the universe according to Emmy Noether

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the universe according to Emmy Noether

Postby vivian maxine on May 6th, 2017, 9:17 am 

Biv, I leave it to you to put this where it belongs: here? in Physics? Anywhere.

There are several good physics discussions going on right now. Because of those, I keep asking if this article contributes anything worth reading. As you know, I am certainly in no position to say. I'll describe it as best I can.

The June 2017 issue of Discover magazine has this article by Steve Nadis which starts out as a small biography of mathematician Emmy Nouther. Her story is sad but she was evidently worth calling in when a problem was found in Einstein's theory of "new theory of gravity, special relativity". (Quote) She resolved the issue head-on, showing that energy may not be conserved "locally" --- that is, in an arbitrary small patch of space --- but everything works out when the space is sufficiently large."

From there, the article goes into another theory of Nouther's: "Every 'continuous' symmetry in nature has a corresponding conservation law and vice versa. The article then explains Symmetry, Conservation (conservation law, conservation of momentum, conservation of electric charge), Color Symmetry, the Standard Model (which is very familiar to me but I need to find what its labels are saying) and the Supersymmetry (which shows again the Standard Model with those same labels beside the Standard Model in reverse with no labels.)

Those who know a bit about physics can decide if this is all worth noting. If not, fine. Just thought I'd offer it.

If someone can, I'd wish to know exactly what she means by "Symmetry in nature". I have some notions that are likely "spacey". A real explanation would be much appreciated so I could see if what I am thinking relates.

Gathered from Discover Magazine, June 2017, "The Universe According to Emmy Noether" by Steve Nadis.
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Re: Anything Physics?

Postby handmade on May 6th, 2017, 9:21 am 

vivian maxine » May 6th, 2017, 8:17 am wrote:Biv, I leave it to you to put this where it belongs: here? in Physics? Anywhere.
.

If someone can, I'd wish to know exactly what she means by "Symmetry in nature". I have some notions that are likely "spacey". A real explanation would be much appreciated so I could see if what I am thinking relates.



Nature balances itself out. Entropy is shared proportionally etc I think that means.
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Re: Anything Physics?

Postby vivian maxine on May 6th, 2017, 9:25 am 

handmade » May 6th, 2017, 8:21 am wrote:
vivian maxine » May 6th, 2017, 8:17 am wrote:Biv, I leave it to you to put this where it belongs: here? in Physics? Anywhere.
.

If someone can, I'd wish to know exactly what she means by "Symmetry in nature". I have some notions that are likely "spacey". A real explanation would be much appreciated so I could see if what I am thinking relates.



Nature balances itself out. Entropy is shared proportionally etc I think that means.


Oh, thank you. Then, that ties back to her solution for Einstein's problem of conservation "locally" vs "universally"?
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Re: Anything Physics?

Postby handmade on May 6th, 2017, 9:41 am 

vivian maxine » May 6th, 2017, 8:25 am wrote:
handmade » May 6th, 2017, 8:21 am wrote:
vivian maxine » May 6th, 2017, 8:17 am wrote:Biv, I leave it to you to put this where it belongs: here? in Physics? Anywhere.
.

If someone can, I'd wish to know exactly what she means by "Symmetry in nature". I have some notions that are likely "spacey". A real explanation would be much appreciated so I could see if what I am thinking relates.



Nature balances itself out. Entropy is shared proportionally etc I think that means.


Oh, thank you. Then, that ties back to her solution for Einstein's problem of conservation "locally" vs "universally"?

Without knowing the details in full I can only second guess, but yes I would say so by your explanation.

E can only be retained locally by ''objects'' , space can not retain energy, however locally always transfers E to distant bodies where some of it is retained and some of it is re-emitted. Then of course vice versus, the distant body transferring energy back, a sort of ping pong between bodies. The universe always tries to find an equilibrium of state, all bodies try to be at room temperature but some bodies such as stars are different to that of the retaining bodies.
In maybe a strange sounding way, the universe is sort of AC, the actual space being the wire and coupling.
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Re: the universe according to Emmy Noether

Postby vivian maxine on May 6th, 2017, 9:50 am 

Thank you, handmade. I understand your explanation and how it works. Much appreciated. I am going to have trouble parting with this issue of Discover. That's for sure.
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Re: the universe according to Emmy Noether

Postby Braininvat on May 6th, 2017, 10:37 am 

Noether's theorem does not apply to non-conserving systems, e.g. systems that would call for a Rayleigh dissipation function.

