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all right let's get into this what are

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natural units in order to understand

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what natural units are we want to know

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what are units so for example what is a

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meter or if you're being Canadian a

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meter I'm based in Toronto if that

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wasn't clear already what is a second

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now you'll get fairly frenzied if you

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think about this for quite some time as

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I have that is metaphysically what the

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heck is a second what is a meter what is

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length a science doesn't answer what is

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questions it's operational science is

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metaphysically agnostic meaning that it

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doesn't actually make a claim onto

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ontology it doesn't tell you what is

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instead science gives operational

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meanings so what is a second it says

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here the second is equal to the duration

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of nine one nine two six three one

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periods of the radiation corresponding

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to the transition between hyperfine

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levels of the unperturbed ground state

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of assisium atom a certain isotope of a

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system atom

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okay so then the natural question that

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comes up is why this number

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so why this and not some other number

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and the reason is because in London many

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decades ago someone in some back alley

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took methamphetamine on a Tuesday night

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and came up with that number now I'm not

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kidding it may as well be that to

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someone studying high energy physics in

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the same way that

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well what the heck is a kilogram what is

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a kilogram it means you go to Paris you

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go outside Paris actually it's on the

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and you deal with people being

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condescending too because you don't

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speak French then you duplicate this

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little metal slab that's in Paris you

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duplicate it 67 times so that you have

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68 of them in total

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I'm just being quick with my writing 68

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of them is in total and then you measure

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yourself on a scale and these two

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numbers will coincide that's what it

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means it's an operational definition now

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physicists like to use units that appear

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in nature so units that appear

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and those we call Natural units there's

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some controversy with what's considered

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natural because when someone comes to

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you with a

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some dish and they say this is a natural

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dish and that's unnatural well what do

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you mean that that those Doritos that

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are unnatural did they come from outside

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this universe from some void because

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it's in everything in this universe

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natural aren't we a product of Nature

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and so what we create is natural okay

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what a physicist means by natural is

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that it's invariants across the universe

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as far as we can tell to be extremely

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precise what we mean when we say natural

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units natural in the natural units is

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natural with respect to our current

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understanding in order to make certain

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equations simpler and remove arbitrary

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human qualities

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some sense even an electron is a human

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construct in the sense that it's there

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because it nature doesn't parse itself

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out into these elements I mean you can

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say elementary elementary seems to be an

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objective quality because of the way

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that we Define what an elementary

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particle is it's an irreducible

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representation of something so the fact

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that it's irreducible means if it could

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be reduced in this block Matrix form

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then we can just decompose it and we'd

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say those elements are Elementary but

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the reason why we set aside some special

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canonical place for the electron is

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because it's useful for us it makes our

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models easier to understand simpler

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outcomes razor Etc there's plenty of

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philosophy that undergirds natural this

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is not usually explained and you'll be

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led astray if you don't understand that

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point now here's another Point that's

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ordinarily not explained observables

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[Music]

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have

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null units

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there

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[Music]

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let's say slash ratios

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Okay now what's meant by that again when

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you say that you weigh 68 kilograms it

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means you take 68 of some other

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reference

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then you stack 68 of them and then you

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get yourself it's actually 68 it's not

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68 kilograms per se you can also think

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of this in another way if you wanted to

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speak to aliens which by the way is

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another topic on this channel not

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speaking to aliens per se but UFOs then

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it would be foolish to say I weigh 68 of

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some product from France now you can

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reverse this and imagine an alien is

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speaking to you and you say well how

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much does your craft weigh and they say

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oh it weighs four garbars and then

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you're like what the heck is a garvar

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then they say well that's how much

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liquid we release from our vorbins every

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two farkles it doesn't provide much

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information so instead we do what you

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see colloquially which is C equals H bar

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equals one okay let's get to some myths

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about natural units before exploring

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exactly what that means so firstly one

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of the myths is that we just simply set

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C to equal 1 to equal H bar this is a

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meaningless statement as it's written

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and the reason is it doesn't they can't

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equal one it means we're now using

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the speed of light and h-bar as a

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reference for some other quantity that

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we're trying to develop if you're

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confused about this now then that means

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you're thinking about this correctly

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because it's not ordinarily explained

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it's left ambiguous

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let's look at this let's imagine what is

