Dazzling Ideas

The history of physics knew many happy guesses that put the whole science on the new track. Of course, the first and most drastic revolution came when people developed the notion of natural regularity that does not require any conscious interference and happen under appropriate conditions regardless of the presence of any sentient beings. The acceptance of this world as it is makes all the rest possible. Otherwise, there is no science. And nothing to philosophize.

It might seem quite obvious that, admitting something beyond human experience, we should be ready to encounter things that are very unlike humans, with all the petty worlds they arrange. However, it has taken many centuries for scientific thought to get rid of anthropomorphic visions in just a few areas of physics, and there are vast domains where anthropocentrism has happily survived the XX century, with fair perspectives for the next. Still, the very ability to fancy the huge outer space swarming with galaxies as well as the hidden infinity of the tiniest perceptible something is an important step forward, towards more theoretical modesty and versatility of viewpoints.

The two greatest achievements of the early XX century, an extended principle of relativity and a generalized notion of observation, have directed the physical science ever since. Though apparently different (and even in conflict), they basically do the same: the objective character of nature is to be expressed in terms of symmetry. The ancient dream of finding "perfect" forms in the foundation of the Universe has thus been echoed on a new level, in a sophisticated mathematical guise.

There is no need to much dwell on how productive this fundamental idea has proved to be. The symmetries of equations and boundary conditions have been directly related to the symmetries of the phase flows; any picture is equally valid, as they refer to the same physical reality. In many cases, important results can be obtained without knowing the details of dynamics, from the overall structure of the model. Relativistic and quantum gadgets have long since become a part of people's everyday life. The Universe has been successfully explained in the scale range of 80 orders of magnitude. Isn't it great?

Unfortunately, bright ideas do not only light up our minds. They also dazzle.

Once having invented a handy instrument, we tend to adapt our activity to the tool, so that the current problems could be solved using the old habits and proven technologies. Our acts become implement-driven rather than purposeful. When all you've got is a hammer, everything looks like a nail. Science transforms into sheer engineering, and there is neither need nor taste for discovery. The question "why?" shoved aside as demagogical philosophy, the only purpose of science is to compute and calculate.

Probably, it's not too bad, as long as enough is enough. The inner inconvenience of just a few should not undermine the mental comfort of many. When it comes to a real social need, a scientific revolution is bound to burst out with all the wild spontaneity of the blind fate. A philosopher might mutter something like that intellectual blindness would not well suit a person of reason... Let them doubt; they do what they can.

Still, even silly doubts may be of some use. At least for the one who doubts. Just because the very presence of a doubt brings some certainty. Thus, one can be certain that there are no absolute hammers fit to nail down the whole Universe. Sticking to one routine, we drive out millions of others. What is good for one may be an obstacle for another. Any theory is only meaningful as a complement to a wider view allowing us to explain what we really mean. Formulas do not explain anything, they only formulate. However, the same idea can be formulated in many ways, while a very different idea may need a drastically new formulation. Trying to reduce physics to a few fundamental principles, we break with physics as such. Science should not postulate nature; science is to describe it.

By the way, for a few centuries, mathematicians have tried to establish the universal foundations of their science. All in vain. Every open door presented more doors to open; answering a question, we raise another one. As a result, we have a number of alternative mathematics, equally consistent and equally lacking justification. Since justifications are never formal.

And now, some physicists try to derive all physics from a mathematical trick. Isn't it silly, to trust mathematics more than it can trust itself?

A few decades ago, there was a wave of formalistic books with the titles like Foundations of Physics, Geometrical Physics, Logical Physics, Quantum and Other Physics as Systems Theory, and so on. The authors were very systematic and neatly fit any known physical law in an axiomatic (or numerological) approach of their own. Did that advance our understanding of physical nature? Not a bit. All such inventory work produced mere ad hoc constructs, incapable of delivering a fresh idea. Probably they were interesting as philosophical experiments. But never as an insight to physical methodology.

Returning to the certainty of doubt, one could observe that the language of differential geometry dominating in modern relativistic mechanics and field theories is very restrictive when it comes to essentially non-stationary phenomena. Formally, it results in mathematical singularities. For a physicist, a formal infinity would only indicate the inadequacy of standard geometry in the critical region and need for a better formulation. All the talks about physical singularities are mere metaphors exaggerated by popular science writers to the extent of a common prejudice, so that many scientists start seriously believing in black holes and the Big Bang.

