From: Subject: Relativity/Quantum Mechanics Date: Fri, 3 Jun 2011 19:48:12 +0200 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01CC2227.2BF72D70" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.6090 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01CC2227.2BF72D70 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable Content-Location: http://web.archive.org/web/20081222192216/http:/home.jam.rr.com/dicksfiles/flaw/Fatalfla.htm =EF=BB=BF Relativity/Quantum Mechanics 3D"Wayback MEI=20 DEC jan 22 3D"Next 2007=20 2008 2009 31=20 captures=20 1 mei 03 - 22 = dec=20 08 = Close Help=20

Resolution of the Relativity/Quantum Mechanics Conflict

By Richard D.=20 Stafford, Ph.D. Copyright =C2=A9 2002, All rights reserved. =

"There is a deep seated fundamental conflict between Quantum = theory and=20 Einstein's theory of relativity. Subtle difficulties become = insurmountable=20 problems when gravity is added1=20 ."

I believe there exists a fundamental error in the common perception = of=20 reality: I hold that this error is the basis of the conflict decried = above. In a=20 nutshell, the error concerns our confused concept of time. Every student = has=20 been told countless times that Newton=E2=80=99s error (which stood for = almost 300 years)=20 was that he assumed everyone=E2=80=99s clock could be set to read the = same. In the same=20 vein, I hold that Einstein=E2=80=99s error (an error which has plagued = science for=20 almost 100 years already) was that he assumed clocks measured time. It = is my=20 position that this perception so blocked his view (as even today it = blocks the=20 view of the whole scientific community) that he made a mistake in his=20 fundamental view of the problem one would not expect of a high school = science=20 student much less a trained scientist.

If you are going to take the position that to criticize Einstein or = his work=20 is beyond the right of a mere mortal, read no further as this message is = not for=20 you; however, if you have the mental capability to temporarily suspend = judgment=20 and are willing to look at a possible alternative, please read on. If = you=20 closely examine my arguments, you may be surprised by what you find. It = is my=20 claim that the most important problem in modern physics is a subtly = confused=20 concept of time. Please note that I am making no argument here against = any of=20 the experimental results which are used to defend Einstein; the argument = is=20 wholly with the interpretation of those results.

The Confusion Concerning Time

If I think the concept of time is confused, it behooves me to clarify = exactly=20 where I believe the problem resides.

To begin with, the concept of time has been around long before the = invention=20 of clocks and the concept never required the existence of accurate = clocks. The=20 most fundamental characteristic of time is that it divides our universe = (the=20 reality within which all experiments conceivable are performed) into two = distinctly different realms: the past and the future! It is an = experimental fact=20 supported by observations extending back to before written history that = nothing=20 can be done to change the past and that we do not know exactly what the = future=20 will turn out to be. The power and dependability of this single idea = (that the=20 past and the future are fundamentally different realms) is the central = reason=20 for the very existence of the concept of time. To forget this fact is to = overlook a very important phenomena fundamental to our very existence. =

As I hold that the current concept of time is confused, it is = necessary that=20 my concept of time must be at least slightly askew of the common = interpretation.=20 Please afford me the small latitude I ask to present my slightly shifted = concept=20 of time. In my argument, I would like to view time from the perspective = of the=20 ancient past and bring that concept forward to what I think would have = resulted=20 if our ancestors had understood everything we know today.

In the beginning, the concept of time was really a subtle reference = to what=20 was known. To refer to a specific moment in the past (usually by naming = a=20 significant event) was to provide a reference to the division between = past and=20 future from the perspective of that event. Time was essentially = delineated by a=20 succession of events. Even prior to the invention of writing, I am sure = it was=20 evident to our ancestors that the motion of the sun (among other = repetitive=20 events) provided a convenient commonly understood event as a easy = reference. It=20 is my position that this is the real source of the idea behind clocks, = devices=20 which could track and label the present. That is, to provide specific = references=20 to the collection of interesting boundaries between the associated = states of=20 past and the future. What should always be remembered here, is that = these=20 references must correspond to a consistent set within our personal = mental image=20 of reality.

Until Newton came along, I think the concept of time was in good = alignment=20 with the needs of mankind; however, I think Newton's great success was = the=20 source of a perspective which was fundamentally erroneous. In essence, = Newton=20 showed that the future mechanical motion of many objects could be = predicted from=20 the past motion via some very simple mathematical relations, time (as a=20 numerical parameter) became a very important scientific concept. This, = in=20 itself, was not at all in violation of the concept of time which I have = laid out=20 here.

