21

Geek Speak / Re: What is 'maths'?

« on: 02/12/2024 00:41:38 »

So what you probably mean by "mathematical truth" is that the statement is true under the systems of mathematics that we do commonly use.   We hope that our preferred systems of Mathematics have intrinsic validity and integrity such as "consistency" - but we will never know.

Except that certain mathematical truths do appear to be entirely consistent with modern physics. So it's always been true that, say, in any given quantum state time is always linear. This is something that is part of proving that a given sequence of quantum "gating operations" on pairs of or on single states will halt properly, with an output.

So quantum logic gives us a kind of backwards narrative: to prove that a theory is mathematically true means proving it can be an algorithm with no errors. No logical errors. If a program works correctly it will have always worked correctly even before anyone builds a computer.

But yes, Godels theorem and Turing aside; we can still prove things except we need axioms and we can't do more than assume they are true. Then we use the logic based on that assumption to show there are no contradictions (or errors in the algorithm).

But, yeah,  time is linear. Who knows why that's true?

I'll try to expound a little: if the only way to "prove" that time is linear in quantum experiments, up to measurement, then what is measurement? How do you prove you measured the output of some internal state? It seems you can't do this algorithmically without assuming that measurement is possible even if the mathematical formulation (in the theory) doesn't predict any such thing.

Moreover, Godel's and Turing's theorems have the same problems with axioms. Time is axiomatic, since, we can't keep any around to prove it exists.

22

New Theories / In four dimensions, must an object move at c in at least one of them?

« on: 01/12/2024 19:45:29 »

In a universe with four dimensions, you have to move at the speed of light in at least one of them.

In the other three, how you can move is restricted by something called mass-we don't really know what that is--but if you have any, you can't move at the same speed in any of the remaining dimensions. Not according to Einstein. The reason you can, and do, move at the speed of light in one dimension--the time dimension--is because time has to vanish from your local frame of reference, if you want to age at all.

That's a weird but true explanation of a theory.

p.s. a hint as to why it works; photons don't age--the universe of matter does and, the ambient space the photon moves in is stretching the wavelength--an isotopy.

23

Geek Speak / Re: What is 'maths'?

« on: 01/12/2024 19:31:43 »

There are some pretty damn good lectures online. My understanding of what is an algebra is now, it's something you can construct. You can start with almost anything, a set of things is better though.

So an incidence algebra of a partially ordered set is given, you define all these operations and show that it gives you a Hopf algebra, or at least a bialgebra. It's really just an example of how mathematics is another form of art, all art is intellectual I think.

If anyone wants to know more, this example explains in very simple terms, what is a tensor product, and how the arithmetic operations of addition and multiplication can be defined on two dual spaces, even what is a homomorphism and why it's a good thing.

24

New Theories / Re: Where does quantization of energy of electromagnetic radiation come from?

« on: 01/12/2024 19:25:10 »

But the electron in question follows a smooth sinusoidal path

I have to say this: you're making an assumption that fits a classical description of electron motion.

25

New Theories / Re: Where does quantization of energy of electromagnetic radiation come from?

« on: 30/11/2024 23:22:57 »

I can generate any frequency of radio waves, continuously, for as long as I like, by an entirely linear and continuous process.

Yes, but the process is continuous because you don't get to see individual, long-wavelength photons. Emission of photons by charged particles is still a hot topic in research labs.

We're talking about the electromagnetic field as if it's fully understood, done and dusted. It's not true, yet.

26

New Theories / Re: Where does quantization of energy of electromagnetic radiation come from?

« on: 29/11/2024 20:17:44 »

Is radio wave also quantized?

All EM radiation is quantized. But there is a problem with measurement and it has to do with the wavelengths.

These days (and actually for all the days before) radio wavelengths mean you need a big enough (in terms of wavelength) transmitting or receiving device. We call them antennas, but that's our business. The need isn't something we can choose to ignore.

27

General Science / Re: Can an electron travel a bit in a copper wire for inertia?

« on: 27/11/2024 00:14:43 »

Apologies, the semiconductor device I mentioned is called a cleaved-coupled x-ray diode or somesuch. A free-electron laser uses alternating magnetic fields. And it's a lot bigger than a diode.

I wouldn't worry too much about producing x-rays because both types of laser are pretty high power and high current, generally not in the milliamp region of most electronics.

28

General Science / Re: Can an electron travel a bit in a copper wire for inertia?

« on: 25/11/2024 19:15:59 »

"If you abruptly stop (or start) charged particles, you get EM radiation."

