someguy1 » April 28th, 2017, 8:55 am wrote:hyksos » April 27th, 2017, 11:35 am wrote:I present the following as strong evidence that the universe is a mathematical structure. (rather than say, a collection of physico-mechanical substances that happen to be describable by math after-the-fact).

Two arguments I just don't get.

One, that just because we have a mathematical formalism whose meaning we don't yet understand, the world must simply "be" that formalism. Isn't it possible instead that someday we'll understand what the formalism means? Just like relativity gave meaning to Newton's formalism of gravitational attraction.

Two, that just because matrices are handy gadgets for computing 3D rotations, matrices have some ontological reality in the world. Couldn't they just be handy gadgets for calculating, the same way the numbers on your grocery receipt aren't actually your vegetables?

The short answer is 'no'.

The long answer: Nuclear quantization of angular momentum( "spin") is not the only example of this perplexing problem in physics. It is, in my opinion, the most violent and strong example of how the universe works in a way that is contrary to physico-mechanicalism. ("gears-turns-gears narratives").

Holomorphic functions map a complex number into a complex number.

`F(z) --> z'.`

Performed over the entire complex plane, holomorphic functions map the complex plane into the complex plane. All holomorphic functions will have a mirror image of their shape below the real axis. The reason for this is because complex vectors all have dopplgangers called

complex conjugate vectors. Example.

`v = 5+7i.`

Conjugate vector

`v* = 5-7i`

Obviously, any sane human being, regardless of this metaphysical prejudices would recognize that

- Humans invented math.
- Complex numbers are mathematical jargon
- Conjugate vectors are conventions of our 'invented' formalism, and should be discarded.

Paul Dirac was not a normal dude. He was very weird and highly eccentric (consult his biography). Even someone as eccentric as Dirac also understood the three points above. Dirac was willing and ready to toss out complex conjugate vectors, because, after all they "mathematical detritous" to be "discarded" because "Humans invent math". Clearly a complex conjugate vector surely does not correspond to something physical in the world -- that would be "silly".

RIGHT? Wrong. Dirac was Ph.d who had grad students working under him. One of his most adept students was named Robert Oppenheimer. (maybe you've heard his name somewhere). Anyways, long story short. Dirac had produced the solution to a relativistic wave corresponding to the electron. The solution admitted two answers: 1) The regular complex vector solution. and 2) the solution corresponding to the complex conjugate vector.

Dirac tossed out the second solution as 'non-physical'. (because ya know, math is "invented by humans" and all that jazz). Young Oppenheimer told Dirac that no --- we left

Sane Regular World 20 years ago. That second solution is a real thing. It must represent an actual physical particle.

Indeed it does. It is the positron. Positrons are real physical objects. They are created in labs by the billions at CERN, SLAC, and other particle colliders.

Just as the mathematics predicts, a positron will be identical to an electron in all ways (spin number, mass, strength of charge) but its charge will be the reverse polarity. Whereas the electron is negatively charged, its doppleganger positron will have a positive charge.

When a positron collides with its partner electron, they "cancel out" and produce a single photon. Just like adding a complex conjugate vector cancels out the imaginary component.

`v+v* = 5+7i+5-7i = 10`

Do you suppose that you could know what this means? Do you suppose that anyone on this forum knows what this "means"?

Initial opening salvos on the metaphysics front produce some bizarre explanations. The physical world appears to "know" about the existence of the square root of negative 1. And that's silly : Even Paul Dirac thought it was silly. It's absurd.

But it's true. Not only does the universe know about i, it seems to know that -i , when added will cancel out the original i and produce zero. Why should the matter and energy of this universe obey and follow the petty little conventions of "human-invented" chalkboard mathematics?

Indeed, angular momentum of nuclei, and the existence of positrons are not the only examples. The history of the development of the Standard Model is rife with such examples. Decade after decade, the nuclear physicists and mathematicians working on the Standard Model found themselves always having to shed all metaphysical prejudice and

simply believe what the equations say.Eugene Wigner was the winner of the Nobel Prize in physics in 1963. He was well-aware of this crazy procedure.

"Shed all metaphysical prejudice. Believe the equations." Time and again, this is exactly how the universe operated. The crazy mantra was wildly successful as a science.

Wigner was scared to his bones by this. Wigner finally broke his silence about physics and wrote a paper where he told the world: "Okay mathematics should be useful for what we are doing, but it should not be this suspiciously effective at predicting how the world behaves.". He then called this effectiveness unreasonable. He also said that this unreasonable effectiveness quote,

"..borders on the mystical."

end-quote.

So you have Dirac discarding secondary solutions as un-physical, and Wigner saying that the universe following math is getting absurd, and bordering on the mystical.

Now we don't have any nobel prize winners on this forum. I ask you to open your ears and hearts to what actual Nobel-prize-winning physicists have said about this topic.