If clocks are seen as mechanical devices designed to provide a = convenient=20 laboratory collection of reproducible repetitive events, then there is = no real=20 conflict with the earlier concept. The clock is then nothing more than = the=20 source of a set of references to the division between past and future = from the=20 perspective of the events being examined in the laboratory. Newton's = error was=20 the presumption that these laboratory clocks provided a valid universal=20 collection of well understood events: i.e. that everybody's clock could = be set=20 to agree. What should be remembered is that this issue, though very = real, in no=20 way reduces the value of the clock; it merely removes the clock from = fulfilling=20 the original concept of time.

The power of Newton's achievements, the ability of his ideas to = analytically=20 predict the behavior of many events, insured the development of clocks = of ever=20 finer precision. In fact, this precision became so important that the = scientific=20 society actually moved to the position that "clocks define time"; = totally losing=20 sight of the fact that the central issue of time was the division of the = past=20 (that which cannot be changed) from the future (that which science is = trying to=20 predict). We had become so sure time could be measured and numerically = labeled=20 that we forgot the underlying purpose of the concept: i.e., to separate = reality=20 into the two distinctly different realms, the past and the future.

Why did such a change raise no signs of difficulty? The issue, very = clearly,=20 is misdirection of attention! Only magicians understand how easily = people can be=20 misled. Misdirection of attention is the very soul of magic; with it = magicians=20 can hide the truth for decades even when we know they are trying to fool = us. In=20 science, attention is focused on new ideas, not on the old concepts = which are=20 presumed to be clear and consistent; how else could Newton's error have = stood=20 for three hundred years?

Consequence of Confusion

Einstein resolved the difficulty brought forth by Maxwell's equations = and the=20 clear requirement of the Lorentz transformations by hypothesizing an = alternate=20 geometry for the universe. His geometric solution to the problem has now = been=20 accepted as incontrovertible. If I hold that Einstein made an error, I = need to=20 display exactly where I think the error was made. Let us return for a = moment to=20 the metric used in Einstein=E2=80=99s space-time, remembering that he = used that metric=20 to define the geometry of the universe2:=20

Under normal circumstances, a person begins with a geometry designed = to some=20 constraints and then deduces the metric after the fact for the purpose = of=20 mathematical analysis. Einstein relied on the fact that the metric was=20 consistent with the Lorentz transformations and concluded that Minkowski = geometry had to be the proper geometry to be used to describe reality. =

What Einstein apparently failed to realize was that, by analytically=20 representing the Lorentz transformations, he had already defined some = aspects of=20 his mental picture which were not actually necessary. The assumption = that clocks=20 measured time was already so solidly embedded in his representation of = the=20 Lorentz transformations that he was unable to see his error even after = he=20 himself actually discovered that clocks measured something else. What he = missed=20 was that they could not be used to define the boundary between the past = and the=20 future. From Einstein's perspective, this was the minor issue that = simultaneity=20 could not be uniquely defined.

This issue was not found to be bothersome because Newton had = established the=20 time dependent mechanical model of reality so powerfully that no one at = the=20 time, saw any need for that ancient division between the two realms of = reality.=20 It was the authoritative scientific position that, if you knew past = exactly, the=20 future would be exactly predictable and the boundary, from the = scientific=20 perspective was unimportant. A very important concept was discarded as=20 unnecessary3!=20 I hold that this is the exact source of the conflict between Relativity = and=20 Quantum mechanics.

Since that time, experimenters have been analytically displaying = their data=20 in Einstein=E2=80=99s picture and searching for relationships without = really ever=20 questioning the applicability of his geometry. In order to understand = Einstein=E2=80=99s=20 error and the consequences of that error we must understand the nature = of what=20 is called "proper time". Proper time is related intimately to the metric = of=20 Einstein=E2=80=99s representation of what he calls space-time4.=20

If one is familiar with Einstein=E2=80=99s theory of relativity, one = should notice=20 two very important facts concerning real experiments which can be = performed. The=20 first fact is that no physical object can follow a path in = Einstein=E2=80=99s space-time=20 if any element of that path requires d to be non real (no physical object may move along = a path where=20 d is imaginary).

