+RimstarOrg Absolutely. Pr. Copeland is one my favorites of the show :) His very smooth voice giving clear explanations, with the twinkle of passion always in his eyes...
I lost track of it too. It reminded me of Uni - a professor writing equations all over the board that took top scientists 10 years work to figure out & I was supposed to absorb it in a few minutes.
Sadly, we will never have another person quite like Albert Einstein. His intuition with regard to the universe was wholly unique, and is very missed to this day.
Prof. Copeland's elementary school teacher tone of voice to explain the most mind-blowing concepts is just perfect! And his "Yes, please" @ 16:48 just made my day! lol
I know you try and keep the maths to a minimum with these videos, and leave it up to people to research more thoroughly if they're interested, but this is probably one of the most interesting videos on your channel (for me, at least), even with the maths.
Believe me - regarding maths in relativity you only see the tip of the iceberg in this vid. He showed the main result of the Einstein equations for an isotropic and honogeneous universe. He skipped how to derive the basic form of the metric by evaluating the cosmological principal, he skipped to derive the energy momentum tensor of a radiation dominated universe and he skipped evaluating the field equations for the Robertson Walker metric - all this taken together yields the equations you've just seen. Great Video though and straight to the point.
16:45 'Yes, please' - I find this a really genuine and heartwarming comment from the professor.
7 ปีที่แล้ว +15
Even Einstein's so called "blunder" (it really wasn't), was genius. It's the constant we now use to describe dark energy and dark matters' effect on the acceleration of the expansion of the universe. Even when he's "wrong" he's still right. He really was a Super-genius.
I would ask him to critique Bell's 1964 paper. What I think would happen is that Einstein would say that since clocks are affected by gravity, the twin particles would not age in phase locked synchrony, so that the presumptive hidden variable would not vanish, but would result in a residual non-zero "beat frequency." And then, Einstein would dub that "spooky timekeeping at a distance."
I love this professor Copeland, he's my favorite. There's a sweet something in his eyes. He seems a very gentle passionate man. Very soothing and easy to listen to.
Professor Copeland is my favorite from these videos. He is just so good at riding the line between explaining a topic so that the "average person" can understand it and diving deeper for those with a larger interest.
+Kobil Shakur Thing is, even Numberphile is not very ''math'' heavy... It's often a lot of playing with numbers or math explained, but purely logically. I agree with what I've seen here; it's very refreshing to see something that isn't dumbed much down, unlike the usual content on Brady's channels (No offense by it, but yeah :P)
I agree, more maths in Physics videos! It does not need to be long derivations of formulas, just equations like this where you can say: look, this here is the term related to the mass of the universe, this is the pressure, this is the cosmological constant. It IS called Sixty Symbols after all, show us the symbols! :-)
Senrade2 It is undeniably heavy on the maths for a Sixty Symbols video. That's in no way to say that it is objectively heavy. So while you are correct that the only maths actually shown in the video is algebra (with the actual solving of all involved differential equations left out for obvious reasons), that's kind of irrelevant.
Niven42 actually my knowledge of the math involved is roughly equivalent to that of a brick. However after each set of equations the prof takes a few seconds to make an easy explanation for us lesser beings that makes it possible for us to keep up with the narrative. So for me it goes.... blah blah equations blah.. what this means is that for this to work this funny squiggle must be zero.... because Maths. Which is fine for me.
+Niven42 I don't have any understanding of the math involved. But explained like this, it was very easy to follow along and get the 'gist' of what he means. Prof Copeland is the best
I really love these slightly more mathematical videos! Brady, i know that you are uncomfortable putting too many equations in your videos, but i think that your audience think they are just they provide just enough intrigue! really enjoyed this video
Excelent video. Please make more longer videos. Especially with prof Copeland and Merrifield. And also let them use more equations. Thank you very much.
"Blunder" is a bit of an overstatement. He did science, he followed an hypothesis and it was proven wrong. It's ok if Einstein was wrong, that's what science is for.
