Important fact, special relativity doesn't say that the laws of physics are the same for everyone, just for inertial observers. GR says that the laws of physics are the same for everyone. Also E=mc² by far isn't the key equation in relativity. I'd write down the Einstein field equations G=8πT, or the metric dS² (as a function of x,y,z,ct) or both. From these you would be able to deduce everything whike E=mc² isn't even coordinate independent
I disagree, the field equations have much less of a profound impact on most applications than mass energy equivalence. E=mc² changed our understanding of all chemical and nuclear reactions. It also made every continuity equation an energy balance. I may be biased tho bc I’m a nuclear engineer
@@ReapersRed I'm also biased since gravity is my field of study. But, when it comes to physics, GR is just insane. It totally changes how we see spacetime. It's dynamical now. It's part of the game, and Einstein's equations tell us how. E=mc² is important but on itself isn't a fundamental equation. P²=-m²c² is the fundamental equation (P is the four momentum). Or E²=m²c⁴+p²c². The way I see it is this (it's rather a physicist's perspective I guess): if someone gives you the formula, tells you about the symbols and what they mean and then lets you play with it (experiment with it), E=mc² will be more useful, that's true (on Earth at least. So many results of GR can't be tested easily here, such as black holes etc) but also, after sometime you'll see that it's wrong (it's frame dependant). It doesn't always work. While Einstein's equations always work (at the Einstein gravity framework let's say, which is much larger than the framework in which E=mc² works). That's what I mean by more fundamental. Especially when it comes to relativity what you'd do is give these equations and then Newton's law (+ geodesic equations) and everything else is derivable from these. dS² is the key of relativity. You know that, you prove everything else. And you find that by solving Eisenstein's equations.
This is incorrect. General relativity does nothing about the "privileged" nature of inertial observers, this is a common misunderstanding. Also a metric is what you get as a solution of the Einstein equations, you can't deduce anything from "the metric" because there is no "the metric", there is infinitely many of them and all are solutions to the EFE.
When first exposed to logarithms people often get hung up on which base is being used (and it is important in some situations - the natural log in calculus for example), but the properties of logarithms used to simplify arithmetic work in every base. That is what makes them so fundamentally useful.
Yes, logarithm was used before exponential arrived on the scene as a method to speed up multiplication by replacing them with addition. Base was something like 1.00001, close to 1.
The description of the Maxwell's equations apply for a vacuum. Charge and current densities are missing here, and thus do not correlate with what you tried to explain afterwards.
One small correction: Maxwell's equations have a different form in the general case. It should be: ∇ · *D* = ρ ∇ × *E* = - ∂ *B* /∂t ∇ · *B* = 0 ∇ × *H* = *j* + ∂ *D* /∂t where *D* is the electric displacement vector(which depends on *E* but also the polarization), *B* is the magnetic induction, ρ is the local charge density, and *j* is the local current density. Also, the 1/c factor in your video comes from Gaussian units, but in standard SI units, there is no 1/c.
The Einstein Field equations should really be shown for relativity instead of E = mc^2. The simplified reduction to rest mass energy is much less important than the other aspects of relativity.
Definitely not. Special relativity pops out of Maxwells equations, but e = mc^2 is truly something revolutionary. It fundamentally changed our understanding of how every conservation equation works at its core. We learned all chemical and nuclear reactions are fundamentally changing from energy to mass or Vice versa. All continuity equations are just energy balance at the end of the day. The only people that care about space-time curvature from general relativity are astrophysicists, but so many fields care about mass energy equivalence.
@@ReapersRed This is the rebuttal I would give too lol. Also how tf can you explain Einstein Field Equations in the same way as E = mc^2, it doesn't exactly roll of the tongue.
Funnily enough the Maxwell Eq's as shown describe none of the effects advertised, bc you only showed the source-free version that can only describe light in an empty space.
@ 0:39 The analogues of the trigonometric rules in non Euclidean geometry are approximately the same as the ones in Euclidean geometry if the sides are very small
Those were Maxwell's equations for vacuum. No charge, no divergence. Same for curl of H: the j current is missing if you want to consider the general case, not only vacuum.
Nah most of is ODE , when working in classical mechanism, i found that. I cant solve Lagrange equation without know how to solve ODE , so i found the paper in library for a month ,then collect pieces of information in many major from economy, fluid mechanic , social science , chemistry, electrical engineer, industry design, architecture , computer science . i found that all that product/model that the majors are currently using is ODE form or a expression of eignvalue of ODE .😅 i take a advantage that school only teach how to calculate, so if i know ODE form i can solve all topic of relevant major, and it true . in accounting and law they mostly using algebra and tree thoery, mixed human factor . then i reveal the world " godfather" according relevant topic both legal and illegal, then it lead me to a rich rss as know as social science. right now. I m development tool to efficiency the knowledge flow , it will be released in further. Moreover , the value which is the partial value of ODE sometime called as "MARCO" , fine, complex, formula ... It have many form, and suffix "ian" ,which mean perform smt ,make the world " mathematician " really have own. meaning. Thanks to visit my TED talk
From the beginning of video to schrodinger i was like oh i know that but after schrodinger it was like oh its whole new level shit i dont even know about one thing in that equations even though video gives me the information about the terms.Still far away from understanding universe.
