Is all physics logically expressible and observable?

In summary, according to the author, mathematics and physics cannot explain all physical reality. However, they have greatly expanded our observable world.
  • #1
Say I observe a physical phenomenon; does that mean I can necessarily mathematicize it? Does possible observation reach only a fraction of physical reality?

Will mathematics ever be able to explain a unification between general relativity and quantum mechanics? If such a TOE is ever realizable, will we be able to experimentally confirm it (re: superstrings)?

Say I am unable, in any frame of reference, to observe a physical phenomenon; does that mean it does not physically exist (re: wavefunction)? Can we state as to what math will, or will not, eventually correlate to physics?
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  • #2
Think about trying to do standard grad-school physics with math that Archemides had. New physics inspires new math. Calculus, tensors, Feynman diagrams, group theory - all were driven by physics. I think as we get close to understanding a phenomenon for which we have no math, we push the old math to ridiculous limits, then invent new math.

The infinitesmals of the French and Italian mathematicians inspired the invention of calculus. Schwinger's conventional but incomprehensible (to anyone but him) formulation of QED inspired the acceptance of Feynman diagrams.

Will we hit a wall? Maybe, but we will probably invent many new schemes of math before then.

  • #3
Is all physics logically expressible and observable?

Not necessarily. An interesting (and relatively unknown) example of this is the alternative extension of the Poincaré algebra. As known, the results of Coleman-Mandula and Sohnus-Haag-Lopuszanski state that the only admissible model for supersymmetry is the Golfan'd-Liktman superalgebra (made famous by Wess and Zumino as supersymmetry algebra, but already discovered by the two preceding guys three years earlier). In 1975 B. Konopelchenko found another admissible extension, which however violated the CMSHL restrictions by a little technicism concerning the supercharges. However, inspite of this anomaly (which is responsible for the superalgebra to have been discarded), the Konopelchenko model allows to recover the GL superalgebra, thus the supersymmetry considerations. The interesting fact is that these effects could not be observed in the alternative model, but on its degeneration to the GL superalgebra.
  • #4
These sound like pretty fundamental questions, on the (smeared) boundary between science and phylosophy.

It is clear that our concept of observable is strongly limited by what we perceive directly with our senses: it took us a while to realize that there are forms of 'light' that we cannot see (electromagnetic waves outside the visible region) or that do not even propagate (electrostatic fields if relax a little our definition of light to encompass all em phenomena). For sure having different senses like dolphins, bats, some fishes, or some reptiles would create a completely different perception of the physical world (and probably also a different system of values and hence a different society).

Nevertheless the development of instruments to enlarge the spectrum of phenomena we can 'see' (take into our field of perception) and the use of math have supplied an astonishing enlargment of our observable/describable world. So nowadays it seems that the real limits are technical and mathematical tools. Is it true? I do not think so, but let me carry on one more second.

These questions are also strongly related to the work of Turing, Godel and others on computability and on the limits of formal languages. We know they have limits, even though we can continuously extend those limits (just think of the new frontiers that will open up once quantum computers will become available).

I think anyway that the real constrain in this process of inquiring reality is that we have to convert phenomena we cannot perceive into phenomena we can perceive and things we perceive into analytical descriptions. There are intrinsic limitation in this process we call science today because of its definition itself.

There are situation where the use of pure logic simply does not help (Turing machine does not produce an answer), sequential reasoning is intrinsically limited, there are phenomena logic alone cannot describe.

In my opinion the real escape here is to point toward a wider concept of knowledge that integrates functions mostly performed by the lefthand side of the brain (logic, analysis) with those performed by the right hand side of the brain (analogy, synthesis). I do not expect this extension of knowledge can ever be put down into formulas but still is observable everyday in important parts of our lives.

Every time we read a formula AND we understand its meaning there is a non-logic step we have performed: meaning attribution is to me beyond the realm of pure logic and yet a phenomenon!

To summarize, I believe we can know everything but math and physics cannot do the whole job!

Good thoughts to you all, Dario

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