Einstein's Famous Blunder - Sixty Symbols

[@ragnkja]

Please let the professors use equations in the videos more often. They made this one so much easier to follow!

[@nishantshah3763]

Yep! agree with you ✌(......🤔)

[@Altorin]

Even if you can't calculate it all it does help to follow along

[@robertelessar]

Absolutely!! He explains them beautifully, and they really help.

[@ahorse7884]

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”

[@Rbedwards94]

16:45 "If I could conjure up Einstein and bring him into the room right now..." *dead serious* "Yes please."

[@Henryguitar95]

That made me laugh so much :D

[@bragg77]

Beyork.

[@robertelessar]

If ANYTHING could persuade the universe to bring Einstein back, surely it would be Professor Copeland's soft, hear felt "Yes, please."

[@elliottmcollins]

That "Yes, please" at 16:85 was kind of sweet.

[@cassandra5322]

+Elliott Collins Yes, he's adorable.

[@shrinidhi111]

+Anders23 was gonna say the same thing. its funny that this player can actually wrap 85 secs in min

[@DanDart]

did it stop being able to now?

[@jesusnthedaisychain]

"Yes, please." I love this guy. He's my favorite.

[@sergiokorochinsky49]

16:44

[@chicoktc]

Such a pure, innocent response! His eyes looks like that of a child who has just been offered ice cream haha

[@jovetj]

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.

[@megamillionfreak]

Jovetj we will.

[@appleslover]

@@jovetj i am sure people said the same thing after Newton

[@RimstarOrg]

I enjoyed Professor Copeland's gentle and interesting telling of the story of those equations! You should unleash him more often, Brady. :)

[@mighty8357]

+RimstarOrg ^This :D

[@ximecreature]

+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...

[@cyprn6600]

he's strangely comforting

[@kelzuya]

Lost track of the maths about halfway through but kept listening :)

[@Bobby-fj8mk]

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.

[@abzanin]

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

[@8ytan]

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.

[@LordOfFlies]

+Ben F The math is the most interesting part.

[@sweetspotendurance]

+Oliver Ocean Agreed.

[@uoy1997]

+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.

[@pabloagsutinnavavieyra2308]

I know, I think the same. Sadly he hadn't follow the trend :(

[@AtotheKres]

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.

[@RemingtonDean]

"You MOCK my equations!" This is how supervillains are born.

[@Henryguitar95]

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..

[@mastershooter64]

Lol yeah, also every supervillan has a PhD, "Dr.this", "Dr.that" you may be onto something!

[@DJTyrrell]

16:45 'Yes, please' - I find this a really genuine and heartwarming comment from the professor.

[@00BillyTorontoBill]

couldnt follow it .....no brown paper.

[@sixtysymbols]

+00Billy that's Numberphile only! :)

[@00BillyTorontoBill]

Sixty Symbols hehe..only watched EVERY video...and never noticed that...lol Thanks.. Still, the brown paper is better !

[@MrMlindsay]

+00Billy ow silly billy

[@Elios0000]

+Sixty Symbols maybe do a 2 hour Numberphile + Sixty Symols GR math video with Prof. Copeland?

[@Overclocked3770K]

+Elios0000 now this is what I want to see. Although PBS spacetime have a great GR playlist

[@CheckeeAintAmused]

16:44 "If I could conjure up Einstein and bring him into the room right now..." "Yes please!"

[@BarryKort]

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."

[@JesseGilbride]

Hah, yeah, Professor Copeland was quick with the "yes please", like a kid being asked if they want candy.

[@Cr42yguy]

thanks for explaining this to thousands of people just like you were talking to a friend!

[@sixtysymbols]

+Cr42yguy he was! :)

[@Cr42yguy]

i know, it's just nice to be able to participate :)

[@Maskinbajs]

+Cr42yguy Exactly the reason why i love Sixty Symbols. :)

[@regpollock9403]

+Cr42yguy I wish I could understand

[@captaintimcurry1713]

He is one of my favorites!

