don’t mean to quote-bomb, but this is so deliciously vicious:
Heisenberg understood first and best how to use mathematics to impress and cow the audience. He also understood first and best how to use mathematics as a tool of propaganda. A math of proper abstraction and complexity could be used to hide all error, to divert all effort, to deflect all criticism. It could be used like a very heavy, very highly decorated quilt, covering the bedbugs beneath. This new abstract math would come not with a foundation, but with a manifesto. It did not have axioms, it had public relations. It was not sold with an explanation, but with an “interpretation”, and this interpretation was to be accepted on authority.
i don’t know what MM says about math yet, but it is possible for something to rest on flimsy theoretical underpinnings but still work for certain types of calculation. what this means is that it will work for limited practical uses, but cannot be applied outside that scope…the problem when such things are applied outside their scope, for status and profit.
There is a tremendous amount of statements and mathematics taken out of context. A great deal.
Hilbert did find the correct formulation of general relativity before Einstein. This is true. However, Einstein was given the credit because Hilbert based his entire formulation on Einstein’s work. It is true that Einstein was weak in the mathematics of differential geometry (differential forms, commutators, Lie derivatives, and so forth)… however, this is SIMPLY because differential geometry was a new mathematics that was never used to describe physical dynamics. This is what many theoretical scientist do… use new mathematics to describe new realms of the universe. Hilbert himself acknowledged this. Up to this point, physicist didn’t use the powerful mathematics of differential geometry. 70 years later differential geometry has become a more mainstream (but powerful) mathematics to describe complex analysis. It’s not obscure mathematics. It’s a form of mathematics that makes calculations much easier to understand in geometric spaces (manifolds). Physicist, chemist, engineers, and mathematicians use it for various problems in their respective fields.
As far as Feynmann’s path integration, it’s a mathematical tool to describe physical reality. IT WORKS PERFECTLY TO DESCRIBE THE ELECTRODYNAMICS OF THE ATOMIC STRUCTURE WITH THE MOST ABSOLUTE PRECISION. As always, I’m always surprised how pop science interprets what physicist use in the laboratory to some crack pot interpretation that has some bizarre meaning. Path integration is a dubious mathematical construction dealing with infinites. It can have absurd interpretations but the mathematical finalization always works out perfectly to physical representations that are tested in the lab. It’s solely the interpretation that is open for debate. However, I can assure you as a physicist, I could care less about interpretation. I only care what I can prove and Feynmann’s electrodynamics does this with more accuracy than any other science. I use it everyday to understand molecular behavior with absolute precision.
Mathematics is nothing more than a tool in physics. It is the most powerful tool. However what differentiates mathematics from physics is that physics only cares about the mathematics that can be applied to physical interpretation. The rest of the mathematics (singularities, infinite dimensions, and so forth) is just mathematics. Derivatives, integration, n-forms, k-theory… ect do have meanings physically.
Heisenberg’s uncertainty principle was not advanced mathematics and he didn’t use it to cow audiences. At the time, matrix algebra and commutator algebra were never used in physics. However, because quantum mechanics is based on the mathematics of the commuators and anti-commutation rules (in vector spaces) it was initially difficult for physicist to understand these new radical principles in physics. It was new mathematics that was only known to the math community. Today any physical chemist or physicist can easily understand these concepts and what they mean conceptually.
I will say while mathematics is essential in the physical sciences. However it has little need in economics. Molecules and atoms behave with predictability… equations can be assigned to atomic and molecular behavior. Humans and social interactions however behave in chaos… there are no equations to predict irrational behavior.
everyone here seems to be acknowledging that things like QED can be used to calculate quantities accurately. the issue is physicists seem to have given up on physical modelling. what is the SHAPE of these particles, waves, or whatever? from the modern physicists we get metaphors but no actual physical models from which to make hypotheses based on the physical mechanisms in the models.
So, here is a “refutation” of Mathis (spoiler: no paragraph makes sense). This tells a lot how seriously you can take Player or Zangelbert. Holocaust denial is one thing, there you only have what others tell you, but this is about lacking elementary logic. Too much.
Quantum electrodynamics is the union of quantum mechanics with electrodynamics (a highly geometric theory that can be easily visualized). QED was constructed because physicist needed a quantum method for describing photons and particles that travel close to the speed of light. In addition, particles contain properties, such as spin, that needed a quantum mechanical reconstruction that could deal with Einstein’s relativity.
The manifestations of QED are all around you. Every time you see light and its interactions with molecules, you are witnessing QED. QED is tremendously rich with visuals (highly geometric because it deals with electrodynamics), but QED deals with things much smaller than non-relavistic quantum mechanics (the quantum theory of single atoms, molecules, proteins, and larger objects). This is where visualization becomes difficult (abstract) because in the quantum realm the universe is not continuos. Energy, matter, and time exists in discrete bits of information called quanta. In addition, QED represents a picture of the universe that is completely alien. For instance, space at this realm is almost completely void. Quantum mechanics has taught us that atoms are literally empty space, and ALL the interactions we see around us deals with the force fields between atoms, sub-atomic particles, and molecules. You never actually touch objects (ie touch other atoms). You only feel the electro field lines between atoms. If atoms were to touch then essentially nuclear fusion occurs.
