Gentlemen, I apologize for the extended delay in this thread. It is the result of real life being real life and the excellent argument posited by you both (which require a bit of thought). I appreciate your patience and I imagine these long delays will continue. For now;

Originally Posted by

**CliveStaples**
A-theory is equivalent to saying that the A-series "slides along" the fixed B-series. So under A-theory, while the *temporal order* of events is fixed, the property *being in the future of the American Revolutionary War ***does** change: people used to be in the past of the American Revolutionary War, then they were contemporaneous with it, and then they were in its future.

Hi CS, sorry to jump in here, but this statement caught my eye. You posited this indirectly earlier in thread and I thought I responded. A theory is not equivalent to a “now” moving along a fixed, extant, ordered timeline. That viewpoint would represent a mixed A/B theory, which some philosophers would put forward, but which usually have several internal problems.

Regardless, it isn't the theory I put forward here or offered in my references. The future is not an existing position we have not yet reached, it is a non-actual state. The best way to highlight this, imo, is to discuss the truth values of the following statements. Assuming it is Feb 25 2014.

1) “Mr. Obama is the President of the United States.” This is a true statement.

2) “Mr. Obama was the President of the United States yesterday.” This is a true statement.

3) “Mr. Obama will be the President of the United States tomorrow.” This statement has no truth value. Under B theory (or the way you described A theory above) the statement is either true or false, we simply don’t have access to the information. However, under A theory, the statement has no actual truth value, it is indeterminate.

To use an analogy, it is not a train moving along a track, but rather like a rail laying train.

Originally Posted by

**CliveStaples**
That doesn't mean that the set of *all coins that go into the vault* is finite.

Correct, it only means that the total amount *in the vault* is finite for any given coin being added. IE there is no specific coin that when added makes the total amount of coins in the vault when added infinite. Or to return from the analogy, there is no specific point, “now” in which the total time, past, is infinite.

And that is the question being asked, imo. The vault represents the total number of points that have been added to the timeline through a continuous process and that vault never becomes infinite through the process we have described here.

Originally Posted by

**CS**
You are assuming that the number of coins in the vault must at some point equal the number of points that "now" has visited.

Perhaps I misunderstand this objection. Are you saying that there is a point in the “vault” (ie in the past) that has not been a “now?”

Originally Posted by

**CS**
Instead of dealing with nebulous phrases like "at any point in the process", where the process hasn't been precisely described, why don't we deal with math?

Because we are using the math to reason by analogy and so far it has seemed to me that the analogies are causing more confusion than they are resolving, almost certainly due to my failings and expressing myself in that analogy. There is a physical reality (or at least a theory of reality) that I am attempting to ensure matches the math we are using to represent it. If we can agree as to the underlying physical process being described then the accompanying mathematical process can be used to explore those consequences more fully.

Originally Posted by

**GoldPhoenix**
Special Relativity is as I defined it in my last post. There's no interpretation issue; __Special Relativity __*is* the theory of Lorentz invariance. You can add metaphysical baggage on top of SR, but they cannot change the predictions of Special Relativity.

This does not seem to be the case as I see it. Perhaps this is due to a translation issue on my part, I’m not sure, but sufficed to say there does seem to be discussion concerning the different interpretation of relativistic phenomena.

One denies the possibility of privileged reference systems, the other postulates the existence of a physically privileged reference system and explains the relativistic phenomena with its help. While the first class is represented by Einstein’s original theory and its most recent formulations, the second involves the Lorentzian, ether-based interpretations of relativity theory as well as theories which while rejecting the Lorentzian ether, introduce an alternative, non ether-based privileged system. For simplicity, we will refer to the theories belonging to this second class as Lorentzian

