The Speed of Light is NOT Fundamental. But THIS is.

you don't have to study physics for very long to meet the fundamental constants of nature things like the speed of light planck's constant boltzmann's constant gravitational constant and these numbers pin down the way that the universe is structured they're very important because if any one of these numbers was even a few percent different the universe probably wouldn't exist and we wouldn't exist to experience them so i thought cool video would be for me to try and go out and find all of these physical constants and collect them together in one video for you to see and this is the story of me doing that but what's interesting is the final list doesn't actually contain any of the constants that we're familiar with it doesn't contain the speed of light planck's constant gravitational constant none of them it contains another set of numbers which are more fundamental and even more fascinating so to find out what the heck is going on keep watching so first of all we have to start off in a familiar place with the formulas of physics that we've encountered before things like the gravitational force between two bodies equals mc squared the energy of a photon and also the force between two charges all of these equations contain one of the physical constants and we need to know the precise value of those constants in order to solve the equations so let's take a closer look at one of them so this is the speed of light it's precisely 299 792 458 meters per second precisely and it's kind of weird that this number is this precise you'd think if you were measuring the speed of light you'd have an error bar on the final number there but this makes sense when you realize that we actually use this value of the speed of light to define our length of the meter and it's a sensible thing to do because what we know or what we believe is that the speed of light is a fixed value everywhere in the universe for all time so it doesn't matter who measures it they'll measure the same thing so we may as well say that that thing is a fixed number and then what we do is we say well we've got this length of a meter so the distance that light travels in one second is exactly this many meters we measure the speed of light and then that sets the size of the meter and in fact since 2019 this is the exact principle which we use to define all of the si units so the unit of time a second is based on a transition of a cesium atom which should be the same no matter where you are in the universe obviously the meter is defined by the speed of light we've also got electrical current is defined by the charge on an electron and the unit of temperature is defined by boltzmann's constant mass is defined by planck's constant and so on this means that we've defined all of these physical constants to be definite values when we measure them we've pushed all of the errors in those measurement onto our units so our definition of a meter is only as accurate as our ability to measure the speed of light which lots of people do and we've measured it to great accuracy [Music] so where are we on my quest to find all of the fundamental constants in physics well we've learned something a bit troubling there's actually nothing special about this value for the speed of light because it depends solely on the units that we're choosing for our meter and our second for example in cgs units the speed of light is a hundred times bigger because we use centimeters instead of meters so scientists like to use the si units as a convention to make sure that we're all on the same page when we do calculations and work on space missions but there's nothing special about that specific set of units it's just human convention so if we didn't use those we could actually pick our unit of length and our unit of time to be sizes where the speed of light actually equals one or boltzmann's constant planck's constant gravitational constant they all equal one these are called natural units instead of si units and this specific choice of physical constants to be equal to one is called planck units not to be confused with planck's constant it was the same dude but different things and i've put the equivalent si units so instead of a meter we now have the planck length and that's a very small value the planck mass and the planck time are very very small and the planck temperature is very big physicists use these units in nuclear physics particle physics and quantum gravity mostly to make the equations a bit simpler for example with these units because the speed of light is equal to one e equals m c squared just becomes e equals m and the energy of a photon instead of being e equals h bar omega just becomes e equals omega but this is weird right just by changing the choice of our units we've actually changed the equations of physics we set speed of light equal to one and it just disappears well not quite we actually have to be very careful to keep track of the speed of light it's still there it's just equal to one and this reveals something deep about the roles that these physical constants play in our equations of physics and to see why we need to look at the dimensions let's go back to our old faithful equation e equals m c squared and what i want to do is look at the dimensions in this equation and by dimensions i don't mean like the three dimensions of space i mean the dimensions we use in physics the physics use of the term which is for those physical quantities we can measure like length time mass temperature the things we need units for so the m in this equation has got the dimension of mass it doesn't matter what units whether we use kilograms or pounds it just needs to be a mass the speed of light has obviously got dimensions of length over time and the units of energy are mass times length squared over time squared and for an equation in physics to make sense the units on both sides of the equation need to equal out this is why in our natural units these equations look so wrong because e equals m is basically saying energy is equivalent to mass which we know doesn't make sense when we look at the dimensions and so when the speed of light is equal to one it still needs to be there because it needs to take care of those dimensions and this tells us something deep about the role that these physical constants play in our equations of physics they're conversion factors that show us how certain physical quantities relate to other ones so the speed of light tells us how mass is related to energy planck's constant tells us how frequency is related to energy boltzmann's constant tells us how temperature is related to energy and the gravitational constant tells us how mass is related to length so here's here's the big picture between every physical quantity mass and time or energy in time or mass and length there'll be a physical constant between them to tie them together and the actual value of those physical constants is not very important because it's dependent solely on our choice of units but what is important are the relationships between the sizes of those physical constants the ratio between those constants because those ratios between all the constants is what sets the particular framework of this universe the recipe that makes this universe stable so is there some parameter some number that captures the relationships between all of these different physical quantities some some number that describes some deep feature of our universe well yes there is it's called the fine structure constant and it's dimensionless here is the fine structure constant alpha you can see its relationship between four of our physical