Toolkit
A person with a new idea is a crank until the idea succeeds. ~ American author and humorist Mark Twain
Math is the tool of the trade for theoretical physics, equations the universal language.
Models are a means of extrapolating from what is known to create proposals for more comprehensive theories with greater explanatory power. ~ American theoretical physicist Lisa Randall
A physical model is a mathematical model, typically geometric or algebraic, providing a symbolic description of the embodied phenomena. The quality of a model is how well it agrees with empirical observations and its predictive power. Newton’s motion laws came from a physical model.
All great discoveries in experimental physics have been due to the intuition of men who made free use of models, which were for them not products of the imagination but representatives of real things. ~ Max Born
A physical theory describes relationships between various measurable phenomena, often considered as cause and effect. A physical theory may include a model of physical events.
In the late 5th century BCE, Greek philosopher Pythagoras explained the relation between the length of a vibrating string and the musical note it produced. In the early 3rd century BCE, Greek polymath Archimedes understood that a boat floats by displacing the water that would otherwise be there.
What is especially striking and remarkable is that in fundamental physics a beautiful or elegant theory is more likely to be right than a theory that is inelegant. ~ American particle physicist Murray Gell-Mann
Physical models bias physics. Physicists are understandably fond of mathematical simplicity, termed elegance, which comes via reducing independent variables. Symmetry is also essential to simplicity.
Otherwise, models become unwieldy if not insolvable, however better they may reflect Nature, and thereby offer predictability. Complexity is considered a nemesis, as it is a hindrance in workability, and an encumbrance to comprehending what are taken to be fundamental operating principles.
The result has been a strong inclination toward simplifying reduction that is often amended with exceptions when a model is found wanting, as most are. Putting a patch on a model lessens its elegance. Applying multiple patches can bring a model to its knees, as predictive power wobbles on an increasing number of variables and/or contingent conditions.
Just because the results happen to be in agreement with observation does not prove that one’s theory is correct. ~ Paul Dirac
Mathematically, any system with 3 or more independent variables is unpredictable. Patches to improve predictability leave room to ponder if something else essential is being left out. Many theories, and the models on which they rely, flounder on these shoals. Such as been the case with the standard cosmological model (ΛCDM) and quantum physics’ standard model.
It is impossible to trap modern physics into predicting anything with perfect determinism because it deals with probabilities from the outset. ~ English physicist Arthur Eddington
Beyond description and prediction lays explanation. The most powerful theories go beyond mere mechanics, yielding insight into the nature of phenomenal relations. Ultimately, this is what physics, and every branch of inquiry, strives for: knowledge.
Although we live in a world of constant motion, physicists have focused largely on systems in or near equilibrium. ~ American physicist Michael Kolodrubetz
A theory is a statement of how a relationship is presumed to behave, based upon some evidence. In contrast, a law is a conclusion of a universal natural tendency.
Whereas a theory is confined to specific relations, a law applies to everything. Laws invariably underpin theories.
While a theory may not necessarily ratify an implied aspect not central to the theory, it at least suggests that any implications of the theory are as valid as the theory’s central tenet. After all, if a theory appears to well-describe its intended target, its ancillary implications intrigue.
Sometimes the implications of a theory turn out to be more important than the target phenomena described, in the doors they open, as questions raised of issues previously unconsidered. Maxwell’s implicit discovery of wave/particle duality, leading Einstein to his relativity theories, is exemplary.
The open-ended nature of mathematics has engendered the belief that the fundamental constructs of physical existence can be formed into formulas.
We exist in a universe described by mathematics. But which math? ~ American theoretical physicist Antony Garrett Lisi
While math has paved a remarkable path, ultimate understanding of existence via science remains as easily reached as the end of a rainbow. Behind every model and theory is insight which only opens more doors. The atomistic unraveling of reality is endless.
The hypotheses we accept ought to explain phenomena which we have observed. But they ought to do more than this: our hypotheses ought to foretell phenomena which have not yet been observed. ~ English polymath William Whewell
