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Invariant Physics

Thomas E. Phipps, Jr.

2210 County Road 0E

Mahomet, Illinois 61853 USA

tephipps137@gmail.com

Abstract. Major revisions of the pillars of physics, Maxwell’s equations and relativity theory, are proposed, based on imposing the requirement of true formal invariance. This theme is further exploited through length invariance and an application of GPS time that permits restoration of a meaningful concept of now. The consequence is a physics from which covariance has been consistently banished in favor of invariance. A crucial experiment is proposed.

Key words: Invariance, Length Invariance, GPS Time, Einstein’s Train, Hertzian Electromagnetism, Acausality.

I. INTRODUCTION

In this paper I shall summarize what I have learned about theoretical physics during a lifetime of intermittent but persistent study. The paper will necessarily be rather long, not because I have learned a lot, but because what I have learned will be unfamiliar to most readers and thus will make special demands on both reader and expositor. I have followed a different path and have seen things from a new angle. In brief, I have been led to propose radical alternatives to the old foundational standbys, Maxwell’s equations and relativity theory. Both need reformation, since they work in intimate togetherness. It is hard to accept departures from what we were all taught. But nobody said theoretical physics was easy.

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II. OVERVIEW

Let us survey the territory to be covered. One central theme has guided all the work to be discussed, the theme of invariance. By this I mean true, literal, formal invariance under physical inertial transformations – in contrast to covariance. Why invariance? Because there is something “out there” that remains identically the same, no matter how we may choose to look at it or describe it; and that something is what physics is about. Successful mathematical representation of the laws of physics (or of nature) may justly be presumed to mimic this defining attribute through form preservation. In brief, Non-invariant = Non-physical.

I might as well be blunt from the start: I have no use for covariance. Covariance masquerades as equivalent to invariance; indeed, as a more sophisticated method of form preservation. But the sophistication lies in redefinition ( 'X Xν

µ µ νν≡ α∑ ) of the quantities whose form is to be preserved;

so the preservation is propaganda, smoke and mirrors. There is more of that in physics than most physicists care to recognize. Under covariance the quantities being transformed are actually not preserved at all. Their appearance of not changing is achieved by applications of prime symbols not to the untransformed quantities themselves but to cunningly-assembled collections of those quantities. Would you do business with a security service that undertook to preserve you by first redefining you in obedience to their rules? Are we to allow unrestricted (arbitrary) redefinitions and still speak of form preservation? A prime can be stuck on anything. Where on this slippery slope do we stop? Covariance, the place where we did elect to stop, has no special virtue except that it is so contrived that Maxwell’s equations can persist without improvement; that is, can remain forever non-invariant. On such a foundation have modern physical theorists built a world.

Maxwell’s equations, as they stand, and as relativity leaves them standing, are invariant under no known transformation, even at first

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order. You would think after all these years that physicists might have got at least their first-order account of electromagnetism right. But no. They have chosen to follow a will-o’-the-wisp (ignis fatuus) known as spacetime symmetry, derived from – wait for it – the symmetry of space and time partial derivatives in Maxwell’s non-invariant equations. Spacetime symmetry provides the only “physical” basis for covariance, and that symmetry derives not from nature but from a set of non-invariant (hence non-physical) equations.

To be sure, there can be no quarrel with Maxwell’s partial space derivatives. Under Galilean inertial transformations they are clearly

invariant ( )'∇ = ∇r r

. However, in view of '

vt t t∂ ∂ ∂

= + ⋅∇ ≠∂ ∂ ∂

rr , we see that the

source of the (Galilean) non-invariance is the partial time derivative. What is to be done?

Very simple. The traditional form of the total time derivative, d wdt t

∂= + ⋅∇

∂

rr , where wr is a new convective velocity parameter, is

invariant under the Galilean transformation (GT). Proof: From the /d dt definition and the Galilean velocity addition law, 'w w v= −

r r r ,

( )' ' ' ''

d dw w v w v wdt t t t t dt

∂ ∂ ∂ ∂ = + ⋅∇ = + ⋅∇ = + ⋅∇ + − ⋅∇ = + ⋅∇ = ∂ ∂ ∂ ∂

r r r r rr r r r r r . q.e.d.

