Can a Coordinate Transformation Contain Physics?

The Special Theory of Relativity SR is identical to the Lorentz coordinate transformation. The General Theory of Relativity involves as an essential step transformations of space-time coordinates. 

Many-Minds Relativity shows, in a careful mathematical analysis, that SR is empty as a theory about real physics. The argument is in brief that since SR is identical to the Lorentz transformation, and a coordinate transformation in itself does not contain any physics, SR is empty of physics. 

Why does a coordinate transformation not contain any physics? Consider for example the coordinate transformation of a pure translation from an $x$-axis to an $x^\prime$-axis, as 1d Euclidean coordinate systems, of the form $x^\prime = x - v$, with $v$ a constant.  One property of such a transformation is that distances are conserved, or are invariant, under transformation: If $x^\prime = x - v$ and $y^\prime = y - v$, then $x^\prime - y^\prime = x - y$. So far no physics has been introduced and so the coordinate transformation cannot have any physical meaning. A natural way to give physical meaning is to say the coordinate $x$ represents the position of a physical body $X$ and $y$ the position of a body $Y$. The positions of $X$ and $Y$ can then alternatively be expressed in terms of $x^\prime$ and $y^\prime$. 

Now, can we say that the transformation contains any physics of the position of the bodies? Can we say that since the transformation expresses that distances are conserved under the transformation, we can conclude a law physics expressing that translation of a rigid body does not change the shape of the body? Is this a law of physics, which may be false, or simply a law of logic or language and not physics which cannot be false? I guess, you we would agree with me that it is not a true law of physics. That a rigid body does not change shape is built in into the meaning of a rigid body, and has nothing to do with physics with the shape of a body determined by physical forces. It cannot be used to say that in a rigid body there are forces which maintain its shape. It would be like pulling a rabbit out of an empty hat.  

Choice of coordinate systems in physics directly connects to the choice of units in physics. If you believe that the choice of units contains physics, that using a meter stick instead of yard stick changes the size of physical objects, then you are well prepared to accept the wonders of SR. If you understand that this is not the case, then you will (like me and many others) have a hard time with SR. 

We can add a common time coordinate $t$ to the $x$ and $x^\prime$ systems into a Galilean space-time transformation of the form 

• $x^\prime = x-vt$, $t^\prime =t$,

between a $(x,t)$-system and a $(x^\prime ,t^\prime)$, with the $x^\prime$-axis translating with respect to the $x$-axis with speed $v$, but still with the same lack of real physics.

The Lorentz transformation of SR is a similar linear coordinate transformation from a a space-time $(x,t)$-system to a space-time system $ (x^\prime ,t^\prime )$-system of the form 

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

where $\vert v\vert <1$, with now also the time variable beeing subject to transformation, and in particular the property that a $x = t$ is transformed into $x^\prime  = t^\prime$ and back.

In order for the Lorentz coordinate transformation to contain physics, the coordinates must be given some physical meaning. Einstein did this by associating space-time coordinates $(x,t)$ to events (of some unspecified physical nature) or rather to observations of events (of some unspecified physical nature), like a body $X$ observed to be at position $x$ at time $t$. Einstein associated the system $(x^\prime ,t^\prime )$ to represent coordinates with the $x^\prime$ axis translating with speed $v$, like in the Galilean transformation, but now with also the time variable being subject to transformation.

Einstein then created SR by drawing conclusions about physics from the Lorentz transformation, like the fact that $x=t$ is the same as $x^\prime =t^\prime$ interpreted by Einstein to mean that a light signal always propagates with speed 1 in any (inertial) coordinate system. Einstein then proceeded to derive properties of space contraction and time dilation from the Lorentz transformation and boldly claimed that he thereby had discovered new truely astonishing real physics (apparently from mysterious forces twisting space and time). 

Many early critics said that this was empty physics, for the reasons exposed above, but somehow Einstein managed to twist the brains of the physical community into believing that he had revealed deep new truths about real physics. This came to serve as footstep into modern physics, as weird empty physics based on transformations of coordinates brought to full bloom in the General Theory of Relativity in curved space-time.  

