Why is the speed of light what it is? Maxwell equations visualized

guys I'm super excited to tell you this video is a collaboration with the history guy channel so while this video is about Maxwell's equations they have simultaneously uploaded a fascinating video on the interesting life of James Clerk Maxwell check out their video at the link in the description think of any high-tech appliance you routinely use your phone your TV your computer your refrigerator toaster lightbulb your car just about anything and I can guarantee that some Engineer somewhere sometime used one of these equations design it almost all modern technology is based on them these are called Maxwell's equations in honor of Scottish physicist James Clerk Maxwell who published them in 1865 he's not as well-known as Newton or Einstein but his contributions to science are arguably among the greatest somewhat like I assign he built in the concepts originated by other scientists but synthesized them and put them in mathematical terms that allowed us to see a new kind of relationship in this case between electricity and magnetism and light he showed that they were really just manifestations of the same phenomena this is one of the most important and practical set of ideas in all of classical physics but I think even Maxwell could not have imagined through huge implications for technology not only do they describe about every electrical and magnetic phenomenon but believe it or not hidden within these equations is a fundamental truth about the nature of light and why it is the ultimate speed of the universe and this truth help set the stage for another famous physicist who would later change our paradigm about the nature of reality itself the explanation is coming up right now [Music] these equations look intimidating but don't worry we're not going to derive them I'm only going to show you what they mean and what they imply in practical terms and we're going to visualize them with graphics that I hope you'll find useful objects have something called a charge this is a property of matter like mass is a property of matter in practical terms what this means for large objects with negative charge is that it has more electrons and protons the first thing I want you to visualize is that if you have a static object with a charge it will affect only other charges and if you have a static magnet it will affect only other magnets it will not affect charges but if you have a moving charge it will affect a magnet and if you have a moving magnet it will affect a charge at the simplest level of description that's what these four equations are telling us it is best to think of this as a field similar to the quantum fields of quantum field theory that I spoke about in another video but for visualization you can think of this as being similar to the gravitational field the first equation is a formula that tells us how electrical charges create electrical fields it's based on concepts developed by Carl Friedrich Gauss it basically tells us that if you have an electrical charge there will be an electrical field emanating from it if you want to know the strength of this electrical field you can calculate it using this equation note that the strength of this electric field is proportional to a constant called epsilon naught this is known as the vacuum permittivity this is a property of the vacuum of space it can be thought of as the resistance of free space against the formation of an electrical field the second equation is referred to as Gauss's law for magnetism it's the equivalent of the same equation for magnetism but it's kind of a negative line it basically says that if you have the same sphere but instead of having a charge inside it was a magnet you'll never find a configuration where the magnetic lines of force always point outward are all this point inward there's always as much field pointed out as there is pointed in it will be in loops in other words a magnet will always have two poles there are no magnetic mount you cannot have a positive magnet or North Pole by itself or a South Pole by itself you might say well I can take this magnet and cut out the North Pole wouldn't that create a monopole no you would just create a smaller magnet with two poles you can keep cutting this in half over and over and you would always have two poles the third equation is called Faraday's law this law basically says that if you move a magnet you will create an electrical field in other words if you change the magnetic field with time it creates an electrical field what does it mean to create an electrical field it just means that you put a charge there it will be affected it will be accelerated this equation tells engineers how to generate electricity from a generator you can take large magnets and rotate them and if you put a wire near it as you move the magnet then electricity will be created in the wire this is because there are electrical charges in the metal wire and as electric field lines are created these charges will move creating a current of electricity the fourth equation is amperes law it basically says that if you have a moving charge through a wire or an electrical current you generate a magnetic field in other words two wires can be attracted to each other if they have current flowing through it the equation will tell you how strong the magnetic field would be so if you have a given current flowing through a wire let's say one amp and you are one meter away how strong with the magnetic field be at that point this requires another concept of nature called mu naught this is known as the permeability of free space this can be thought of as the ability of free space to allow magnetic lines of force to go through it note that there are two terms in this equation one term tells you that moving electrical charges can create magnetic fields and the second term tells you that moving electrical fields can also create magnetic fields this idea of magnetic fields being created from electrical fields was Maxwell's addition to amperes law and he just thought it up in his head it was not based on any experiment he figured that there should be some symmetry with Faraday's law because if moving magnets could create electric fields then moving electrical fields should also create magnetic fields now I want you to take note of epsilon naught and mu naught both of these constants have to be measured since they are inherent properties of nature they are not derived from anything you might say at this point well you're just talking about electricity and magnets what does this have to do with life so here comes the most interesting part let's take what we've gleaned from Maxwell's equations and now put it to practical use put yourself in Maxwell's shoes at this point you're working with equations and concepts that other people really don't know about much in the early 1860s and you are staring at them for a long time trying to see some patterns here and you are mathematically trying to figure out what these equations are telling you so now you think to yourself maybe I'll do a thought experiment what if I take an electric charge and put it on a pole outside my house and I just move it up and down up and down what will this cost well if you did that