One has been taught that physical inertial transformations, which used to be described by the GT, are now to be described by the Lorentz transformation (LT). This could be more smoke and mirrors, since no experiment has proven that inertial motion is better described by the LT than by the GT. Despite much talk and the passage of many years, experimentalists have felt little need to validate the superiority of the LT for describing physical inertial motions: easier to assume it; also easier to muddy the waters by inventing the misnomer “Lorentz invariance” (the correct term being “Lorentz covariance”). In speaking of the GT, by the way, we shall find presently that the operational definition of the time

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parameter appearing there is open to negotiation; so invariance under the formal GT is not yet a fully developed physical concept. Let us be patient and see where this is heading.

So far, our reasoning has led us from Maxwell’s non-invariant form of the equations of electromagnetism to a GT-invariant form first proposed (to cite history) by Heinrich Hertz1, wherein the Maxwell partial time derivatives are everywhere replaced by invariant total time derivatives; thus, Hertz’s field equations in the simplest case take the GT-invariant form

1 4

1

0

4

mdEB j

c dt cdBE

c dtB

E

π∇× − =

∇× = −

∇⋅ =

∇⋅ = πρ

r rrr

rrr

rrrr

. (1)

Note that there is no spacetime symmetry. Here, in the total derivative with respect to the time parameter (the operational definition of which will be discussed presently), we may write the convective velocity as dvr ,

dd vdt t

∂= + ⋅∇

∂

rr , (2)

in order to call attention to the fact that the only tangible object connected with the field is the radiation field absorber or detector; so dvr

represents the velocity of the field detector relative to the observer or his inertial frame. This is a new parameter not present in traditional field equations; rather, it is present as the velocity of the “test particle” in an add-on known as the Lorentz force law. Here we see it incorporated directly in the field equations (1). This is surely an improvement in logical economy, as well as coherence, since it is a very strange anomaly that the only parameter suited to making a connection with observable physics is absent from Maxwell’s form of the field equations. The

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revised field equations (1) now do the whole job, there being no need for a separate “force law.” The force action is right there in (1), to be inferred from observable motions of the field detector acting as test particle. Proof: In terms of potentials, the Maxwell form of the electric field is

1MaxE A

c t∂

= −∇φ −∂

r rr. The Hertzian invariant counterpart is 1 dAE

c dt= −∇φ −

rr r.

The latter (expressing the simplest and most fundamental form of the law of electromagnetic force on unit charge – the full and correct meaning of the E

r-field) is derived from the second of Eqs. (1), using the

fact that in both Maxwellian and Hertzian theory B A= ∇×r rr

, and observing that any quantity whose curl vanishes can be set equal to minus the gradient of a scalar φ . Thus, from Eq. (2), the Hertzian electric

field is ( ) ( )1 1d Max dE v A E v A

c t c∂ = −∇φ − + ⋅∇ = − ⋅∇ ∂

r r r rr r rr r . The vector identity

( ) ( ) ( ) ( ) ( )a b a b b a a b b a∇ ⋅ = ⋅∇ + ⋅∇ + × ∇× + × ∇×r r r r rr r r r rr r r r r , with ( )da v t≡

r r and b A≡r r

,

simplifies to ( ) ( ) ( )d d dv A v A v A⋅∇ = − × ∇× + ∇ ⋅r r rr r rr r r . [The detector is idealized as a

point particle or small, non-rotating rigid body ( )dv tr , not a “mollusc” or

velocity field ( ), , ,dv x y z tr .] It follows that ( )1dMax d

vE E B v Ac c

= + × − ∇ ⋅rr r r rr r . Thus

qEr

is the Lorentz force on “test charge” q, plus a gradient term that

integrates to zero around any closed curve. Since current is popularly thought to flow only in closed circuits, it is clear that most ordinary experiments would not reveal the existence of this extra force term. (It might affect the behavior of plasmas – with unexpected effects on Tokamaks?) Both observed “magnetic” and “electric” forces are therefor included in the Hertzian electric force qE

r. Effects attributed to

magnetism are actually electrical, incident to the motion of electric charge. q.e.d.

