John Gabriel - Another "Strict Finitist" like Mathis

This is a weird coincidence with John Garbriel's calculus and Mathis' theories. Both are nearly identical. Gabriel's were published a few years before but apparently discovered independently from Miles Mathis. He, like Mathis, is a strict "finitist" in that you cannot have a "curve" without measurable angles (hence Pi=4):

http://web.mit.edu/andersk/Public/John-Gabriel.pdf

http://johngabrie1.wix.com/newcalculus (main site)
https://www.facebook.com/thenewcalculus
http://www.filesanywhere.com/fs/v.aspx?v=8b6c678a5a656f75ad6c (files and .pdfs on theory)
New Calculus:
http://drive.google.com/file/d/0B-mOEooW03iLT0VrWHFmN2NOUTg/view?pli=1

When I read Mathis on entanglement, I looked to youtube to help envision the bell inequality, the bell tests, chsh inequality, etc

I found extremefinitism.com had an offering that helped me. The vid was this one
outube.com/watch?v=yOtsEgbg1-s
https://www.youtube.com/watch?v=yOtsEgbg1-s

He has several on infinity.
One requested help in banishing it from math!
I am going to reach out to him and drop MM's links, see what he says.

Here is his vid listing, Karma Peny
outube.com/channel/UC3blYLgZ6JiGdEL1M8EThGw/videos?view=0&sort=dd&shelf_id=1
https://www.youtube.com/channel/UC3blYLgZ6JiGdEL1M8EThGw/videos?view=0&sort=dd&shelf_id=1

Yeah 3rd Doorman, it seems that if you want to measure the distance around a curve in 2D versus measuring in the real world traveling it actually you will end up inevitably with Mathis. At the basic level as a kid, you had to adjust the handle bars of your bike at times if you traveled a true circle on the play ground...just like the Manhattan metric.

There was never an infinitesimal to close the wheel of your bike with the "curve"...you had to turn the handlebars. If you started with a good angle, you would still see little pyramids on the curve as you right-angled your travel.

http://extremefinitism.com/ is interesting site btw. There are some physicists now saying the universe as we know it may be infinite in size. The limitation on making the claim is only instruments used to measure it.

Old paper from Miles: The calculus is corrupt by Miles Mathis

http://milesmathis.com/calcor.html

This Mathis paper is always a good one:
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http://milesmathis.com/angle.html

Angular Velocity and Angular Momentum



by Miles Mathis

One of the greatest mistakes in the history of physics is the continuing use of the current angular velocity and momentum equations. These equations come directly from Newton and have never been corrected. They underlie all basic mechanics, of course, but they also underlie quantum physics. This error in the angular equations is one of the foundational errors of QM and QED, and it is one of the major causes of the need for renormalization. Meaning, the equations of QED are abnormal due in large part to basic mathematical errors like this. Because they have not been corrected, they must be pushed later with more bad math.

Any high school physics book will have a section on angular motion, and it will contain the equations I will correct here. So there is nothing esoteric or mysterious about this problem. It has been sitting right out in the open for centuries.

To begin with, we are given an angular velocity ω, which is a velocity expressed in radians by the equation

ω = 2π/t

Then, we want an equation to go from linear velocity v to angular velocity ω.
Since v = 2πr/t, the equation must be

v = rω

Seems very simple, but it is wrong. In the equation v = 2πr/t, the velocity is not a linear velocity. Linear velocity is linear, by the equation x/t. It is a straight-line vector. But 2πr/t curves; it is not linear. The value 2πr is the circumference of the circle, which is a curve. You cannot have a curve over a time, and then claim that the velocity is linear. The value 2πr/t is an orbital velocity, not a linear velocity.

I show elsewhere that you cannot express any kind of velocity with a curve over a time. A curve is an acceleration, by definition. An orbital velocity is not a velocity at all. It cannot be created by a single vector. It is an acceleration.

But we don't even need to get that far into the problem here. All we have to do is notice that when we go from 2π/t to 2πr/t, we are not going from an angular velocity to a linear velocity. No, we are going from an angular velocity expressed in radians to an angular velocity expressed in meters. There is no linear element in that transform.

What does this mean for mechanics? It means you cannot assign 2πr/t to the tangential velocity. This is what all textbooks try to do. They draw the tangential velocity, and then tell us that

vt = rω

But that equation is quite simply false. The value rω is the orbital velocity—even according to current definitions—and the orbital velocity is not equal to the tangential velocity. The velocity may be labeled "tangential," but what is derived in the historical proofs is the orbital velocity.

I will be sent to the Principia, where Newton derives the equation a = v2/r. There we find the velocity assigned to the arc.1 True, but a page earlier, he assigned the straight line AB to the tangential velocity: "let the body by its innate force describe the right line AB".2 A right line is a straight line, and if Newton's motion is circular, it is at a tangent to the circle. So Newton has assigned two different velocities: a tangential velocity and an orbital velocity. According to Newton's own equations, we are given a tangential velocity, and then we seek an orbital velocity. So the two cannot be the same. We are GIVEN the tangential velocity. If the tangential velocity is already the orbital velocity, then we don’t need a derivation: we have nothing to seek! If you study Newton's derivation, you will see that the orbital velocity is always smaller than the tangential velocity. One number is smaller than the other. So they can't be the same.

