Can Cinderella be violated?

The previous post ended with a question: when a physicist plays with clocks and rods and kinematic concepts like time, displacement, velocity, acceleration… what is his or her Cinderella, that is to say, the practical purpose that he or she has in mind?

Seeking an illustration for the answer, I reviewed the problems posed in a standard physics book. Unfortunately, the questions stopped at the abstract level. They asked, for example, about the velocity of a projectile after the lapse of a time interval. However, they would have been more amusing (and probably more pedagogical) if they had spoken out any reason why that velocity may matter. For instance: will the projectile fired by the villain arrive “in time” to hit the heroine, before the latter receives a warning message from the hero? We could think of many analogous situations and, in my opinion, in all of them should we find the same leitmotiv: they sound like causality. The shape of the question may be whether an agent causes an effect or whether it avoids it or how many times it does it…; all those are variations over the same theme, which is the old story about causes and effects.

So causality is the Cinderella of motion concepts. This is the essence, the “spirit” of these notions, which –as you can appreciate- is, paradoxically, a pretty material thing: our pious Cinderella is a practical goal, made of tangible matter.

Thus we have identified the end. The means, as commented in the previous post, is the physical instrument with which we measure: in my metaphor, it is Cinderella’s slipper; in the context of kinematics, it is clocks and rods (or, if we take a modern stance, based on Special Relativity, electromagnetic waves with which you measure both space and time). In between those two elements, there lies the third ingredient of concepts: the  logical reasoning explaining how, on the basis of what the instruments have measured, you can find the solution to the problem at hand.    

Given this, how come that, according to certain interpretations, causality (our lovely Cinderella!) can be violated?

So… you have a challenge, you need to find Cinderella, you get hold of one of her slippers as a clue for unmasking her identity, you start playing with this instrument and… the mother of all wonders! Just because of these manipulations, you suggest that… somewhere else, Cinderella may be suffering some nasty effect… she is negated, she is somehow vexed, she is breached …

Yes, it sounds ridiculous but that is the nature of intellectual process leading to the fantasies that put in question causality. It is a simple epistemological error. You invent a concept for solving a problem and in the end you get so entangled in the intricacies of the idea, you fall so much in love with it, that you become sort of fetishist: you forget your problem and feed on the instrument.

I will finish with another metaphor borrowed from the philosopher Eckhart Tolle. Concepts are pointers at solutions to practical concerns. For instance, a signboard with an arrow pointing to Rome. However, you do not remain there, gazing at the arrow. That may be entertaining if the arrow is beautifully drawn. But it is not the aim. And for sure you would never pay attention to the bizarre idea that, because of the very existence of the signboard, Rome may be set on fire.

Slippery concepts

I have a model to explain what a concept is. It is a very pragmatic one. It has three elements and they are all tainted by empirical / practical features:

a) An end. This is the practical concern, the solution to any problem of day-to-day life that is nagging you.

b) A means. In physics, this is the instrument with which you carry out measurements and obtain values.

c) The logical link between the former two, the reason why you think that b) is a clue that solves a). This should also be tested in practice: it is good if it works.

To put it graphically, a concept is like Cinderella’s slipper. Yes, I believe that fairy tales have, amongst other things, an epistemological value. Especially, Cinderella’s tale may be interpreted as a metaphor of knowledge-seeking. Those wanting to improve their Spanish and being patient enough to read a long and verbose philosophical joke... can find a development in www.idearemos.com (sorry, this site is not available any more).  But in the end the metaphor is simple: 

a) The Prince has a problem: he needs a wife and a (future) queen.

b) After several failures, he hits on an idea: he puts glue on the stairs of the palace so that a piece of his beloved, a model of her foot, gets stuck therein.

c) For a number of reasons, he thinks this is a good clue for catching Cinderella, that the slipper adequately “mirrors” the girl who satisfies his needs.

Please note what a modest approach this is. We do not “know” what reality is. We just solve problems. We do not even “describe” nature. Strictly speaking, we only describe the results of our measurements, that is to say, the score of our interaction with nature. Somehow, this is downsizing science and art to the level of technique. We, the self-called knowledge-seekers, are just crafty detectives.

And, getting to the point, I believe that Einstein’s theory of Special Relativity brilliantly exemplifies and illustrates this approach. See this quote from “The Meaning of Relativity”:

The only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy. I am convinced that the philosophers have had a harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to the intangible heights of the a priori. For even if it should appear that the universe of ideas cannot be deduced from experience by logical means, but is, in a sense, a creation of the human mind, without which no science is possible, nevertheless this universe of ideas is just as little independent of the nature of our experiences as clothes are of the form of the human body. This is particularly true of our concepts of time and space, which physicists have been obliged by the facts to bring down from the Olympus of the a priori in order to adjust them and put them in a serviceable condition.

I would not find it strange if Einstein had read Cinderella (specifically, the version of the Grimm Brothers, in beautiful German) the day before drafting this passage. He wants the idea of time to be fed with real, empirical input. Ideas are enrooted in sense perceptions or, if you want to be more precise, objective measurements. They are built upwards, not the other way round. Why? Because only this way do concepts play their function of “mirroring” a practical problem and providing the solution thereof. The process goes as follows: the measurement embraces the concept and the concept embraces the solution, just as clothes embrace the form of the human body… In particular, if time is relative, because it depends on the state of motion of the reference frame, that is it. No more discussion. We must put up with that constraint and feed our equations and geometric pictures with relative time measurements. We just need to re-adjust the latter so that they are consistent with the real nature of their raw material. That is what the Lorentz Transformation and other related equations do.

Let us remark the difference with Newton’s assertion:

Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

Newton was wrong in arguing that mathematical time should be the non-measured one. The equations must be alimented with the real value, otherwise they will not lead to a sensible solution to the real problem!

Hence… should we thus ban the very idea of "absolute time" from our vocabulary? Should we refuse to even discuss what it may at all mean? Should we reject it as an inexistent slipper? I do not think so. That would be misunderstanding what I explained before: how concepts work, how slippers serve for catching Cinderellas. Yes, slippers may be "ideal", purely mental constructions, too, when that comes helpful in finding the beloved solution to our concerns. But what is our practical goal when we play with clocks and rods? What is the physicist's Cinderella...?