ENTROPY? MEASURE OF DISORDER? Completely incorrect, entropy has nothing to do with order. Entropy is related to the number of possible micro states, which increase in the path to equilibrium.
1:18 “The most common bases are 10 and 2”
Natural log/log base e: am I a joke to you?
They are *ln*
@@akshat_senpai too bad for me! i thought they're Out
I thought that too. haha.
@@akshat_senpaiactually mathematicians just use log and it’s understood that we mean ln
@@justinjames2436 i was taught that if you put log it means you have base 10
Important fact, special relativity doesn't say that the laws of physics are the same for everyone, just for inertial observers. GR says that the laws of physics are the same for everyone. Also E=mc² by far isn't the key equation in relativity. I'd write down the Einstein field equations G=8πT, or the metric dS² (as a function of x,y,z,ct) or both. From these you would be able to deduce everything whike E=mc² isn't even coordinate independent
I disagree, the field equations have much less of a profound impact on most applications than mass energy equivalence. E=mc² changed our understanding of all chemical and nuclear reactions. It also made every continuity equation an energy balance. I may be biased tho bc I’m a nuclear engineer
@@ReapersRed I'm also biased since gravity is my field of study. But, when it comes to physics, GR is just insane. It totally changes how we see spacetime. It's dynamical now. It's part of the game, and Einstein's equations tell us how. E=mc² is important but on itself isn't a fundamental equation. P²=-m²c² is the fundamental equation (P is the four momentum). Or E²=m²c⁴+p²c². The way I see it is this (it's rather a physicist's perspective I guess): if someone gives you the formula, tells you about the symbols and what they mean and then lets you play with it (experiment with it), E=mc² will be more useful, that's true (on Earth at least. So many results of GR can't be tested easily here, such as black holes etc) but also, after sometime you'll see that it's wrong (it's frame dependant). It doesn't always work. While Einstein's equations always work (at the Einstein gravity framework let's say, which is much larger than the framework in which E=mc² works). That's what I mean by more fundamental. Especially when it comes to relativity what you'd do is give these equations and then Newton's law (+ geodesic equations) and everything else is derivable from these. dS² is the key of relativity. You know that, you prove everything else. And you find that by solving Eisenstein's equations.
well ur biased maybe because ur newton and einstein stole ur fame feel u bro
This is incorrect. General relativity does nothing about the "privileged" nature of inertial observers, this is a common misunderstanding.
Also a metric is what you get as a solution of the Einstein equations, you can't deduce anything from "the metric" because there is no "the metric", there is infinitely many of them and all are solutions to the EFE.
thank you for your wise words isaac
When first exposed to logarithms people often get hung up on which base is being used (and it is important in some situations - the natural log in calculus for example), but the properties of logarithms used to simplify arithmetic work in every base. That is what makes them so fundamentally useful.
Yes, logarithm was used before exponential arrived on the scene as a method to speed up multiplication by replacing them with addition. Base was something like 1.00001, close to 1.
The description of the Maxwell's equations apply for a vacuum. Charge and current densities are missing here, and thus do not correlate with what you tried to explain afterwards.
Then why don’t you make a video instead of complain g in the comments?
@@levelup2014he pointed out a flaw in the video so that we can all be better informed, this is not a negative thing
@@levelup2014hey, if i want to criticise a president, does that mean i have to be a president first to be able to?
@@levelup2014why don't you grow some balls and realise he just pointed out mistake for people who are interested
Damn nigga tf ia current density that's sounds tuff asf gotta learn about to it
1:19 What, no love for the natural log, base _e??_
i was gonna say it had to be higher than base 2 even
you just earned a new subscriber!
One small correction: Maxwell's equations have a different form in the general case. It should be:
∇ · *D* = ρ
∇ × *E* = - ∂ *B* /∂t
∇ · *B* = 0
∇ × *H* = *j* + ∂ *D* /∂t
where *D* is the electric displacement vector(which depends on *E* but also the polarization), *B* is the magnetic induction, ρ is the local charge density, and *j* is the local current density. Also, the 1/c factor in your video comes from Gaussian units, but in standard SI units, there is no 1/c.
The Einstein Field equations should really be shown for relativity instead of E = mc^2. The simplified reduction to rest mass energy is much less important than the other aspects of relativity.
Definitely not. Special relativity pops out of Maxwells equations, but e = mc^2 is truly something revolutionary. It fundamentally changed our understanding of how every conservation equation works at its core. We learned all chemical and nuclear reactions are fundamentally changing from energy to mass or Vice versa. All continuity equations are just energy balance at the end of the day. The only people that care about space-time curvature from general relativity are astrophysicists, but so many fields care about mass energy equivalence.
@@ReapersRed This is the rebuttal I would give too lol.
Also how tf can you explain Einstein Field Equations in the same way as E = mc^2, it doesn't exactly roll of the tongue.
@@freniisammiiI mean, it's relatively easy to explain it in layman's terms. The hard part of the EFEs isn't the concept, it's the mathematics.