interpretations or Lorentzian-type theories independently of whether they establishes the privileged reference system by the introduction of the ether (as Lorentz did it) or does it in a different way. [The mean stream of various Lorentz-like interpretations are connected to H. Ives, regularly cited in the Anglo-Saxon literature and characterized by M. C. Duffy as the “Ives Group” of Lorentzian theories (Duffy 2008). Duffy lists the representatives of this group of theories as H. Ives, G. Builder, S. V. M. Clube, H. Erlichson, J. Levy, S. J. Prokhovnik and F. Wintenberg. (ibid. pp. 23, 30). He also mentions a Hungarian physicist, Lajos Jánossy (ibid. p. 32), who did not belong to this group but who not only worked out one of the most comprehensive and mathematically most elaborated Lorentzian theory, but also provided a clear metatheoretical foundation of this kind of interpretations (Jánossy 1971; Székely 2009). Unfortunately, Jánossy’s work is unfairly ignored by the members of the “Ives Group” and other Anglo-Saxon authors working on the topic. He had nevertheless a great

influence as it is indicated by the acknowledgments to him by such significant authors as Bell and Brown (Bell 1976, Brown 2005, vii.). Among the representatives of the Lorentz-like theories it can be also mentioned a recent Hungarian physicist/philosopher L. E. Szabó. (Szabó 2010)]

Source

Many naturally occurring phenomena require theoretical treatment utilizing complex analysis by methods such as the Cauchy-Riemann relations using hyper-geometrical spaces which treat inherently nonlinear, non-dispersive, collective nonlocal resonant states of a quantum system, so as to be consistent with the nonlinearity inherent in General Relativity. Typical quantum approaches form linear approximations limiting the ability to formulate a quantum consistent Relativity Theory. The fundamental nature of remote connectedness is exemplified by Young’s double slit experiment, Bell’s Theorem, nonlocality, Mach’s Principle and operation of a Foucault pendulum, which may imply the existence of an aether. We demonstrate that a geometric aether is not precluded by the structure of Relativity, although Einstein excluded a fixed reference aether frame. In fact, certain observable phenomena, such as Mach’s Principle, Bell’s Theorem and Young’s double-slit experiment imply the existence of a fixed geometric spacetime aether. A basic tenet of this aether is the quantum principle of nonlocality understood in terms of the soliton-solitary wave solutions of the Schrödinger equation solved in complex relativistic Minkowski space. Formulation of the complex modified relativistic multidimensional aether allows us to understand the fundamental nature and mechanism of nonlocality allowing experimental designs to further evaluate the properties of nonlocal coherent collective phenomena. The structure of quantum theory using the Schrödinger equation, covariant Dirac equation and sine-Gordon equation are solved in a complex hyper-eight dimensional relativistic geometric space. The symmetry of this space possesses relativistic Lorentz invariance for nonlinear hyper-dimensional geometry, nonlocality, and nonlinear coherent states which are expanded in terms of quantum soliton solutions

Source

The Lorentz transformation (the LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de Broglie, regarding the underlying unity of matter and radiation. To show the nature of these changes, a massive particle is modeled as a standing wave in three dimensions. As the particle moves, the standing wave becomes a travelling wave having two factors. One is a carrier wave displaying the dilated frequency and contracted ellipsoidal form described by the LT, while the other (identi.ed as the de Broglie wave) is a modulation de.ning the dephasing of the carrier wave (and thus the failure of simultaneity) in the direction of travel. The superluminality of the de Broglie wave is thus explained, as are several other mysterious features of the optical behaviour of matter, including the physical meaning of the Schrödinger Eqn. and the relevance to scattering processes of the de Broglie wave number. Consideration is given to what this Lorentzian approach to relativity might mean for the possible existence of a preferred frame and the origin of the observed Minkowski metric.

Source

General relativity has a geometric and a field interpretation. If angular momentum conservation is invoked in the geometric interpretation to explain experiments, the causality principle is violated. The field interpretation avoids this problem by allowing faster-than-light propagation of gravity in forward time. All existing experiments are in agreement with that interpretation. This implies the existence of real superluminal propagation and communication of particles and fields, free of causality problems. The introduction of real physical faster-than-light propagation into gravitation, electrodynamics and quantum theory has important consequences for physics

Foundations of Physics 32 (7):1031-1068 (2002)

Physicists’ understanding of relativity and the way it is handled is at present dominated by the interpretation of Albert Einstein, who related relativity to specific properties of space and time. The principal alternative to Einstein’s interpretation is based on a concept proposed by Hendrik A. Lorentz, which uses knowledge of classical physics to explain relativistic phenomena. In this paper, we will show that on the one hand the Lorentz-based interpretation provides a simpler mathematical way of arriving at the known results for both Special and General Relativity. On the other hand, it is able to solve problems which have remained open to this day. Furthermore, a particle model will be presented, based on Lorentzian relativity, which explains the origin of mass without the use of the Higgs mechanism, based on the finiteness of the speed of light, and which provides the classical results for particle properties that are currently only accessible through quantum mechanics.