As far as particles existing as a wave or particle- that is a much more complicated understanding but the answer to many outside the physics and chemistry community is unsatisfactory (but makes sense). Unless you study and understand the experimentation and physics it won’t make sense. Essentially, it’s the experiment that determines whether a particle exist as a wave or particle. However, wave-particle duality does exist and it’s been proven countless times in laboratories. X-ray crystallographers, solid state chemist, condensed matter physicist, & other scientist witness it everyday in the lab when we use x-rays (high energy photons) to probe into molecules.
The visualization that is difficult to understand with QED is the mathematical path in achieving the answers, not the answer themselves (or final visualization). QED employs a mathematical technique called path integration that is sophisticated, but works out very elegantly in the end. It essentially deals with removing and teasing out other fields in the quantum realm. It’s analogous to calculating the weight of an object in water. You first have to remove the surrounding structure of water before you can figure out the weight of that object. Visually that is difficult to picture but conceptually easy to understand.
Other types of visualization in the quantum world is abstract, nonetheless, because you’re dealing with properties that are completely outside of human experience. Again the quantum world is different because it is not continuos. It’s lumpy because it deals with the most discrete properties of nature.
i don’t endorse Mathis or his pi=4 proof, as i don’t understand it and haven’t read his background reconception calculus which is required to understand the long paper anyway. (by the way, he says it is only valid for measurement of motion within his re-worked system of calculus; not that if you wrap a string around a dowel rod the length of string required won’t be pi times the diameter of that dowel rod, as that would be obviously wrong. one cannot just look at his pi=4 and call him insane without looking first through his reconception of calculus and calling it wrong or right. he is making a very specific claim, not the one that you would generally think of as pi=4.)
the main criticism i would lob at mathematical physics is that is has ceased to make physical hypotheses, or that when it does it proposes absurdities that are easily shown as absurdities.
how is a force field a physical hypothesis, any more than the holy ghost is a physical hypothesis? how are field lines physical things? they are metaphors or heuristics, are they not? this is my point.
again not defending Mathis, but the refutation scineram posted completely misses the point that his pi=4 proof only applies to measurement of motion. the refutation explicitely rejects his proof because “Mathis is absolutely obsessed with idea that drawing something is absolutely critically important”. but the reason he is “absolutely obsessed” with “drawing” is that he is talking ONLY about physical objects tracing out orbits and the like. he makes this perfectly clear at the very start of his paper, and the refuter makes it perfectly clear that he has not acknowledged that qualification. so the rest of the refutation is called into extreme question, as he clearly does not even understand what he is supposed to be refuting.
by the by, this is typical with “anti-crank” sites, and Austrians ought to be used to it. strawmans a-plenty, just like with Krugman.
it is puzzling the kneejerk reactions and claims of “logic” from people who have most probably not verified any of the underlying math themselves. this is appeal to authority disguised as an appeal to logic.
Magnetic and electric field lines are physical objects. Just like light. Electric magnetic field lines help generate electricity.
This was taught at a young age in physical sciences. You have a magnet and you put iron fillings around the magnet. The fillings position themselves spontaneously into the geometric field lines of the magnet.
The electricity that you and I, and the world uses relies on are created by electro-magnetic force fields, in a electrical plant, that generates electron production that gives way to electricity. That same electro-magnetic force is present within molecules, atoms, and sub-atomic particles.
the link scineram posted goes much deeper than that, to the very heart of Mathis’s confused thinking.
An analogy would be if Mathis claimed the emperors new clothes weighed 4 pounds, and were not weightless as some assert, because the emperor was constantly in motion bla bla. Scineram’s link then showed that the clothes were weightless because the emperor was naked in the first place.
According to wikipedia, physical objects have mass, which I doubt magnetic fields have. I think a more accurate statement would have been that magnetic fields are physical phenomena [=force fields], whose influence is readily observable on physical objects, those iron filings.
As Newton taught us all, the physical world we live in is contains two things. There are “objects”, which have mass, and there are “forces”, which do not.
Wilipedia on force:
In physics, a force is any influence that causes a free body to undergo a change in speed, a change in direction, or a change in shape. Force can also be described by intuitive concepts such as a push or pull…
So a force is an “influence”. Nice and vague, but there it is. Newton postulated as an axiom that these things called forces exist. We cannot see them, for they are invisible and have no mass. All we can see is the result of their influence.
So that indeed you are correct in saying that all you can see are the magnet, the filings, and some regularity in their motion. But Newton asked himself “What makes that motion happen?” And he answered, after that apple conked him on the head, that there must be some invisible hand pushing those filings and making them move. He called the invisible hands [whose existence he assumed] “forces”.
The only reason everyone accepted this very odd way of looking at things is that it works.