Funnily enough the Maxwell Eq's as shown describe none of the effects advertised, bc you only showed the source-free version that can only describe light in an empty space.
THIS IS AMAZING STUFF!!!!
hopefully one day i ll come back to this video, truly undrerstanding all the equations.
slight mistake, eulers polyhedra formula only states true if the body has no holes aka isnt a torus in topology
This kinda looks like one of Ian Stewart's books
Everyone is complaining about the lack of source fields in Maxwell’s Equations while I can’t believe you wrote them in GAUSSIAN UNITS 😭
@ 0:39 The analogues of the trigonometric rules in non Euclidean geometry are approximately the same as the ones in Euclidean geometry if the sides are very small
7:16 slight mistake, the divergence of the E-field is not 0. Other than that amazing video 😁
Those were Maxwell's equations for vacuum. No charge, no divergence. Same for curl of H: the j current is missing if you want to consider the general case, not only vacuum.
Bell's Inequality, Euler's Identity
Woke mathematical justice warriors, whinging about equality and identity maths.😆
No.... There not
@@LordMarcusyour accounts older than me,dang
Nah
@@LordMarcus is this satire
7:38 div.E= rho/r ( in which rho is density and r is distance of point charge) isn't it?
Great video!)
Nice
Informative
Yes, I've read "17 equations that changed the world" too.
Isn't black-scholes just navier stokes partial solution recontextualized? Why is navier stokes on there twice?
5:42 interesting set of limits
Yes, he took an interval [a,b], and kicked it all the way to the left so that we don't see it again...
I sent this to my friend who hates math to make him faint. 😂
euler lagrange equation?
Bro you just explain the book of the king Ian stewart but it s cool
3:50 number 0 comes under the whole number set
Love your channel!!!!!
Decibels are the logs I roll!
3:50 Isn't 0 an Integer, not a Natural number?
You do realise that natural numbers are integers?
It depends. In Peano arithmetic, 0 is a natural number. Other constructions of N don't include 0 however.
@Tsbwi82 All natural numbers are integers but not all integers are natural numbers
SCIENCE IS AWESOME🗣🗣🗣🗣🗣🔥🔥🔥🔥🔥🔥💯💯💯💯💯💯💯
What is V + F - E = 2 useful for?
Important in material science
Important for graph theory
Topology
It was literally explained in the video that it was crucial for topology and physics
for finding the penile length, here V = 2 (2 balls), F = 4 (Number of sperm ducts + fallopian tubes) and E = 2 (Mental agility)
principle of least action?
Where is the variational principle?? Giving birth to the principle of stationary action, basically the most fundamental principle in physics.
Schrodingers equation, at its core,is actually a variant of the heat equation
And not the wave equation?
New subscriber
ΔU = Q - W
I'm so mad, at least you included entropy lol
1:12 TPOT mention lol
Retard. Retard.
Where are the dual bases equations bruh
Uhm, the standard model langrangian?
laplacian?
Lagrangian
@@Quant_mL i was confused with the laplace transform
The normal distribution misses a minus in the exponential. Good video otherwise :)
Maybe he intends it for imaginary x 😂
Yang-Mills wasn't here lol
Note the word ***Crucial***
V+F-E=2
Nah most of is ODE , when working in classical mechanism, i found that. I cant solve Lagrange equation without know how to solve ODE , so i found the paper in library for a month ,then collect pieces of information in many major from economy, fluid mechanic , social science , chemistry, electrical engineer, industry design, architecture , computer science . i found that all that product/model that the majors are currently using is ODE form or a expression of eignvalue of ODE .😅 i take a advantage that school only teach how to calculate, so if i know ODE form i can solve all topic of relevant major, and it true . in accounting and law they mostly using algebra and tree thoery, mixed human factor . then i reveal the world " godfather" according relevant topic both legal and illegal, then it lead me to a rich rss as know as social science. right now. I m development tool to efficiency the knowledge flow , it will be released in further.
Moreover , the value which is the partial value of ODE sometime called as "MARCO" , fine, complex, formula ... It have many form, and suffix "ian" ,which mean perform smt ,make the world " mathematician " really have own.
meaning.
Thanks to visit my TED talk
Cool
DRAKE's equation
From the beginning of video to schrodinger i was like oh i know that but after schrodinger it was like oh its whole new level shit i dont even know about one thing in that equations even though video gives me the information about the terms.Still far away from understanding universe.
🤣 same
Not trying to sound in rude and toxic tone
I never made any content for you and I am not present in this video or any content
Stop talking like that.
I thought I was the only one who noticed
ENTROPY? MEASURE OF DISORDER? Completely incorrect, entropy has nothing to do with order. Entropy is related to the number of possible micro states, which increase in the path to equilibrium.
entropy is a measure of disorder, more possible microstates = more disorder
@@sanjeev9581Correct. Entropy is defined as the degree of disorderness or randomness only.
Kewl
It‘s not Leonard Euler. It‘s Leonhard Euler. Please learn how to pronounce the names correctly.
since when logarithms are equations at all lol
BREATHE
E = 89875517873681764m