Source

Originally Posted by

**GP**
Emphasis mine. Absolute and relative simultaneity are logical opposites of each other, you have to pick which one Lorentzian relativity supports.

I understand your confusion with that response. In post 200 what I was implying was that the Lorentzian Relativist isn’t arguing that there is data showing relative simultaneity to be incorrect, but rather that he points out that its existence arises from an assumption that the speed of light is constant. IE that this is a fundamental assumption of ER that LR does not assume as valid indeed cannot be shown experimentally if you use Poincaré–Einstein synchronization because it assumes it to be true (just as it would become automatically false if you used Lorentzian synchronization because it assumes it to be false). (more on this later of course)

Originally Posted by

**GP**
SR is a model. You seem to be under the false impression that Lorentzian relativity is merely a different interpretation of the model, SR. If Lorentzian relativity implies different predictions than SR, then Lorentzian relativity is inherently __not an interpretation of the results of SR__; it is a new, competing model. That makes it --categorically-- not "metaphysics" as you have been arguing, __it makes it a new model that is in competition with Special Relativity__. This makes it "physics".

First, as I pointed out earlier, I’m not arguing this is metaphysics, but physics and that this is a physics debate occurring between physicists.

Second, I largely agree with you, however I think your language is slightly imprecise. Einsteinian Relativity (ER) is a form of SR in which a set of results are predicted. Lorentzian Relativity (LR) is a different form of SR which predicts the same set of results, but which the mechanism that produces the experimental data is different.

Physicists’ understanding of relativity and the way it is handled is at present dominated by the interpretation of Albert Einstein, who related relativity to specific properties of space and time. The principal alternative to Einstein’s interpretation is based on a concept proposed by Hendrik A. Lorentz, which uses knowledge of classical physics to explain relativistic phenomena. In this paper, we will show that on the one hand the Lorentz-based interpretation provides a simpler mathematical way of arriving at the known results for both Special and General Relativity. On the other hand, it is able to solve problems which have remained open to this day. Furthermore, a particle model will be presented, based on Lorentzian relativity, which explains the origin of mass without the use of the Higgs mechanism, based on the finiteness of the speed of light, and which provides the classical results for particle properties that are currently only accessible through quantum mechanics

Source

---------- Post added at 08:12 PM ---------- Previous post was at 08:09 PM ----------

Originally Posted by

**GP**
Does the Lorentzian relativity model obey Lorentz invariance? If not, then I

you explain why Nature looks the way it does. (Again, see point #7).

As I stated earlier, in LR, the invariance is apparent, not fundamental. It is the result of physical distortion of matter caused by motion relative to an absolute reference frame. Remember, invariance applies to any two frames moving relative to each other, that comparison nets out any effects arising from motion relative to an absolute frame.

Sorry the equations don’t quite paste quite right (I’ve tried to paste it as best I can, but will reference the equation number listed clearly).

For the student of physics, there comes a moment of intellectual pleasure as he or she realizes for the first time how changes of length, time and simultaneity conspire to preserve the observed speed of light. Yet Einstein’s theory [1] provides little understanding of how Nature has contrived this apparent intermingling of space and time.

The language of special relativity (SR) may leave the impression that the Lorentz transformation (the LT) describes actual physical changes of space and time. Thus we have Minkowski’s confident prediction that, Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows and only a kind of union of the two will preserve an independent reality [2].

The impression that the LT involves some physical transmutation of "spacetime" might seem consistent with the change of that nature contemplated in general relativity (GR). But in GR a change in the metric aspects in like manner all that occupies the region of space in question. In SR it is necessary to distinguish what actually changes from what is merely "observed"1 to change...