constants the electric constant speed of light planck's constant and the elementary charge the actual value of this is approximately equal to one over 137 but the actual value is slightly smaller than that and what's cool about this number is that all of the dimensions on the right hand side actually cancel out so this is a dimensionless number it doesn't matter what unit system you measure it in you'll reach the exact same number we've got no idea why it's this precise number the origin of this constant comes from studying the atomic spectra of hydrogen it's the electron orbitals doing their thing but as soon as you add in relativistic effects you get a splitting of energy levels called a fine structure splitting hence the name find structure constant but since then we've realized that this constant is actually more general and more fundamental and now it forms a core part of the theory of quantum electrodynamics which is the theory that unites electromagnetism quantum physics and special relativity and the phone structure constant sets the strength of the interaction between electrons and photons so this number the specific way is kind of sets our entire experience of the world everything we touch and feel is mediated by electrostatic forces and everything we see is from light so if this number was any different our experience of the universe would be completely different in fact the universe probably wouldn't exist and this is a puzzle that's been challenging theoretical physicists for a very long time feynman called this the greatest damn mystery in physics it's a magic number his words and the reason is the universe just gives us this number and there's no underlying theoretical framework to tell us why it is this specific value also this is a brilliant number to send to aliens to prove that you're intelligent all you have to do is say one over one three seven and those aliens know immediately that you know electromagnetism quantum physics and special relativity although probably best to send it as a binary number instead of in base 10 because they've probably got i don't know 11 fingers or something so now we've got to a true universal fundamental dimensionless physical constant and this is the reason why we don't include the speed of light planck's constant gravitational constant as fundamental constants because they're not dimensionless so the question is is the fine structure constantly only one or are there others well there are others in fact there's a total of 26 that set the structure of our universe so let's take a look at those [Music] so this final set of universal dimensionless constants is given to us by our best theories of physics a combination of the standard model of particle physics and also general relativity now most of these numbers 25 of them come from the standard model there's only one number that comes from general relativity and that's the cosmological constant this is the energy density of empty space otherwise known as the vacuum energy and it's closely related to the expansion of space what we call dark energy even though we don't really know what dark energy is but we have measured it pretty accurately moving on to the standard model which you can see here this is just all of the different particles in the standard model now 15 of these dimensionless physical constants come simply from the masses of the particles that have mass and they're the mass in kilograms divided by the planck mass to give us a dimensionless constant then we have a thing called the electromagnetic coupling constant but this is actually just another name for the fine structure constant so we've already met this there's also another coupling constant that sets the strength of the nucleus strong force so we add that in there would also be one for the nuclear weak force but we can actually derive that from the other constant so we don't need to include it on our list so that gives us 18 of our fundamental dimensionless physical constants 26 in total so we've got eight left the final eight come from interactions of the fundamental particles with each other and i'll be honest i don't fully understand the underlying physics of these but i'll i'll tell you as much as i know four of these numbers come from the interaction of the w boson with the quarks in something called the this matrix giving you four parameters that define those interactions and then you get another four parameters from the higgs boson interacting with the neutrinos in the this matrix but we're really hitting the limits of our knowledge about physics here because there's still lots of things we don't understand about neutrinos like how they get their mass and other things to do with their handedness and whether they're their own anti-particles so this set of numbers might change in the future based on new physical theories or new evidence in fact theoretical physicists would love to be able to get this set of fundamental constants down to a smaller set but to do that we'll need some revolution in the foundations of physics we need some new fundamental physical theory that would explain why these numbers are the way that they are so we finally did it we got to the final set of universal dimensionless constants that the laws of physics gives us quite why they are the specific numbers that they are is still a complete mystery if you've got any ideas leave them in the comments below i'd love to hear your thoughts and thanks for coming along on this journey with me i hope it's been enlightening i'm aware that the destination might be a bit more abstract and hard to understand than we were anticipating when we set out but i've linked to all of my original source material in the description below so if you want to dig deeper on your own that's a great place to start and i'd like to tell you about the sponsor of this part of the video brilliant if you want to learn something new brilliant is the place to do it brilliant a website an app that makes learning accessible and fun and is an excellent way to dive deeper into the subjects in my videos their approach is based on problem solving and active learning seeing concepts visually and interacting with them and then answering questions that get you to think their courses are laid out like a story and broken down into pieces so that you can tackle them a little bit at a time there are no exams or grades just pick a course based on what you're interested in and you can happily make mistakes getting help from the explanations under each problem there's something for everybody whether you want to brush up on the basics of algebra learn programming or learn about cutting-edge topics like quantum computing just go to brilliant.org dos or click on the link in the description below which lets them know that you've come from my channel and yeah thanks again for watching and i'll see you on the next video which i'll be posting pretty soon thanks bye i think it's good how you can just sit in your kitchen and think about physics and go on a sort of journey through the nature of reality [Music] it's cool takes your mind off things anyway

Channel: Domain of Science

Views: 354,742

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Id: aYIbC25GNKs

Length: 16min 34sec (994 seconds)

Published: Fri Oct 30 2020

Reddit Comments

[u/AdamsOnlinePersona]

TLDW: By definition fundamental physical constant is unitless. Whereas physical constant can have units.

So speed of light is not fundamental.

There are a bunch of constants that are unitless expressed in terms of constants with units where units cancel out. Those are fundamental.

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