Transcripted Video: On the Radius (and the Fine Structure Constant)

In this video

Modified Unit Analysis: THE RADIUS

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today we're going to talk about modified unit analysis and the radius now you may

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think that it is overkill to make a whole video on the radius but I think

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you will see that this is an important topic and it needs to be dealt with

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now I think everyone will agree that we can't really talk about the radius unless we're talking about the circle

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okay so the radius is the distance from the center of a circle to the outer edge

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of a circle now if you had an ellipse then you could maybe have two radii one

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for the long axis and one for the short axis but for now we're just talking about the radius of a circle

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and of course the relationship between the circumference of a circle and the

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radius of the circle is circumference equals 2 pi times the radius so if you

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have the radius of a circle you can calculate the circumference and if you have the circumference of a circle you

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can divide by 2 pi and calculate the radius

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and it is well known that the standard units of radius the units of radius that

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you would find in the nist standard is the meter and this is what I'm calling a

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question in this video in modified unit analysis the units of the radius are not

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the meter and as you likely remember from my

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previous videos the circumference of a circle is also equal to the wavelength

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of the circle so circumference and wavelengths are intimate and intimately

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connected in this manner in this manner and I've shown you a video of how this works but this is actually geometrically

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more accurate the circumference of this circle is approximately the wavelength

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of this wave and so I actually equate the circumference of a circle with the

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wavelength of a wave and they both have units meters per cycle

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and so um wavelengths and circumference are 360 Degrees okay so this is really saying

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meters per 360 degrees or you could say meters per 2 pi or

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um I could make up a unit called the Doge okay in the Doge you one turn

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around the circle is 720 degrees or sorry 720 Doge and one doge is equal to

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a half a degree and so once around the circle is is 720 Doge so that's what the

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units would look like but here's the problem I don't want to put numbers into the unit section that's why I put a

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symbol here okay it's meters per whatever units I'm using in my

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experiment so if I'm using degrees so here's an example so here's the

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relationship between circumference and wavelength okay here you have a circle people with 30 60 90 120 degrees being

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marked out and here is a wave with 30 60 90 120

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whatever degrees up to 360 degrees so this is 360 degrees and once around the

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circle is 360 degrees so long story short in the domain of

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wavelength in the domain of circumference in the domain of cycle a

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AKA 360 Degrees the wavelength circumference has units

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meters per cycle okay so the units of

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wavelength in my language is meters per cycle and of course you already know

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that in a similar manner the units of radius

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in modified unit analysis are meters per radian so basically all I'm doing is com

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converting from meters per cycle to meters per radians so as I mentioned in

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a previous video the the radian one radian is the angle such that the arc

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length The Arc Length equals to the radius so radius and radian are intimately

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connected and as okay as

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um 360 degrees 360 Degrees has units meters per cycle

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57 degrees has units meters per radian

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so one cycle is 360 degrees one radian is 57.29 degrees okay and so the

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circumference of a circle one wavelength has units meters per cycle and one radian so one partial cycle

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because this is not a complete cycle one incomplete cycle of one radian has units

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meters per Radian so meters per cycle are the units of a

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the circumference of a circle in meters per radian are the units of a partial

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circumference of the circle which just happens to equal the radius so whenever

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I see radius I'm going to assume we mean these because you're not going to have a radius unless you have a circle or maybe

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an ellipse but you're not going to have a radius unless we're talking about a circle and I think because the radius

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equals this Arc Length here that in we are in fact at least in the own particle

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in the own particle model and in modified unit analysis I'm actually referring to this Arc Length here so

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whenever I see radius yeah I'm going to think about the radius of the circle but I'm also going to think about the arc

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length of the circle and then the question I want to ask you is is radius

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fundamental is radius fundamental that is the question I am asking in this video is

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radius fundamental does nature care about radius is the

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radius of a circle a fundamental measure of nature should when when we take all

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of the constants of Nature and combine them together and get something that get the units of the meter are we going to

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assume it is a radius or where are we going to assume it is the circumference of a circle or maybe it's the diameter

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of a circle but is the radius important because radius does seem to be very important in physics okay I'm not saying

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it's not useful I'm just saying the question is does nature

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care about the radius if it were going to spit out fundamental constants would

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those constants be you know in terms of radius and so here is just something a quick

Does nature care about radius?

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picture of what I mean when you want to measure the radius of a tree you cannot

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measure the radius radius of a tree of course unless you chop down the tree so the way you measure a tree is you put

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a string around it you put a measuring tape around it and you measure its circumference and then if you need the

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radius for whatever reason you can calculate the radius or if you need the diameter you can calculate the diameter

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but really you cannot physically measure the radius of a tree

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in out in nature without cutting down the tree so again is radius fundamental is does

Is radius FUNDAMENTAL?