This is the first sign that something is amiss here! If no object may = follow=20 such a path, why does Einstein's proposed geometry of the universe = include such=20 a path? That this is not a trivial question is pointed out by the fact = that the=20 issue of objects following such paths is a serious question considered = by modern=20 physicists. This is the impetus for the search for tacheons: particles = which=20 travel at speeds in excess of the speed of light. Anyone competent in = relativity=20 can show that the existence of such particles yield demonstrable = violation of=20 causality: essentially, they allow the past to be changed! Serious = scientists=20 usually dismiss this issue as a flight of fancy; however, if that is the = case,=20 we are back to the original question: why should the geometry include = such a=20 possibility?

The second fact, which is also of under appreciated significance = (dismissed=20 as insignificant by everyone), is the fact that each and every object = which has=20 any internal dynamic properties can function as a clock and that all = such clocks=20 exactly measure d: i.e., proper time. This fact is true even under = acceleration;=20 a point seldom pointed out by any authority on relativity5.=20

If one wishes to be exactly correct, any competent physicist knows = that, when=20 he performs an experiment, there exists no clock in the universe which = yields=20 the correct time for the reference frame used in the calculation of the=20 consequences of his experiment (such a clock would have to be in an = absolutely=20 perfect rest frame). He will hold that the errors are negligible and=20 unimportant. I agree that they may,by care, be made as negligible as = desired but=20 I deny that they are unimportant.

Please notice that, if one is to be exactly correct, a subtle problem = has=20 been handed to the experimentalists. They take measurements on the real = world:=20 x,y,z and "some clock reading". They then display that data in = Einstein=E2=80=99s=20 geometry (the display is usually via analytic and not graphic methods = but it is=20 display none the less). Somehow, they always manage to perceive the fact = that=20 all clocks measure proper time to be a trivial issue, not really = significant to=20 their problems. But Einstein=E2=80=99s coordinate system requests they = display x, y, z=20 and time (not proper time). This error leads the experimenter into an = almost=20 insoluble problem. His problems are only shielded from his personal = realization=20 by the superb power of the mathematics available to him or the usually = small=20 relativistic effects.

In order for you to understand the depth of the = experimenter=E2=80=99s abstract=20 dilemma, consider the following circumstance. What kind of success would = you=20 expect of a student who took data in an experiment = (ai,bi)=20 and then displayed that data in a geometry using the coordinates a and = c; where=20 he had defined b (one of his measured variables) to be path length of = his=20 finished plot in the geometry. By selecting such a geometry, the student = has=20 presented himself with an almost impossible problem: he must know the = solution=20 (the consistent set of ci which go with his measurements=20 ai,bi) before he can display his data. If his data = produces straight lines, the problem is straight forward; but if the = data=20 produces curves, finding the corresponding data set (ci) will = become=20 a mathematical chore that the very best of us would rather avoid.

That problem is exactly the problem the physics community has been = faced with=20 solving during the last century. As would the student above, they have=20 discovered that the problem is quite easy so long as the data falls = along=20 straight lines (special relativity, i.e., no acceleration) and time is = linearly=20 related to proper time; but, just let a little acceleration confuse the = issue=20 and to merely display the data analytically drives one to mathematical = notation=20 so complex that very few (if any) experimentalists even bother to = attempt a=20 "correct" representation. Most do not even develop the skills necessary = to do=20 so.

The fundamental problem is two very different concepts of time. One = concept=20 of time is the idea that there is a state called the present which = divides the=20 universe into two different realms: the past which cannot be changed = from the=20 future which cannot be exactly known. The second concept of time is that = it is=20 the reading off a clock. These concepts are fundamentally inconsistent = with one=20 another.

Two issues ignored by the scientific community should be looked at = very=20 closely here. First, any competent physicists knows that it is = impossible to=20 construct a device which will provide a universal division between past = and=20 future for all possible reference frames. This being the case, they = simply=20 ignore that concept of time as being of no scientific significance. = Quantum=20 mechanics, on the other hand, seriously confronts that concept.

The second issue is the fact that all clocks are dynamic physical = entities=20 controlled by the laws of physics. Since the fundamental axiom of = relativity is=20 that the laws of physics are not frame dependent, the readings on a = clock cannot=20 possibly be frame dependent! Note that the only measure in the theory of = relativity which is totally independent of the reference frame is = Einstein's=20 invariant interval which, as luck would have it, is exactly what all = clocks=20 measure. Scientists avoid thinking about this issue by placing their = reference=20 clocks in specific reference frames as if these frames are of special=20 significance.