Prof. Copeland, you can see the passion in your eyes and hear it in your voice, almost like child like wonderment, I love it! I so wanna sit in on one of your lectures; I don't know if I would have the background to understand most of it, but it would be freaking amazing :D
More equations, please. They are the meat of physics and therefore should not be shunned upon. This is, by far to me, the best Sixty Symbols video precisely because it explains physics as physics are: formulae, and their interpretations.
Francis Galiegue Except he did an awful job at actually explaining any of them. Equations are fine, but meaningless and even obfuscating if you're just going to carelessly skim over the terms and relationships.
Francis Galiegue My bet is you're either afflicted by an inflationary sense of comprehension, or have some background in physics and are simply as poor a communicator as buddy in the video.
For me, Maths helps me understand Physics. I can look at an equation and gain some insight into the relationship of the terms. Please, in future increase the amount of Maths on the channel as it allows people like me to see where relationships come from in Physical systems.
Albert Einstein new about "Mass-SPACE relation", however he applied "Static" = "Infinite sponge" = "Non-Space-Expandable Universe" (just added to Newton "Sponge Structural-Geometrical Deformation Ability") (logic - if space is infinite= can't further to expand) into General Relativity model and than Edington "proved it" (he "measured" light bend - 0,00000000000000000000000000000001% of a single radius degree, as a "Flag Evidence".. hmm "how u can measure if its a wave" so precisely anyway, by tracking single photons?) in 1925 or 1919? ...but then Mr Edwin Hubble in 1929 completely demolished Einstein's "Static Universe" by discovering that "Universe is expanding" (they just didn't realise that it was "Space Expansion"), but false statements never been dismissed. They were "updated" - new solutions/transformations added to the equations, but "main conclusion" that "mass not curves, but expands space=distance effectively", never been noticed ("Cosmological Constant" MIA) and this is the reason why Invisible Ghosts of Dark Energies" overtaken XX century physics.
"This" is a "Real Physics" = description of the energy transformation mechanism. What u "practicing" with "math calculations" (can u explain what "physical truths" you reveal with your mathematics?) got nothing to do with the real physical model.
You can even do and call it "Master degree of the Universe Math Champions", but that has nothing to do with a real physics which is description of energy transformations. As a pupil or scientists you got no idea even about ATOM EXPANSION POSSIBILITY (and that's BASICS OF THE THERMODYNAMICS) , you got no idea either about MACROSCOPIC UNIVERSE where mass cumulating in nucleuses of stars and galaxies expands space . So honestly i got no clue what is all about... when you claim : "math helped me to understand physics" (how that could happen).
Great video and a great explanation. I love the use of "more maths" in this video while still keeping it on a reasonable level for people like me (some math knowledge but far from an expert).
I am no mathematician, but more equations please, Brady. Particularly with the explanatory glosses you added. They really helped me understand better. Thanks for a fascinating video!
Professor Copeland is really always very clear and he has a way to use equations which is xtremely understandable. Please make more videos with him and its equations.
_If I could conjure up Einstein and bring him into the room now- - Yes, please._ * little smile * The whole thing is great, but this is my favorite part of the interview.
I would ask him to critique Bell's 1964 paper. What I think would happen is that Einstein would say that since clocks are affected by gravity, the twin particles would not age in phase locked synchrony, so that the presumptive hidden variable would not vanish, but would result in a residual non-zero "beat frequency." And then, Einstein would dub that "spooky timekeeping at a distance."
I have always thought these videos needed both a layman explanation as well as a more rigorous explanation for those more knowledgeable or curious. Needless to say, despite Brady not wanting all the math, I very much appreciated it. Thanks for the video!
As many others, looking at the posts before this, I also liked the equations. Having them clearly explained while writing them down, made them really helpful understanding it all. More equations please.
At 5:05 essentially what youre saying is that at some point when the density of mass = 0 which will happen eventually if I am not mistaken about the eventual fate of our universe is that double flux alpha will be 0 in which case our universe will stop expanding
This is exactly why I'm so intrigued by physics. That fact that you can describe such a complex concept like the curvature and form of space with math and that the answers to that equation tell you so much about it. It is just wonderful :)
Edmund "Ed" Copeland is a theoretical physicist, cosmologist, and professor of physics working in the Faculty of Science at the University of Nottingham, United Kingdom. Copeland won the 2013 Rayleigh Medal and Prize awarded by the Institute of Physics for his work on particle/string cosmology.
