Einstein translated in terms of tau (2π)

[Spectrum744]

Einstein written in terms of tau (2π) makes a beautiful equation visible and helps to understand GR: https://vixra.org/abs/1805.0304. I hope someone enjoys.
 

From the abstract: I propose to rewrite the volume equation for the non-euclidian spherical Universe in terms of tau (2π) instead of π. Written this new way, a truly elegant equation and deeper structure becomes visible. Further, I postulate that the Universe is the Fundamental Theorem of Calculus, i.e. that the 3-dimensional Universe we live in is the derivative-surface of its 4-dimensional hypersphere volume.

1805.0304v2.pdf

[swansont]

!

Moderator Note

The rules mandate that discussion take place here

 

from rule 2.7: Attached documents should be for support material only; material for discussion must be posted. Documents must also be accompanied by a summary, at minimum.

 

 

[studiot]

1 hour ago, Spectrum744 said:

I propose to rewrite the volume equation for the non-euclidian spherical Universe in terms of tau (2π) instead of π.

Fair enough.

Now let us see this equation and please explain why there is any essential difference since the substitution of the diameter for twice the radius in calculations makes no essential difference.

Edited June 7, 2021 by studiot

[Spectrum744]

Your correct question should have been: "the substitution of the diameter for the radius" (see Euler's 1787 E7 "Essay explaining the Phenomena of Aire" where it all began, he still correctly used both pi and tau). It just make things much more elegant and understandable. I have attached the Pdf. After you've read it, please then come back with questions. 

[swansont]

1 minute ago, Spectrum744 said:

Your correct question should have been: "the substitution of the diameter for the radius" (see Euler's 1787 E7 "Essay explaining the Phenomena of Aire" where it all began, he still correctly used both pi and tau). It just make things much more elegant and understandable. I have attached the Pdf. After you've read it, please then come back with questions. 

!

Moderator Note

1. "more elegant and understandable" is subjective

2. If you are going to ignore the rules then I will go ahead and lock this. Is that the path you wish to take?

 

[Spectrum744]

Dear Swansont, yesterday I just stumbled on the Scienceforums.net while doing some research. Honestly, I just discovered it. I was really amused by, actually, your comments and I had the impression that you had good understanding of physics. This is the reason why I posted my paper here. Elegance and symmetry are underlying principles of mathematics, group theory, ... Let me cite Paul Adrian Dirac: "What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating. The theory of relativity introduced mathematical beauty to an unprecedented extent into the description of Nature."  Unfortunately, why it is more elegant - in most cases - to use tau instead of pi cannot be defined. A French croissant tastes imo better than a croissant from country y, but I would have great difficulties to explain why, it is difficult to define taste. (As a sidenote, with respect to tau, I may suggest you to read the Tau Manifesto: https://tauday.com/tau-manifesto). 

[iNow]

9 minutes ago, Spectrum744 said:

A French croissant tastes imo better than a croissant from country y, but I would have great difficulties to explain why

It's known as the subjectivity bias, and you seem uninterested in recognizing that this is no way to arrive at an accurate or useful model of the cosmos (or simply following the rules to which you agreed when creating your account here). 

[studiot]

39 minutes ago, Spectrum744 said:

Your correct question should have been: "the substitution of the diameter for the radius" (see Euler's 1787 E7 "Essay explaining the Phenomena of Aire" where it all began, he still correctly used both pi and tau). It just make things much more elegant and understandable. I have attached the Pdf. After you've read it, please then come back with questions. 

Yes I'm back and my simple question remains unanswered.

Why is 2πR  different from τD  ?

[Spectrum744]

(I’m working in between) thank you for your questions. 2πR = τR

[swansont]

33 minutes ago, Spectrum744 said:

Dear Swansont, yesterday I just stumbled on the Scienceforums.net while doing some research. Honestly, I just discovered it. I was really amused by, actually, your comments and I had the impression that you had good understanding of physics. This is the reason why I posted my paper here. Elegance and symmetry are underlying principles of mathematics, group theory, ... Let me cite Paul Adrian Dirac: "What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating. The theory of relativity introduced mathematical beauty to an unprecedented extent into the description of Nature."  Unfortunately, why it is more elegant - in most cases - to use tau instead of pi cannot be defined. A French croissant tastes imo better than a croissant from country y, but I would have great difficulties to explain why, it is difficult to define taste. (As a sidenote, with respect to tau, I may suggest you to read the Tau Manifesto: https://tauday.com/tau-manifesto). 

My prior comments have nothing to do with any understanding of physics. I have been relaying the pertinent rules you agreed to follow when you joined the site.