A Path out of Confusion?

The answer to the dilemma is frightfully simple: one should work = directly=20 with the experimentally measured variables. That is to say, we should be = displaying our data in a geometry where the coordinates along the path = of the=20 objects of interest are x,y,z and proper time. Notice that this change = does=20 absolutely nothing to the data describing the universe! This change = constitutes=20 no more than a different representation of exactly that same data and = must obey=20 all the equations obeyed by the data in the original representation. It = is no=20 more than a different (and, in some ways, more convenient) display. = Please note=20 that I am not proposing either absolute time or any kind of "ether" = theory; all=20 I am saying is that one may, at any time, choose a reference frame = within which=20 to plot their data.

In order to see the consequences of displaying our data in this = geometry, let=20 us rewrite the differential relationship derived from the Lorentz = consistent=20 metric deduced by Einstein with the proper time under the radical; thus=20 discovering the metric of our suggested geometry consistent with physics = driving=20 the change in the measured variables.

Several surprising things have occurred; two of which are apparently = quite=20 unreasonable6.=20 One of the most astounding things about that metric is that it is = exactly the=20 form we would expect for a Euclidean metric. Who, in their right mind = would have=20 expected the Lorentz consistent transformations required by Maxwell's = equations=20 to have lead us to a Euclidean space? The second rather different aspect = of this=20 picture is that "t" has returned once more as a parameter of the motion, = not a=20 coordinate.

On the other hand, two other consequences seem, at least at first = glance, to=20 be in direct conflict with reality. First, if the measure along any path = is cdt=20 and t is a parameter of the motion, the speed of every entity described = in this=20 geometry is identical to the speed of light (a comment seemingly = contradictory=20 to any experience). The other equally strange consequence, that tau = apparently=20 represents a real axis totally and completely on par with the other = three axes,=20 seems also to be in direct conflict with reality. This geometry is a = four=20 dimensional Euclidean geometry and it is counter to our intuition that = there=20 could exist another axis totally equivalent to x,y and z which is not=20 perceivable.

I would like to take time out to assure everyone who has managed to = get this=20 far, that there is no physics here at all! We have done nothing except = propose=20 to plot object paths in an alternate geometry; any problems which appear = to=20 arise must arise because our mental picture does not map these events = properly=20 into our common perception of reality (as seen in Einstein's space-time=20 continuum). I will therefore proceed with a proposed mapping which I = think makes=20 sense.

Mapping the Picture into Reality

This fourth dimension, which arose from the path length from = Einstein's=20 theory (his invariant interval), must be given as a function of t (the = parameter=20 of the motion). It should be evident that c is a measure (confined to the space-time path of = the event of=20 interest) of the total path length of that entity since it was created = (the=20 integral of cd along that space-time path). Clearly, the start = point is=20 either the beginning of the universe or some other point of interest. = With=20 regard to that "point of interest", if we have two entities interacting, = it is=20 quite rational to conclude their position in c coincide.

Now, that idea immediately generates some major problems. If you = start laying=20 out your data in such a picture, it is very easy to set up the following = problematical situation:

Start with two entities interacting at some time t=3D0 (we are free = to set our=20 zero of the parameter of motion to any value). Presume that, following = the=20 interaction, one proceeds into the future with a relativistic velocity = whereas=20 the other proceeds at some much smaller velocity. Then allow the two to = interact=20 later via a photon exchange. Clearly, from what we have said above, the = two=20 entities no longer have the same value of and yet they interact via an entity which has the = property=20 that has exactly the same value everywhere on its path = (the=20 invariant interval along the path of a photon is exactly zero always). = We=20 clearly have a logic problem in our picture.

How is it that this problem showed up here but not in Einstein's = picture? As=20 I said earlier, all we are doing is re-plotting our data in an alternate = coordinate system! The fact is that exactly the same difficulty showed = up in the=20 conventional view only it was never brought to our attention. = Essentially, we=20 failed to mention the well know fact that clocks need not read the same = for=20 entities associated with those clocks to interact (remember, is exactly what is measured by clocks!) It follows = that, in=20 our mental picture of the situation in our new coordinate system, differences must be projected out; they have = nothing at all to=20 do with whether or not an interaction can take place.