My eyes go blind at the equations, even when pausing the vid, but I followed the principles and loved the notion of checking to see if there is stability in the equation - extra insight. I can only consider my interest in physics from a lay perspective, but I watch these and always walk away with a bit more each time and a bit deeper down. I love em
I enjoyed the maths here, please keep it up guys. If possible I have a suggestion here: I like the way you explain things but sometimes you don't go sufficiently into details and it seems too superficial, so I suggest that you categorize your videos to categorize your videos to 3 types: level 1: general public level 2: scientists and engineers in general level 3: specialists of the field of the talk and experts You can put a label indicating the category of the video that keeps showing in (let's say) the top left corner of the video With respect
Is there a book that describes the history of physics in terms of dates and people involved with the theory (or at least main points) of their papers like we have in 15:58 ?(obviously with greater detail than this, I give the timestamp only as a reference to what I am looking for in general)
Does Einstein say at 0:42 "es ist mir eine Freude, und zusatz eine Ehre"? (I'm learning German and I'm not sure if that is what he says, or I am misunderstanding).
I don't understand if Lamda or Dark energy contributing negatively in that Friedman equation then how it causes the universe's expansion. It is helping gravity in that equation so it should be the cause for the contraction of the universe. please answer!
LOVE that Prof. Copeland worked the equations! I feel I know (this aspect) of GR better. Of course, Prof. Copeland teaches it very well. Brady: more equations (well taught), please.
do a video about deriving e=mc2. i wana know how its done, someone explaining it in the way i can understand. minutephysics did it but he was way2 fast and didnt explain propely.
+bastard You ultimately want to understand where E=mc^2 comes from, I recommend first starting where the Lorentz Transformations come from (they're the equations that show how frame of reference affects space and time in relativity). After that E=mc^2 is a short derivation away. But without understanding the Lorentz Transformations first, no derivation of E=mc^2 will ever make sense to you.
+bastard I recently did a derivation of E=mc^2, and I'll tell you that unless you're comfortable with four vectors and stuff, you won't get much of a derivation. The key is the time part of the momentum four vector, but most people show that it's equal to E/c by assuming already that E=mc^2 or assuming the total energy, which seems like cheating. I was only able to do it by "intuitively" defining the momentum four vector and comparing the time part to the momentum four vector as it's derived from the action equations of motion. The "intuitive" bit started with the position four vector with (ct) as the time part.
Zuzu Superfly yup i just checked out those, looked like a headache. i have better things to do with my life at this point, its exam week going on. didnt look too overwhelming but i will give that a look once i have time
I would actually love to see more of the mathematics in these videos. Really wonderful stuff to think about whilst drinking a cup of coffee in the morning. Maybe I'm weird.
I really like this video, it's one of my favourite Sixty-Symbols ones so far :). The equations didn't detract from the video - the opposite is the case, they greatly aided my understanding. Thanks guys!
im so pleased when i look at the comments and see people not being scared off by the equations, embrace them! they are the best way to understand physics imo. wonderfully explained as well.
Thank you for offering a clear explanation, particularly around perturbation. It left be wondering if young Einstein had known about dynamical systems or tensors if he would have spent so much time on the cosmological constant.
Isn't making the "non relativistic matter assumption" you quote at 9:30 already excluding the speeds at which today the universe is being observed to expand? So Einstein used his assumption in a way that is less transparent than it is made to appear in the video, when you deduce the formula relating k, Lambda etc?
November 1915 was when the E-man published the four seminal papers on his general theory of relativity. Champagne corks pop for the passage of 10^2 years, which is of great significance to those of us with ten fingers.
So this space equation, what system is it in relation to? I mean like is it like drawing a volume around the entire universe and assuming it is like a uniformly distributed sphere? So is it a conservation of something equation?
Eisnteins belief that there was an elegant order to the world was his success, but once he discovered that order, his belief in it stopped him from going any further...
Please let the professors use equations in the videos more often. They made this one so much easier to follow!
Yep! agree with you ✌(......🤔)
Even if you can't calculate it all it does help to follow along
Absolutely!! He explains them beautifully, and they really help.