As for my understanding of physics, I personally am not befuddled by the location of a factor of 2, as the constants of proportionality and similar terms are IMO the least interesting part of an equation. (I am an experimentalist, though, so this does not extend to setting everything to 1, as I do want to be able to calculate physically meaningful results)

Your croissant comment serves to reinforce the notion that this is personal taste, i.e. subjective, so it is an overreach to say one is better than the other. Better for you perhaps, but there's nothing inherently better about it.

6 minutes ago, Spectrum744 said:

(I’m working in between) thank you for your questions. 2πR = τR

IOW they are the same. It's a notation difference, i.e. a triviality.

[studiot]

5 minutes ago, Spectrum744 said:

(I’m working in between) thank you for your questions. 2πR = τR

Yes you are right, my mistake, 2πR = τR =2πR = τD/2 = πD

Why is this the most important thing to start your thesis with ?

[Spectrum744]

😅 I just have 5 minutes (need to run to school). I’ll try to explain it quickly. In Einstein’s 1917 paper on Cosmological Considerations etc (last pages)., and also in his book on ‘The Special and the General Theory’ he describes the Universe as 2π^2r^3 but that is a little bit an ‘ugly’ equation that doesn’t do justice to the beauty of it, namely if you wright it in terms of tau (2π), the same equation equals the Circle (τr) times the Area of the circle (1/2τr^2) which is a pattern underlying many physics equations, and which also give you the equation for the surface of a hypersphere. But I need to explain more (I’ll try to do this a little later), which in turn makes clear that the Universe we live in is the derivative-surface of its hypersphere’s etc. 

Edited June 7, 2021 by Spectrum744

[swansont]

18 minutes ago, Spectrum744 said:

😅 I just have 5 minutes (need to run to school). I’ll try to explain it quickly. In Einstein’s 1917 paper on Cosmological Considerations etc (last pages)., and also in his book on ‘The Special and the General Theory’ he describes the Universe as 2π^2r^3 but that is a little bit an ‘ugly’ equation that doesn’t do justice to the beauty of it, namely if you wright it in terms of tau (2π), the same equation equals the Circle (τr) times the Area of the circle (1/2τr^2) which is a pattern underlying many physics equations, and which also give you the equation for the surface of a hypersphere. But I need to explain more (I’ll try to do this a little later), which in turn makes clear that the Universe we live in is the derivative-surface of its hypersphere’s etc. 

It's the area multiplied by the circumference if you put it in terms of π, as well. 2π^2r^3 = 2πr * πr^2 

Nothing actually changes when you put it in terms of tau.

[Ghideon]

As far as I know proper time in relativity is denoted by tau (τ). Personally I find pi (π) more practical (or "elegant") with less room for confusion in this context. Maybe you are aiming at replacing the symbol of proper time as well?

Edited June 7, 2021 by Ghideon

[studiot]

20 minutes ago, Spectrum744 said:

In Einstein’s 1917 paper on Cosmological Considerations etc (last pages)., and also in his book on ‘The Special and the General Theory’ he describes the Universe as 2π^2r^3

He does indeed as in the attached, but I'm pushed to find a tau in either document.

 

If Pi was good enough for good old Albert, why is it not good enough for you ?

 

In respect of diameter v radius,

There are good practical reasons for retaining both measurements.

 

In respect of your other commitments, you have reached your 5 posts in your first-24-hours anti-spam limit.

So I suggest you use that time to consider your reply and also think very carefully about the SF rules.

 

 

[LaurieAG]

14 hours ago, Spectrum744 said:

In Einstein’s 1917 paper on Cosmological Considerations etc (last pages)., and also in his book on ‘The Special and the General Theory’ he describes the Universe as 2π^2r^3 but that is a little bit an ‘ugly’ equation that doesn’t do justice to the beauty of it, namely if you wright it in terms of tau (2π), the same equation equals the Circle (τr) times the Area of the circle (1/2τr^2) which is a pattern underlying many physics equations, and which also give you the equation for the surface of a hypersphere. But I need to explain more (I’ll try to do this a little later), which in turn makes clear that the Universe we live in is the derivative-surface of its hypersphere’s etc. 

If you write things in terms of tau (2π) universally you just end up with numerology.

[Spectrum744]

I’ve been thinking about this. The first pages of my paper are easy to understand but to understand the last part of my paper, where you start to mix e.g. 1d momentum (p = mv = τr) with 2d energy (K.E. = 1/2 mv^2 = 1/2 τr^2) and so on - and you thus immediately see why you need to use τ instead of π - into the 4d Energy-Momentum Tensor Tμν, you need to understand the tensors that are used in GR, and you need to be able to grasp (‘vizualize’) the difference between the 3d hypersurface and 4d hypervolume, something Einstein had clearly understood but which is not that easy to ‘see’.

In the future I’ll write a didactical paper for the young (the easy part) and old (the part with GR and the connection between classical mechanics and quantum mechanics which appears visible).

