Where math meets physics

socratus

socratus
Dec 10, 2008
940
3
18
Israel
www.worldnpa.org
Where math meets physics
---
Math and physics are two closely connected fields.
For physicists, math is a tool used to answer questions.
For example, Newton invented calculus to help describe motion.
For mathematicians, physics can be a source of inspiration,
with theoretical concepts such as general relativity and
quantum theory providing an impetus for mathematicians
to develop new tools.
----
But despite their close connections, physics and math research
relies on distinct methods. As the systematic study of how matter
behaves, physics encompasses the study of both the great and
the small, from galaxies and planets to atoms and particles.
Questions are addressed using combinations of theories, experiments,
models, and observations to either support or refute new ideas about
the nature of the universe.
---
In contrast, math is focused on abstract topics such as quantity
(number theory), structure (algebra), and space (geometry).
Mathematicians look for patterns and develop new ideas and
theories using pure logic and mathematical reasoning.
Instead of experiments or observations, mathematicians
use proofs to support their ideas.
---
While physicists rely heavily on math for calculations in their work,
they don’t work towards a fundamental understanding of abstract
mathematical ideas in the way that mathematicians do.
Physicists “want answers, and the way they get answers is by doing
computations,” says mathematician Tony Pantev. “But in mathematics,
the computations are just a decoration on top of the cake.
You have to understand everything completely, then you do a computation.”
----
This fundamental difference leads researchers in both fields to use the analogy
of language, highlighting a need to “translate” ideas in order to make progress
and understand one another. “We are dealing with how to formulate physics
questions so it can be seen as a mathematics problem” says physicist Mirjam Cvetič .
“That’s typically the hardest part.”
----
Kamien works on physics problems in that have a strong connection to geometry
and topology and encourages his students to understand problems as mathematicians do.
“Understanding things for the sake of understanding them is worthwhile, and connecting
them to things that other people know is also worthwhile,” he says.
---
“A physicist comes to us, asks, ‘How do you prove that this is true?’
and we immediately show them it’s false,” says mathematician Ron Donagi.
“But we keep talking, and the trick is not to do what they say to do
but what they mean, a translation of the problem.”
----
Adding extra symmetries makes string theory problems easier to work
with and allows researchers to ask questions about the properties
of geometric structures and how they correspond to real-world physics.
---
Using their physics intuition, Lawrie and Lin were able to apply
their knowledge of math to make new discoveries that wouldn’t
have been possible if the two fields were used in isolation.
“What we found seems to suggest that theories in five dimensions
come from theories in six dimensions,” explains Lin.
“That is something that mathematicians, if they didn’t know
about string theory or physics, would not think about.”
----
Lawrie adds that being able to work directly with mathematicians
is also helpful in their field since understanding new math research
can be a challenge, even for theoretical physics researchers.
“As physicists, we can have a long discussion where we use a lot of intuition,
but if you talk to a mathematician they will say,
‘Wait, precisely what do you mean by that?’ and then you have to pull out
your important assumptions,” says Lawrie. “
It’s also good for clarifying our own thought process.”
---
https://penntoday.upenn.edu/news/where-math-meets-physics
============
 

Attachments

  • Euler - i - e - pi .jpg
    Euler - i - e - pi .jpg
    12.2 KB · Views: 0

socratus

socratus
Dec 10, 2008
940
3
18
Israel
www.worldnpa.org
Adding extra symmetries makes string theory problems easier to work
with and allows researchers to ask questions about the properties
of geometric structures and how they correspond to real-world physics.
https://penntoday.upenn.edu/news/where-math-meets-physics

The mathematicians have no problem to create many - many
extra symmetries . . . but would '' they correspond to real-world physics'' ?
===
 

Attachments

  • Question.jpg
    Question.jpg
    5.5 KB · Views: 1

socratus

socratus
Dec 10, 2008
940
3
18
Israel
www.worldnpa.org
New Math Makes Scientists More Certain About Quantum Uncertainties
---
New statistical calculations suggest the fundamental quantum limits
of some sensitive measurements may have been off by a factor of pi
By Mark Anderson , 11 Feb 2020
----
The practical Heisenberg limits in measuring some quantities
up to the ultimate quantum sensitivity may be larger than
expected—by a factor of pi.
This new finding would, according to physicist Wojciech Górecki
of the University of Warsaw in Poland, represent “an impediment
compared to previous expectations.”
---
As Werner Heisenberg famously theorized in 1927, the product
of uncertainties of these two observables can never dip below a
very small number equal to Planck’s constant divided by four times pi (h/4π).
----
https://spectrum.ieee.org/nanoclast...ists-more-certain-about-quantum-uncertainties
====
 