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the speed of let's say some car on the

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highway

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equals we would say 100

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per hour

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these are the units

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and that's the magnitude with respect to

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those units so if I wanted to say what

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is the speed

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sorry that's already speed what is the

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speed of light

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what we mean is two nine nine seven nine

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two four five eight again it's one of

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those numbers you try to show how clever

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you are when you're a child by

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memorizing meters per second

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now look this is actually what C is C

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refers to all of this C doesn't just

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refer to the magnitude C refers to the

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entirety of it including the units so

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when someone says C equals one C equals

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one what they actually mean is that we

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are now using units where we've taken

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that two nine nine seven nine two four

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five eight meters per second and we've

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placed it in here so we've taken this

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guy and we've placed it in here see all

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of this is not ordinarily explained and

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it's because

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as an undergraduate you're especially

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used to writing with reference to a

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coordinate basis which is why I said try

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to do everything you can coordinate free

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if you have an instructor you're lucky

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enough to have an instructor you always

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ask how can you represent these

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equations coordinate free another way of

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thinking about this is that we have

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graphs in physics and math constantly

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plot and those etchings are akin to

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choosing a unit the fact that we put

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lines with etchings means we've chosen a

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coordinate so these etchings outward are

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it implicitly a choice of coordinates

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but nature but if you look again like I

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mentioned that there's no detector that

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can detect the coordinates much like if

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you take a picture with your phone and

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you then look at it on the screen and

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you zoom in you see pixels the pixels

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are an artifact of you taking a picture

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and trying to manipulate it in some

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manner the world itself is not pixelated

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unless you're to believe Thomas Campbell

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or Donald Hoffman another reason to

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think coordinate free is you'll start to

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construct constructions that actually

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depend on your coordinates when they in

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fact don't in nature and then you'll

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wonder why are you getting an incorrect

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answer so for example in physics and so

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on we often use

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let's see this and then we represent it

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in some symmetry this is how theoretical

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physicists generally reference matrices

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they don't like them so they call them

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symmetries these rows and columns but

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then you also would reference this same

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object

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with numbers in a similar manner

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however they transform completely

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differently so one is an endomorphism

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then the other is a two form or a

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bilinear form and they transform

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completely differently and which is why

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you have transpose which is it's not an

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ill-defined object but it's a strangely

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defined object the inverse of a matrix

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is more copacetic but the transpose is a

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strange one so this one is a two form a

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bilinear form the metric in the with the

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Einstein equations is a 2 4 is a

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bilinear form and also the determinants

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of endomorphism is a completely

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different object it's invariant compared

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to the determinants of a two form or a

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bilinear form and then as you start to

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understand this coordinate free you'll

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realize that there's a special place in

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hell for the person who developed the

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transpose it's an unwieldy object

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another one that will confuse you if you

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think in terms of coordinates is that

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the wave function you ordinarily think

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of the wave function that's going from

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to

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guy is a section

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on a c line bundle and you need to

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understand bundles in order to

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understand it coordinate free so that

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you can do not only polar coordinates

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and you wonder why the heck does the

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derivative change well that makes sense

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when you understand it in terms of a

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principal bundle and then the associated

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bundle but also in terms of no longer

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staying in Rd what if you want to move

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to a curved space for quantum mechanics

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what if you want to do quantum mechanics

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on a curved space this is why one should

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try their best to understand what the

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heck is going on without reference to

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coordinates and then go to coordinates

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when you're actually making a

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calculation that's why this is a myth we

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just simply set C to equal one to equal

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H bar by the way what is h bar well

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that's a bit more abstract you don't

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need to understand that for the sake of

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this video but this is an ill-defined

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equation there's actually a caveat here

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that will come into play later another

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way of thinking about it is imagine you

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have one USD one US dollar

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sometimes you would say it equals 127

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Yen it doesn't actually equal 127 Yen

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otherwise when you have a US dollar it

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would just be 127 Yen what it means is

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that there's something called value or

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some monetary equivalent that's another

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way of thinking about it conversion what

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it means that you go here with some

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mapping let's say m and then here with

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some mapping that's that's called let's

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say m Prime

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what it means is that you do

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let's say m Prime

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inverse see we have to make all these

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constructions now and then that's after

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you've already done M so you've gone