Just throwing that out for anyone who wants to go a bit further.

This is also helpful, getting a sense of how symmetry works in physics....

https://en.m.wikipedia.org/wiki/Symmetry_(physics)

Also this, on Lie Groups....

https://www.quora.com/What-is-a-Lie-Group-in-laymans-terms
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Re: the universe according to Emmy Noether

Postby vivian maxine on May 6th, 2017, 10:50 am 

Thank you, Biv. I'm onto it. All very interesting. More so because I begin to understand it.

Lie Group does definitely relate to the magazine article except that it goes into the math part which those who know Discover would not expect the magazine to do.

The Wiki article is going to require packing lunch and not budging from my chair for a few hours. Very, very good. Many good points that do relate to some of our conversations.

Thanks again.
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Re: the universe according to Emmy Noether

Postby vivian maxine on May 6th, 2017, 1:33 pm 

Braininvat » May 6th, 2017, 9:37 am wrote:Noether's theorem does not apply to non-conserving systems, e.g. systems that would call for a Rayleigh dissipation function.

Just throwing that out for anyone who wants to go a bit further.

This is also helpful, getting a sense of how symmetry works in physics....

https://en.m.wikipedia.org/wiki/Symmetry_(physics)

Also this, on Lie Groups....

https://www.quora.com/What-is-a-Lie-Group-in-laymans-terms


Biv, I have a question. In the ordinary world of everyday accomplishments, where does all this fit in? In what fields of study and professions is this used? Things like inversion transformations, Lorentz covariance, arbitrary differentiable coordinates (that one went over my head), etc.

I suppose the first answer is they help us understand how the universe works. But, I mean closer to home. Who must actually use this for what? Please?
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Re: Putting a Noether Spin on it!

Postby Faradave on May 6th, 2017, 1:46 pm 

Hi Viv,

There's a lot to learn from Emmy Noether. Besides being brilliant, she heroically pursued her subject, acting as a professor, even without pay (as respectable universities couldn't be seen to have mere women on the pay role as professors). On the other hand, this shouldn't be too surprising to anyone with any sort of talent. If you're born with wings, you fly, whether anyone is paying you or not. Emmy refused to walk, just because that's what other humans happen to do.

I like BiV's Wiki reference but don't think the one on Lie groups is for you. Too much abstraction can lead to abandonment of intuition and even blind experts to the obvious. Flying is great but it's important to do it with eyes open.

The most compact definition of "symmetry" I've found is "transformational invariance". This indicates a change in situation for which an object appears unchanged. If you rotate the letter "N" by 90° it looks changed into a "Z". That's not invariant so its not a symmetry. However, if you rotate an "N" by 180°, it still looks like itself so that is a symmetry under 180° rotation. The fact that a particular quantity of rotation must be specified, makes it a "discrete" symmetry.

The circle like "o" appears the same under any amount of rotation (within its plane), so it is said to have "continuous" symmetry.

That tells us something about symmetry under rotation. But if you type here an "N", then type it over here "N", it looks the same. It turns out that "N" is continuously invariant under spatial translation (displacement). The same is true if you watch "N" age. It is continuously symmetric under time translation. Where Noether's theorem applies to physics is that the Laws of Nature are found to exhibit symmetries. In particular, there is an "exact" (the most powerful kind) conservation law corresponding to every continuous symmetry and vice versa. For example, the mass-energy of a closed system is invariant under time translation. This corresponds to the exact law: conservation of mass-energy. Symmetries and conservation laws provide extremely valuable insights into nature. For example, because of symmetry, what is learned about part of a sphere reveals a great deal about the rest of it.

You can skip this next part, since it deals with the "blindness" of physicists referred to above.