You can really understand why they say what they say when you have equations as opposed to when they go “so we crunched the numbers”
16:45
"If I could conjure up Einstein and bring him into the room right now..."
*dead serious* "Yes please."
That made me laugh so much :D
Beyork.
If ANYTHING could persuade the universe to bring Einstein back, surely it would be Professor Copeland's soft, hear felt "Yes, please."
I enjoyed Professor Copeland's gentle and interesting telling of the story of those equations! You should unleash him more often, Brady. :)
+RimstarOrg ^This :D
+RimstarOrg Absolutely. Pr. Copeland is one my favorites of the show :) His very smooth voice giving clear explanations, with the twinkle of passion always in his eyes...
he's strangely comforting
Lost track of the maths about halfway through but kept listening :)
I lost track of it too.
It reminded me of Uni - a professor writing equations all over the board that took top scientists 10 years work to figure out & I was supposed to absorb it in a few minutes.
"Yes, please."
I love this guy. He's my favorite.
16:44
Such a pure, innocent response! His eyes looks like that of a child who has just been offered ice cream haha
Sadly, we will never have another person quite like Albert Einstein. His intuition with regard to the universe was wholly unique, and is very missed to this day.
Jovetj we will.
@@jovetj i am sure people said the same thing after Newton
That "Yes, please" at 16:85 was kind of sweet.
+Elliott Collins
Yes, he's adorable.
+Anders23 was gonna say the same thing. its funny that this player can actually wrap 85 secs in min
did it stop being able to now?
Prof. Copeland's elementary school teacher tone of voice to explain the most mind-blowing concepts is just perfect! And his "Yes, please" @ 16:48 just made my day! lol
"You MOCK my equations!"
This is how supervillains are born.
You may mock my equations, mortal, but I shall rule the world with the power to create atom bombs........ wait. That was a bit too real..
Lol yeah, also every supervillan has a PhD, "Dr.this", "Dr.that" you may be onto something!
I know you try and keep the maths to a minimum with these videos, and leave it up to people to research more thoroughly if they're interested, but this is probably one of the most interesting videos on your channel (for me, at least), even with the maths.
+Ben F The math is the most interesting part.
+Oliver Ocean Agreed.
+Oliver Ocean it's very basic math too. And it's seeing the scientists' interpretations of the equations that is the most intriguing part for me.
I know, I think the same. Sadly he hadn't follow the trend :(
Believe me - regarding maths in relativity you only see the tip of the iceberg in this vid. He showed the main result of the Einstein equations for an isotropic and honogeneous universe. He skipped how to derive the basic form of the metric by evaluating the cosmological principal, he skipped to derive the energy momentum tensor of a radiation dominated universe and he skipped evaluating the field equations for the Robertson Walker metric - all this taken together yields the equations you've just seen. Great Video though and straight to the point.
16:45 'Yes, please' - I find this a really genuine and heartwarming comment from the professor.
Even Einstein's so called "blunder" (it really wasn't), was genius. It's the constant we now use to describe dark energy and dark matters' effect on the acceleration of the expansion of the universe. Even when he's "wrong" he's still right. He really was a Super-genius.
thanks for explaining this to thousands of people just like you were talking to a friend!
+Cr42yguy he was! :)
i know, it's just nice to be able to participate :)
+Cr42yguy Exactly the reason why i love Sixty Symbols. :)
+Cr42yguy I wish I could understand
He is one of my favorites!
16:44
"If I could conjure up Einstein and bring him into the room right now..."
"Yes please!"
I would ask him to critique Bell's 1964 paper.
What I think would happen is that Einstein would say that since clocks are affected by gravity, the twin particles would not age in phase locked synchrony, so that the presumptive hidden variable would not vanish, but would result in a residual non-zero "beat frequency."
And then, Einstein would dub that "spooky timekeeping at a distance."
Hah, yeah, Professor Copeland was quick with the "yes please", like a kid being asked if they want candy.
couldnt follow it .....no brown paper.
+00Billy that's Numberphile only! :)
Sixty Symbols hehe..only watched EVERY video...and never noticed that...lol Thanks.. Still, the brown paper is better !