Back in the early 80's a free-electron laser was made for the first time. It utilises a small gap between two semiconductor crystals to generate coherent x-rays.
The electrons move freely across the gap, and emit radiation when they reach the other crystal surface. Electrons are extremely small objects and the gap is enormous by comparison, a whole handful of micrometers!
You can google it.

29

Geek Speak / Re: What is 'maths'?

« on: 25/11/2024 04:30:17 »

I think mathematics is something we consider is a tool. For a long time the only counting we did, presumably, was because we traded goods.

But then mathematical truth is something that again presumably, has always been true. Pythagoras' theorem was true before it was written down. It was true before humans evolved. So when was it "first" true? Is that even a question?

If you want to study postgrad math, you need to get your head around constructing algebras, and proofs. Pretty much all the current research is about constructible mathematical theories. Physics likes to borrow the ideas and see if they have any practical use, in particle theories (physics joke there).

30

General Science / Re: Can an electron travel a bit in a copper wire for inertia?

« on: 25/11/2024 04:12:22 »

A length of copper wire might seem like a simple thing, or cutting it might too. But I guarantee there are literally shelves of books on physics that will say otherwise.

The electrons in a metal are in a state before you do anything to the wire, so if you do something, even accelerate the wire, the electrons change state, relatively speaking since, everything is relative.

Anyhoo, to "fully" understand electrons in metals and how current actually moves, you need a lot of undergrad physics. If you study electronics they don't tell you. It's just assumed that current flows, or that a source of current or voltage is lying around.

If you also do theoretical postgrad stuff, you might learn about a Fermi gas, or Dirac sea, and Landau levels--all important stuff in solid state physics. A metal wire is a Fermi gas of "free" electrons, Landau levels appear when there is an electric potential or gradient; i.e. when a current flows in the wire. The individual electrons don't move in straight lines either, and only a small fraction contributes to a flow of current.

What I think I'm trying to say here is something like a complete description of the flow of electrons might need a path integral formulation, which would be outrageously complicated. So a simpler description-one that is fit for the purpose--will have to do, at least until some future genius discovers something better,

This simplification is what you have in electronics, at the engineering level you just ignore quite a lot of detail, it isn't relevant even if it is true.

31

Physics, Astronomy & Cosmology / Re: Liquid surface waves in an acoustic resonator

« on: 16/11/2024 18:42:19 »

Try it in zero gravity.

Gravity is the reason the liquid stays where it is. It's part of the construction.

Without gravity, arranging a liquid so it presents a flat surface is difficult. But you can't help but notice how gravity simplifies the problem.

One other detail; if you don't apply a smooth rubbing motion to the edge of the glass, you get chaotic patterns on the surface of the, ah, electrostatic fluid, near the glass.

32

Physics, Astronomy & Cosmology / Liquid surface waves in an acoustic resonator

« on: 15/11/2024 03:30:53 »

That sounds like a fancy title for what happens when you partly fill a wineglass and rub the edge.

Well, it is. The acoustic waves in the glass see a response in the liquid in the glass--waves start forming.
The kinds of waves can depend to some extent on the kind of glass. With lead glass, it seems to be easier to get a standing radial pattern on the surface of the water.

My conjecture is that these waves are not because the bulk of the liquid is vibrating, the surface pattern can't be very deep. So it's likely entirely electrostatic--the glass is vibrating so is producing an electric field displacement, this is projected over the surface of the water.

But I bet that's not the only causative agency--plasma physics is complicated and, the dipole moment of water molecules means it does act somewhat like a plasma does, when subjected to an oscillating electric field. The difference between tension at the surface and tension below it is why the surface responds and the pattern isn't destroyed.

Or is this all off the wall?

33

Physics, Astronomy & Cosmology / Re: Has anyone heard of tresino theory?

« on: 14/11/2024 22:07:43 »

I don't see how a particle can be a phase of matter at all,

In some modern experiments, electrons can "de-phase" into separate quasiparticles with charge, with magnetic potential, and with mass. It involves fairly complex geometries in the 2d substrate, these are the fixed waveguides, I would say.
Moreover, when electrons propagate in matter, they are quasiparticles, not free electrons. There is some change in an abstract phase, in a Hilbert space of course.

34

Just Chat! / Re: Where do I get my confidence to challenge established theories?

« on: 14/11/2024 18:24:53 »

What do you think is the biggest flaw in my arguments in philosophy, and what can be done to improve or correct it?

One argument is that you don't need philosophy to perform an experiment. The experiments you've been doing are the product of your curiosity.

I once pulled a lawnmower apart, completely, because nobody told me I didn't have to if I wanted to fix it. I was 8 years old though. So you could say I learned a lot from that one. But I don't remember thinking about the Zen of lawnmower maintenance, or much at all except how to dismantle.