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nature care about radius do we see radius in our equations that we use to

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describe nature well it we it looks like we do it looks like we do what we find

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is in the gravitational equation and the electric charge equation where you're

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calculating a force in this equation you see something that looks like radius in

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the equation but is this really a radius so when you look at charges okay let's

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look at the charge one first when you look at charges now this equation only really cares about the distance between

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the charges there's no like orbit going on here where you have the radius of an

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orbit there's no radius in this picture right here all you have is distance between the charges and so really this

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this equation should read like this where this is a d for distance and not R

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for radius because there is no radius in this picture

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a similar thing can be said in terms of the gravitational constant okay gravity

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doesn't care about radius okay yes if this object is orbiting around this

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object then this is going to be the radius of the orbit but this equation

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here really only cares about the distance between these objects and really this is just a at any snapshot in

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time all we have are the distance between these two objects and so

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regardless of whether one is smaller than the other and so um basically

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what used to be thought of as a radius should in fact be a distance between

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particles distance between planets distance between planetary objects and

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so you can see clearly here that radius at least in these two equations radius

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is not fundamental distance between objects is fundamental we need to know

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distance between objects but in both these cases this has nothing to do with

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radius in the OM particle model I only care

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about the circumference of the circle which is the Compton wavelength and the

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distance between these two objects here which is a distance and not a radius

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although in the ohm particle model the distance between these two points here

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actually does equal the radius of this circle so that is actually just a

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coincidence of the model but but I would never put radius into my equations

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because I'm not talking about radius I'm talking about the circumference of the circle and I'm talking about the

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distance between these two points so in physics you often run into these

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two characters okay this is the Greek character Lambda and this is Lambda with

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a stick through it I'm not sure if that has a name but so this symbol is the

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symbol they use when they're talking about wavelength and this symbol here is uh what they use

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when they're talking about reduced wavelength well what is reduced wavelength

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reduced wavelength is actually wavelength divided by 2 pi okay so when

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you divide wavelength by 2 pi what's happening is your is you're switching from the domain of the cycle to the

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domain of the the radian so if you're talking about a circle when you switch

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from um from Lambda to from the wavelength to divided by 2 pi to the reduced

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wavelength you are switching from the domain of this cycle to the domain of

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the radian or the domain of the circle to the domain of the radius so when

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you're talking about a circle you're switching from the domain of the circle to the domain of the radius and when

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you're talking about waves you're switching from the domain of the cycle the domain of the wavelength to the

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domain of the radian okay the arc length of one radian and so you're switching

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from a perfect perfectly complete cycle to a not perfectly complete cycle okay

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you're switching from the domain of the cycle to the domain of the radians and this is what I'm trying to avoid okay

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I'm trying to avoid this I'm trying to do all of physics in the domain of the cycle and that cycle is either once

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around a circle or that cycle is once along this length

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now when you look at this diagram you can see clearly that okay once around

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the circle is one complete wavelength okay halfway around the circle is half a

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wavelength okay radian is somewhere in here so you have

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0 30 60 90 okay one radian is 57.29

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degrees so it's in here somewhere so when you look over at the maps you can

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see Zero is here 30 in the circle is over here on the wave 60 on the circle

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is over here so 60 degrees in terms of a

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wave is right here and so um 57.29 degrees is somewhere in here so it

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is a non it's a very arbitrary location on the curve okay one radian one radian

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57.29 degrees lands around here on the curve and this is a completely arbitrary location on

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this curve so when people switch from the domain of wavelength from the domain of the

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complete wavelength to the domain of reduced wavelength they are basically

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um Counting uh or they are switching to an arbitrary position on phase in the wave

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and making that fundamental okay they're making that fundamental this is not fundamental this is the

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point I'm trying to make radius is not fundamental nature doesn't care about radius and Radian

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right here on the curve is not one radian is nothing special it's just an

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arbitrary position on this curve and for some reason um the standard physics wants to do

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everything in the domain of the radian they want to do angular frequency and

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they want to switch everything to the domain of the radian and that is what I'm trying to avoid I'm actually getting

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a lot better interpretations when I switch to the domain of a cycle because

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nature cannot be called is not quantized by the radian nature is quantized by the

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cycle so where else is radius being used where

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else in the language of theoretical physics is a radius a thing okay so

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there's this one right here this is actually the equation for the

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classical electron radius what you see here is a bunch of supposedly Universal

