Is Physics a Matter of Applying or Deriving Mathematics?

[thinkandmull]

Hi,

Does "calculus based physics" just mean the study of the phenomenon that displays calculus activity? I read a book recently by Heisenberg that confused me on this. He said our measurements of phenomenon are irreversible. Are scientists deriving mathematical activity from the world, or applying a mathematical structure to something in order to understand it? I don't quite understand what the later means. Heisenberg wrote that, at least at that time, scientists were disagreed on how to reconcile relativity and quantum physics when dealing with momentum and high energy. He said that the math could be tweaked though in order to find a resolution. Could someone explain what this means to me? Thanks!

 

[jedishrfu]

Here's a prior thread on the differences:

https://www.physicsforums.com/threads/calc-based-or-not-non-physics-major.172552/

And here's one such example of calculus-based physics:

http://www.anselm.edu/internet/physics/cbphysics/

and here's another that doesn't use Calculus:

http://www.lightandmatter.com/cp/

Problem-wise non-calculus problem would feature forces that remain the same whereas a calculus problem might incorporate a changing force as in the time for an object to fall from 100ft up vs the time to fall from thousands of miles up where now you must incorporate the changing gravitational force using f=GMm/r^2 instead of F=mg.

 

[gianeshwar]

Nature in quantum world behaves in discrete sense due to limits like smallest energy unit(plank energy I think).To study it we need to invoke thinking in terms of Abstract Algebra(groups,rings etc.).We need to study different states of systems.In Calculus we study systems assuming continuous changes.So calculus works well in Common sense (macro) world.

 

[aikismos]

In regards to the difference of the mathematics that describe relativity and quantum mechanics, what Heisenberg was trying to express is that the fundamental difference isn't so much in the discrete versus analog methods of mathematics (see the mathematics of a particle's wave function and compare it to those of Minkowsi space), but rather the certainty that undergirds each. The originator of the Heisenberg Uncertainty Principle was stricken, instead, by the fundamental difference in the certainties at play in the two mathematics, since the mathematics of quantum phenomena is essentially statistical or probabilistic in nature (and as a minority argue contains "hidden variables"). Whereas we can put a satellite in orbit around Pluto years into the future with a minimum of fuss, the complex interplay of even a small group of particles and their properties is almost mind-warpingly difficult. We can shoot a projectile out of the sky, these days, with another projectile, with some degree of accuracy, but we can't even tell where a photon will appear as a particle when it travels through a double-split. Why is that? It's what the Quantum Greats called "spooky". Even recent research into the quantum tunneling, entanglement, and superposition has made it clear that we stand at a fundamental barrier in using mathematics to understand and predict certain types of systems. The concept of measurement being irreversible, and someone more knowledgeable can correct me if I'm wrong, is based on a clear understanding that as we are ourselves information-tight information systems, our very interaction with systems such as quantum particles to generate information within ourselves (the observer) forces the system into a measurement in a somewhat random manner. Think about measuring a photon, which is fundamentally both a particle and a wave. If we measure it AS a particle, then our math is the mathematics of particles, and if we measure it AS a wave, then our math is the mathematics of waves, and from that event forward, our understanding (itself a model) has committed the potential being into a particular mathematical state (that of wave or particle), and our future and the decisions we make upon it are irreversible. Once we make that particle a wave at a point in time, we are committed to the idea that it IS a wave at that point in space-time forever. Does math describe the phenomenon? Yes. Do we choose which aspect of the phenomenon to observe? Yes. Does that mean in effect we are imposing the mathematics of our observation onto the phenomenon thereby altering physical relativity in our internal worldview? Yes. The division between quantum and macro-sized phenomena, and our role as 2nd-order cybernetic systems interacting with them is very much at the heart of a great philosophical revolution that occurred in science, and is still the subject of much philosophical wrangling.

 

[thinkandmull]

Does the Bell theorem's show that there is a truly a subjective side to the world and the study of it?

 

[aikismos]

I don't think you need Bell's Theorem to show that the study of the world is replete with subjectivity. Knowledge itself is a social construct, and therefore demonstrative of the subjectivity of information. All human thought requires selectivity of data, and it is this selectivity that makes knowledge subjective. What science has brought to the table (in comparisons of ontologies) is the insistence on intersubjectivity as a means to eliminate contradiction and encourage consistency of knowledge. Bell's Theorem (or rather the empirical efforts to validate it so far) merely substantiates the non-locality of the fundamental particles of the universe. In my mind, physical causality of fundamental particles shouldn't be seen as subjective versus objective since subjectivity requires an information-tight physical system which stores models of information.

 

[sophiecentaur]

Maths is based on axioms. When life is being good to us, we can devise a mathematical formula /method which models a certain (measured) scientific phenomenon to within acceptable accuracy. It is a matter of faith (and experience) that we can extrapolate and use the same formula to predict the outcome of some (or even many) other experiments. That's really how Physics works. It so happens that more than one approach can often produce satisfactory models and that they can both / all yield good predictions. On some occasions, the ranges of the variables over which the models work best will differ from model to model. That can upset some people because they have not accounted for the fact that the Maths is the servant of Reality and not the other way round.
As a pragmatist, I just reckon it is lucky that our Maths is such a useful tool and that it so often does a pretty good job of producing reliable (but limited - of course) models.