So, our problem is solved. All we need do is remember that anytime = x,y,z and=20 t are the same (independent of the value of ) entities can interact. If we keep that fact in = mind, it is=20 not difficult to show that both pictures yield exactly the same = experimental=20 results (as they have to)7.=20 However, it does lead us to thoughts we might not have within Einstein's = picture.

Some thoughts about Quantum Mechanics

In this unconventional picture, we have a real coordinate, , who's actual value vanishes from the physics = while the impact=20 of the time dependent changes in value remain significant. I do not know = how=20 that strikes the reader, but I find myself drawn to the Heisenberg = uncertainty=20 principal. If one takes the uncertainty in to be infinite, then one can only conclude that = the momentum=20 in the direction is most probably quantized! What impact = would such=20 an alteration in our mental picture have on the physics?

and, most important to this discussion8:=20

Clearly, in terms of our new metric, since tau is a real axis just = like x, y=20 or z, momentum in the tau direction must be mass. This fact has far = reaching=20 consequences. Who among you has ever performed an experiment in the = total=20 absence of quantized mass? Every experimentalist I know of works in a = laboratory=20 where almost everything he deals with is in a mass quantized state with=20 uncertainty in tau (half life) at least on the order of the age of the = universe.=20 In fact, I would say that it is absolutely obvious that our day to day=20 experience is built on observations of nothing but mass quantized = entities!

=20

It follows, absolutely and unconditionally, that the uncertainty in = tau must=20 be infinite for any common physical measurements9.=20 That is, it follows directly that every entity in the universe that we = deal with=20 on a day to day level can have no measurable irregularities in the tau=20 direction. The magnitude of the wave function which describes that = entity and=20 its motion can not be a function of tau; clearly, the cross section=20 perpendicular to tau of any macroscopic object is absolutely and = unconditionally=20 uniform over any range within our conception. Two physical consequences = of this=20 fact jump immediately to mind: the tau dimension, real or not, yields no = directly measurable phenomena thus vanishes from any possible perception = and=20 secondly, the fact that clock readings have nothing at all to do with=20 interactions occurring does not contradict the picture at all.

Although the existence of a real tau axis could not possibly be = directly=20 perceived, its existence does yield some subtle consequences. It = follows, from=20 our total inability to perceive the tau dimension, that only those = components of=20 motion perpendicular to tau can be perceived. Thus it becomes quite = clear that,=20 although everything in the universe (in this mental picture) travels at = the=20 speed of light, we only perceive velocities less than c (we are = describing a 4=20 dimensional Euclidean universe and, in Euclidean geometry, a component = of a=20 vector cannot be larger than the magnitude of that vector).

In the picture just constructed, the only case where an entity can be = perceived to travel at the velocity of light occurs when its motion is = entirely=20 perpendicular to tau. In that particular case, its momentum in the tau = direction=20 must be zero: i.e., it is a massless object10.=20 On the other hand, in order for a massive object to approach the = velocity of=20 light, it needs to have an almost unbelievably high momentum in the = direction of=20 perceivable space as its momentum in the tau direction (its rest mass) = is fixed.=20 Please note again that all of special relativity must be valid in this = picture=20 as we have actually done absolutely nothing except re-plot our data in a = different geometry; all numbers, all equations, and all relationships = remain=20 exactly the same as they would be were we to use Einstein's preferred = geometry.=20

What first appeared to be problems with the new metric turn out not = to be=20 problems at all. In fact, as I have shown, direct detection of such a = real axis=20 violates quantum theory. The beauty of the picture is that we are now = dealing=20 with a Euclidean universe, much much simpler to mentally handle than = Einstein's=20 space-time construct. Problems which were difficult to explain to a = novice are=20 now simple. Time is once again a simple parameter of the motion. = Simultaneity is=20 an well defined concept; in fact it can be shown that the universe in = this=20 perspective is dynamically Newtonian in many respects. Time, as = displayed in our=20 reference frame is an interaction parameter and is, in fact, the = division=20 between past and future as per the original concept of time.

One should make one further observation about this frame and how it = brings=20 consistency to our picture. Simultaneity is easy to define in any given=20 relativistic space-time frame; the problem is that individuals in = different=20 frames will not agree with one anothers definition. However, all = observers will=20 agree with the order of specific related interactions (a result often = shown in=20 any examination of the subtleties of relativity3).=20 The solution here arise from the fact that "time", as define in this = picture, is=20 not a measurable variable (it is rather a mental construct providing the = separation between past and future). The standard Lorentz = transformations=20 distort the entire geometry without disturbing that final result. A = consequence=20 I will demonstrate to any interested party.