We now investigate how this particle must change if it is to acquire a velocity v in the frame of the laboratory, when subject to the constraint that its constituent influences (rays) must retain the velocity c with respect to that frame. (We are thus assuming for the moment that the inertial frame in which this particle has the form (4), which we have called the laboratory frame, is at the same time the preferred or privileged frame supposed by Lorentz. To simplify matters further the amplitude jrj1 is omitted in what

follows).

What we require now is not a standing wave but a travelling wave. Its form can be established in either of two ways, and it will be instructive to consider both. The first is by construction, and we begin by considering rays, directed forward and rearward along the direction of travel, which we will take to be the positive x-direction. At rest in the preferred (laboratory) frame, the composition of these rays results in the one-dimensional standing wave

EQUATION 5

This standing wave becomes a travelling wave of velocity v if the wave characteristics of the rays directed forward and rearward (which we now label 1 and 2 respectively) become,

EQUATION 6

where is again the Lorentz factor (1), and since,

EQUATION 7

both rays retain as required the velocity c with respect to the preferred frame. We then have by composition,

EQUATIONS 8 AND 9

which from relations (6) may also be written,

EQUATION 10

and is a travelling wave of the kind illustrated in Fig. 2(b). This one-dimensional travelling wave already displays features that will become more apparent when we consider the full three-dimensional travelling wave, namely a carrier wave of velocity v (the .rst factor in Eqn. (10) ) and a superluminal

modulation (or beating) of velocity c2=v (the second factor).

The structure of the full model wave at velocity v is now obtained by noticing that (as shown in Fig. 3) the amplitude of this wave at any point P at time t, when the centre of the wave has reached B, results from the interference of the outgoing ray that left the particle centre when it wasat A at the earlier time t t1, with the incoming ray that will reach the particle centre when it is at C at the later time t + t2. (To an observer in the frame of the moving particle, the paths of these rays will appear to coincide, but they do not coincide in the laboratory frame)….

Travelling wave (15) displays all the effects predicted by SR – length contraction, time dilation and failure of simultaneity. If all matter changed between inertial frames in the same manner as our model particle, this would explain why Mary considered Buzz to have changed in accordance with the LT. But the transformation is here a change of wave structure, not of space, nor even yet of reference frame. There has been no opportunity, let alone necessity, for some additional transformation of "spacetime"…

While there would seem little doubt that the laws of physics are the same for all observers, one might ask why this should be so. In the context of ESR this satisfying situation would seem fortuitous. However, a consideration of the wave nature of matter may suggest at least a partial explanation for

this invariance

Notice firstly the unusual effects that would result if the LT were not exactly as it is, for instance if the Lorentz factor was not (1 v2=c2)1=2 but had some other value a (a being a real number other than unity). Consistently with relations (7), a wave travelling at any desired velocity v could still be constructed, but as in the case of a = 0, which is the Galilean transformation, the preferred frame would then be detectable. In the Galilean case, longitudinal contraction is replaced by transverse contraction that in-

creases with acceleration away from the preferred frame. For other values of a, contraction or expansion (both longitudinal and transverse), time dilation and simultaneity would be observed to differ according to whether velocity were increased or decreased with respect to the preferred frame. The laws of physics would not then be invariant, and the Universe would be rather more curious and less elegant than it is. But that alone does not explain why it is not so.

Consider now, however, the stability of matter. The elementary particles exist in a limited variety of precisely defined characteristic forms. Why that should be so is not apparent, but what is apparent is that they are constrained by those forms and by their wave-like nature to combine in a limited number of ways, as is well illustrated by the Bohr conditions (18). Even in matter that we would think of as stationary, underlying micro processes are occurring at relativistic speeds, as illustrated well enough again by the Bohr orbits. For these processes to remain undisturbed by a change of inertial frame, dynamic relationships between particles must be preserved, including for instance relative velocities, accelerations, masses and polarizations. In other words, the laws of physics must be the same for all inertial observers, and this is so only at a = 1.

Considered in this way, Lorentz invariance is not the fortuitous cause, but rather the inevitable e¤ect, of the manner in which the constituent elements of matter must persist and combine. It is not then the metric that determines how matter transforms, but the stability of matter that determines the LT and the bserved (Minkowski) metric. Of any pre-existing or primordial metric little can be said, except that the simplest possible metric, the Euclidean, was that assumed by Lorentz.