Note that this improvement in parameterization of the field equations [inclusion of ( )dv tr ] is achieved as a direct result of demanding genuine

invariance, with the least possible further disturbance of Maxwell’s

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equations. The other parameters in (1) are the same as Maxwell’s, except that the possibility of detector motion ( 0dv ≠

r ) introduces an extra

convective current density source term, m Maxwell dj j v≡ − ρr r r . [In Ref. [2] it is

proven that under the GT 'm mj j=r r

, where mjr

is the Hertzian measured current density. It is also verified that ' , 'E E B B= =

r r r r in (1), thereby

confirming true invariance of the Hertzian field equations, as distinguished from covariance.]

The Hertzian wave equation, derived from (1), is

2

22 2

1 0d EEc dt

∇ − =rr

. (3)

Employing (2) in (3), we obtain the surprising solution2 for wave propagation speed:

dku c v

k k ω

= = ± + ⋅

rr . (4)

Proof: Look for a solution of form ( )E E p=r r

, where p k r t≡ ⋅ − ωr r . Then

( ) ( )2 2E p k E p∇ =rr && and ( ) ( ) ( )( ) ( )

22 2

2 d dd E p v E p v k E pdt t

∂ = + ⋅∇ = ω− ⋅ ∂

rrr rrr r && , whence

from Eq. (3) ( )dck v k= ω − ⋅rr and Eq. (4) follows. q.e.d.

In view of the dvr term in (4), the photon may be said to be

convected by the detector’s motion relative to the frame of the observer. This is new physics, wholly unexpected, though perhaps foreshadowed by quantum nonlocality. (Few think of classical fields as what they are physically, viz., non-classical objects embodying purely quantum processes.) It remains true that emitter motion has no effect on light speed; but the hidden hand, the absorber or detector, has a hitherto unsuspected direct influence. This has many far-reaching consequences. For instance, it can be shown2, by revisiting Einstein’s train problem3,

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that the modification (4) to the speed of light makes distant simultaneity absolute, not relative. We shall confirm this crucial point presently.

The restoration to physics of distant simultaneity permits a decisive simplification of space description and leads to an essential further manifestation of invariance; namely, length invariance. Let two straight sticks slide past each other at an arbitrary speed and in any spatial orientation. Given that distant simultaneity is physically valid and meaningful, if the end points of the two sticks coincide simultaneously, then the sticks are of the same length and length invariance holds independently of the speed of sliding. There is no realistic possibility of motion-correlated contraction or expansion, or of any “appearance” or “perception” of such. (But wait, what if both sticks contract equally—the way both twins age more than each other? In that case let a third stick not participating in their relative motion be so aligned that a triple distantly simultaneous coincidence of end points occurs. Then the sticks are all of the same invariant length, whether in relative motion or not.) In sum, relative motion has no effect on the length of a structure. This eliminates from physics not only Lorentz’s never-verified ether (dynamically responsible for Lorentz contractions), but the Herglotz5 stresses or Dewan-Beran6 stresses that have been thought to play a corresponding role in Einstein’s “kinematics.” Thus, in addition to restoring distant simultaneity we have effected an important simplification of space mensuration. The two go together: if length is invariant, then distant simultaneity can be defined by inverting the sliding-stick argument. An important proviso: “Length,” as used here, refers to material object length—that is, not to wavelengths, but to lengths of objects capable of bearing stress and showing strain.

Turning now to established relativity, we note that Einstein’s special theory does contain one invariant element, the proper time τ of the individual particle. Unfortunately, it is a miserable parameter to

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work with, being different for each differently-moving particle, and having an inexact (path dependent) differentialdτ . This last feature is unbearable. It makes consistent description of more than one particle at a time inordinately difficult. Physics (particularly of the many-body problem) needs a time parameter that is not only invariant but possessed of an exact differential, so that it can be universalized across all particles (integrable, path independent) and can serve as a coordinate in the way Einstein’s “frame time” does in the Minkowski representation. Is this an impossible goal? No, we need not stir a brain cell; it has already been done and proven in practice.