To anyone with open eyes*, a table of the exact laws has two conspicuous omissions, which I believe are related.
1. Laws exist for both temporal and spatial translation but only about spatial axes for rotation.
2. A non-spatial, primary quantum spin axis (σ) should list with the spatial axes for Conservation of angular momentum.
A Noether Spin b.png
It makes no sense to purport 4D of translation (rows 1+ 2) and yet pretend only 3D available for rotation (row 3), especially in the absence of an identified primary spin½ axis (σ added), which is widely acknowledged to be non-spatial.

"[Quantum] Spin is often depicted as a particle literally spinning around an axis, but this is only a metaphor: spin is an intrinsic property of a particle, unrelated to any sort of motion in space."

Replacing σ with t for a temporal spin axis (i.e. "chronaxial spin") satisfies both omissions and provides a simple, explicit model for the current mystery of "spin½".

*Alas, so far that's no one.
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Re: the universe according to Emmy Noether

Postby vivian maxine on May 6th, 2017, 2:11 pm 

Thank you, Faradave. I shall save all of that. The last part needs some studying. The article does tell about her teaching with no pay. She was fortunate to have family who would support her. No doubt, very proud of her. That "no women allowed" was a long time a-dyin'. It does my heart good to see today's young women getting a better chance.

I can't leave without saying this. Steve Nadis is one great writer. He knows his audience and how much to give them. After reading his article (several times, I confess), I gleaned a lot from the Wiki article that I would not have before. I must watch for more of his works.
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Re: the universe according to Emmy Noether

Postby mitchellmckain on May 7th, 2017, 2:41 pm 

vivian maxine » May 6th, 2017, 8:17 am wrote:Biv, I leave it to you to put this where it belongs: here? in Physics? Anywhere.

There are several good physics discussions going on right now. Because of those, I keep asking if this article contributes anything worth reading. As you know, I am certainly in no position to say. I'll describe it as best I can.

The June 2017 issue of Discover magazine has this article by Steve Nadis which starts out as a small biography of mathematician Emmy Nouther. Her story is sad but she was evidently worth calling in when a problem was found in Einstein's theory of "new theory of gravity, special relativity". (Quote) She resolved the issue head-on, showing that energy may not be conserved "locally" --- that is, in an arbitrary small patch of space --- but everything works out when the space is sufficiently large."

From there, the article goes into another theory of Nouther's: "Every 'continuous' symmetry in nature has a corresponding conservation law and vice versa. The article then explains Symmetry, Conservation (conservation law, conservation of momentum, conservation of electric charge), Color Symmetry, the Standard Model (which is very familiar to me but I need to find what its labels are saying) and the Supersymmetry (which shows again the Standard Model with those same labels beside the Standard Model in reverse with no labels.)

Those who know a bit about physics can decide if this is all worth noting. If not, fine. Just thought I'd offer it.

If someone can, I'd wish to know exactly what she means by "Symmetry in nature". I have some notions that are likely "spacey". A real explanation would be much appreciated so I could see if what I am thinking relates.

Gathered from Discover Magazine, June 2017, "The Universe According to Emmy Noether" by Steve Nadis.

Worth noting??? uh! We are talking about some of the most significant elements of modern physics -- both of which I have referred to in other posts of this forum. The first is the energy-time uncertainty principle which lead to Hawking's famous discovery that black holes radiate (Hawking radiation). And Noether's theorem which you stated here is one of the central principles of Quantum Field theory and it is the basis for my claim that symmetry and thus geometry is at the heart of this most successful theory of modern physics.
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Re: the universe according to Emmy Noether