---------- Post added at 08:15 PM ---------- Previous post was at 08:12 PM ----------

Originally Posted by

**GP**
Support or retract all of this, and do it with equations. I'm serious about that last bit. You've been using a lot of vague words that you clearly don't understand, so please do us both the favor and explain, using equations, why this is true.

Hmm, I’m not sure why I would need to use an equation to discuss why this assumption is required for each method. To reiterate, we are discussing here my assertion that the validity of the underlying postulate to ER (constancy of the speed of light for all observers) has not been shown because the method used to measure that speed.

In Einsteinian synchronization you use a radio wave between two reference frames to adjust for the displacement caused by relativistic effects. Given ER you operate on a postulate that no reference frame is privileged and the speed of light is constant for all observers right?

http://en.wikipedia.org/wiki/Einstei...on#cite_note-1

That synchronization assumes the speed of light to be constant to calculate the relative simultaneity of the events. In a similar, but opposite affect, Lorentizan synchronization assumes a privileged frame and thereby a variable speed of light.

Perhaps to lend a bit more weight than just my opinion.

Contrary to special relativity, aether theory does not assume that the time itself is affected by motion; the reading displayed by the moving clocks results from two facts: 1/ Due to their movement through the aether, they tick at a slower rate than in the aether frame.2/ The usual synchronization procedures generate a synchronism discrepancy effect. These facts give rise to an alteration of the measurement of time which, as we shall show, exactly explains the experimental results…

This study does not question the experimental results brought about by relativity theory since, as we shall see, at least in the cases studied here, it predicts the same clock readings as SR provided that we use the standard measurement procedures. It nevertheless gives another interpretation of the experimental data (demonstrating that the procedures used entail measurement distortions and that the results obtained conceal hidden variables)…

Contrary to relativity theory, the motion of bodies does not affect the time, but the motion through the aether causes a slowing down of the moving clocks. The real two-way transit time of light, along a rod attached to a certain ‘inertial’ frame, is the same for the observers of all frames, but, due to clock retardation, the reading displayed by clocks moving relative to the rod will depend on their speed with respect to the rod [2, 8, 9]…

3.2.1. We shall first assume that the clocks placed at points A and A’ are exactly synchronized. Let us label as 2 t_{0} the two-way transit time of the light signal that would be displayed by clocks attached to the co-ordinate system S_{0}.

Due to clock retardation the clock readings in S_{1} and S_{2} are related to t_{0}as follows:

EQUATION 3

and

EQUATION 4

(Note nevertheless that the true time, needed for half a cycle, measured with clocks not slowed down by motion, is t_{0} for all observers).From (3) and (4) we infer:

EQUATION 5

Assuming that v_{02}/C<<1, this expression reduces to first order, to:

EQUATION 6

Noting that (as in section 3.1.) t_{2} = t_{2app} = L/C, this expression is different from the relativistic formula (2) which reduces to:

EQUATION 7

__Therefore if clocks were exactly synchronized, there would be an obvious difference between the two theories. __

3.2.2. Practical consequences of the clock synchronization procedures used. We should note that, in practice, in order to determine the duration of a cycle in S_{1} we must subtract the reading displayed by clock A when the signal starts from this clock, from the reading displayed (after reflection in B) by clock A’ when the signal reaches this clock, and therefore we must synchronize the clocks A and A’ beforehand.

According to aether theory if the synchronization of clocks was perfect we would have obtained formula (5). Yet, synchronizing the clocks perfectly is a difficult problem, and, with the standard synchronization procedures, (Einstein-Poincaré method (E. P) or slow clock transport), we make an unavoidable systematic error in measuring the time, (synchronism discrepancy effect) [2, 9, 10]

The apparent duration of a cycle measured in S_{1} is therefore equal to the difference between 2 t_{1app} and the synchronism discrepancy effect (SDE) that will be derived in the text which follows. (The SDE, which was defined by Prokhovnik for the first time, enables to resolve a number of paradoxes in physics).