[@funkycude57]

you guys should have more videos that have math

[@kobil316SH]

+Ansh Shah no, go to numberphile for that

[@funkycude57]

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.

[@kobil316SH]

Ansh Shah look it up, you're def going to enjoy it

[@justarandompally]

+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)

[@funkycude57]

+justarandompally true story.

[@ariessweety8883]

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.

[@richmelchr]

Really heavy on the maths this time, I like it :)

[@BSN9ne]

+Richard Melcher Could be even more for me. Maybe in a bonus video for those who want it :)

[@vincentpelletier57]

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]

+Richard Melcher Really heavy? This is only algebra.

[@richmelchr]

+Senrade2 really heavy compared to usual.

[@RQLexi]

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.

[@zZputterZz]

Professor Copeland is absolutely phenomenal at explaining things, what a privilege it must be to attend one of his courses.

[@mignik01]

THANK YOU. FINALLY...... Something that is not dumbed down beyond recognition.

[@ragnkja]

+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.

[@Niven42]

+poseidon Agreed. I think most of us who would watch videos like this have already some basic understanding of the math involved.

[@Kizron_Kizronson]

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.

[@faddenmandolo9638]

+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

[@waynelast1685]

I totally agree . This video is useful. I’m tired of dummed down fluffy arguments.

[@prezwhitehouse]

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.

[@mattlm64]

I do not fear the equations.

[@trevorthompson6155]

Plug and chug or You shall not pass.

[@00bean00]

You merely adopted the field equations.

[@avinotion]

In Soviet Russia, _equations_ fear *you*

[@AlchemistOfNirnroot]

@@avinotion Because all you're going to do is manipulate the poor bastards.

[@pseudonymousbeing987]

"I'm not afraid" "You will be, _you will be._ "

[@Dazbog373]

Can't discuss these topics in depth without the maths. Keep it coming!

[@fr0nage]

"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.

[@brcardoso00]

Einstein himself called it a blunder.

[@brainimp]

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 .

[@Frisbieinstein]

@@brainimp His "blunder" was his failure to make yet another brilliant conjecture to stun the world of science.

[@heh2393]

@@brainimp It wasn't even known then if the universe included objects beyond the Milky Way. Give them some space.

[@acenog123]

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.

[@chillyshotorbitus5152]

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.

[@acenog123]

What, exactly, does this have to do with Maths helping me understand Physics?

[@chillyshotorbitus5152]

"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.

[@acenog123]

I do a Physics degree. Everything I do is explaining the physical significance of the maths.

[@chillyshotorbitus5152]

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).

[@mosab643]

wtf brady? i like this math. and i'm pretty sure most of ur viewers appreciate it as well.

[@MyYTwatcher]

Excelent video. Please make more longer videos. Especially with prof Copeland and Merrifield. And also let them use more equations. Thank you very much.

[@ericisawesome476]

You should do another round of long interviews w prof Copeland, those were great!

[@buzhichun]

_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.

[@BarryKort]

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."

[@ScottMorgan88]

I read a book about the universe, and I'm pretty sure that Lambda is going to turn out to be 42.

[@kentudahl6511]

That's great!

[@pillettadoinswartsh4974]

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.

[@Matiburon04]

"If I could conjure Einstein and bring him into the room--" "Yes please"

[@nateblubaugh729]

This is one of my very favorite videos on the sixty symbols channel.

[@mighty8357]

This is my favorite Professor :)

[@tomwhiteley4126]

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

[@francisgaliegue6645]

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.

[@Ones_Complement]

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.

[@francisgaliegue6645]

***** awful job?? That is your opinion; my opinion is quite the opposite, his explanation was spot on

[@Ones_Complement]

Francis Galiegue "Spot on" is irrelevant in a discussion concerning effective communication.

[@francisgaliegue6645]

***** if _this_ communication was not effective to you, I don't know what communication will ever be, to be honest.

[@Ones_Complement]

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.

[@rockyraccoon]

"Yes please." That was the highlight of the video for me. Can't stop smiling.