Postby socrat44 on August 7th, 2017, 10:29 pm 

In 1918 Emmy Noether published theory that every differentiable symmetry
of the action of a physical system has a corresponding conservation law.
Noether's theorem has become a fundamental tool of modern theoretical physics,
both because of the insight it gives into conservation laws, and also,
as a practical calculation tool. ‘
https://en.wikipedia.org/wiki/Emmy_Noether
So, thanks  to  Noether the symmetries were legitimate in physics.
============================.
Emmy Noether was a great and famous mathematician, but bad physicist.
Why?
Because  there isn’t such law in physics  as  ‘ conservation law ’
or  ‘The law of conservation of mass’.
If you read in Wikipedia:
https://en.wikipedia.org/wiki/Conservation_of_energy
https://en.wikipedia.org/wiki/Conservation_of_mass
it is half-truth. Half-true  theory is deceitful theory.
You cannot believe half-true  explanation.
The true theory says - there is  only
‘Law of conservation and transformation energy/mass’.
We cannot talk about one without talking about the other.
The law of conservation and transformation energy/mass
is a law about a symmetry and asymmetry in the Nature.
If somebody think that  “ The Law of conservation and
transformation of energy/ mass “ is a simple
bookkeeping calculation of debit-credit   he  is  mistaken.
It is a primitive judgment about one of the most important Law in Nature.
Why?
The bookkeeping calculation of debit-credit is 
“ a symmetry law” - like 1$ is equal 100 cents.
But in the Universe we see the laws of symmetry and we see
the laws of breaking of symmetry.
The Life in the Universe is connected  with  symmetry and  with breaking of symmetry.
The forms of living creatures are almost always symmetrical.
But sooner or later comes time of breaking symmetry.
And a  "broken symmetry"  doesn’t  look as  symmetric thing.
( It means : 1$ is not exactly  equal to 100 cents.)
Between symmetry and asymmetry  the effect of ‘transformation’ appears.
But nobody explains what the  ‘transformation’ means according to one
single quantum particle.
=.
If somebody takes only one part of the law (conservation )
and ignore the second part of it (transformation) then abstract ideas
appear in physics  and we lost sight of the real picture of Nature  .
=============================================.
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Re: Approximately right?

Postby Faradave on August 9th, 2017, 12:14 pm 

You seem to be ignoring the distinction made between "exact" and "approximate" conservation laws.
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Re: Approximately right?

Postby socrat44 on August 10th, 2017, 3:17 am 

Faradave » August 9th, 2017, 12:14 pm wrote:You seem to be ignoring the distinction made between "exact" and "approximate" conservation laws.


The Law of Conservation of Energy states that energy cannot be created or destroyed,
just transformed from one form to another.
These forms can include kinetic and potential energy .
. Since energy cannot be created or destroyed,
the amount of energy present in the universe is always the same.
It is simply being transformed and transferred over and over again.
===
So, conservation laws cannot be understand without transformation laws:
they are like two different sides of the same coin.
Physicists explain one side and nobody explains the other side -
- the transformation of the one single quantum particle.

================
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Re: Enough to make your head spin

Postby Faradave on August 11th, 2017, 12:05 am 

socrat44 wrote:Physicists explain one side and nobody explains the other side -- the transformation of the one single quantum particle.


That's our job! Conservation laws are a great place to start.

The kinetic energy of single particles equates to the potential energy of a collection of them (such as the pressure of jar of gas).

Rest mass may be considered potential energy. I personally model this as energy associated with its quantum spin, because there is real, measureable angular momentum attributed to quantum spin. It's hard to imagine angular momentum not associated with energy. We're left to consider what kind of object is spinning and how.
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Re: Enough to make your head spin

Postby socrat44 on August 11th, 2017, 2:45 am 

Faradave » August 11th, 2017, 12:05 am wrote:
socrat44 wrote:Physicists explain one side and nobody explains the other side -- the transformation of the one single quantum particle.


That's our job! Conservation laws are a great place to start.

The kinetic energy of single particles equates to the potential energy
of a collection of them (such as the pressure of jar of gas).

Rest mass may be considered potential energy.
I personally model this as energy associated with its quantum spin,
because there is real, measureable angular momentum attributed to quantum spin.
It's hard to imagine angular momentum not associated with energy.
We're left to consider what kind of object is spinning and how.