Galileo of course understood that his coordinate transformation does not contain any real physics. Why do modern physicists insist that the Lorentz transformation contains real physics?  Lorentz did not believe so, but he was quickly side-stepped by not being modern enough. 

Modern physics is in deep crisis. Why? Is it time now for post-modern physics?

The crisis is expressed in the obsession of modern physicists to focus efforts on a Theory of Everything a ToE, with the aim of explaining the basic four forces (electromagnetic, weak and strong nuclear and gravitation) as different manifestations of one basic force/interaction. No progress towards an answer has been made and the mystery of the origin of the four forces is as mysterious today as ever.   

Einsteins "Scientific Method": Magic Physics from Definition

Einstein "scientific method", which brought him immense fame as the greatest physicist of all times, consists of:

• Start from a definition, convention or stipulation/law without physical content, and then draw far-reaching consequences about the physics of the world.

It is not hard to understand that such a "method" cannot work: You cannot draw meaningful conclusions about the world simply from a definition empty of physics content. You cannot develop a meaningful scientific theory from a definition that there are 100 centimeters on a meter. 

Einstein cleverly covered up by naming his definitions or conventions or stipulations/laws, "principles":

1. Equivalence Principle: Gravitational mass is equal to inertial mass.
2. Relativity Principle: Observations in inertial coordinate systems moving with constant velocity with respect to each other, are to be connected by the Lorentz transformation.
3. Covariance Principle: Physical laws are to have the same form independent of the choice of coordinate system.

Here 1. is an empty definition, because there is only one mass, and that is inertial mass, which measures acceleration vs force and gravitational force is a force. Gravitational mass is equal to inertial mass by definition. Attempts to "prove/verify" this experimentally, which are constantly being made with ever increasing precision and always with the same result of equality, are as meaningful as experiments attempting to verify that there are 100 centimeters on a meter, which could very well be the next grand challenge for LHC, in the spirit of Einstein.

2.  stipulates that different physical phenomena are to be viewed to be the same. This is because the Lorentz transformation is not invariant with respect to initial conditions, and thus Einstein stipulates that  two waves satisfying the same form of wave equation, but having different initial conditions, shall be viewed to be the same. No wonder that with this play with identities, all sort of strange effects of time dilation and space contraction can be drawn out of  a magicians hat.

It is clear that physical laws in general take different forms in different coordinate systems, and thus 3. is an absurd stipulation. Alternatively, it is trivial and just says that a physical law will have to transform when expressed in different coordinates so that the law has the same physical content. So 3. is either absurd or trivial, in both cases devoid of physics.

It is depressing that none of this can be understood by leading modern physicists. Nada. Even more depressing is that the discussion is closed since 100 years.

Simultaneity as Non-Physical Convention along with Special Relativity

The book Concepts of Simultaneity: From Antiquity to Einstein and Beyond is presented by:

• Max Jammer's Concepts of Simultaneity presents a comprehensive, accessible account of the historical development of an important and controversial concept—which played a critical role in initiating modern theoretical physics—from the days of Egyptian hieroglyphs through to Einstein's work in 1905, and beyond. 
• Beginning with the use of the concept of simultaneity in ancient Egypt and in the Bible, the study discusses its role in Greek and medieval philosophy as well as its significance in Newtonian physics and in the ideas of Leibniz, Kant, and other classical philosophers. 
• The central theme of Jammer's presentation is a critical analysis of the use of this concept by philosophers of science, like Poincaré, and its significant role in inaugurating modern theoretical physics in Einstein's special theory of relativity. 
• Particular attention is paid to the philosophical problem of whether the notion of distant simultaneity presents a factual reality or only a hypothetical convention. The study concludes with an analysis of simultaneity's importance in general relativity and quantum mechanics.

In earlier post on I have argued that simultaneity in time at distant points in space is a man-made convention, which is useful to humanity in many ways including GPS, but as convention has no role in describing the physics of material bodies without GPS receivers.  Jammer presents much evidence supporting this view without closing the door to simultaneity as some form of factual reality.