+00Billy ow silly billy
+Sixty Symbols maybe do a 2 hour Numberphile + Sixty Symols GR math video with Prof. Copeland?
+Elios0000 now this is what I want to see.
Although PBS spacetime have a great GR playlist
I love this professor Copeland, he's my favorite. There's a sweet something in his eyes. He seems a very gentle passionate man. Very soothing and easy to listen to.
Professor Copeland is my favorite from these videos. He is just so good at riding the line between explaining a topic so that the "average person" can understand it and diving deeper for those with a larger interest.
you guys should have more videos that have math
+Ansh Shah no, go to numberphile for that
Kobil Shakur most of physics is based on math , I don't see why they don't include Math in their videos.
P.s - I know what numberphile is.
Ansh Shah look it up, you're def going to enjoy it
+Kobil Shakur Thing is, even Numberphile is not very ''math'' heavy... It's often a lot of playing with numbers or math explained, but purely logically. I agree with what I've seen here; it's very refreshing to see something that isn't dumbed much down, unlike the usual content on Brady's channels (No offense by it, but yeah :P)
+justarandompally true story.
Professor Copeland is absolutely phenomenal at explaining things, what a privilege it must be to attend one of his courses.
Really heavy on the maths this time, I like it :)
+Richard Melcher Could be even more for me. Maybe in a bonus video for those who want it :)
I agree, more maths in Physics videos! It does not need to be long derivations of formulas, just equations like this where you can say: look, this here is the term related to the mass of the universe, this is the pressure, this is the cosmological constant. It IS called Sixty Symbols after all, show us the symbols! :-)
+Richard Melcher Really heavy? This is only algebra.
+Senrade2 really heavy compared to usual.
Senrade2 It is undeniably heavy on the maths for a Sixty Symbols video. That's in no way to say that it is objectively heavy. So while you are correct that the only maths actually shown in the video is algebra (with the actual solving of all involved differential equations left out for obvious reasons), that's kind of irrelevant.
I do not fear the equations.
Plug and chug or You shall not pass.
You merely adopted the field equations.
In Soviet Russia, _equations_ fear *you*
@@avinotion Because all you're going to do is manipulate the poor bastards.
"I'm not afraid"
"You will be, _you will be._ "
Can't discuss these topics in depth without the maths. Keep it coming!
wtf brady? i like this math. and i'm pretty sure most of ur viewers appreciate it as well.
THANK YOU. FINALLY...... Something that is not dumbed down beyond recognition.
+poseidon In my opinion, including the equations made the whole thing a lot easier to follow. I hope other physics topics get the same treatment.
+poseidon Agreed. I think most of us who would watch videos like this have already some basic understanding of the math involved.
Niven42 actually my knowledge of the math involved is roughly equivalent to that of a brick. However after each set of equations the prof takes a few seconds to make an easy explanation for us lesser beings that makes it possible for us to keep up with the narrative. So for me it goes.... blah blah equations blah.. what this means is that for this to work this funny squiggle must be zero.... because Maths. Which is fine for me.
+Niven42
I don't have any understanding of the math involved. But explained like this, it was very easy to follow along and get the 'gist' of what he means. Prof Copeland is the best
I totally agree . This video is useful. I’m tired of dummed down fluffy arguments.
I really love these slightly more mathematical videos! Brady, i know that you are uncomfortable putting too many equations in your videos, but i think that your audience think they are just they provide just enough intrigue! really enjoyed this video
Excelent video. Please make more longer videos. Especially with prof Copeland and Merrifield. And also let them use more equations. Thank you very much.
You should do another round of long interviews w prof Copeland, those were great!
This is one of my very favorite videos on the sixty symbols channel.
This is my favorite Professor :)
"Blunder" is a bit of an overstatement. He did science, he followed an hypothesis and it was proven wrong. It's ok if Einstein was wrong, that's what science is for.
Einstein himself called it a blunder.
The blunder is he already had the solution in some of his equations but removed it because he was too stubborn to accept the universe was expanding .
@@brainimp His "blunder" was his failure to make yet another brilliant conjecture to stun the world of science.