That's our job! Conservation laws are a great place to start.
/ Faradave /
Conservation laws are a great place to start . . . . but not place of ending.
    / israel /

The kinetic energy of single particles equates to the potential energy of a collection of them
(such as the pressure of jar of gas).
/ Faradave /
Don;t agree.
A single q/particle can have Dirac's potential energy :- E=Mc^2
And by pressure like ''gas in jar'' , maybe, can create effect of Hiroshima and Nagasaki.
  / israel /

Rest mass may be considered potential energy.
I personally model this as energy associated with its quantum spin,
because there is real, measureable angular momentum attributed to quantum spin.
It's hard to imagine angular momentum not associated with energy.
We're left to consider what kind of object is spinning and how.
/ Faradave /
Agree.
Spin - angular momentum can be associated with energy.
But . . .
Wave - particle duality introduced in quantum physics a property called  spin.
Book:
  ''A brief history of time'' , by Stephen  Hawking,  edition July 2016.
'' One way of thinking of spin is to imagine the particles as little tops spinning
about an axis.  However, this can misleading , because quantum mechanics
tells us that the particles DO NOT HAVE any well - defined axis.''
   / page  75 /
My question:
Do we know the geometrical form of quantum particle which allow
   as to speak about AXIS ?
====================..
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Re: the universe according to Emmy Noether

Postby socrat44 on August 11th, 2017, 2:48 am 

   Noether's theorem of differentiable symmetries  cannot contain any breaks.
So it can be associated with conservation laws.
  But asymmetry is associated with some kind of  breaks, some kind of transformation.
  And the conservation  laws and transformation laws
are like two different sides of the same coin.
A coin without  picture on one side   doesn't have value.

=======================.
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Re: Coordinated Effort

Postby Faradave on August 12th, 2017, 2:44 am 

Stephen Hawking wrote: …quantum mechanics tells us that the particles DO NOT HAVE any well-defined axis.

socrat44 wrote:Do we know the geometrical form of quantum particle which allow as to speak about AXIS?

Hawking represents the entire QM literature in denying an explicit primary spin axis for fermions, instead relying on an abstract (i.e. made up) "intrinsic" axis. It's possible that they are victims of an unfortunate legacy – a bad set of presumed coordinates, which obscure the quantum spin axis.

I noted above that the table of Exact Conservation Laws itself reveals an asymmetry in that it gives 4D of translation axes and yet only 3D of axes for rotation. Like the QM scientists, it ignores the possibility of a temporal spin axis, without a stated justification. There are two reasons why this might be:

1. Spin around time would be essentially instantaneous, thus violating universal speed limit c at any non-zero radius.
But fundamental fermions are point particles (i.e. have zero radius) so, this restriction does not apply.

2. If time is orthogonal with 3D of space, a temporal spin axis should make no projections on space. Yet quantum spin components are found in every spatial direction (always ±ħ/2).
Things change if simpler coordinates are employed.

Here are equivalent representations of the same algebraic expression in two different geometries.
Coordinated Effort 1.png
Left: A right triangle in familiar, Euclidean geometry exhibiting the theorem of Pythagoras (longest side c is hypotenuse).
Right: A right triangle in non-Euclidean geometry (longest side c is a leg, i=√-1).

The interval equation of Special Relativity has an identical algebraic form, again presented in two geometries.
Coordinated Effort 2.png
Right: Conventional Minkowski hyperbolic spacetime geometry.
Left: Leg d implies interval, rather than spatial, coordinates.
d is an interval, r is a spatial span where r = √(x²+y²+x²), t is elapsed proper time, universal speed limit c = 1 is implicit.

With interval-time coordinates, a temporal spin axis (my "chronaxial spin") would make equal projections in every spatial direction, exactly as observed.
C-Spin Field.png
Primary spin½ vector (σ) projects symmetric ±ħ/2 components on space. For clarity, spatial arc (±r) is shown locally flat, with exaggerated inclination in Euclidean coordinates.
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Re: Coordinated Effort

Postby socrat44 on August 12th, 2017, 9:20 am 

Faradave » August 12th, 2017, 2:44 am wrote:
Stephen Hawking wrote: …quantum mechanics tells us that the particles DO NOT HAVE any well-defined axis.

socrat44 wrote:Do we know the geometrical form of quantum particle which allow as to speak about AXIS?