Classical Electron Radius

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constants that we know measured constants like the speed of light permittivity of free space the mass of

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the electron and the charge of the electron okay these are all plugged into a formula and because the units because

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when you combine all these units and simplify you get the units of the meter they refer to this as the classical

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electron radius but why did they assume that this was a

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radius right why did they assume it was a radius and not the circumference of a circle or the way the length of a wave

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so why did they assume this was a radius just because these values spit out the

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units of the meter doesn't mean that this is a radius so if it's not a radius then what is it

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well in the ohm particle model there are two choices it could either be the

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circumference of this circle or it could be the distance between these two points here okay so but

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actually I don't see classical electron radius in my own particle model okay I

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can't find it it's just not there so it's not the distance between if the

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circumference of this circle is the Compton wavelength which it is in my

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model then this cannot be the classical electron radius because it does not work

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out to be the correct value so what if instead of assuming that this

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is a radius why not assume that it is a wavelength

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okay so what happens when you assume it's a wavelength well um in terms of

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the own particle model that actually doesn't help me much because this is also not the value of the circumference

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of my circle which is supposed to be Compton wavelength and the or the

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distance between these two points okay and so uh what I want to know I

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want to know what's the relationship between this modeled as a wavelength

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what is the relationship between this and the Compton wavelength because in my

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model the circumference of the of the circle and or the wavelength of my own

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particle model is um is the Compton wavelength and so what

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happens when you divide the these two what happens if you take the classical

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electron wavelength now we're gonna we're just modeling this as a wavelength

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for pretending it's a wavelength okay so this wavelength divided by the Compton

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wavelength which my model assumes as the circumference of the circle or the

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wavelength of the wave when you divide these two together you get this number here now anyone out

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there that's a little Savvy will recognize it recognize this as the

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anomalous Magnetic Moment okay so this is the anomalous Magnetic

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Moment if you pretend that the classical electron radius is a wavelength and you

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divide it by something that I am modeling as a wavelength so you're comparing Apples to Apples here you're

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comparing something I believe is a wavelength with something that I believe is a wavelength you get the anomalous

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Magnetic Moment so what happens when we do model this as

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a radius when we and compare it to the Compton wavelength of the electron and

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so when we model this as a radius and compare it to the Compton wavelength of

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the electron we need to divide by two Pi so we need to convert this to radians

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AKA radius so when you uh when you do this right here when you convert this to

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the domain of the radian of the radius and compare it to this radius you get

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this value here and of course you'll recognize this value here as the fine structure

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constant so I find this really interesting okay

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so although the classical electron radius this value here has no meaning in

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my own particle model okay since this has no meaning this is

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not meaningful but when I apply this conversion factor when I can apply this

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conversion factor to the to this value here the classical electron radius you

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end up with the in the domain you end up with actually calculating the distance

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between these two points which also happens to be the radius of this circle

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now in the case of the when you model the classical electron radius as a

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wavelength when you model it as a wavelength we get the anomalous Magnetic Moment

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and so to me it seems like the both the anomalous Magnetic Moment and the fine

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structure constant um basically are two sides of the same coin

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when you're in the domain of the radius when you are in the domain of the radian

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so when you take the circumference and divide it by 2 5 2 pi you're in the

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domain of the radian when you're in the domain of the radian aka the domain of the radius you need to use the fine

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structure constant and when you're in the domain of the wavelength when you

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model this as a wavelength you use the anomalous Magnetic Moment so these two

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appear to me to be two ways of expressing the same thing okay here is

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the fine structure constant in the domain of the radius and the domain of the radian and here is the

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anomalous Magnetic Moment In the domain of the wavelength okay so these appear

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to be two sides of the same coin they appear to me as some sort of conversion factor

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the uh and I think I know what the problem is so I'm just going to give you

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a brief slide explaining uh what what I think the problem is and then uh give

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you time to think about it before I elaborate more

Re-calibrating Charge

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so what I'm going to do is I'm going to switch to the domain of the wavelength I'm going to assume that this is a

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wavelength and then I'm going to have a look at this a little closer to see

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whether maybe there is a problem in here and so these are all fundamental

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constants this is the permittivity of free space in fact this right here is

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the coulomb constant now I don't know why they have to write it like this I would rather see a little letter K here

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for the coulomb constant but this is in fact the coulomb constant and the mass of the electron is known and the speed

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of light is is measured and known and so and supposedly this is measured and

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known but we are going to have a closer look at this

Planck Charge

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so there is another quantity of charge that is found in the literature and this

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is referred to as plank charge and this can be calculated in two ways so there

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are two calculations for this one of them uses Planck's constant straight up

