/spatial presence, it has to be given up, as Einstein did. Galilean invariance is meaningful, but not Lorentzian.

I have argued that the two postulates of SR themselves are empty of physics. It is possible to give SR a restricted physical meaning by combining the postulates with Maxwell's equations in vacuum showing some compatibility with experiments.  But adding physics in the form of gravitation has shown to not be compatible with experiments. It is now time also for us to give up SR, following Einstein.

Or restrict SR to the domain of its postulates without combination with any physics, in which case SR is empty of physics and carries no incompatibility with observation of physics.

PS In the debate with Ulf Danielson in a previous post, it was not made clear what physics was appended to the two postulates of SR themselves empty of physics, which led to a lot of confusion. Let's see if UD will take up the challenge and comment this post...

Does the Period of a Harmonic Oscillator Change under Uniform Translation?

High speed trains in China in uniform translation with identical clocks.

The most basic of all clocks is a harmonic oscillator consisting of a body of unit mass connected by a linear spring to a fixed point, described by the differential equation expressing Newton's 2nd Law:

• $\frac{d^2x}{dt^2}=(x_0-x)$   (1)

where $x(t)$ is the position of the body at time $t$ on an $x-axis$ and $x_0$ is the fixed point with $x_0-x$ the spring force. The solution $x(t)$ is periodic in time with period $2\pi$.

Suppose now we introduce another coordinate axis with coordinate $x^\prime = x-vt$, where $v$ is a given constant velocity, expressing that the $x^\prime$-axis moves with the constant velocity $v$ with respect to the $x$-axis in uniform translation. Substituting $x=x^\prime +vt$ into (1), we get

• $\frac{d^2x^\prime}{dt^2}=(x_0^\prime-x^\prime )$   (2),

because $\frac{d^2(vt)}{dt^2}=0$. We see that (1) reads identically the same as (2) sharing the same time $t$. We thus see that the motion of a harmonic oscillator is Galilean invariant since the equation describing the motion reads the same in the two space coordinate systems connected by the Galilean transformation $x^\prime = x -vt$ of uniform translation.

One way to express our experience is to say that the motion of a harmonic oscillator including the period is independent of uniform translation. This is what we expect: It is unthinkable that the physics including the period of a harmonic oscillator, could be influenced by uniform translation. Your clock must tick the same rate waiting for the train in the train station and in the train in uniform translation. Anything else is unthinkable, based on the basic Newtonian mechanics of a harmonic oscillator. 

But the special theory of relativity SR says that the clock in motion ticks at a slower rate. 

What is your conclusion? Evidence that SR is correct or false from a physical point of view?

PS1 Note that (1) has the same form in all inertial systems under uniform translation and thus satisfies Einstein's Relativity Postulate. What is then wrong with (1) from the view of SR? Well, SR is obsessed with the speed of light, but a harmonic oscillator has nothing to do with light because it is a mass-spring system. So what is wrong with the harmonic oscillator form the point of view of SR is that it is mechanical, but is it anything wrong with being a mechanical system?  Isn't a harmonic oscillator an example of basic physics?  If not, what physics is then SR?

PS2 To see that (1) is not Lorentz invariant as required in SR, recall this post. It means that (1) from the point of view of SR is not a law of physics. Einstein thus claims that a harmonic oscillator is not physics.  Do you agree?

PS3 Things like this appears to be impossible to discuss with physicists seemingly brain-washed by special relativity.

Special Relativity Theory for One Observer?

A One-King system can be very stable.

Einstein's special theory of relativity concerns the relation between observations (of "events" without spatial extension recorded by space-time coordinates (x,t)) made by different observers using different inertial coordinate systems moving with constant velocity with respect to each other.

Suppose there is only one observer making observations in only one coordinate system in which the observer is at rest. Let us refer to this as a one-system situation. Can there be any special relativity theory for this one-system with its single observer/inertial system? Of course not. With only one  inertial system there is no room for comparison with observations in another moving inertial system. The special theory of relativity is empty for a one-system.

Now, the GPS system is a one-system based on the WGS84 spherical (ellipsoidal) coordinates system we are used to with latitude, longitude and height for spatial location, and an Earth based master clock setting common time, which is what your GPS receiver can report to you. The GPS system is thus a one-system and as such has no use for the special theory of relativity. In this one-system, the position of moving satellites are recorded by one master observer at rest on Earth and satellite clocks are synchronized with the master clock to UTC Universal Central Time (with nanosecond precision). There are no observers, sitting in the satellites making observations in moving inertial systems requiring coordination using the special theory of relativity. This is a one-master one-system for which the special theory of relativity has nothing to contribute.

This is yet another observation that GPS does not depend on the special theory of relativity.

PS We may compare with Deng Xiaopin's idea of one country - two systems, which we now see is collapsing in Hong-Kong. A one-system appears to be more stable, which is also what we expect from GPS.