Attachments

  • Math.jpg
    Math.jpg
    59.6 KB · Views: 0

socratus

socratus
Dec 10, 2008
940
3
18
Israel
www.worldnpa.org
1 - Heisenberg’s Uncertainty Principle (h/4π) is about limit
of one (single) quantum particle.
2 - Wojciech Górecki Uncertainty can be a limit of statistical
calculations of quantum system (system of many-many quantum particles)
And therefore Wojciech Górecki '' observations of the universe are
a little bit fuzzier than we imagined.''
=====
 

Attachments

  • H.jpg
    H.jpg
    6.1 KB · Views: 1

socratus

socratus
Dec 10, 2008
940
3
18
Israel
www.worldnpa.org
Mathematics + Physics: By Beauty it is Beautiful.
----
About 2500 years ago, according to Plato, Socrates said: ‘' I do not go so far as to insist upon the precise details; only upon the fact that it is by Beauty that beautiful things are beautiful.'’
#
Book '‘Albert Einstein'’ . . . ‘'Minkowski mathematical genius put Einstein’s ideas into a new geometrical form that fully revealed their beauty and simplicity'' / by Leopold Infeld , Page 45 /
#
“There are occasions when mathematical beauty should take priority over agreement with experiment.” / Dirac /
This can be illustrated by referring to Einstein's SRT: 4D, light cone . . . Nobody knows what 4D really is, nobody knows what light cone really is , but these beautiful constructions were took as basis for many modern scientific works.
#
'' . . . . faith in beautiful math has become pervasive in the community. And that’s despite the fact that relying on beauty as a guide to new natural laws has historically worked badly: The mechanical clockwork universe was once considered beautiful. So were circular planetary orbits, and an eternally unchanging universe. All of which, it turns out, is wrong.'' / Posted By Sabine Hossenfelder on Sep 16, 2019, Mind the Gap Between Science and Religion /
------
Without précises physical details, like: volume (V ), temperature (T ) and density ( P) the Minkowski ''beautiful and simple'' spacetime (-4D) is a pure mathematical game, and as result of such beautiful game the paradoxes come in physics.
======================
 

Attachments

  • Lightcones - A-Physicists-Favorite-Tool.jpg
    Lightcones - A-Physicists-Favorite-Tool.jpg
    96 KB · Views: 0

socratus

socratus
Dec 10, 2008
940
3
18
Israel
www.worldnpa.org
Physicists Prove That the Imaginary Part of Quantum Mechanics Really Exists!
By Faculty of Physics University of Warsaw on Apr 27, 2021
-----
“In physics, complex numbers were considered to be purely mathematical in nature.
It is true that although they play a basic role in quantum mechanics equations,
they were treated simply as a tool, something to facilitate calculations for physicists.
Now, we have theoretically and experimentally proved that there are quantum states
that can only be distinguished when the calculations are performed with the indispensable
participation of complex numbers,” explains Dr. Streltsov.

==========
 

Attachments

  • Math and Physics.jpg
    Math and Physics.jpg
    8.3 KB · Views: 1

socratus

socratus
Dec 10, 2008
940
3
18
Israel
www.worldnpa.org
'' . . . complex numbers are an integral, indelible part of quantum mechanics . . . ''

/ Dr. Streltsov /

" The mathematics of QM is straightforward, but making the connection

between the mathematics and an intuitive picture of the physical world is very hard"

/ Claude N. Cohen-Tannoudji . Nobel Prize in Physics 1997 /

---------------

Do Complex Numbers Exist?

175,946 views•6 Mar 2021


--------

Is imaginary science real?

If this is true, then it is possible that we live in metaphysical reality

----

‘’Imaginary numbers are a fine and wonderful refuge of the divine spirit,

almost an amphibian between being and non-being.’’

/ Gottfried Leibniz /

=====