Interpretational problems in Quantum Mechanics and SR

ggarret1 · is under review Joined: 29 Apr 2006 Posts: 1

I have been studying the interpretive dilemma in quantum mechanics relating to Bell’s inequality and other experiments. As a layman I am more interested in the theory on a conceptual level and its epistemological implications than the math. (It is not really that I am not interested in the math but that most of it is beyond me.)

I have always had problems with the conceptual meaning of physical quantities. For instance, entropy is defined by a simple equation; delta S equals q reversible over T. While the formula is simple the concept is not. Put simply, it is not intuitively obvious what a quantity purported to represent the relative order or disorder of a system (formally the number of micro states associated with a macro state) has to do with heat and temperature. Obsessing over meaning has often hindered my progress in mastering the formalism.

I feel quite certain that there are many very productive scientists out there, using the Schrödinger equation, happily shuffling symbols about the paper without any clear understanding of what those symbols mean. Using scientific equations to solve real world problems is highly commendable and, indeed, we owe the existence of televisions and computers to people like them more than to people like me (those with an obsessive need for understanding and logical consistency.) Never the less, striving to understand meaning can yield practical benefits. An example is Einstein’s Special Theory of Relativity.

Lorenz had deduced the transformation equations for time and distance before Einstein wrote his paper and there is circumstantial evidence that Einstein had seen them. However, Lorenz viewed his t prime as some kind of imaginary time, a quantity useful in solving problems in electro dynamics but having questionable physical meaning. The achievement of Special Relativity lies not so much in the formalism or the math (indeed the math is so simple it is easily accessible even to a rank amateur like me) but in Einstein’s recognition that t prime represented the physical time. In Special Relativity Einstein’s genius is largely interpretational.

The interpretational problem in QM keeps bringing me back to a problem I have with Special Relativity which I have been obsessing over, on and off, for thirty some odd years, namely, the Twin Paradox. Since the student of physics has no doubt contemplated this mystery in some depth at some point in his career and made some kind of peace with it, much of what I have to say will be nothing new. Please bear with me.

Two observers are traveling at relativistic speeds relative to each other and as they pass they synchronize clocks. In observer A’s coordinate system observer B’s clock is running slower than A’s and in B’s coordinate system A’s clock is running slower. The explanation of this contradiction is that time and distance are two facets of separation and, as such, a local phenomenon. Now let me say that I do not for a moment doubt that the velocity of light is a constant for all observers nor do I doubt in any way the correctness of the formalism of Special Relativity. My problem is not so much with what Special Relativity implies about external reality but in what it implies about perception.

Our ancestors, no doubt, believed that the primary colors were a property of external reality, a fact of nature. As it turns out, the reason there are three primary colors is because there are three kinds of cells in the retina of the human eye sensitive to three different wave lengths of light. The primary colors do not exist in external reality. They are not a fact of nature but an artifact of human nature. There are many examples where our perception of reality differs dramatically from reality.

I have no problem believing that perceptions of time and distance can differ between observers or even that time and distance do not exist in external reality. However, even dreams are real in the sense that they are real dreams and perceptions are real in the sense that they are real perceptions. The one thing every human knows with absolute certainty is “I perceive what I perceive.” I see what I see, I hear what I hear and I feel what I feel. And, this statement is true regardless of the nature of external reality. In fact, all of our information about external reality is based on perception. Scientific observations are also perceptions. Is the assumption not implicit that perceptions are real (in the sense of being real perceptions) and that perceptions obey the basic laws of logic such as transitivity.

In this light the paradox relating to Bell’s inequality could be restated thus – one set of perceptions (or actions) seem to be influencing another set of perceptions in a way that is non-local and (arguably) a-temporal. But, to my mind, a similar interpretational problem was already implicit in Special Relativity.

In the above example with observers A and B, let us say the observers agree to flip a coin at some predetermined time, in their respective coordinate systems, to decide if they will change directions. One quarter of the time they will continue on their way. One quarter of the time they will both change directions. Half the time one but not the other will change directions. When they meet and compare clocks absolute time will be defined by the observer who remained at rest with respect to his own coordinate system. If A changes direction but not B, we must assume that A’s perception of time was running slower “the whole time” whatever that means. If B changes direction but not A the converse is true. It would seem that A and B’s perception of time on their outward journey is contingent on a coin flip which has not yet happened. This effect seems, to my mind, non-local and a-temporal.

By framing this argument in terms of perception I do not mean to imply that I assign some special role to consciousness. The experiment could just as easily have used clocks and machines. I focus on perception for two reasons. One: “I perceive what I perceive” is the one thing each observer knows with absolute certainty and A’s perception of time agrees with his clock. Two: Regardless of what you say about clocks and time as a property of external reality, it is none the less true that observers perceive the passage of time. If we are to make any sense of our experiences we must assume that perceptions are transitive. I.e. A greater than B means B not greater than A. Since the formalism of Special Relativity is clearly correct, I can either accept that perceptions are intransitive or there is an interpretational problem.

I wonder if this interpretational problem is an “elephant in the room.” Everybody sees it but tradition forbids pointing it out. Some observations on Special Relativity: First, it is based on two assumptions, that the velocity of light is a constant for all observers and the laws of physics are the same for all observers. These assumptions are both simple and grounded in observation. Second, Special Relativity is (internally) logically consistent. Third, the formalism has been verified by numerous experiments. And, finally, as I previously pointed out, Einstein’s achievement is largely interpretational. The success of Special and General Relativity has elevated Einstein to a god among scientist. To question Einstein’s interpretation of Special Relativity is a heresy of the highest order. I do so secure in the knowledge that, not being a physicist, I have no career or reputation to jeopardize. Since I have shown myself a heretic and, arguably, a lunatic, I may as well compound my sin by offering the following. Possible interpretational solutions to quantum mechanics my also apply to Special Relativity.

For instance, the Transactional Interpretation posits waves traveling backward through time. These waves are said to carry information from particles in the present, or even the future, to particles in the past. This reversal of cause and effect is assumed only to apply to the microscopic. If we extend this alleged phenomenon to the macroscopic, is it conceivable that such waves could affect clocks and perception of time.

Of more interest to my mind is the Multiple World interpretation. There is a principle by which a theory may be evaluated that says something like – we should not posit things not known to exist (not directly observable) unless there is no logically consistent alternative. Physicists are surely aware of this principle. Yet, some prominent physicists have held this Multiple World interpretation, apparently feeling that the evidence from quantum experiments is sufficiently strong to justify positing such seeming absurdities.

In Special Relativity, it seems, at least to me, that we are faced with two realities. One in which observer A’s perception of time is slower than B’s and one in which B’s perception is slower. In a Multiple World system, there are multiple realities, multiple observer A’s and multiple observer B’s. If such a system is real, can we be certain that the observer A who synchronized clocks with B at the beginning of the experiment is the same Observer A who compares clocks with B at the end of the experiment?