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and one of them uses H bar which is Planck's constant divided by 2 pi now

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this is the one we're going to be using because I am in the domain of wavelength

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so I am in the domain of wavelength in all of the cosmology that I'm doing I am

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switching from radians to to the domain of radians to the domain of cycle and so

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I am always going to use H Planck's Constant and I'm never going to use H

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bar and so I'm avoiding the radians as soon as I use H bar I have to use

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Omega I have to use angular frequency and I don't want to use angular frequency I want to use 6 click frequent

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frequency so every calculation that I do you can assume that I'm using H and not

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H bar so what I'm going to do for fun here is

Elementary Charge

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I'm going to replace Elementary charge here Elementary charge squared with

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Planck charge squared okay so I'm going to perform the same

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calculation only I'm going to replace Elementary charge squared with Planck

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charge squared and when you do that what you end up with is the Compton wavelength of the

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electron when you plug these values into this formula you end up with the Compton

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wavelength of the electron so this is really nice for my own

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particle model because the ohm particle model has the circumference of the um of

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the model the circumference of the circle is the Compton wavelength of the

Compton Wavelength of the Electron

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electron okay so or if this was the proton if you plugged in the mass of the

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proton here you would get the Compton wavelength of the proton

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so this uh to me looks really fundamental so what happened to Alpha so

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where did they find structure constant and the anomalous Magnetic Moment come

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from well it turns out when you take Elementary charge squared and divide it

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by Planck charge squared now keep in mind this one was calculated using H

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Planck's Constant and not reduced planes constant when you do this operation here

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you get the anomalous Magnetic Moment but when you take Elementary charge

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squared and divided by Planck charge squared that I calculated using using H

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bar so reduced um Planck charge basically you get the

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fine structure constant okay so you get the anomalous Magnetic Moment if you use Planck charge where I used H and you get

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the fine structure constant when you use Planck charge calculated using H bar

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okay so clearly clearly you can see that

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the anomalous Magnetic Moment and the fine structure constant are related and

Fine Structure Constant

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they have something to do with the relationship between the charge as we calibrated it in our

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system with um with Planck charge but regardless when I substitute Planck

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charge for elementary charge in this formula that's meant for calculating the

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classical electron radius I get something that is familiar to me I get the

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um the wavelength or the circumference of my own particle model of the electron

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okay and again if this were the if if I replace the mass of the electron with

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the mass of the proton then this value would end up being the um the Compton wavelength of the proton

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and as everyone knows probably by now the both the anomalous Magnetic Moment

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and the fine structure constant which are the same thing which are not two

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different things they are the same thing when you're in the domain of wavelength you use the anomalous magnetic moment

Anomalous Magnetic Moment

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and when you're in in the domain of radius radians you use the fine structure and constant regardless uh the

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this constant whether it be in wavelength or in radians is

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um is a unit with value and whenever as a computer scientist in the 3D

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ultrasound acquisition software that I develop when I find a unitless value but

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I don't know why I don't know why it almost always turns out to be a

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calibration error and so to me it seems like maybe we calibrated charge wrong or

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maybe charges calibrated for those the domain of electronics but maybe it shouldn't be used here

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I'm not sure okay I'm not sure but it looks like when I use playing charge I

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get values that I am familiar with I get values that match what I expect to find

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in my model and so that gives a little bit of to me it gives a little Vindication to my model in the fact that

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I'm able to calculate one of the parameters from my model using the constants of Nature and so so that is

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the point I want to make the main point I want to make is that the units of the

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units of the radius are meters per radian in modified unit analysis okay so

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I'm going to be very strict about that okay but I'm going to try to avoid the domain of the radians I'm going to

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always stick to the domain of the cycle and the domain of the um the

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circumference of a circle and not the radian okay so I'm going to try to avoid radians whenever I see angular frequency

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I'm going to convert to frequency whenever I see wavelength I'm going to convert to frequency so I'm going to

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stick to the frequency domain and I'm going to stick to the domain of the cycle one complete cycle not one partial

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cycle and so that was the main point I took a little journey here on this video but that was the main point I want to

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make in this video and so hopefully you you kind of get the

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point that the circumference of the circle and the wavelength of a wave are

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really two ways of looking at the same thing and so the circumference of my own

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particle model um is also the wavelength of the

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particle as a if you can think of this as a standing wave this is a wave that

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is propagating in place um and light is where our waves that

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propagate in through space okay so this is the OWN particle model this is an

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electron this is a proton uh probably other particles too but for now I you know I you know I want to focus on the

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electron and the proton okay so that's about it I hope you're

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having a good day and I'll be back