It is in the nature of science to seek for regularities, mass reproduction of the same objective behavior. Science never deals with the unique. Indeed, we just don't need science that would not give us a stable platform for common activities replicated from one day to the next. But we also don't need science that would not give us a certain perspective, a range of choices to consciously shape our future. The essential stationarity of a scientific theory is to be complemented with a critical attitude towards the present forms of our knowledge and openness to (if not active search for) any alternatives. The principal goal of science is to develop a bunch of complementary models applicable in the respective regions of stability, while the transitions between the stationary domains remain out of grasp, beyond any science at all. We can find regularities in the very modes of transition and make them the object of science. This will give yet another science, with its limits of applicability and the necessity of alternatives covering the domains out of reach (similarly to the development of nonlinear dynamics). Boundary sciences do not transform one model into another; they only refer to their own (independent) domain, and their formalism cannot be "translated" into any other, even in the asymptotic sense. For instance, thermodynamics cannot be derived from mechanics or physical kinetics, nor interfere with their specific models. These are independent sciences, each following the logic of the respective object area. Similarly, general relativity may fairly well describe the structure of gravitational field relatively far from a very massive object; to describe the interior of that object, we need a different theory (or, maybe, just a different form of the same theory, like the inner Schwarzschild solution); however, to speak of the physics of the regions close to the boundary (which, of course, does not assume any physical singularities), we need something new, unlike the "outer" and "inner" theories.

The necessity of switching to a different model at the boundary of the applicability region closely resembles the well-known physical effect of phase transition. There is no smooth transformation; the very meaning of a boundary is a qualitative change, a leap. On a different level, this boundary may be smoothed, or even entirely disappear; but the very change of level is a qualitative leap, and there is no direct correspondence between the levels.

In a way, quantum physics came to cope with such essentially non-stationary processes involving abrupt changes out of control, qualitative leaps. As we know, quantum theory has only revealed a new kind of stationarity, so that the observable non-stationary effects could be considered as an artifact of level change, a statistical ("macroscopic") aggregation of quite deterministic virtual ("microscopic") transitions. This level fusion lead to the mystical interpretations of quantum mechanics, as if bare human will, mere presence of a human observer, might influence the light from the distant stars.

The geometrical picture of space-time is an acceptable model for some areas of our experience. However, this does not forbid search for other representations, possible more adequate in a wider domain including numerous levels of scaling characterized each with its own velocity range. Unfortunately, modern scientists, blazed with the apparent success of relativistic theories, have entirely abandoned the attempts to fancy anything unusual beyond the relativistic cage. We blindly accept the Universe as a 3+1 (or N+1) dimensional manifold, and the very question about the special conditions and the limits of this coupling is an absolute taboo.

In general, any kind of dimensionality should be understood as a result of physical dynamics. Yes, various "theories of everything" include folding and unfolding of spatial dimensions at certain energetic boundaries (with energy intimately related to time). But such theories still admit an absolute "background" symmetry that can only be violated in many ways, but never transform into a different symmetry, or reveal a symmetry of an entirely different kind. The group theory formalism has subdued creative imagination, suggesting us the clones of the same theory instead of drastically new models. And, so far, nobody can tell why time gets stubbornly coupled to space still retaining an obviously privileged role. Even a child understands that, to make a box, one needs to somehow fasten its walls to each other; similarly, to build a 2-dimensional space, we need a "glue" to stick one dimension to another, and a different kind of "glue" is needed to bind time to space. Dynamic dimensionality has already found its place in nonlinear dynamics, albeit restricted to the geometry of flows in a "classical" space-time. What prevents us from considering space production in a manner we describe many-body quantum systems, using dimension creation or folding operators? Which, of course, is also a limited picture, admitting the existence of notions beyond our present comprehension (and yet never beyond any comprehension at all).

In the same manner, bluntly postulating the equivalence of the inertial and gravitational masses, we stop any questions about the origin of mass in general, and hence the possibility of different kinds of mass and the physical conditions required for relative (or local) equivalence. Formal elegance has eclipsed the physical sense.

In the same manner, demanding the stationarity of action in the variational formalism, we refuse to consider non-stationary systems (or higher levels of stationarity). The origin of the action principle goes back to simple equilibrium conditions practically important for medieval architecture. Newtonian dynamics could be derived from a quasi-equilibrium, introducing fictitious forces associated with the motion of the bodies (which is virtually justified by the diversity of the forms of energy and the possibility of their mutual transformation). However, such stationary dynamics is implicitly based on the presence of dynamical symmetries, and hence the famous Noether's theorem contains, in fact, a logical circularity.

One could readily collect many more dazzling ideas from all branches of physics. Do we really need such examples? This is the first principle of science: all we can is inventing models, and every model is only right within the limits of its applicability. For truly scientific rigor, every statement must be appended with a stipulation: "where appropriate". We omit this phrase, just to avoid excessive wording. However, a lighter text is no excuse for a looser thought. A limited character of any formulation never goes away. The author should always mean it; the reader is to mentally restore the required reservations. Introducing a function, we refer to a particular domain and a definite range. Writing down an integral, we assume that integral formulation is acceptable in the object area of interest. Suggesting a symmetry group, we must clearly realize that any symmetry is approximate, and the results may be inapplicable in a less symmetric dynamic (on a different level of stationarity).

The laws of science are like legal laws: they tell us what is admissible, but they can never forbid anything. The law prescribes a proper conduct in the standard situations; but it is of no help in a real mess. Eventually, new laws summarize the precedents and establish a standard to cover a wider range of legal acts. But nature is the greatest criminal of all: there is no law it would not violate. So, take it with a funny bone. Dazzling ideas are no stupefying mystery; they are to sharpen our vision, and not to blind us.