Pi will certainly continue to exist, Euler used the same term ‘pi’ for both pi and tau, but tau is certainly more elegant (as is the Dozenal system imo).

Let me just hope that if someone comes along and understands my paper, (s)he senses a glimpse (Universe = ⭕️🔴) of the Beauty which good old Albert would certainly have seen too. 

[exchemist]

26 minutes ago, Spectrum744 said:

I’ve been thinking about this. The first pages of my paper are easy to understand but to understand the last part of my paper, where you start to mix e.g. 1d momentum (p = mv = τr) with 2d energy (K.E. = 1/2 mv^2 = 1/2 τr^2) and so on - and you thus immediately see why you need to use τ instead of π - into the 4d Energy-Momentum Tensor Tμν, you need to understand the tensors that are used in GR, and you need to be able to grasp (‘vizualize’) the difference between the 3d hypersurface and 4d hypervolume, something Einstein had clearly understood but which is not that easy to ‘see’.

In the future I’ll write a didactical paper for the young (the easy part) and old (the part with GR and the connection between classical mechanics and quantum mechanics which appears visible).

Pi will certainly continue to exist, Euler used the same term ‘pi’ for both pi and tau, but tau is certainly more elegant (as is the Dozenal system imo).

Let me just hope that if someone comes along and understands my paper, (s)he senses a glimpse (Universe = ⭕️🔴) of the Beauty which good old Albert would certainly have seen too. 

I have to say this whole exercise strikes me as pointless. A factor of 2 is not going to make a material difference to how an expression is seen, to anybody who is even remotely used to algebra. As you yourself say, 2π pops all over the place. So  "2π" is read and recognised as a familiar symbol already, in its own right.  Replacing it by τ won't reveal anything. It may in fact momentarily confuse people who are not used to seeing τ used in this way, as it has other meanings in physics. 

[studiot]

38 minutes ago, Spectrum744 said:

I’ve been thinking about this. The first pages of my paper are easy to understand but to understand the last part of my paper, where you start to mix e.g. 1d momentum (p = mv = τr) with 2d energy (K.E. = 1/2 mv^2 = 1/2 τr^2) and so on - and you thus immediately see why you need to use τ instead of π - into the 4d Energy-Momentum Tensor Tμν, you need to understand the tensors that are used in GR, and you need to be able to grasp (‘vizualize’) the difference between the 3d hypersurface and 4d hypervolume, something Einstein had clearly understood but which is not that easy to ‘see’.

Instead of being rude and condescending about our abilities why not just post the requested information and see if we understand it ?

I note you have ignored my comment about diameters v radii.

Using diameters instead of radii is equivalent to asking "what is the diameter of curvature in differential geomery ?"

[Spectrum744]

It is just that I need at least like 20-30 pages to explain everything and I need also that you are willing to read the paper which I had attached, even only the first 5-6 pages. Unfortunately, I have the impression that you still haven’t done this. And I already explained that pi and tau will be continue to be used, but that is really of no importance here. Thus, for me it makes more sense to write a didactical explanatory paper for some curious student in the future. Luckily for me, some people have read and understood it and, as Feynman said, the pleasure of finding things out is more than a sufficient recompense 🤷🏻‍♂️

[swansont]

1 hour ago, Spectrum744 said:

I’ve been thinking about this. The first pages of my paper are easy to understand but to understand the last part of my paper, where you start to mix e.g. 1d momentum (p = mv = τr) with 2d energy (K.E. = 1/2 mv^2 = 1/2 τr^2) and so on

2d energy? KE is a scalar. and it’s not 1/2 τr^2 which has the wrong units.

And it’s better to write KE as Qv^2, where Q = m/2. Much better.

 

[Spectrum744]

Indeed, if Q = m/2 then KE = 1/2mv^2. 

[swansont]

3 minutes ago, Spectrum744 said:

 

And?

Nothing here says KE is 2d. It says it’s quadratic.

 

[Spectrum744]

Well, ok, yes, but these equations all follow the same pattern and you can mix this up into ‘4d’. 

Einstein declares that the Universe equals 2pi^2r^3. Ok, fair enough, a bit strange vs.

Einstein declares that the Universe equals a circle ⭕️ times the area of a circle 🔴 which corresponds to a pattern that can be found in many physics equations, which equals - multiplied together - the hypersurface and, and at the same time, this geometric pattern that these physics equations follow, is extended into 4d and corresponds to Conservation laws.

Edited June 8, 2021 by Spectrum744

[swansont]

20 minutes ago, Spectrum744 said:

I’m afraid I’m close to my 5 post maximum limit.

That only applies on day 1

 

Quote

these equations all follow the same pattern

They’re contrived; several of those equations are not valid in general (e.g. a composite system can have p=0 and have kinetic energy)