Euler's Equation and the Reality of Nature.

[s0cratus]

Euler's Equation and the Reality of Nature.
=.
Mr. Dexter Sinister wrote:
‘ I understand Euler's Identity,
and I know what it means, and I know how to prove it,
there's nothing particularly mystical about it,
it just demonstrates that exponential, trigonometric,
and complex functions are related.
Given what we know of mathematics it shouldn't surprise
anyone that its various bits are connected.
It would be much more surprising if they weren't, that would
almost certainly mean something was badly wrong somewhere.’

Mr. Gary wrote:
Mathematics is NOT science.
Science is knowledge of the REAL world.
Mathematics is an invention of the mind.
Many aspects of mathematics have found application
in the real world, but there is no guarantee.
Any correlation must meet the ultimate test:
does it explain something about the real world?
As an electrical engineer I used the generalized
Euler's equation all the time in circuit analysis:

exp(j*theta) = cos(theta) + j*sin(theta).

So it works at that particular level in electricity.
Does it work at other levels, too?
Logic cannot prove it.
It must be determined by experiment, not by philosophizing.
====..
Thinking about theirs posts I wrote brief article:
Euler's Equation and Reality.
=.
a)
Euler's Equation as a mathematical reality.
Euler's identity is "the gold standard for mathematical beauty'.
Euler's identity is "the most famous formula in all mathematics".
‘ . . . this equation is the mathematical analogue of Leonardo
da Vinci’s Mona Lisa painting or Michelangelo’s statue of David’
‘It is God’s equation.’, ‘ It is a mathematical icon.’
. . . . etc.
b)
Euler's Equation as a physical reality.
"it is absolutely paradoxical; we cannot understand it,
and we don't know what it means, . . . . .’
‘ Euler's Equation reaches down into the very depths of existence’
‘ Is Euler's Equation about fundamental matters?’
‘It would be nice to understand Euler's Identity as a physical process
using physics.‘
‘ Is it possible to unite Euler's Identity with physics, quantum physics ?’
==.
My aim is to understand the reality of nature.
Can Euler's equation explain me something about reality?
To give the answer to this question I need to bind
Euler's equation with an object - particle.
Can it be math- point or string- particle or triangle-particle?
No, Euler's formula has quantity (pi) which says me that
the particle must be only a circle .
Now I want to understand the behavior of circle - particle and
therefore I need to use spatial relativity and quantum theories.
These two theories say me that the reason of circle – particle’s
movement is its own inner impulse (h) or (h*=h/2pi).
a)
Using its own inner impulse (h) circle - particle moves
( as a wheel) in a straight line with constant speed c = 1.
We call such particle - ‘photon’.
From Earth – gravity point of view this speed is maximally.
From Vacuum point of view this speed is minimally.
In this movement quantum of light behave as a corpuscular (no charge).
b)
Using its own inner impulse / intrinsic angular momentum
( h* = h / 2pi ) circle - particle rotates around its axis.
In such movement particle has charge, produce electric waves
( waves property of particle) and its speed ( frequency) is : c>1.
We call such particle - ‘ electron’ and its energy is: E=h*f.

In this way I (as a peasant ) can understand the reality of nature.
==.
I reread my post.
My God, that is a naïve peasant's explanation.
It is absolutely not scientific, not professor's explanation.
Would a learned man adopt such simple and naive explanation?
Hmm, . . . problem.
In any way, even Mr. Dexter Sinister and Mr. Gary
wouldn't agree with me, I want to say them
' Thank you for emails and cooperation’
=.
Best wishes.
Israel Sadovnik Socratus.
=.
P.S.
' They would play a greater and greater role in mathematics –
and then, with the advent of quantum mechanics in the twentieth
century, in physics and engineering and any field that deals with
cyclical phenomena such as waves that can be represented by
complex numbers. For a complex number allows you to represent
two processes such as phase and wavelenght simultaneously –
and a complex exponential allows you to map a straight line
onto a circle in a complex plane.'