@@brainimp It wasn't even known then if the universe included objects beyond the Milky Way. Give them some space.
Yay Ed! We need more Ed videos. I'd like one on how Feynman developed his diagrams and how they solve problems in new and interesting ways.
I wish that in other videos you guys used MORE equations! This was wonderful!
"Yes please." That was the highlight of the video for me. Can't stop smiling.
I think the community is ready for more math heavy videos . I am sure the professors will be happy. Awesome work Brady and the professors
I would absolutely love more videos like this explaining the Mathematics behind relativity and quantum mechanics!
Prof. Copeland, you can see the passion in your eyes and hear it in your voice, almost like child like wonderment, I love it!
I so wanna sit in on one of your lectures; I don't know if I would have the background to understand most of it, but it would be freaking amazing :D
This was fantastic! I would love it if this channel did a seminar or lecture type video on physics with all the mathematics included.
Thank you very much for including some equations. it makes everything more clear
More equations, please. They are the meat of physics and therefore should not be shunned upon.
This is, by far to me, the best Sixty Symbols video precisely because it explains physics as physics are: formulae, and their interpretations.
Francis Galiegue Except he did an awful job at actually explaining any of them. Equations are fine, but meaningless and even obfuscating if you're just going to carelessly skim over the terms and relationships.
***** awful job?? That is your opinion; my opinion is quite the opposite, his explanation was spot on
Francis Galiegue "Spot on" is irrelevant in a discussion concerning effective communication.
***** if _this_ communication was not effective to you, I don't know what communication will ever be, to be honest.
Francis Galiegue My bet is you're either afflicted by an inflationary sense of comprehension, or have some background in physics and are simply as poor a communicator as buddy in the video.
For me, Maths helps me understand Physics. I can look at an equation and gain some insight into the relationship of the terms. Please, in future increase the amount of Maths on the channel as it allows people like me to see where relationships come from in Physical systems.
Albert Einstein new about "Mass-SPACE relation", however he applied "Static" = "Infinite sponge" = "Non-Space-Expandable Universe" (just added to Newton "Sponge Structural-Geometrical Deformation Ability") (logic - if space is infinite= can't further to expand) into General Relativity model and than Edington "proved it" (he "measured" light bend - 0,00000000000000000000000000000001% of a single radius degree, as a "Flag Evidence".. hmm "how u can measure if its a wave" so precisely anyway, by tracking single photons?) in 1925 or 1919? ...but then Mr Edwin Hubble in 1929 completely demolished Einstein's "Static Universe" by discovering that "Universe is expanding" (they just didn't realise that it was "Space Expansion"), but false statements never been dismissed. They were "updated" - new solutions/transformations added to the equations, but "main conclusion" that "mass not curves, but expands space=distance effectively", never been noticed ("Cosmological Constant" MIA) and this is the reason why Invisible Ghosts of Dark Energies" overtaken XX century physics.
What, exactly, does this have to do with Maths helping me understand Physics?
"This" is a "Real Physics" = description of the energy transformation mechanism. What u "practicing" with "math calculations" (can u explain what "physical truths" you reveal with your mathematics?) got nothing to do with the real physical model.
I do a Physics degree. Everything I do is explaining the physical significance of the maths.
You can even do and call it "Master degree of the Universe Math Champions", but that has nothing to do with a real physics which is description of energy transformations. As a pupil or scientists you got no idea even about ATOM EXPANSION POSSIBILITY (and that's BASICS OF THE THERMODYNAMICS) , you got no idea either about MACROSCOPIC UNIVERSE where mass cumulating in nucleuses of stars and galaxies expands space . So honestly i got no clue what is all about... when you claim : "math helped me to understand physics" (how that could happen).
please do more videos like this where the equations are included. This was so much more elegant than just explaining it with words only.
Great video and a great explanation. I love the use of "more maths" in this video while still keeping it on a reasonable level for people like me (some math knowledge but far from an expert).
I am no mathematician, but more equations please, Brady. Particularly with the explanatory glosses you added. They really helped me understand better. Thanks for a fascinating video!
Professor Copeland is really always very clear and he has a way to use equations which is xtremely understandable. Please make more videos with him and its equations.