The necessary work has been done for us by scientists of the Global Positioning System (GPS). They recognized that it would facilitate the working of a global-scale satellite system if all clocks could be induced to run in synchrony – to tell the same “time.” As a reminder, the idea of GPS time is that all clocks in the universe, no matter how they may be moving or in what gravity environments, are set to run exactly in step with a Master Clock at rest in a fiducial inertial system, considered to be the system of common origin of all clocks. (For the GPS this is called the Earth Centered Inertial system.) GPS time is thus the frame time of the Master Clock. The latter — which may be purely notional – keeps its undisturbed proper time, and the slave clocks elsewhere are each corrected according to individual requirements by application of known “relativistic” laws. Atomic clocks are used, and the symmetry of the Lorentz transformation is ignored. That is, the slave clocks are each objectively speeded up to compensate relativistic running-rate slowing (“time dilation” by the factor 2 21/ 1 /dv cγ = − , dv

being slave clock speed in orbit measured with respect to the fiducial system). But there is no pretence that the Master runs reciprocally slower than the moving slaves; hence no twin paradox. That aspect of current theory is mercifully disregarded. (Good riddance to bad theory.)

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Clock slowing is a real physical phenomenon consequent upon asymmetrical energy (or action) state change. The misconception that kinematics can cope with the physics of this asymmetry is as naïve as it is widespread. (Why study physics, if kinematics can carry the whole load?)

How does GPS time handle effects of varying gravity? Compensation is made for the real, asymmetrical running-rate speeding that results from moving a slave clock into a region of weaker gravity. Einstein’s complicated mathematics, designed to eliminate the special status of inertial systems, led at the observable lowest order in 2c− to Newton’s gravity potential, so the correction factor f to be applied to the number of atomic oscillations that define the “second” (thereby compensating the running rate of a clock put into orbit so as to nullify the rate change effected by nature) is of the general character

2

42 2 2

1 1 ( )/ 2

vf O cc c c

−∆Φ= = − + +

γ − ∆Φ, (5)

where

orb surf orborb earth

GM GMr R

∆Φ = Φ − Φ = Φ = − + , (6)

the gauge being chosen so that 0surfΦ = . Here G is Newton’s gravity

constant, M is mass of the earth, etc. Eq. (5) is based on the simplest supposition, that clock energy (or action) changes, both kinetic and gravitational, may be treated as additive. Other forms of f have been proposed2, differing at higher orders not yet subject to verification. The upshot is that all clocks everywhere, when synchronized, run in step with the Master Clock. That is, they all agree to tell the same “time,” the corrections being continually up-dated to maintain permanent synchrony.

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This new type of time, pioneered by the GPS, I have ventured to rename2 Collective Time (CT), since it is shared among all clock-particles. Relativists think of it as the result of simple applications of Einstein’s theories of special relativity and gravity, because his formulas are used in making the running rate corrections. But Einstein’s 1905 second postulate of light speed constancy is violated by CT or by proper time, one or the other. (Measured light speed constancy is thought to require the use of proper time clocks, from which CT clocks have been deliberately set to differ in their running rates in certain environments; so, if proper time clocks measure c, CT clocks must sometimes measure not-c, and vice versa.) We have seen that invariance implies a non-Einsteinian behavior of light that fits (as we shall show) with CT being the kind of time that measures light speed c.

In what sense is CT invariant? First, it is trivially invariant under choice of clock or of the clock’s state of motion or environment. Secondly, it is operationally defined in all systems, and those (clock correction) operations, although not numerically invariant, are of identical form in every system. It would seem that CT is not invariant under choice of fiducial inertial system, since the running rate of the entire set of clocks varies with that choice. However, what varies for different choices may be said to be the “rate of time flow,” which is without objective physical counterpart in nature. That is, time can be thought to flow fast or slow without altering the form of the laws of nature, therefore leaving the physics invariant. (This principle was known already to Newton, who called it his Principle of Similitude.) We see this, for instance, from Newton’s second law, which does not depend on choice of time units or time flow rate. Invariance of this sort might be termed formal invariance, to distinguish it from numerical invariance. (Caution: As a reminder, the term formal invariance is also applied to covariance; but that means invariance with redefinition of the quantities being transformed.) It is formal invariance that speaks to the laws of

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nature, and thus expresses our aim concerning physical description. Numerical invariance (implying an absolute or universal time) is unimportant; but if we want it we can have it by a two-stage clock running-rate correction, the first stage being as described, whereby all slave clocks are brought into step with the Master, the second being a simple change of all clock rates (including the Master) by a common factor equivalent to a units adjustment. Again, this definition is an operational one.