Einstein's special relativity came out from an a simple thought experiment showing that agreement on distant simultaneity defined by a certain conventional form of clock synchronization set up by Einstein, cannot be established for different observers moving with speeds comparable to the speed of light with respect to each other. 

Einstein thus started from a certain ad hoc man-made convention and from the impossibility of making the convention work for moving observers Einstein jumped to the conclusion that our concepts of the physics of space and time will have to be fundamentally changed. And the world  jumped along. But is it possible to change physics by man-made convention? Can we change physics by changing our man-made conventions to measure time and space, by changing from yard to meter? I think not. 

Why believe that special relativity is real physics, when special relativity is based on an impossibility to make a certain man-made convention work?

I have stressed that the notion of distant simultaneity is present in the standard form of Newton's law of gravitation as Poisson's equation $\Delta\phi =\rho$, seemingly creating a gravitational potential $\phi (x)$ depending on a Euclidean space coordinate $x$ from instant action at distance by a primordial matter distribution $\rho (y)$ with $y$ different from $x$,  represented as $\phi =\Delta^{-1}\rho$ with the inverse $\Delta^{-1}$ a non-local (integral) operator.

On the other hand, viewing the gravitational potential $\phi$ as primordial and $\rho =\Delta\phi$ as derived by local differentiation, there is no need to explain the physics of instant action at distance, which Newton left open under the criticism of Leibniz and which has resisted all attempts after Newton.

We conventionally view matter $\rho$ as primordial, since we can see matter at distance if it is sending out light, while we cannot see the gravitational potential $\phi$, only feel that it is there. 

But with a different eyes we may be able to see the gravitational potential $\phi$, but not $\rho$, and we would then naturally view $\phi$ to be primordial. With such eyes we might be able to see a gravitational potential of dark matter and dark energy, which we now cannot see, only feel that it is there.   

Instant Action at Distance and Simultaneity not Needed in New Theory of Gravitation including Dark Energy

                           Einstein won the game. But what was the game about? Simultaneity?

Einstein's theory of relativity grew out from a question of simultaneity in time of events at different locations in space, which Einstein could not answer in a non-ambiguous way and then jumped to the conclusion that a fundamental revision of our concepts of space and time was necessary. Einstein took so on the responsibility in the service of science and humanity to make the revision and thereby open the door to a modern physics of "curved space-time" with all its wondrous new effects of time dilation and space contraction, albeit too small to be detected.

It is clear that simultaneity plays an important role in our society, to set schedules and allow people to meet at the same place and for these purposes we all have clocks synchronized to a reference clock. And to decide which scientist first submitted an article reporting a certain new scientific break-through and to navigate...

But what role does simultaneity play in physics? In what sense do distant physical objects care about simultaneity? Do they all have synchronised clocks? Of course not. What they do is to react to local forces acting locally in time, and no simultaneity with the action of distant objects is involved.

Or is it? What about gravitation, isn't it supposed to act instantly over distance and thus require a form of exact simultaneity? Yes, it so seems because in Newtonian gravitation the Earth is instantly acted upon by a gravitational force from the Sun directed towards the present position of the Sun, and not towards the position where we see the Sun because of the 8 minute time delay of the light from the Sun.

The standard view on gravitation, is thus that the presence of matter instantly generates a gravitational potential/force (Newton) or "curvature of space" (Einstein) at distance. This view comes with the following questions:

1. What is the physics of the instant action at distance? Gravitons?
2. What is the physics of the simultaneity associated with instant action? 

Since no progress towards any form of answer has been made over all the centuries since Newton, it is natural to shift and instead view the gravitational potential $\phi$ as primordial from which matter density $\rho$ is obtained by the differential equation acting locally in space and time:

• $\Delta\phi =\rho$.    (*)      

With this view there is no instant action at distance to explain and no associated simultaneity, since the action of Laplacian $\Delta$ as differential operator is local is space and time. 

It may thus be that the questions 1. and 2. are not the right questions, and then also that Einstein's relativity originating from a question about simultaneity, is not the right answer to the right question.