_If I could conjure up Einstein and bring him into the room now-
- Yes, please._ * little smile *
The whole thing is great, but this is my favorite part of the interview.
I would ask him to critique Bell's 1964 paper.
What I think would happen is that Einstein would say that since clocks are affected by gravity, the twin particles would not age in phase locked synchrony, so that the presumptive hidden variable would not vanish, but would result in a residual non-zero "beat frequency."
And then, Einstein would dub that "spooky timekeeping at a distance."
This 19 min was packed with real insights and maths of the story behind cosmological constant. Awesome presentation!
Brady should do more sixty symbol videos with maths like in this video. really enjoyed it.
One of the best Sixty Symbols videos. Thanks for not editing out the equations!!
One of your best videos, Brady. Great work! And kudos to Prof. Copeland as well.
Brady let the man speak, we are not afraid of equations! This is good stuff!
I have always thought these videos needed both a layman explanation as well as a more rigorous explanation for those more knowledgeable or curious. Needless to say, despite Brady not wanting all the math, I very much appreciated it. Thanks for the video!
more videos with math like this! Love to see it even more in depth.
It is nice to see the maths behind physics once in a while. I think that you guys should show it more frequently
As many others, looking at the posts before this, I also liked the equations. Having them clearly explained while writing them down, made them really helpful understanding it all. More equations please.
What a delight to listen to Ed Copeland talking about early 20th century cosmology and Einstein's evolving stance on it.
I read a book about the universe, and I'm pretty sure that Lambda is going to turn out to be 42.
That's great!
The equations are lovely, definitely want more
I wish people would realise that just because they don't understand mathematics, it does not mean that the rest of use don't either.
At 5:05 essentially what youre saying is that at some point when the density of mass = 0 which will happen eventually if I am not mistaken about the eventual fate of our universe is that double flux alpha will be 0 in which case our universe will stop expanding
This was very interesting. I'd be interested in seeing more videos about Einstein.
This is exactly why I'm so intrigued by physics. That fact that you can describe such a complex concept like the curvature and form of space with math and that the answers to that equation tell you so much about it. It is just wonderful :)
Wonderful talk! Please let there be more equations Brady. I'm sure 60-70% of your audience here can keep up with the equations.
Edmund "Ed" Copeland is a theoretical physicist, cosmologist, and professor of physics working in the Faculty of Science at the University of Nottingham, United Kingdom. Copeland won the 2013 Rayleigh Medal and Prize awarded by the Institute of Physics for his work on particle/string cosmology.
Personally, I like the videos that go through the actual equations. I tend to understand that easier than trying to use words
"If I could conjure Einstein and bring him into the room--"
"Yes please"
Thanks for this explanation. It seems like this perspective was really needed to be shown because it sorta clears a lot of things up.
My eyes go blind at the equations, even when pausing the vid, but I followed the principles and loved the notion of checking to see if there is stability in the equation - extra insight. I can only consider my interest in physics from a lay perspective, but I watch these and always walk away with a bit more each time and a bit deeper down. I love em
I enjoyed the maths here, please keep it up guys. If possible I have a suggestion here: I like the way you explain things but sometimes you don't go sufficiently into details and it seems too superficial, so I suggest that you categorize your videos to categorize your videos to 3 types:
level 1: general public
level 2: scientists and engineers in general
level 3: specialists of the field of the talk and experts
You can put a label indicating the category of the video that keeps showing in (let's say) the top left corner of the video
With respect
Love the excitement at 16:45 on Professor Copeland's face when Brady mentioned getting Einstein into the room.
Is there a book that describes the history of physics in terms of dates and people involved with the theory (or at least main points) of their papers like we have in 15:58 ?(obviously with greater detail than this, I give the timestamp only as a reference to what I am looking for in general)
I very much enjoy this type of video where equations are included but not a lot of detail for deriving them is given
Does Einstein say at 0:42 "es ist mir eine Freude, und zusatz eine Ehre"? (I'm learning German and I'm not sure if that is what he says, or I am misunderstanding).
Thanks so much for this upload! Brilliant video! :D
+Palvindar Chhokar you're welcome
I don't understand if Lamda or Dark energy contributing negatively in that Friedman equation then how it causes the universe's expansion. It is helping gravity in that equation so it should be the cause for the contraction of the universe. please answer!