Let the parameter measuring CT be designated 0t . Then we may

consider equations such as (1)-(3) to hold with 0t written for t , and may

understand a solution such as (4) to involve speeds all calculated with respect to CT, that is, as measured by CT clocks. In this way we exploit the exactness of the differential 0dt . Eq. (4), thus understood, shows that

light speed c is what is measured by CT clocks. (The first-order term in

dvr is cancelled in a manner illustrated by Einstein’s train analysis,

reviewed below.)

I am now ready to say what I mean by inertial transformation. I mean the GT, modified by use of CT as the time parameter:

0

0 0

''''

x x vty yz zt t

= −

=

==

(7)

As far as I can determine this should adequately describe the physics of inertial motions. Time dilation is automatically incorporated in the invariant time parameter by the CT clock corrections. These, it will be recalled, are asymmetrical between Master and slaves; so that is how the non-physical symmetry of the LT (twin paradox) is avoided.

In recognition of the obvious analytic advantages of CT over proper time, at this point I am going to take a bold step, which is to

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postulate that the validity of a relativity principle is contingent on the use of CT clocks:

Modified relativity principle: The form of the laws of nature is invariant under changes of inertial system, provided time is measured by CT clocks.

There is no need for a separate light speed postulate, since that is a matter of electromagnetism, already subject to the postulate of Eq. (1), written in terms of 0t .

It might seem that this is all nonsense, since proper time clocks (those that run undisturbed at their natural running rates) have always been unquestioningly assumed at all stages of relativistic theorizing to be the ultimate arbiters of time. But the experiments confirming this presumption mostly involve static laboratory conditions, unchanging gravity, and/or field detectors at rest ( )0dv =

r , so that CT and proper time

do not differ, as may be seen by identifying the lab system with the fiducial system. In most instances where this is not the case the principal relativistic effect observed is that of time dilation, which is automatically incorporated in CT. I do not wish to imply that there is no physical use for proper time. On the contrary, each of us certainly needs it to keep track of our personal aging; and CT is itself a sort of universalizing of a particular kind of proper time, that of the Master Clock. But the analytic advantages of CT, because of the exactness of 0dt , are so overwhelming

that it seems worth the gamble to create new CT-based theory and test the consequences.

III. TEST PROBLEMS

First let us review Einstein’s train problem3. Two lightning strikes occur at the ends of a train simultaneously in the view of the embankment observer, at the same time a mid-train rider R passes him. If the train

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moves left to right at speed dv and the flashes travel rightward from the

rear at speed rv and leftward from the front at speed fv , the half-length

of the train being L¸ we deduce that R at the middle of the train, whose eye constitutes a radiation field detector moving rightward relative to the embankment at speed dv , sees the right-going flash from the rear of

the train after a propagation time rRt given by the solution of

d rR r rR rRr d

Lv t L v t tv v

+ = → =−

. Similarly, R receives the left-going flash from

the front after a time delay fRf d

Ltv v

=+

. Letting r fv v c= = , by Einstein’s

second postulate, we see that the propagation intervals from front and rear are not the same; so, because R is at the train’s mid-point, the flashes could not have originated simultaneously in R’s system, whereas they did so originate in the embankment observer’s view. Hence the relativity of simultaneity. This Einsteinian analysis supposes all velocities to be measured by proper time clocks at rest on the embankment.