What is time dilation all about? It is very simple! Clocks simply do = not=20 measure time: i.e., the rate at which we go into the future. They = measure only=20 the undetectable tau component of our motion. On the other hand, any = motion=20 through space must correlate directly with propagation into the future. = In=20 ordinary circumstances, the component of our velocity perpendicular to = tau is so=20 small that only the tau component of our motion is significant and that = leads us=20 into the delusion that what is displayed on our clocks is time. The = actual fact=20 is that all clocks, including our biological clocks, measure only tau=20 displacement (proper time!). Any movement in space perpendicular to tau = forces=20 us into the future without changing either our personal clocks or our = perception=20 of time passage.

=20

If we were to move one light year extremely quickly (that is, little = time=20 would pass on our personal clock) we would find ourselves roughly an = additional=20 year in the future not indicated on our clock. Remember, clocks do not = measure=20 time, they measure proper time: i.e., change in tau! What we have = actually done=20 in this case is to make our tau component of movement very small. Since = our=20 actual velocity is always c, the space component of our velocity must, = in this=20 example, be approaching c. Any outside observer (who only perceives = motion=20 perpendicular to tau) will immediately conclude that we were traveling = at very=20 close to the speed of light. It should be eminently clear that we can = never=20 appear to exceed the speed of light because we merely end up going more = quickly=20 into the future: that is, we simply go into the future without our = clocks=20 changing!

Kinematically speaking, it is not difficult to show that the two = seemingly=20 violently different pictures of the universe (Einstein's and mine) yield = absolutely identical results as they must11.=20

There are two points I would like to make here: first, Einstein's = relativity=20 is an extremely valuable perspective for expressing the laws of physics = in a=20 form which are truly independent of our frame of reference but that fact = should=20 be taken as a convenient mathematical structure and not a statement = about the=20 "true" structure of reality. And second, if anyone is interested, it is = not=20 difficult to show the analogous extent ion of this work into the area of = General=20 Relativity. The results are much simpler than Einstein's machinations = and also=20 produce a few subtle differences which I think are worth looking at=20 experimentally.

End Notes

1. Paul Renteln, "Quantum Gravity", American=20 Scientist, 79, 508-527 (1991).

2. John David Jackson, Classical = Electrodynamics,=20 (John Wiley & Sons, Inc., New York, New York,1963), p. 369.

3. Just as an aside, I would like to point out = that anytime=20 this difficulty is brought up (in any of its many possible guises), it = is always=20 quite quickly dismissed as being of no consequence. Anyone competent in=20 relativity can show very easily that the finite speed of light yields = the fact=20 that you can choose any reference frame you wish and, in detail, = demonstrate=20 that no real difficulties exist. What I want the reader to comprehend is = that it=20 is not the mathematical results of Einstein's theory of relativity with = which I=20 argue. It is with the interpretation; an issue not yet clarified here: = i.e.,=20 please delay judgment until my arguments are completed.

4. Jackson, Op. Cit.

5. This statement is true by definition: i.e., = even in=20 Einstein's own picture, the path length is given by the integral of = icd along the path.

6. Please note that I say apparently. I say = apparently=20 because I know I am only representing the data in a different geometry = and that=20 the results cannot violate experiment; the difficulties are bothersome = because=20 they imply my mental picture is in error.

7. So long as we remain in one, non accelerating = reference=20 frame (which is true here as our purpose is nothing more than to display = data)=20 there is nothing in Einstein's Theory of Relativity to deny us the = option of=20 defining simultaneity. The difficulty occurs when we attempt to make = such a=20 definition universal (true in anyones frame of reference).

8. Nothing more than the uncertainty in=20 m0c2 (Energy) in the unstable particle's rest = frame!

9. If not infinite then something in excess of=20 3x1020 light years (that estimate is based on a rather = conservative=20 estimate of the stability of protons). Note that this is over a billion = times=20 the standard three dimensional diameter of the universe. You will excuse = me if I=20 use a mental image of infinity.

10. Note that although the tau component of its = velocity is=20 zero, its tau dimension is still infinite!

11. This is just a different way of ploting = exactly the=20 same information.

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