Hawking represents the entire QM literature in denying an explicit primary spin axis for fermions, instead relying on an abstract (i.e. made up) "intrinsic" axis. It's possible that they are victims of an unfortunate legacy – a bad set of presumed coordinates, which obscure the quantum spin axis.

I noted above that the table of Exact Conservation Laws itself reveals an asymmetry in that it gives 4D of translation axes and yet only 3D of axes for rotation. Like the QM scientists, it ignores the possibility of a temporal spin axis, without a stated justification. There are two reasons why this might be:

1. Spin around time would be essentially instantaneous, thus violating universal speed limit c at any non-zero radius.
But fundamental fermions are point particles (i.e. have zero radius) so, this restriction does not apply.

2. If time is orthogonal with 3D of space, a temporal spin axis should make no projections on space. Yet quantum spin components are found in every spatial direction (always ±ħ/2).
Things change if simpler coordinates are employed.

Here are equivalent representations of the same algebraic expression in two different geometries.
Coordinated Effort 1.png

The interval equation of Special Relativity has an identical algebraic form, again presented in two geometries.
Coordinated Effort 2.png

With interval-time coordinates, a temporal spin axis (my "chronaxial spin") would make equal projections in every spatial direction, exactly as observed.
C-Spin Field.png


Quantum particles have different properties of spin:  0, 1, 1/2, . . etc
and therefore it is impossible to image all them as a triangle.
=============================.
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Re: the universe according to Emmy Noether

Postby socrat44 on August 12th, 2017, 9:31 am 

     Book:
  ''A brief history of time'' , by Stephen  Hawking, pages 75 - 77, edition July 2016.
 
'' One way of thinking of spin is to imagine the particles as little tops spinning
about an axis.  However, this can misleading , because quantum mechanics
tells us that the particles DO NOT HAVE  ANY  WELL - DEFINED AXIS .''
================.
Hawking explains why ''the particles DO NOT HAVE  ANY  WELL - DEFINED AXIS .''
Because these particles have different properties of spin:  0, 1, 1/2, . . . etc. and
therefore they look different from different directions.
a) ''' A  particle of spin 0 is like a dot: it looks the same from every direction.''
b) ''On the other hand, a particle of spin 1 is like an arrow: it looks different from
different directions. Only if one turns it round a complete revolution (360 degrees)
does the particle look the same.''
c) A  particles of spin 1/2  . . .  looks the same ''if you turned it through two revolutions.''
     (720 degrees)
=========================..
I will try to understand situation.
/ Faradave / wrote:
''I personally model this as energy associated with its quantum spin,
because there is real, measureable angular momentum attributed to quantum spin.''

If  spin  ( linear and  angular momentum)  is responsible of energy then:

a) ''' A  particle of spin 0 is like a dot: it looks the same from every direction.''
               is particle of rest mass and potential energy.
b) A  particle of spin 1 is like an arrow,   has linear momentum,
              and it is photon (for example) 
c)  A  particles of spin 1/2,  has angular momentum and it is an electron (for example).
   '' It's hard to imagine angular momentum not associated with energy.'' / Faradave /
     Usually the form of electron  seems as  a ''ball''.
===========================.
So, it seems that Hawking is right:  ''the particles DO NOT HAVE  ANY  WELL - DEFINED AXIS .''
=================================..

Thank you / Faradave /
======================================.
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Re: Coordinated Effort

Postby BurtJordaan on August 12th, 2017, 10:08 am 

Faradave » 12 Aug 2017, 08:44 wrote:With interval-time coordinates, a temporal spin axis (my "chronaxial spin") would make equal projections in every spatial direction, exactly as observed.

FD, have you ever considered a 5th dimension for your "spin axis"?

Following my terminology in the thread on gravity in hyperspace-propertime, I guess it should then be rather called "hyperaxial spin". This might remove one of the grounds for scientists rejecting your "chronaxial spin". I'm not saying it will make your proposition for quantum spin correct and acceptable, I'm just curious.

BTW, what you referred to as "interval-time coordinates" looks to me the same thing as standard space-propertime coordinates in SR.

PS: the discussion on quantum spin continues under Private Theories here.
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