This website first considered the subject of relativity in terms of a learning process of ‘accepted science’ under the heading ‘A Relative Perspective’. However, at the end of this initial process, doubts had emerged about the logic and scope of the verification process surrounding many aspects of relativity, especially in terms of any causal mechanisms that explained the fundamental idea of time dilation or length contraction. As a consequence, the idea of a wave model was reviewed, initially in terms of the WSM model as proposed by Milo Wolff, where the ‘Relative Effect’ on different reference frames was further considered. However, as the WSM model appeared to have issues of its own, the idea of a ‘Wave Theory of Everything (WSE)’ was developed, not as a new model, but rather as the requirements that had to be placed on any wave model that wished to address the perceived problems associated with both the relativistic and quantum models – see Quantum Issues for more details of the latter. Under the WSE heading, the issues associated with relativity, both special and general, were again outlined. Later, a more detailed review of the MMW model widen the review of the ‘scope of assumptions’ of this wave model and its potential implications on accepted science. While aspects of the MMW model have also been questioned, its author, Gabriel LaFreniere, has possibly provided a coherent description as to why time dilation and length contraction might physically take place within the structures of his wave model.
Note: While the various reviews cited above never claimed to be authoritative, they appeared to highlight too many fundamental issues associated with Einstein’s model of relativity to simply be ignored. However, it appears that most of the wave models reviewed may also have limitations, even though they may provide a more plausible explanation of the causal mechanisms underpinning fundamental reality than simply relying on mathematical models.
Today, there are many papers that have attempted to highlight the errors in Einstein’s mathematical derivations associated with special relativity, which are broadly based on the Lorentz transforms. However, few of these papers even attempt to forward any causal mechanisms that might physically explain why time dilation and length contraction might actually occur. For this reason, this discussion will essentially be a summary of some of the salient arguments forwarded by the MMW model in respect to the Doppler effect, the Lorentz transforms and relativity. However, there is possibly some benefit in initially outlining some of the historic developments and assumptions that surround SR along with some links to additional information. Prior to SR, Newtonian physics, inclusive of the laws of motion and gravitation, had broadly defined the central ideas of classical physics. Then, in 1905, Albert Einstein proposed the Theory of Special Relativity that has now been generally accepted to supersede Newton’s idea of space and time.
- Newton’s Assumptions: An infinite number of inertial
frames can exist and relative uniform motion between any two inertial
frames can be conceptually measured. Within this model, time is absolute
and therefore universally applies to all frames of reference, such that
the Galilean transforms can be used to translate between two inertial
- Einstein’s Assumptions: The velocity of light [c] is a constant across all frames of reference and is independent of the velocity [v] of the source or receiver. The velocity [c] of light in a vacuum is the maximum velocity between any two reference frames. This leads to the idea that time is no longer absolute and each reference frame experiences its own ‘local’ time, such that the Lorentz transforms are required to translate between any two inertial frames, where the laws of physics are assumed invariant in all inertial frames.
Note: The idea that the velocity of light [c] is independent of the velocity [v] of the source is often initially presented by analogy to the velocity [u] of an object thrown from a train with velocity [v], such that it results in a combined velocity [v+u]. However, sound waves in air might be a better analogy, which are known to be independent of the velocity of the source or receiver, as the velocity of sound [c’] is the property of the propagation media, although Doppler Effects can confuse this situation.
As part of this initial introduction, the following concepts are simply highlighted for reference:
- Isotropy of Space: An
[μ], which is uniform in all directions of the medium, e.g.
of Space: Assumes that the property of space is consistent at every
point and has no irregularities, at least, when considered on the scale
of the universe. However, this definition of homogeneity is often based
on the particle or energy density within a volume of space, not space
itself. Therefore, the homogeneity of ‘space’ requires an actual
definition as to whether ‘space’ has a ‘material substance’
to which any properties can be assigned, otherwise space is reduced
to a mathematical coordinate construct.
- Frames of
Reference: In 1632, Galileo Galilei postulated that no absolute
and well-defined state of rest exists. In SR, Einstein limited Galileo’s
principle of relativity to inertial reference frames, such that all
physical laws that apply to a coordinate system [S] must also apply
to any other co-ordinate system [S’] moving in uniform translation to
- Special Relativity (SR): Is a model of space and time first published in 1904, where the relative measurement of length and time can depend on the relative velocity [v] of an inertial reference frame, although most effects will only be apparent when velocity [v] approaches [c]. Under these conditions, an observing reference frame perceives a length contraction and time dilation within the moving frame. However, SR also rests on the assumptions of two postulates underpinned by a mathematical expression called the Lorentz transforms. We might introduce the postulates as follows:
- The laws of physics take the same form in all inertial frames
- When measured in an inertial reference frame, the velocity of light is always [c] and independent of the velocity [v] of the source or receiver.