The problem is that those who came after Newton notated them the same. He himself understood the difference between tangential velocity and orbital velocity, but he did not express this clearly with his variables. The Principia is notorious for its lack of numbers and variables. He did not create subscripts to differentiate the two, so history has conflated them. Physicists now think that v in the equation v = 2πr/t is the tangential velocity. And they think that they are going from a linear expression to an angular expression when they go from v to ω. But they aren't.

This problem has nothing to do with calculus or going to a limit. Yes, we now use calculus to derive the orbital velocity and the centripetal acceleration equation from the tangential velocity. But Newton used a versine solution in the Principia. And going to a limit does not make the orbital velocity equal to the tangential velocity. They have different values in Newton's own equations, and different values in the modern calculus derivation. They must have different values, or the derivation would be circular. As I said before, if the tangential velocity is the orbital velocity, there is no need for a derivation. You already have the number you seek. They aren't the same over any interval, including an infinitesimal interval or the ultimate interval.

This false equation vt = rω then infects angular momentum, and this is where it has done the most damage in QED. We use it to derive a moment of inertia and an angular momentum, but both are compromised.

To start with, look again at the basic equations

p = mv

L = rmv

Where L is the angular momentum. This equation tells us we can multiply a linear momentum by a radius and achieve an angular momentum. Is that sensible? No. It implies a big problem of scaling, for example. If r is greater than 1, the effective angular velocity is greater than the effective linear velocity. If r is less than 1, the effective angular velocity is less than the effective linear velocity. How is that logical?

To gloss over this mathematical error, the history of physics has created a moment of inertia. It develops it this way. We compare linear and angular energy, with these equations:

K = (1/2) mv2 = (1/2) m(rω)2 = (1/2) (mr2)ω2 = (1/2) Iω2

The variable "I" is the moment of inertia, and is called "rotational mass." It "plays the role of mass in the equation."

All of this is false, because vt = rω is false. That first substitution is not allowed. Everything after that substitution is compromised. Once again, the substitution is compromised because the v in K = (1/2)mv2 is linear. But if we allow the substitution, it is because we think v = 2πr/t. The v in K = (1/2)mv2 CANNOT be 2πr/t, because K is linear and 2πr/t is curved. You cannot put an orbital velocity into a linear kinetic energy equation. If you have an orbit and want to use the linear kinetic energy equation, you must use a tangential velocity.

The derivation of angular momentum does the same thing

L = Iω = (mr2)(v/r) = rmv

Same substitution of v for rω. Because v = rω is false, L = rmv is false.

But this angular momentum equation is used all over the place. I have shown that Bohr uses it very famously in the derivation of the Bohr radius. This compromises all his equations.

Because Bohr's math is compromised, Schrodinger's is too. This simple error infects all of QED. It also infects general relativity. It is one of the causes of the failure of unification. It is one of the root causes of the need for renormalization. It is a universal virus.

The correction for all this is fairly simple, although it required me to study the Principia very closely. We need a new equation to go from tangential or linear velocity to orbital velocity, which I am calling ω. Newton does not give us that equation, and no one else has supplied it since then. We can find it by following Newton to his ultimate interval, which is the same as going to the limit. We use the Pythagorean Theorem. As t→0,

ω2 → v2 - Δv2
and, v2 + r2 = (Δv + r)2
So, by substitution, ω2 + Δv2 + r2 = Δv2 + 2Δvr + r2
Δv = √ v2 + r2) - r = ω2/2r

v = √[(ω4/4r2) + ω2]
ω = √[2r√v2 + r2) - 2r2]
r = √[ω4/(4v2 - 4ω2)]

Not as simple as the current equation, but much more logical. Instead of strange scaling, we get a logical progression. As r gets larger, the angular velocity approaches the tangential velocity. This is because with larger objects, the curve loses curvature, becoming more like the straight line. With smaller objects, the curvature increases, and the angular velocity may become a small fraction of the tangential velocity. And if v and ω diverge greatly, as with very small particles, this equation can be simplified to

v = ω/r

Yes, it is just the inverse of the current equation.

This means that the whole moment of inertia idea was just a fudge, used to make v = rω. Historically, mathematicians started with Newton's equations, mainly v = 2πr/t, which they wanted to keep. To keep it, they had to fudge these angular equations. In order to maintain the equation v = rω, the moment of inertia was created. But using my simple corrections, we see that the angular momentum is not L = mvr = Iω. The angular momentum equation is just L = mω. We didn't need a moment of inertia, we just needed to correct the earlier equations of Newton, which were wrong. (more at link)