Referring to the SDE that would affect the clocks if they were not slowed down by motion as Δ, the SDE affecting the clocks attached to the coordinate system S_{1} is:

δ= Δ√(1-v_{01}^{2}/C^{2})

The apparent (measured) two-way transit time of the signal (from A to B and to A’)is therefore:

2T_{1app} = 2t_{1app} - Δ√(1- v_{01}^{2}/C^{2})

__It is this apparent time which is in fact measured when a SDE between the clocks A and A’ exists. __

(a)Derivation of the synchronism discrepancy effect, and clock synchronization. The Einstein-Poincaré method (E. P) consists in sending a light signal from clock A to clock A’ along the x’-axis, at an arbitrary instant where the reading of clock A is set at t=zero. After reflection in A’, the signal comes back to A. The clocks are considered synchronous if upon reception of the signal by clock A’, this clock displays a reading equal to half the reading displayed by clock A upon return of the signal.

(The alternative synchronization method, referred to as the slow clock transport procedure, has been shown to be equivalent to the former by different authors[2, 10])…

The comparison of formulas (6) and (7) demonstrates that relativity and aether theory are fundamentally different. Nevertheless, paradoxically, due to the systematic measurement distortions mentioned above, aether theory leads to a clock reading given by formula (15), which presents a mathematical form identical to formula (2);yet for relativity, the formula is regarded as exact, while for aether theory it results from the measurement distortions. Aether theory provides also an explanation of why formulas (1) and (17) can be both rationally justified, although at first sight they appear incompatible. Aether theory explains that due to the synchronism discrepancy effect formula (17) is observed instead of formula (16), an explanation which solves the paradox. Special relativity obtains the same result but cannot give a rational explanation of it. In conclusion, the choice of one theory rather than the other is not simply a question of philosophical preference.

http://www.scribd.com/doc/78608645/J...-Time-Dilation

The author also wrote another paper:

Although the mathematical form of the equations we have derived is identical to that of the Lorentz-Poincaré transformations, their meaning is completely different because they relate distorted co-ordinates and are dependent on an arbitrary synchronization procedure. Yet, these transformations are those which result from the experimental measurements.

As we have seen in formulas (15) and (16), they can be qualified as Lorentz-Poincaré transformations only when they connect the aether frame with any other ‘inertial frame’.

The difference is all the more evident, as these transformations are derived from the extended space-time transformations, which assume the variability of the one-way speed of light when this speed is exactly measured, and show that the apparent invariance of the speed of light results from measurement distortions. If the synchronization were perfect, the speed of light would prove dependent on the relative speed between the fundamental frame and the frame where it is measured, a fact which would enable us to measure the absolute speed of this

13

frame in contradiction with Poincaré’s relativity principle [1]. And a near perfect clock synchronization is not a priori an objective impossible to reach.

It is clear that, if no preferred frame did exist, the celestial bodies, taken as reference systems would, in all probability, move in an almost absolute vacuum. In this case, the existence of near perfect inertial frames would be possible. Indeed, no physical effect could distinguish one frame from another. As a result, the laws of physics, relating exactly measured variables, would be identical in all these reference frames. But, as we demonstrated in ref [1], a number of experimental and theoretical arguments lend support to the existence of a preferred aether frame.

http://arxiv.org/pdf/physics/0607067v2

Originally Posted by

**GP**
6.) Whatever you final position is, to re-iterate, I

you to explain how your theory is consistent with what we know about physics.

As I think I’ve shown above, it is consistent with all observational evidence in support of ER. There seems to be a health discussion going on concerning which interpretation best fits the data set and how the few scenarios in which different results are predicted could be tested. Sufficed to say, the sources I provided above argue that LR and ER are currently observationally identical, which would seem to meet the requirement of this challenge.

Originally Posted by

**GP**
7.) Clive has mentioned to me that it seems likely that (one of) your sources of error lie in the fact that you likely think that Lorentz invariance is a metaphysical postulate of Special Relativity.

I appreciate the attempt at clarity. I do not think that Lorentz invariance is a metaphysical postulate. I think I gave a relatively succinct definition in post 192. IE that Lorentz Invariance is the requirement that all non-gravitational laws will produce the same results for two reference frames moving relatively to each other.

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