Quite otherwise is the analysis in terms of CT. There, light propagation is ruled by Eq. (4), which yields r du v c v= = + , since

( )/ d dk k v v⋅ =r r , whereas f dv c v= − . Putting these altered light speeds relative

to the fiducial (embankment) system into the above propagation time

expressions, we get ( )rR

d d

L Ltc v v c

= =+ −

, and ( )fR

d d

L Ltc v v c

= =− +

. Thus the

train rider receives the flashes not only simultaneously but at the same clock time /L c the embankment observer sees them. By that time R has progressed down the track past the embankment observer a distance ( )/dv L c . So, although simultaneous in time, the flash reception

events occur at different places. When CT is used the states of motion of the observers or of their radiation detectors have no effect on propagation time. The latter (no matter where absorption occurs) is determined by the

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spatial separation of emitter and absorber at the instant of emission, divided by c. Distant simultaneity is absolute. This implies that our intuition of “now” as meaningful throughout the universe is substantiated. This is one of the major consequences and payoffs of our determination to explore without compromise the physical implications of genuine formal invariance. Moreover, in view of the measured propagation times /L c , it will be noted that the ( )/ dk k v⋅

r r departure from speed c

shown in Eq. (4) cancels, leaving observable propagation speed c.

To repeat: the light convection by the light detector shown in Eq. (4) has the effect of cancelling (or being cancelled by) the effect of detector motion during the propagation interval; so the resulting measurable light speed is uninfluenced by detector motion: the train can move or not, the train rider and non-rider both see the same thing at the same time (CT), albeit in general at different places. It is all rather as if the photon had foreknowledge of its absorber. Light of this ilk is obviously non-Maxwellian and non-Einsteinian. It might be termed Feynmanesque, in recognition that “Nobody understands quantum mechanics” (most especially the mechanics of light quanta).

Next consider Einstein’s train (or, with neglect of gravity change, a passing earth satellite) in which a Feynman light clock4 (two facing mirrors separated by a rigid rod, aligned with the train’s or satellite’s motion, wherein a light pulse oscillates), plus a CT clock for timing the pulses, is at rest. Consider things from the viewpoint of the train rider (or orbiting observer). With respect to him the Feynman light clock, viewed as a light-speed measuring apparatus (LMA), is at rest, 0dv = .

Since CT is being used, light propagation within the LMA is governed by Eq. (4). In consequence of 0dv = the CT clock on the moving platform

measures light speed c. (Remember that the “moving” clock is always the one that has changed its energy or action state from that of the fiducial state.)

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What does a commoving proper time clock measure? Leaving gravity aside, we recall that the motional correction applied to the CT clock involved speeding it up by a γ -factor, redefining the second as a reduced number of atomic oscillations, to compensate for time dilation; so the proper time clock, not speeded up, runs slower by that factor, with the result that it measures less elapsed time per light pulse oscillation within the LMA. Consequently, with a smaller elapsed time denominator, if the numerator is fixed by rod length invariance, the measured light speed quotient is increased to cγ . Thus light speed measured by the proper-time clock commoving with the LMA differs from c. This violates the relativity principle referred to proper time. (For the embankment observer, doing the same experiment with an LMA at rest with respect to himself, does of course measure speed c with his proper time clock. Hence the outcomes of identical experiments differ in the two inertial systems.) But we have seen that when the relativity principle (as modified) is referred to CT there is no violation of relativity or of the speed-c rule. That is, our modified form of the relativity principle (above) is required by the physics. (For, again, the embankment observer with a stationary LMA measures light speed c with his stationary CT clock, because CT and proper time are identical in the fiducial system.) CT results are thus consistent between moving and stationary systems and consistent with length invariance. It is clear (if length cannot be both invariant and variant) that the relativity principle cannot be valid with respect to both CT and proper time. The physicist must choose. The same is true of speed-c measurement.

To check on the foregoing, consider the moving LMA experiment from the viewpoint of the embankment observer. By definition his elapsed time measurements using his CT clock are identical with those of the moving observer, when both use CT, because of the universal equality of CT clock running rates. Length invariance further implies that both observers measure identical apparatus length. So the speed

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quotient is the same for the embankment observer as for the moving one; namely, both measure light speed c with respect to CT, as shown above for the moving observer. This indicates that our speculative reformulation of the relativity principle in terms of CT has some substance to it. It is in fact required by logic, the argument being ultimately driven by the requirement of length invariance (itself a logical consequence of the restoration of distant simultaneity, as shown by the sliding-stick argument).