/ Book: The great equations. Chapter four.
The gold standard for mathematical beauty.
Euler’s equation. Page 104. /

#
Euler's e-iPi+1=0 is an amazing equation, not in-and-of itself,
but because it sharply points to our utter ignorance of the
simplest mathematical and scientific fundamentals.
The equation means that in flat Euclidean space, e and Pi happen
to have their particular values to satisfy any equation that relates
their mathematical constructs. In curved space, e and Pi vary.
/ Rasulkhozha S. Sharafiddinov . /
===============…

 

[s0cratus]

Intuitive Understanding Of Euler’s Formula

http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/#comment-190704
=====….

 

[SLushhYYY]

I have a whole electrical engineering class based on this identity next quarter. I too am in awe of it.

 

[s0cratus]

Euler's Equation Crackpottery
Feb 18 2013 Published by MarkCC under Bad Math, Bad Physics

One of my twitter followers sent me an interesting piece of crackpottery.
I debated whether to do anything with it. The thing about crackpottery
is that it really needs to have some content.
Total incoherence isn't amusing. This bit is, frankly, right on the line.
==.
Euler's Equation and the Reality of Nature.
a) Euler's Equation as a mathematical reality.
Euler's identity is "the gold standard for mathematical beauty'.
Euler's identity is "the most famous formula in all mathematics".
‘ . . . this equation is the mathematical analogue of Leonardo
da Vinci’s Mona Lisa painting or Michelangelo’s statue of David’
‘It is God’s equation’, ‘our jewel ‘, ‘ It is a mathematical icon’.
. . . . etc.
b) Euler's Equation as a physical reality.
"it is absolutely paradoxical; we cannot understand it,
and we don't know what it means, . . . . .’
‘ Euler's Equation reaches down into the very depths of existence’
‘ Is Euler's Equation about fundamental matters?’
‘It would be nice to understand Euler's Identity as a physical process
using physics.‘
‘ Is it possible to unite Euler's Identity with physics, quantum physics ?’
My aim is to understand the reality of nature.
Can Euler's equation explain me something about reality?
To give the answer to this. question I need to bind Euler's equation
with an object – particle. Can it be math- point or string- particle
or triangle-particle? No, Euler's formula has quantity (pi) which
says me that the particle must be only a circle .
Now I want to understand the behavior of circle - particle and
therefore I need to use spatial relativity and quantum theories.
These two theories say me that the reason of circle – particle’s
movement is its own inner impulse (h) or (h*=h/2pi).
a) Using its own inner impulse (h) circle - particle moves
( as a wheel) in a straight line with constant speed c = 1.
We call such particle - ‘photon’.
From Earth – gravity point of view this speed is maximally
. From Vacuum point of view this speed is minimally.
In this movement quantum of light behave as a corpuscular (no charge).
b) Using its own inner impulse / intrinsic angular momentum
( h* = h / 2pi ) circle - particle rotates around its axis.
In such movement particle has charge, produce electric waves
( waves property of particle) and its speed ( frequency) is : c.
1. We call such particle - ‘ electron’ and its energy is: E=h*f.
In this way I can understand the reality of nature.
==.
Best wishes.
Israel Sadovnik Socratus.

==.
Euler's equation says that . It's an amazingly profound equation.
The way that it draws together fundamental concepts is beautiful
and surprising.
But it's not nearly as mysterious as our loonie-toon makes it out to be.
The natural logarithm-base is deeply embedded in the structure of
numbers, and we've known that, and we've known how it works
for a long time.
What Euler did was show the relationship between e and the
fundamental rotation group of the complex numbers.
There are a couple of ways of restating the definition of that
make the meaning of that relationship clearer.
For example:

That's an alternative definition of what e is. If we use that, and we
plug into it, we get:

If you work out that limit, it's -1. Also, if you take values of N,
and plot , , , and , ... on the complex plane, as N gets larger,
the resulting curve gets closer and closer to a semicircle.
An equivalent way of seeing it is that exponents of are rotations
in the complex number plane. The reason that is because if you take
the complex number (1 + 0i), and rotate it by radians, you get -1: .
That's what Euler's equation means.
It's amazing and beautiful, but it's not all that difficult to understand.
It's not mysterious in the sense that our crackpot friend thinks it is.
But what really sets me off is the idea that it must have some
meaning in physics. That's silly.
It doesn't matter what the physical laws of the universe are:
the values of and e will not change.
It's like trying to say that there must be something special about
our universe that makes 1 + 1 = 2 - or, conversely, that the fact that
1+1=2 means something special about the universe we live in
. These things are facts of numbers, which are independent
of physical reality. Create a universe with different values for all
of the fundamental constants - e and π will be exactly the same.
Create a universe with less matter - e and π will still be the same.
Create a universe with no matter, a universe with different kinds
of matter, a universe with 300 forces instead of the four that
we see - and e and π won't change.
What things like e and π, and their relationship via Euler's equation
tell us is that there's a fundamental relationship between numbers
and shapes on a two-dimensional plane which does not and cannot
really exist in the world we live in.
Beyond that, what he's saying is utter rubbish.
For example:
These two theories say me that the reason of circle – particle’s
movement is its own inner impulse (h) or (h*=h/2pi).
Using its own inner impulse (h) circle - particle moves ( as a wheel)
in a straight line with constant speed c = 1.
We call such particle - ‘photon’.
From Earth – gravity point of view this speed is maximally.
From Vacuum point of view this speed is minimally.
In this movement quantum of light behave as a corpuscular (no charge).

This is utterly meaningless.
It's a jumble of words that pretends to be meaningful and mathematical,
when in fact it's just a string of syllables strung together nonsensical ways.
There's a lot that we know about how photons behave.
There's also a lot that we don't know about photons.
This word salad tells us exactly nothing about photons.
In the classic phrase, it's not even wrong: what it says doesn't have
enough meaning to be wrong. What is the "inner impulse"
of a photon according to this crackpot?
We can't know: the term isn't defined.
We are pretty certain that a photon is not a wheel rolling along.
Is that what the crank is saying? We can't be sure.
And that's the problem with this kind of crankery.
As I always say: the very worst math is no math.
This is a perfect example.
He starts with a beautiful mathematical fact.
He uses it to jump to a completely non-mathematical conclusion.
But he writes a couple of mathematical symbols,
to pretend that he's using math.
http://scientopia.org/blogs/goodmath/2013/02/18/eulers-equation-crackpottery/

==.

 

[Chad]

Interesting what was the point?

Call me curious.

You posted a made up hypothesis and then you debunked your own Hypothesis.

 

[s0cratus]

Interesting what was the point?

Call me curious.

You posted a made up hypothesis and then you debunked your own Hypothesis.

I am searching for the truth.
=

 

[Chad]

Fair enough.

Is it that you like the first synopsis but later you realized that it had already been debunked.

 

[s0cratus]

Euler's Equation Crackpottery
Feb 18 2013 Published by MarkCC under Bad Math, Bad Physics

Create a universe with different values for all
of the fundamental constants - e and π will be exactly the same.
Create a universe with less matter - e and π will still be the same.
Create a universe with no matter, a universe with different kinds
of matter, a universe with 300 forces instead of the four that
we see - and e and π won't change.
What things like e and π, and their relationship via Euler's equation
tell us is that there's a fundamental relationship between numbers
and shapes on a two-dimensional plane which does not and cannot
really exist in the world we live in.
http://scientopia.org/blogs/goodmath/2013/02/18/eulers-equation-crackpottery/

==.