However, in 1904, neither of these postulates had been physically verified and, even today, many aspects of SR are still discussed in terms of Einstein’s thought experiments, or Gedanken experiments. Both of the postulates cited above put conditions, and restrictions, on how relativity maps spatial [xyz] and time [t] coordinates in one reference frame to another based on the constancy of the velocity of light [c=1] in all reference frames, as per the second postulate, and the relative velocity [v] between the frames. However, the first postulate allows any inertial reference frame to assume itself to be stationary [v=0], such that it assumes the laws of physics are unaffected, irrespective of whether the frame is in motion, but more on this aspect in later sections. The coordinate mapping inferred by SR is based on the Lorentz and inverse transforms, as shown in , where the symmetry of velocity [±β] in the two forms is required by the first postulate – see Lorentz Transforms for derivation details.
By way of initial clarification, the primed [x’,t’] notation relates to a frame [S’] moving with velocity [β=v/c] relative to the unprimed frame [S], but where a comoving observer-S’ may assume itself to be stationary [β=0]. As such, any local measure of [x’,t’] done by observer-S’ must reflect the variables without any relativistic effects. The notation [β] is the ratio of velocity [v] to the velocity of light [c], which along with the factor [ϒ] is introduced in , but discussed in more detail in later sections.
Note: SR allows a relative inertial perspective to be reversed, such that it leads to the assumption that time can simultaneously be running slower in both frames. In a wave model, the propagation media provides the reference frame for the wave velocity [c], such that time dilation would be relative to the velocity [β] with respect to the reference frame of the light propagation media. However, the results of the Michelson-Morley experiment, first carried out in 1887, questioned whether space could be the propagation media for light – see this discussion of the Michelson-Morley Experiment for an alternative interpretation within a wave model.
Einstein also used Minkowski’s idea of a four-dimensional vector space as a way to present his SR concepts. In Minkowski’s model, events in a unified spacetime are defined as four-vectors, although it has to be highlighted that this may only be a mathematical convenience rather than a verification that space [xyz] and time [t] can be physically merged – see 4-Vector Notation for more details. However, we might first anchor the laws of classical physics to Newton’s 2nd law of motion.
The first postulate of SR states that any physical law is not affected by a reference frame in uniform motion. As such, the physical law in  must apply to all inertial frames, irrespective of the relative velocity [v] to each other. As such, there should be no effect on the measurement of [F] or [m] within any local reference frame, but we might wish to question this assertion as follows:
In , velocity [vA] is the relative velocity of frame [A] to frame [B], while velocity [vB] is the relative velocity of frame [B] to frame [A], where both are equal to each other. As shown, acceleration [aA, aB] in [A] and [B] is determined as the rate of change of velocity with local time [tA,tB] in each reference frame. However, if the rate of time in each frame is different, due to time dilation, but velocity invariant, we might need to question whether Newton’s second law of motion [F=ma] can remain consistent in each frame. However, relativity also suggests that mass [mA, mB] is also subject to another relativity effect, which may maintain . Again, we might seek causal mechanisms that physically explain what is actually happening.
So, has the first postulate of SR really been proved?
From the definition of force [F] in , we can proceed to define the ‘work done [W]’ on a system, which is related to the energy transferred.
In , we see the general definition of the work done [W] by a constant force [F] acting over a distance denoted by three common forms of notation, i.e. [x, s or d]. However, in the case of a variable force, where distance might be denoted by [r] along a path [C] between [r1] and [r2], a line integral is required to define the work done, as shown in .
A conservative force is a variable force that is a function of [r] acting upon a particle that moves from [r1] to [r2] along any path [C], such that it aligns to . Gravitational and electrostatic forces are conservative forces. If a particle has mass [m] and velocity [v], it has kinetic energy [Ek], such that it can also be used to quantify the work done [W], if we initially ignore any implications of potential energy [Ep] in the system.
At this point, we might also make reference to the Lorentz force law and also introduce Maxwell's equations, which define how the movement of charge particles both create and change the electric and magnetic fields. Maxwell’s equations include the universal constants for the permittivity of free space [ε0] and permeability of free space [μ0].
Note: The implication of Maxwell’s equations have to be understood within the context of electromagnetic fields – see discussion of Maxwell’s Equations by way of an introduction of their historic and mathematical development.
Based on the introductory links in the note above, we might immediately jump to a simplification of Maxwell’s equations for free space, in the later differential form, where charge density [r] and current density [j] are both set to zero.
Each of these equations requires further explanation in order to provide some physical interpretation of what they are really trying to tell us about electromagnetism, which can be found by following the links in the note above. While the issue of ‘EM Propagation’ also requires more detail, this discussion will simply introduce a generic form of the EM wave equation and how it is derived from Maxwell’s equations:
In [9a], the variable [A] can be substituted for either the ‘amplitude’ of the electric [E] or magnetic [B] field strength at some given point in space and time; while [9b] alludes to a relationship between the propagation velocity [c] of an EM wave in vacuum and the electric and magnetic constants of free space.
Note: It is highlighted that Maxwell’s propagation equation is essentially
a derivation based on classical sinusoidal wave equations. While the
subsequent development of the photon light model sits within the framework
of a quantum model, the exact details of the photon structure or how
it propagates are far from clear – see
Photon Issues for more details.