These results depend jointly on Eq. (4) and on the assumption of length invariance of the rod in the Feynman light clock. Einstein’s analysis is of course quite different. His way of thinking treats the relativity principle as valid with respect to proper time, and applies the Lorentz contraction to the orbiting rod, so the γ -factors in numerator and denominator of the light speed quotient cancel, with resulting light speed c, as measured by the orbiting proper time clock. The trouble with treating the relativity principle as valid with respect to proper time is that proper time is limited to simple description of only one particle. It takes just one other differently moving particle to spoil this garden party. We then have rival invariances and unlimited descriptive misery. That second clock-particle will measure not-c if the first measures c. In choosing between the two clock-particles, philosophers will recognize the circumstance that induced the starvation of Buridan’s ass. This follows Einstein in supposing the Lorentz contraction to have some physics in it; that is, to be something definite associated with the first clock-particle. Else at the same time two different Lorentz contractions? In that case relativity is empty of physics. Do you see why universal invariance is the missing life preserver in this rising sea of subjectivity?

The test problems just considered clearly validate CT. This is surely no accident. The failure of proper time to yield physically consistent results is a consequence primarily of the assumption of length

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invariance. Proper time does not fit well with that. The reason is that if clocks are going at all sorts of inconsistent rates, while length is behaving consistently, one should expect trouble with speed quotients. Einstein makes a threefold mistake: (1) He uses non-invariant electromagnetic theory. (2) He uses uncorrected clocks. (3) He lets length vary. These three wrongs, taken together, make a number of experimental rights. But for how long will nature keep on kidding us?

IV. CRUCIAL EXPERIMENT

Let a light-speed measuring apparatus (LMA), together with a dual-function atomic clock be put into orbit. By dual-function clock I mean one designed to measure both CT and proper time simultaneously. This is accomplished by using a single cloud of atoms, e.g., cesium. Two counters are installed, one set to count as the “second” of proper time (at zero temperature) 9,192,631,770 oscillations of the cesium atom, the other set with whatever corrections are called for by GPS protocols, to define CT in the orbiting environment. It may be presumed that one or the other counter will record elapsed times (reflection periods) within the LMA corresponding to a measurement of light speed c. It would be quite embarrassing if neither did, and altogether impossible that both should. Relativity predicts that the proper time counter will be the winner. I predict invariance of the apparatus length, in which case the CT counter should win. I cannot foresee an ambiguous outcome, but if there were one the experiment might have to be repeated at different speeds and altitudes. The experiment is most simply thought of as a test of length invariance, which is itself a make-or-break test of the whole invariance approach to physical description.

V. PHOTON FANTASY

What are we to make of the strange behavior of light revealed by an invariant reformulation of electromagnetism? The most likely response

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is to ignore it; but I suggest that the most intelligent is to learn from it. We have over-simplified our picture of the photon, anthropomorphized it: As we ourselves might do, it travels from one place to another – its propagation an expedition into the unknown, a journey of exploration. Off it goes, alpenstock in hand, knapsack on back, an adventuresome little pilgrim … like the boll weevil, just a-lookin’ for a home.

But Eq. (4) suggests that the world is quite differently structured at its foundation. The light quantum has no human attributes. It is a monster, with extensible fingers that directly connect emitter and absorber. Before the energy transfer we picture as photon propagation can happen, acceptance at the destination must already have been established. The journey itself is quite possibly instantaneous. There is no causal “guidance by a wave,” the wave being far too slow, as well as ignorant of what lies ahead of it. Eq. (4) shows the photon to be possessed from the start of its apparent journey of information about its specific absorber that it simply cannot have on the basis of any causal model. For a parallel case one thinks of the Machian model of inertia, wherein the principal instant-actor is the distant matter of the universe (not four-index tensor symbols). The Machian (gravitational) action in a large universe cannot be causally delayed; else increasingly distant matter would continually be making its action felt locally, with time-changing inertial properties at all localities.

I have concentrated attention here on the absorption process, and found it quite mysterious. Reflect, then: how much more mysterious must be the process of emission! Yet physics, according to authorities, is almost finished? Rather, almost begun.