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from here and then you go back up there

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they're not the same so another way of

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thinking about this is imagine you want

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to change lengths instead of using

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meters because you think meters are

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strange for some reason you want to

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measure everyone in terms of Lady Gaga

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so you have Lady Gaga here which I'm

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going to call

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LG so now let's say we want to measure

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someone else let's say some let's say

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Goku so what is Goku Goku

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equals maybe one and a half Lady Gaga's

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in length so you take half of Lady Gaga

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and you stack that again on Lady Gaga

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and you get a Goku in terms of Link how

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about Tony Robbins well that's let's say

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two Lady Gaga's now what we're doing

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here is we're saying I'm going to make

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all my future length measurements in

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terms of Lady Gaga for whatever reason

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in the same way that generally speaking

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prices can be made in reference to the

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US dollar and then you do some

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conversion to find out its equivalent

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monetary value in some other currency in

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the same way what we're doing right here

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is we're referencing everyone's height

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in terms of Lady Gaga's height and it

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just as foolish as it would be to say

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Lady Gaga equals one equals the USD just

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as foolish as this equation is it's

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tantamount to saying C equals one equals

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H bar there's so much that goes into a

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statement like that that's just seeing

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that gives the impression oh physicists

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are just setting it equal to one so no

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this statement is foolish and what's

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underneath that is saying hey I'm going

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to now measure everything in terms of

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the speed of light so I want to measure

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my car maybe it's a millionth of the

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speed of light I don't know I don't want

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to do the calculation right now but

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let's say it's a millionth of a speed of

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light so then I say well the speed of

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walking let's say

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0.0005 I'm making this up of these speed

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of light units that's what it means okay

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so this is all including by the way this

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you have to understand what's lurking

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underneath so in this example the value

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is what's being referenced when I see

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the real world that's what I mean is

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that there's something else that's

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tangible that I'm trying to represent my

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quantity in reference to so from now on

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we're going to no longer say that this

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is moving at 500 meters per second we're

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going to say that this is moving at a

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fraction of the speed of light by the

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way this should be a definition and that

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refers to the entire object there not

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just this this is just the magnitude and

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that's where this is misleading because

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it's just showing you the magnitude how

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the heck can c equal this in the same

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way how the heck can Lady Gaga equal the

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US equals one that is myth number one

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now myth number two is that the

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advantage

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welcome to the theories of everything

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podcast you just watched a clip from a

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00:13:16,730 --> 00:13:15,420
much larger two hour video Lesson

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including what to do with these natural

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units such as how to calculate the

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radius of a black hole in five seconds

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no joke as well as the vacuum energy of

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the universe as well as the pressure

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00:13:28,370 --> 00:13:26,220
inside a neutron star some facts about

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extra dimensions and quantum gravity to

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watch it click here and also this video

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00:13:33,829 --> 00:13:32,519
was sponsored by brilliant brilliant is

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a website where you can go to learn math

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00:13:37,009 --> 00:13:35,399
science and engineering through these

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00:13:38,930 --> 00:13:37,019
bite-sized Interactive Learning

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experiences I keep saying this on the

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show and I mean it that at some point I

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would like to speak to Chiara marletto

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or David Deutsch on Constructor Theory

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and that's heavily based in information

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00:13:50,870 --> 00:13:49,560
Theory and thus as preparation for that

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00:13:52,730 --> 00:13:50,880
I went through brillian's course on

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information Theory and random variables

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and from there I was able to finally see

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why the formula for entropy is the way

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that it is it's handed to you on high

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00:14:02,930 --> 00:14:01,139
from above and it looks Baroque and

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highly manufactured but after going

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00:14:06,710 --> 00:14:04,200
through their course you can see that

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it's an extremely organic choice for a

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formula visit the link brilliant.org toe

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00:14:14,030 --> 00:14:12,720
to get 20 off your annual subscription I

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00:14:16,850 --> 00:14:14,040
personally recommend that you don't stop

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00:14:17,990 --> 00:14:16,860
before four lessons keep going even if

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00:14:20,269 --> 00:14:18,000
you feel like you're not making progress

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00:14:22,009 --> 00:14:20,279
on the first second or third go to four

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00:14:24,050 --> 00:14:22,019
and you'll be extremely surprised that