Dear MarkCC.
Thank you for paying attention on my crackpottery article.
I like your comment.
Very like.
==.
You say:
Create a universe with no matter, a universe with different kinds
of matter, a universe with 300 forces instead of the four that
we see - and e and π won't change.
=..
Now Euler’s equation plays a role in quantum theory.
In quantum theory there isn’t constant firm quant particle.
The Pi says that a point-particle or string-particle cannot be
a quant particle. The Pi says that that quant particle
can be a circle and it cannot be a perfect circle.
If e and π belong to quant particle then these numbers
can mutually change.
Doesn’t it mean that Pi ( a circle ) can be changed into sphere?
Doesn’t Euler’s equation cosx + isinx in = e^ix can explain
this transformation / fluctuation of quant particle ?
You say:
What things like e and π, and their relationship via Euler's equation
tell us is that there's a fundamental relationship between numbers
and shapes on a two-dimensional plane which does not and cannot
really exist in the world we live in.
=.

But this ‘a fundamental relationship between numbers and
shapes on a two-dimensional plane’ can really exist
in two-dimensional vacuum.

All the best.
socratus.

==…..

 

[SLushhYYY]

What differs the quantum world from the expression of the quantum world?

 

[s0cratus]

My questions are:
Can ‘dirac’s virtual particles’ have geometrical form of circle?
Can we use Euler equation to this circle- particle ?
Which physical laws can we use to this circle- particle ?
How can be tied Euler equation, physical laws and
circle- particle into one theory ?
==..
I say that there is circle-particle that can change /
transformed into sphere-particle and vice versa
and Euler’s equation cosx + isinx in = e^ix can explain
this transformation / fluctuation of quantum particle
I try to understand more details.
I have circle- particle with two infinite numbers: (pi) and (e).
I say that this circle-particle that can change into sphere-particle
and vice versa. Then I need third number for these changes.
The third number, in my opinion, is infinite a=1/137
( the fine structure constant = the limited volume coefficient)
This coefficient (a=1/137) is the border between two
conditions of quantum particle. This coefficient (a=1/137) is
responsible for these changes. This coefficient (a=1/137) unite
geometry with the physics ( e^2=ah*c)
=..
If physicists use string-particle (particle that has length but
hasn’t thickness -volume) to understand reality
(and have some basic problems to solve this task) then why don’t
use circle-particle for this aim.
It is a pity that I am not physicist or mathematician.
If I were mathematician or physicist I wouldn’t lost the chance
to test this hypothesis.
=..
Best wishes.
Israel Sadovnik Socratus
==…

 

[Vrecknidj]

Mathematics is an invention of the mind.

Whose mind?

 

[s0cratus]

Whose mind?

Math and Physics.

Klein &Lachièze-Rey,
THE QUEST FOR UNITY – The Adventure of Physics.
=.
Mathematics is an indispensable and powerful tool where it has been
demonstrated that it applies to a real world experience. However,
it is inappropriate and, as Dingle points out, potentially dangerous,
to give credence to deductions arising purely from the language
of mathematics. The problem is that mathematicians now dominate
physics and it is fashionable for them to follow Einstein’s example,
with fame going to those with the most fantastic notions that defy
experience and common sense. So we have the Big Bang, dark matter,
black holes, cosmic strings, wormholes in space, time travel,
and so on and on.
It has driven practically minded students from the subject.
There is an old Disney cartoon where the scientist is portrayed with
eyes closed, rocking backwards in his chair and sucking on a pipe,
which at intervals emits a smoke-cloud of mathematical symbols.
Much of modern physics is a smoke-screen of Disneyesque fantasy.
Inappropriate mathematical models are routinely used to describe
the universe. Yet the physicists hand us the ash from their pipes
as if it were gold dust. If only they would use the ashtrays provided.
“It seems that every practitioner of physics has had to wonder
at some point why mathematics and physics have come to be
so closely entwined. Opinions vary on the answer.
Bertrand Russell acknowledged
“Physics is mathematical not because we know so much about
the physical world, but because we know so little.” …
Mathematics may be indispensable to physics,
but it obviously does not constitute physics.”
=.
Klein & Lachièze-Rey,
THE QUEST FOR UNITY – The Adventure of Physics
===…