VI. SUMMATION

After more than a century it is high time that physicists had second thoughts about covariance, universal or otherwise. There is something

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simpler, better, more honest and true to life. That is invariance, which may be had at the sacrifice of the conviction that the Lorentz transformation better describes physical inertial motions than does the Galilean transformation. I realize that relativists are going to dig in their heels on this point. The LT is too dear to their hearts to abandon without immense trauma. I am challenging their religion (their unquestioned belief system) and asking them to change it. It takes little knowledge of human nature to anticipate the outcome of that. So, realistically, this paper is not addressed to relativists, but to those rare spirits who have already sensed flaws in the LT and begun by their own brainpower to question the belief system that prevails today among physicists.

Physics needs rebuilding from the ground up. I have made a case here to establish that the missing ingredient in the physics of our time is an unswerving demand for genuine invariance on all fronts. This includes length invariance on the space side and a sort of physical invariance on the time side, which I have associated with a simplified type of timekeeping I call Collective Time (CT), patterned on GPS time. This offers an exact differential, is shared among all particles, and is “invariant” under inertial transformations of its fiducial reference system, in the sense that such transformations do not alter the form of the laws of nature … invariant, then, in its physical implications. The reader unconvinced on this point may be reminded that a two-stage method of clock correction can, if desired, operationally define an absolute version of CT about which there can be no misunderstanding.

The clock corrections inherent in the definition of CT offer a simplification of physical description analogous to that effected by the correction of thermometer readings in thermodynamics. The use of raw instrument readings to define either temperature or time results in vast and unnecessary complication of physical theory. In the case of time the exclusive use of proper time (uncorrected clocks) leads not only to

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motion-dependent time interval measurements but to corresponding variations of measurement units, with consequent inordinate complexity of analysis. “Standard” units of time and other physical quantities are lost. All that complexity is eliminated by the use of invariant descriptors, beginning with CT.

The speed of light is c, regardless of the motions of either the emitter or absorber, as measured by CT. (This is not a postulate but a deduction.) Thus propagation time equals the separation of emitter and absorber at the instant of emission, divided by c. In the case of absorber motion, this results from “light convection by the absorber,” a modification of light speed that cancels the effect of absorber motion during the propagation interval. This acausal mechanism has hitherto been hidden by the traditional form of Maxwell’s equations and is revealed only by an invariant reformulation of electromagnetism. Those who reject acausal thinking might try answering why light propagation time is unaffected by absorber motion.

Among the most readily recognized benefits of the CT approach is the reinstatement of the concept of a universal now. This has such intuitive appeal that I suspect it has never really been abandoned, even by the savants who have demoted it to fiction. The conception is undeniably helpful in organizing our thinking about the world. This new “now” results from a restoration of distant simultaneity (consequent upon making Maxwell’s equations GT-invariant), which in turn entails the invariance of object length under relative motions.

This paper has made no attempt to apply its alternative theorizing to comparisons with specific experimental results. I hope enough has been said about the basics to let others carry on that major part of the job. I have suggested a crucial experiment. Let it rest there.

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VII. POSTSCRIPT ON MY PAST WRITINGS

For many years I have dithered on topics related to this paper. In the first (2006) edition of a book I wrote2 I made essentially the same prediction about a crucial experiment in orbit as is made here. In the second edition (2012) I got a different notion and predicted the opposite. Nowhere in that book did I emphasize the unifying theme of invariance. I believe I have finally got a consistent story to tell -- based on the Hertzian formalism with CT as its time parameter -- and hope my attempt to tell it in this paper has succeeded.

REFERENCES

1H. R. Hertz, Electric Waves, translated by D. E. Jones (Dover, NY, 1962), Chapter 14.

2T. E. Phipps, Old Physics for New (Apeiron, Montreal, 2006 and 2012)

3A. Einstein, Relativity: the Special and General Theory, translated by R. W. Lawson (Dover, NY, 2001).

4R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics Definitive Edition (Addison-Wesley, San Francisco, 2006).

5G. Herglotz, Ann. Phys. (Leipzig) 36, 493 (1911).

6E. Dewan and M. Beran, Am. J. Phys. 27, 517 (1959).