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Resolution of the Relativity/Quantum Mechanics Conflict

By Richard D. Stafford, Ph.D. Copyright © 2002, All rights reserved.

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

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

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

To begin with, the concept of time has been around long before the invention of clocks and the concept never required the existence of accurate clocks. The most fundamental characteristic of time is that it divides our universe (the reality within which all experiments conceivable are performed) into two distinctly different realms: the past and the future! It is an experimental fact supported by observations extending back to before written history that nothing can be done to change the past and that we do not know exactly what the future will turn out to be. The power and dependability of this single idea (that the past and the future are fundamentally different realms) is the central reason 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 my concept of time must be at least slightly askew of the common interpretation. Please afford me the small latitude I ask to present my slightly shifted concept of time. In my argument, I would like to view time from the perspective of the ancient past and bring that concept forward to what I think would have resulted if our ancestors had understood everything we know today.

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

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

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

The power of Newton's achievements, the ability of his ideas to analytically predict the behavior of many events, insured the development of clocks of ever finer precision. In fact, this precision became so important that the scientific society actually moved to the position that "clocks define time"; totally losing sight of the fact that the central issue of time was the division of the past (that which cannot be changed) from the future (that which science is trying to predict). We had become so sure time could be measured and numerically labeled that we forgot the underlying purpose of the concept: i.e., to separate reality 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, is misdirection of attention! Only magicians understand how easily people can be misled. Misdirection of attention is the very soul of magic; with it magicians can hide the truth for decades even when we know they are trying to fool us. In science, attention is focused on new ideas, not on the old concepts which are presumed to be clear and consistent; how else could Newton's error have stood for three hundred years?

Consequence of Confusion

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

Under normal circumstances, a person begins with a geometry designed to some constraints and then deduces the metric after the fact for the purpose of mathematical analysis. Einstein relied on the fact that the metric was 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 representing the Lorentz transformations, he had already defined some aspects of his mental picture which were not actually necessary. The assumption that clocks measured time was already so solidly embedded in his representation of the Lorentz transformations that he was unable to see his error even after he himself actually discovered that clocks measured something else. What he missed was that they could not be used to define the boundary between the past and the future. From Einstein's perspective, this was the minor issue that simultaneity could not be uniquely defined.

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

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

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

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

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

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

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

In order for you to understand the depth of the experimenter’s abstract dilemma, consider the following circumstance. What kind of success would you expect of a student who took data in an experiment (ai,bi) and then displayed that data in a geometry using the coordinates a and c; where he had defined b (one of his measured variables) to be path length of his finished plot in the geometry. By selecting such a geometry, the student has presented himself with an almost impossible problem: he must know the solution (the consistent set of ci which go with his measurements ai,bi) before he can display his data. If his data produces straight lines, the problem is straight forward; but if the data produces curves, finding the corresponding data set (ci) will become 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 solving during the last century. As would the student above, they have discovered that the problem is quite easy so long as the data falls along straight lines (special relativity, i.e., no acceleration) and time is linearly related to proper time; but, just let a little acceleration confuse the issue and to merely display the data analytically drives one to mathematical notation so complex that very few (if any) experimentalists even bother to attempt a "correct" representation. Most do not even develop the skills necessary to do so.

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

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

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

A Path out of Confusion?

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

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

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

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

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

Mapping the Picture into Reality

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

Now, that idea immediately generates some major problems. If you start laying 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=0 (we are free to set our zero of the parameter of motion to any value). Presume that, following the interaction, one proceeds into the future with a relativistic velocity whereas the other proceeds at some much smaller velocity. Then allow the two to interact later via a photon exchange. Clearly, from what we have said above, the two entities no longer have the same value of and yet they interact via an entity which has the property that has exactly the same value everywhere on its path (the invariant interval along the path of a photon is exactly zero always). We clearly have a logic problem in our picture.

How is it that this problem showed up here but not in Einstein's picture? As 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 conventional view only it was never brought to our attention. Essentially, we failed to mention the well know fact that clocks need not read the same for entities associated with those clocks to interact (remember, is exactly what is measured by clocks!) It follows that, in our mental picture of the situation in our new coordinate system, differences must be projected out; they have nothing at all to 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 t are the same (independent of the value of ) entities can interact. If we keep that fact in mind, it is not difficult to show that both pictures yield exactly the same experimental results (as they have to)7. 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 of the time dependent changes in value remain significant. I do not know how that strikes the reader, but I find myself drawn to the Heisenberg uncertainty principal. If one takes the uncertainty in to be infinite, then one can only conclude that the momentum in the direction is most probably quantized! What impact would such an alteration in our mental picture have on the physics?

and, most important to this discussion8:

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

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

Although the existence of a real tau axis could not possibly be directly perceived, its existence does yield some subtle consequences. It follows, from our total inability to perceive the tau dimension, that only those components of motion perpendicular to tau can be perceived. Thus it becomes quite clear that, although everything in the universe (in this mental picture) travels at the speed of light, we only perceive velocities less than c (we are describing a 4 dimensional Euclidean universe and, in Euclidean geometry, a component of a 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 perpendicular to tau. In that particular case, its momentum in the tau direction must be zero: i.e., it is a massless object10. On the other hand, in order for a massive object to approach the velocity of light, it needs to have an almost unbelievably high momentum in the direction of perceivable space as its momentum in the tau direction (its rest mass) is fixed. Please note again that all of special relativity must be valid in this picture as we have actually done absolutely nothing except re-plot our data in a different geometry; all numbers, all equations, and all relationships remain exactly the same as they would be were we to use Einstein's preferred geometry.

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

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

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

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

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

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

End Notes

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

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

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

4. Jackson, Op. Cit.

5. This statement is true by definition: i.e., even in 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 because I know I am only representing the data in a different geometry and that the results cannot violate experiment; the difficulties are bothersome because they imply my mental picture is in error.

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

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

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

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

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