Science and philosophy – 2

I just finished reading “dreams of a final theory” by Steven Weinberg. The book is somewhat less technical than I had expected. Despite having a chapter titled “Against Philosophy”, Weinberg deals with several issues that have more to do with the methodology of science than with its content, such as reductionism, “aesthetics” in science, positivism, belief in God etc. Overall, the book is quite enjoyable. I am interested in developing a better understanding of several of the issues Weinberg discusses, so this book has given me a lot of starting material.

To me, the most interesting arguement that Weinberg makes is that “aesthetics” has played a significant role in the formulation as well as the acceptance of several of the theories that have been developed in the last century. I had encountered similar claims before but had not taken them very seriously. But Weinberg makes his case quite convincingly. He argues that validating a theory by means of experiment is not as simple as it may seem. There can be any number of reasons for an anomaly in experimenal results. In judging whether a theory may be valid, whether it is worth trying to validate, physicists necessarily rely on “aesthetic” judgements. As an example, he argues that physicists were more or less certain of Einstein’s theory of general relativity before it was conclusively validated by experiment. As another example, he argues that physicists were sceptical of the theory of quantum electro-dynamics although it was in agreement with experimental results because some calculations based on it involved “ugly” infinities in intermediate steps. He writes that part of this “beauty” lies in simplicity – not the simplicity of the equations but of ideas. Another part of this beauty lies in what he calls logical isolation or rigidity. For example, he writes that no one has yet found a way to make a small modification in the principles of quantum mechanics without destroying the theory altogether. It would make little difference in Newton’s inverse square law of gravitational force if the exponent were changed to 2.01 instead of 2, but even the introduction of a small non-linear term in the linear equations of quantum mechanics produces nonsensical results. Such a theory does not explains why it should be correct but it explains why it cannot be just a little wrong. Concluding a chapter titled “Beautiful Theories” Weinberg writes

We believe that, if we ask why the world is the way it is and then ask why that answer is the way it is, at the end of this chain of explanations we shall find a few simple principles of compelling beauty… the beauty of present theories is an anticipation, a premonition, of the beauty of the final theory. And in any case, we would not accept any theory as final unless it were beautiful. (emphasis mine)

The last sentence in that excerpt sums up most of what Weinberg is saying about beauty. If one keeps asking why as Weinberg does, there will come a point where one will have to stop. How does one decide what that point is? For Weinberg that point will have been reached when we have a simple and logically isolated theory that “explains” everything including the values of what we call universal constants.

In my next post in this series, I will try to present my own thoughts on what it means for a theory to explain something and on beauty.

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4 Responses

  1. It would make little difference in Newton’s inverse square law of gravitational force if the exponent were changed to 2.01 instead of 2, but even the introduction of a small non-linear term in the linear equations of quantum mechanics produces nonsensical results.

    If Wienberg said that, he is wrong. Plain wrong. (Regardless of which university granted him tenure.)

    I also recollect that Feynman, too, has somewhere waxed eloquent about the exponent 2 being a little different. I don’t remember where; perhaps in the context of electromagnetic fields. In doing so, Feynman, too, was showing a similarly poor understanding of both: (i) the structure of the physics theory under discussion, and (ii) the nature of physics, mathematics, and their inter-relationship.

    … That’s what happens when you are too busy calculating. Or, are too preoccupied lionizing mathematics in physics.

    But then, unfortunately, not even Harriman has got it right.

    –Ajit
    [E&OE]

  2. I suppose you mean that conceptually, it would make a lot of difference if the exponent were slightly different. I haven’t given it enough thought to hold any particular position about this in particular or the role of math in physics in general.

    b.t.w. I did get Harriman’s The Logical Leap yesterday. Will read it when I get time… am quite busy right now… and ponder this/

  3. The point would require a blog post or two, but here is the gist (which is primarily addressed to the Nobel laureate(s)):

    Don’t just mathematically stare at the number 2. Think of the physics that leads to that number. It’s a very very simple matter, but a profound one. It’s simple—it’s directly written in all (good) college-level text-books, but never granted the importance it deserves. (And, which, perhaps is not written with as much attention as below.)

    You have to think of a physical entity (the source of the field), one closed mathematical surface enveloping it, and a second closed surface enveloping the first. The surfaces serve to measure the action of the enveloped entity.

    Given this physical and physical-mathematical setup, the meaning of the inverse-square law is this:

    (i) *Some*thing physical physically flows from the source to the other physical entities (like the test mass/charge).

    (ii) The quantity of that which flows across the first (inner) enveloping surface is the same as that across the second (outer) surface. Some kind a conservation statement is implied, the conserved quantity being that which flows.

    (iii) Implicit in such a description is also this fact: The enveloped entity is the only source of that flow in such a description—else, the inverse-square law would not hold.

    Alter the exponent by a small fraction, and the interesting thing you get is not just a mathematically nonlinear behavior. The most interesting *physical* implication is this: The flow would begin to physically arise (or get weakened) even in the absence of any physical entity to act as a source or a sink, in such a description.

    Before complex phenomena can be causally described, one must have a simpler underlying basis. Before causal statements can be made, one must first isolate the entities that act in a description (the causes) and certain of their actions (the effects). In the case of the inverse-square laws, to state that the exponent is the integer 2 is to state that the causal description is *complete*—that there are no other agents (or sources/sinks) of the flow.

    To accept a Nobel for physics, and still to keep questioning why the integer 2 cannot be a real 2, without ever caring to look at the nature of the theorization (e.g. as above)—in one’s lectures, seminars, or books—is to demonstrate one’s “love” of engaging one’s powerful intellect in some floating abstractions without taking any care to tie it to reality, as a matter of habit.

    And more. To grant such purposeless, even meaningless, mental gyrations the prestige of one’s Nobel, and to encourage and invite one’s students, readers, colleagues, etc., into launching similar meaningless gyrations in their minds. All those gyrations are OK, so long as they are mathematical in nature, and are being done in the context of physics.

    When you introduce an artificial division of Newtonian mechanics and their hallowed Quantum mechanics (which cannot be understood by anyone, you take care to add), and then proceed to wax eloquent about how physics is an “experimental” method and how American (and European etc.) experimentalists have “validated” Newton’s law to 1 part in million/billion/zillion, you already are displaying a compartmentalizing mentality that goes defunct except for the narrow concerns for which you are paid (and perhaps not even well enough there—Nobel, or no Nobel).

    When you go further and add that it would make “little” difference to Newton’s law if 2 were to be different, without looking into the nature of the causal description contained in it, what you display is an enhanced or more acute version of the same incompetence as in the immediately preceding paragraph.

    …If only these idiots knew physics—and the nature of it.

    Enough.

    I will post this at my blog too.

    –Ajit
    [E&OE]

  4. Very nicely explained. Thanks. I do now remember reading that kind of explanation (for the Coulomb’s law, I think) but either the implications were not fully clear or I failed to grasp them.
    It is surprising how Weinberg can say that.

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