More precisely, simultaneity does not appear to be a matter of the physics of the world, since atoms are not equipped with a man-made system of synchronised clocks, and so it is not reasonable to make a complete revision of Newtonian mechanics starting from an ad hoc idea of probably little significance.        

The equation (*) further suggests that with $\phi$ primordial there is no reason to insist that $\rho$ as a derived quantity must be non-negative, thus (*) opens to the possible existence of matter density $\rho$ of both signs, that is to both positive and negative matter. 

This idea is explored in the app Dark Energy on App Store with in particular a simulation of a universe resulting from a fluctuation of the gravitational potential with associated positive and negative matter, with the negative matter forcing a positive matter world into accelerating expansion, which may be the missing dark energy you are looking for. Try it!

Physics Illusion 3: Explanation of Michelson-Morley Null Result

In the previous post we considered a system of two distant resonators E and R connected by electromagnetic waves in a vacuum between the resonators, which can take the following form

• E = radio mast - vacuum - R = radio receiver
• E = mobile phone mast - vacuum -  R = mobile phone
• E = radio star - vacuum - R = radio telescope
• E = visible star - vaccum - R = telescope/eye.  

The velocity of the  E-vacuum-R system is here irrelevant as the system acts like one unity with E and R being connected by standing waves carried by an immaterial vacuum, which can be assumed to "move along with" E and R. 

The Michelson-Morely experiment was set up to detect possible motion of the Earth through an "ether medium" carrying electromagnetic waves, by comparing the travel time of light signals in two perpendicular directions using a system of mirrors: 

But no motion could be detected as if the "ether medium" was "dragged along" by the Earth. This was viewed as a contradiction to classical electromagnetics described by Maxwell's equations. To handle the illusion of contradiction, relativity theory was developed seeking to explain the Michelson-Morely null result by entirely new phenomena of length contraction and time dilation, which sent modern physics into a nightmare of mysteries.

However, it is possible to explain the Michelson-Morley null result without resort to mysteries of relativity: If we consider each pair of mirrors as a rigid system connected by standing electromagnetic waves in a vaccuum, then the orientation and velocity of the system will not affect the inner working of the system. The system acts like a clock ticking at the same rate independent of orientation and velocity. 

The key is that electromagnetic waves are carried by a vacuum which by its immaterial nature can be viewed to move along with the pair of mirrors. The immaterial nature makes it possible to envision many different vacuui. We cannot eat the same piece of food, but we can share the same immaterial ideas with any number of people.  

This is developed further in Many-Minds Relativity based on the principle that each observer is fixed to the origin of a Euclidean coordinate and relies on Maxwell's equations in this coordinate as a representation of the vacuum carrying electromagnetic waves. Different observers moving with respect to each other thereby use different coordinate systems or vacuui. Different observers will then have the same experiences inside their respective systems as a reflection of the Michelson-Morley null result. Different observers will be able fully agree about certain observations such as Michelson-Morley and the speed of light, but not fully about all observations. Full coordination is not possible but nor necessary. 

Einstein's special relativity seeks to establish full coordination by a dicate, but as any dictate against natural order, it is destructive.

Note that the resonators communicating by electromagnetic waves in a vaccum, connects to the New View of Motion under Gravitation without Classical Mysteries, where large scale material motion is an illusion created by real small scale circular wave motion. Energy is thus transferred from one resonator to the other by transversal electromagnetic wave motion in a vaccum, but there is no stream of "particles as packets of energy" through the vacuum connecting the resonators.

Physics Illusion 1: Gravitational Attraction as Instant Action at Distance

In New View of Motion under Gravitation I suggest to view gravitational potential $\phi (x,t)$ as primordial and matter density $\rho (x,t)$ generated by $\phi$ by action of the Laplacian: $\rho (x,t) =\Delta\phi (x,t)$ which is local space and time, with $x$ a Euclidean space coordinate and $t$ time.

With this view there is no action at distance, which is the main unresolved mystery of Newton's mechanics with matter density $\rho$ primordial and gravitational potential $\phi$ as the solution of the differential equation $\Delta\phi =\rho$.  Istant action at distance has never been explained.