35

Physics, Astronomy & Cosmology / Re: Theoretical information

« on: 11/11/2024 18:56:16 »

...which is still an approximation to the analytic statement.

There is something a bit weird about analytic continuation. If you expand a unitary "space" by functionalising it, that is, you map a pair of complex matrix exponentials, along with their inverses such that their product is 1, but you still have a Taylor series.

Because of continuity you can show that you still get Euler's formula, even with just the first three terms of the Taylor polynomial.  Unitarity is a real thing though. It also has something to do with normalisation and measurement.

One way I think about the Taylor expansion is, how many dots do I need to see a pattern that isn't random? The dots, their positions, are the "polynomial expression", it has to be unitary in that, I need a large enough volume for all the individual probabilities to add up to "a pattern".

If that's no help at all, yeah, I guess. I've been watching Sir Roger Penrose on Youtube, talk about Schrodinger and how that man was sure he had it wrong, even though it works.

That stuff about expanding matrix exponentials was part of an online MIT course by Seth Lloyd, the goal was to show that for electrons, or charged particles generally, an external magnetic field can rotate some abstract angle. I recall the three normalised real unit vectors were in there, this was meant to be something that fermions do in real 3-space, or as physicists like to call it, a lab.

36

Physics, Astronomy & Cosmology / Re: Theoretical information

« on: 11/11/2024 06:52:29 »

Here's the story, or at least a version of.

Suppose a program is written which does everything that Newton's Laws of motion say objects with mass can do, when forces act on them. This program though, has no specification that it outputs anything, but it works and it can be proven that it does.

An output is then a kind of postcondition, a requirement that is imposed--the program has to be observed to be working, not just proven. Where does this go? Algorithms have no "duty to report", unless we add that to them.

Just saying. That this seems to connect observation of motion to whether a program outputs anything. As long as the program faithfully represents the same motion.

37

Physics, Astronomy & Cosmology / Re: Theoretical information

« on: 04/11/2024 22:30:43 »

But it doesn't have anything to do with polynomials!

That depends on how you define polynomials. The rule seems to be you start with a field.
If you can show there is a way to grade your expressions over this field, then you have polynomials.
Derivatives can be first, second, etc order so there's the graded algebra. ODE and PDE expressions are polynomials.

And, in physics it's usually possible to expand any expression into a Taylor polynomial.

38

Physics, Astronomy & Cosmology / Re: Theoretical information

« on: 03/11/2024 23:56:49 »

Refinement is what gives an algebra a way to generalise, and to unify concepts. Maxwell eventually unified all forms of electricity with all forms of magnetism, his theory proposed that it was all because electric and magnetic fields behave the same way, in free space as in conductors, or when interacting with other forms of matter.

The forms  of matter that lie in the domain of kinematics are often pendulums with oscillatory motion. This motion is a common feature of all kinds of physical pendulums i.e. plug in some real physical stuff and the equations are the same.
So oscillatory motion is a physical thing which itself unifies the different kinematic systems, and this has some dual kind of unification (replace L and C with other kinds of reactive devices).

Or at least, that's the theory.

39

Physics, Astronomy & Cosmology / Re: Theoretical information

« on: 03/11/2024 00:08:47 »

Another observation.

Equations in differential form that define oscillations in a LC circuit have the same form as equations in kinematic oscillations. So you could posit a "theory of oscillatory motion". Say this theory has a basis of ODE "polynomials" whose form is an invariant of the theory.

In Maxwellian dynamics, the symmetries of an obviously more complex system than a simple string or spring pendulum, have a problem with algebras of rotations, or with the quaternions. Although there is a quaternionic representation of Maxwell's "theory of electromagnetism", it doesn't have an obvious map to any Hopf algebra structure.

Hopf algebras are ubiquitous in physics, so this makes the obstruction an interesting kind of algebraic problem. Sometimes knowing why the math won't work can be as informative as knowing why it does. A theory that does or doesn't preserve structure of an algebra is the vehicle needed.

And no, I don't really have much idea why there's a problem, or even if it matters.

40

General Science / Re: Does All Of Mathematics Come Down To Simple Arithmetic?

« on: 02/11/2024 04:24:26 »

Another way to understand any distinction (perhaps there isn't one except if we say so), between arithmetic and algebra.

Arithmetic can be modular. Like with hours, and addition, that's arithmetic modulo 12. Or 24 if you want.
And in the army, they do want.

So that, we can choose any number and do arithmetic modulo that number, on the integers. But then we have an algebra because we can show that it is at least a vector algebra. Other kinds might follow, but it depends what you want to do with it. If you also can prove you have an object called a ring (might be easy peasy), that can open the door so to speak.