LOVE that Prof. Copeland worked the equations! I feel I know (this aspect) of GR better. Of course, Prof. Copeland teaches it very well. Brady: more equations (well taught), please.
Can you make a video on deriving the equations like why is it 4 pi G and 3p over c^2 and why is some of the terms added and some multiplied
Very happy to see The professor Ed Copeland back on Sixty Symbols. Thank you Brady!
do a video about deriving e=mc2. i wana know how its done, someone explaining it in the way i can understand. minutephysics did it but he was way2 fast and didnt explain propely.
+bastard jsan
+bastard You ultimately want to understand where E=mc^2 comes from, I recommend first starting where the Lorentz Transformations come from (they're the equations that show how frame of reference affects space and time in relativity). After that E=mc^2 is a short derivation away. But without understanding the Lorentz Transformations first, no derivation of E=mc^2 will ever make sense to you.
+bastard I recently did a derivation of E=mc^2, and I'll tell you that unless you're comfortable with four vectors and stuff, you won't get much of a derivation. The key is the time part of the momentum four vector, but most people show that it's equal to E/c by assuming already that E=mc^2 or assuming the total energy, which seems like cheating. I was only able to do it by "intuitively" defining the momentum four vector and comparing the time part to the momentum four vector as it's derived from the action equations of motion. The "intuitive" bit started with the position four vector with (ct) as the time part.
Zuzu Superfly i just went thru a college long mathematics vector class so im not scared of few vectors
Zuzu Superfly yup i just checked out those, looked like a headache. i have better things to do with my life at this point, its exam week going on. didnt look too overwhelming but i will give that a look once i have time
I would actually love to see more of the mathematics in these videos. Really wonderful stuff to think about whilst drinking a cup of coffee in the morning.
Maybe I'm weird.
I really like this video, it's one of my favourite Sixty-Symbols ones so far :). The equations didn't detract from the video - the opposite is the case, they greatly aided my understanding. Thanks guys!
Bring Einstein back?
Yes, please.
Made me cry a little.
We all want longer videos, deeper explanations and more Ed Copeland. :)
Awesome explanation! Copland made it so easy to grasp to a non-physicist like me. Nobody's beyond blunder even if he's Einstein!!!
im so pleased when i look at the comments and see people not being scared off by the equations, embrace them! they are the best way to understand physics imo. wonderfully explained as well.
16:45 hahahaha that reaction/look on his face though "yes please".
We need more maths in those videos Brady!! It's interesting to see the actual maths behind the theory.
is ρ in the numerator or not? what is this notation to write numbers floating next to numerator of a fraction?
Where can I find the proof of equation at 4:11
Is the scaling factor a(t) continuous function?
Thank you for offering a clear explanation, particularly around perturbation. It left be wondering if young Einstein had known about dynamical systems or tensors if he would have spent so much time on the cosmological constant.
Isn't making the "non relativistic matter assumption" you quote at 9:30 already excluding the speeds at which today the universe is being observed to expand? So Einstein used his assumption in a way that is less transparent than it is made to appear in the video, when you deduce the formula relating k, Lambda etc?
I kind of like having the equations. It's cool to look at them and actually understand that each term actually means something.
This was so exciting to see in my subscription feed! Great video! :D
I love how the view count shows how much the info in these videos trumps the subpar video production
Lovely math. Been wanting this out of this channel for awhile.
November 1915 was when the E-man published the four seminal papers on his general theory of relativity. Champagne corks pop for the passage of 10^2 years, which is of great significance to those of us with ten fingers.
Love the equations and working out in this one!
What did Mr. Einstein say at 0:45 ? It sounded a bit unclear to me.
So this space equation, what system is it in relation to? I mean like is it like drawing a volume around the entire universe and assuming it is like a uniformly distributed sphere? So is it a conservation of something equation?
This is the best numberphile video sixty symbols has ever done.
I really wish they used more equations on this channel.
Eisnteins belief that there was an elegant order to the world was his success, but once he discovered that order, his belief in it stopped him from going any further...