then according to amperes law if an electric field moves or changes with time it would create a magnetic field perpendicular to that and because of the changing movement of up and down that you're making with the charge the magnetic field will also be changing with time and according to Faraday's law the moving magnetic field would create another new set of electrical fields now since the same thing is happening to these new electric field lines that is they're changing over time they would in turn create new magnetic fields and the new moving magnetic fields would create yet more electrical field lines so this becomes like an unstoppable positive feedback loop of electric fields creating magnetic fields creating electrical fields creating magnetic fields and so on each is produced by the movement of the other you have just created a self propagating wave this is analogous to throwing a rock in a lake it disturbs the water so the water starts to oscillate and it pulls its neighboring molecules up so the first way will pull its neighboring molecules up which isolates more water which moves more of the molecules from neighboring water and this is the way a water wave propagates so now you're mr. Maxwell and you're trying to figure out what kind of wave you've just created this wave must be occurring in nature because electricity and magnetism exist so you think about that well what would this wave look like how fast is the wave moving so you calculate using what you think the speed could be about manipulating the equations that you have you do this by using advanced multivariable calculus which Maxwell was exceptionally good at you won't go through how it's done here but what Maxwell comes up with is 1 over V squared is equal to epsilon naught times me R naught and solving for velocity you get that it's equal to the square root of 1 over epsilon naught times me or not so what the equations are saying is the velocity of this wave is inversely proportional to the permittivity and permeability of free space does this even make sense well permittivity can be thought of as I said earlier as the resistance of free space against the formation of an electrical field think of this like viscosity a more viscous fluid like molasses would be harder to swim through than water you wouldn't swim very fast in molasses similarly a wave flowing through a substance with warm permittivity would propagate faster for free space epsilon naught is equal to the following number and permeability can be thought of as the resistance of a material against the formation of a magnetic field and it's equal to this number so it makes sense that the velocity of any wave would be inversely proportional to the resistance of the substance it's traveling it you might at this point ask well why our mu naught and epsilon naught those exact values that's a real good question no one knows why these are just the constants of nature these are properties of free space that tell us how fast magnetic fields and electrical fields can interact with each other if there's a finite speed at which the electrical and magnetic fields can interact with each other then it sets a limit on how fast these fields can propagate through space in a different substance or a different universe these constants could be different now we take the measured values of these two constants and do some simple math lo and behold what you find is that the wave you've just created moving at about 300,000 kilometers per second this is really fast this would go all the way around the earth almost eight times or close to the distance of the moon in one second what kind of wave moves this fast your Maxwell and you say to yourself wait a minute you remember that in 1728 English astronomer James Bradley had calculated what the speed of light is it's about two hundred ninety seven thousand kilometers per second and a huge Eureka moment hits him that light must really just be a manifestation of electricity and magnetism it is an electromagnetic wave can you imagine how Maxwell's insight from this must have felt there was a point in time when Maxwell was the only person in the world who realized this now he could not prove it at the time but about twenty years later I in records proved experimentally that Maxwell was absolutely right and the rest of the story is that about 40 years later another great scientist by the name of Albert Einstein did his own thought experiments inspired by Maxwell's equations and his thought experiment was based on one simple assumption he asked himself if the speed of light is an inherent property of space why would the speed be any different based on the speed of the observer it shouldn't matter whether you measured the speed of light moving at a fast train or whether you measured it standing still it should be the same regardless of your reference frame and it was from the simple assumption that he came up with a special theory of relativity in 1905 which changed our ideas about the nature of time later in his life when people suggested to Einstein that he stood on the shoulders of Newton he corrected them and said no I stand on the shoulders of James Clerk Maxwell the man who inspired not only Einstein but to a large extent is responsible for creating the equations used by every electrical engineers to create some of the most cherished and useful technologies that we use today is James Clerk Maxwell and as the history guy likes to say this is history worth remembering guys if you want to learn more about the interesting life of James Clerk Maxwell check out the superb video on the history guy channel at the link in the description click like button if you liked this video and post a question in the comments I try to answer all them and I will see you in the next video my friend

Channel: Arvin Ash

Views: 1,176,826

Rating: 4.9314237 out of 5

Keywords: maxwells equations, speed of light, electromagnetic radiation, electromagnetic wave, magnetic field, electric field, electromagnetic waves, gauss law, maxwells equations explained, why is the speed of light what it is, why is the speed of light the limit, why is the speed of light the speed of light, amperes law, maxwells equations and light, maxwells equations for dummies, let there be light, electric fields, magnetic fields

Id: FSEJ4YLXtt8

Length: 13min 19sec (799 seconds)

Published: Wed Mar 25 2020

Reddit Comments

[u/zyxzevn]

Note: the video explains the speed in only a very small segment.

The basis for constant speed of light are the maxwell equations.
Based on that, if these stay constant when moving, the speed of light should also stay constant.

Personally I am curious if this really holds true.

As we can clearly see that the maxwell equations are very similar to (Stokes) fluid-equations. And the equations are not time-sensitive. With this I mean that a loop integral around a changing field, can not account for distant changes in these fields. In other words: It does not account for the delay of the field to reach the edge.

And in some cases they don't work well. Like in the homopolar motor. That is because some of the equations are related to circuits/loops and not to other cases.

So, the speed of light is based on a system that is not completely consistent to begin with.