What Is Special Relativity without the Lorentz Transformation?

Many-Minds Relativity MMR is an alternative to Einstein's Special Theory of Relativity SR. Let us bring out the essential difference between MMR and SR.

Let us start noting that MMR and SR share the same basic Postulate:

• The speed of light is the same in all internal systems.

An inertial system is a spatial Euclidean coordinate system with space coordinate $x$ combined with a time coordinate $t$ into a space-time system with coordinates $(x,t)$. Inertial systems move with constant velocity with respect to each other.

The set-up in MMR is a collection of observers $X$ equipped with inertial systems with space-time meter-second scales set by the 1983 SI standard with meter defined as a certain fraction of a lightsecond and second defined by a standard cesium clock. The light speed will then be the same in all inertial systems. 

MMR studies the relation between descriptions of physics by different observes using different inertial systems in which the observer is stationary. MMR contains in particular physics which can be expressed in one privileged system in which the observer is stationary (like an Earth based observatory).

The set-up in SR is different. In basic form SR boils down to the Lorentz transformation as a coordinate transformation connecting coordinates in different inertial systems, which is supposed to be a consequence of the Postulate.  SR is thus empty of content in the case of one privileged system since the Lorentz transformation involves two systems. In the case of two systems with two observers $X$ using an $(x,t)$-system and $X^\prime$ an $(x^\prime ,t^\prime )$-system, SR dictates that an event labeled $(x,t)$ to $X$ will have to be labeled $(x^\prime ,t^\prime )$ to $X^\prime$ by the Lorentz transformation. The effect is that $X^\prime$ will see effects of space contraction and time dilation in the $(x,t)$-system vs her/his own system, and vice versa. In particular, $X^\prime $ will see a slowing down of the clock/time of $X$, and vice versa.  

MMR studies the same physics as experienced by different observers in different inertial systems. MMR is meaningful with just one observer. MMR is compatible with the 1983 SI standard.

SR assumes that observations by different observers in different systems are identical, as an expression of relativity according to Einstein. Instead SR is concerned with the view of one observer on the observations by another observer in another system. SR has no meaning for just one observer, does not compare the observations of different observers in different systems (because they are supposed to be identical), and is concerned instead with the view of one observer on something described in another system than her/his own. This connects to Matthew 7:3:

• Why do you look at the speck of sawdust in your brother's eye and pay no attention to the plank in your own eye?

SR also has a most unclear relation to the SI standard.

In MMR each observer makes observations in her/his own system, and compares with that of other observers in other systems if there are more than one.

In SR each observer focusses interest not on observations in her/his own system, but on observations made in other systems, and so has nothing of interest to say alone from observations in her/his system. 

Hopefully this discussion can help to clarify what SR is about, which is truely mysterious as witnessed by all leading physicists as a wonderful new aspect of modern physics, which however connects back to the Dark Age rather than Enlightenment.

PS The basic theories of physics take the form of physical laws expressed as differential equations such as Newton's 2nd law and law of gravitation, Euler's equations for fluid mechanics, Boltzmann's equations for gas dynamics, Maxwell's equations for electromagnetics, Schrödinger's equation for atom physics, and even Einstein's field equations. SR does not have this form, but is instead basically a coordinate transformation. There is no other theory of physics which has this form. Can a coordinate transformation contain any physics? Does a transformation from meter to yard bring in any physics?