[@parasdsingh]

Wonderful talk! Please let there be more equations Brady. I'm sure 60-70% of your audience here can keep up with the equations.

[@Harlequin314159]

Brady let the man speak, we are not afraid of equations! This is good stuff!

[@DanielFoland]

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.

[@alexkolberg9589]

Personally, I like the videos that go through the actual equations. I tend to understand that easier than trying to use words

[@NeedsEvidence]

What a delight to listen to Ed Copeland talking about early 20th century cosmology and Einstein's evolving stance on it.

[@jamieg2427]

I wish that in other videos you guys used MORE equations! This was wonderful!

[@GaelinEruien]

Bring Einstein back? Yes, please. Made me cry a little.

[@enderwiggins8248]

The equations are lovely, definitely want more

[@kongotech2]

16:45 hahahaha that reaction/look on his face though "yes please".

[@curiosity9678]

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

[@saddamalgafsi6721]

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

[@JiveDadson]

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.

[@911gpd]

Thank you very much for including some equations. it makes everything more clear

[@8nwidth]

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.

[@asymptoticspatula]

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).

[@sumdumbmick]

Regarding the discussion starting at 16:45 - This is what I'm talking about when I ask questions about GR and people come in thinking they're providing satisfying answers by repeating basic, basic stuff they heard about it from somebody years ago, and accept as true but don't actually understand. If all you have to fall back on is this type of silly footstomping then you don't understand well enough to attempt an explanation to anyone and you should bow out of a discussion if you cannot participate in it accordingly. It is truly refreshing to see someone admit that GR is not fully understood.

[@cesarjom]

This 19 min was packed with real insights and maths of the story behind cosmological constant. Awesome presentation!

[@sunnysood8702]

Brady should do more sixty symbol videos with maths like in this video. really enjoyed it.

[@Bring_MeSunshine]

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

[@CrackheadMagnate]

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

[@comochinganconesto]

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

[@Philc854]

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!

[@ericpuse5151]

Exactly the amount of math I can understand before getting lost. It's good to let Ed off the reins a little. There is probably a correlation between the amount of symbols used in a video and user comprehension. For me, this is the peak.

[@arthurdent9160]

please do more videos like this where the equations are included. This was so much more elegant than just explaining it with words only.

[@spinvalve]

0:42 Gee, I didn't know Einstein sounded like a chipmunk.

[@RFC3514]

+spinvalve - He did have a pretty high pitched voice, but that clip sounds _too_ high. It may have been filmed at 18 fps and played back at 24. Or it may have been filmed from the top of a train going at 99.8% of the speed of light, of course.

[@joebankerful]

+RFC3514 But i thought the human eye cant see above 1 fps :/

[@RFC3514]

***** - While old microphones weren't very sensitive to low frequencies (leading to a kind of unbalanced "tinny" tone), they couldn't really _shift_ the frequency. Doing that requires either a lot of complex spectral processing or (in 99% of cases) playing the sound back at a different speed (play it faster and the pitch goes up, play it slower and it goes down). Between the 1920s and 1950s it was common to shoot film at 18 fps or less (sometimes the speed even varied _during_ the clip, because the camera was cranked by hand - though that was mostly in the silent era), and there were no embedded timecodes or sync signals (or, in many cases, even a label on the reel saying what speed it had been recorded at). When those films get played back at the "modern" standard of 24 fps (or sometimes even directly at 30 fps for TV, if the telecine operator is _really_ incompetent), the result is that everyone moves very fast and talks with a high-pitched voice. Even a small difference (ex., assuming the film was shot at 18 fps when in fact it was shot at 16 fps) can lead to a noticeable shift in audio pitch.

[@spinvalve]

RFC3514 Figures then. But what has always intrigued me is how Google managed to keep videos from sounding chipmunky even when we speed them up on KZbin.

[@Garbaz]

+spinvalve That isn't really that new of a concept. Most decent pieces of audio software have it built in. Google might be your friend (if you are nice).

[@xXguzman98Xx]

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 :)

[@StrangeAstro]

This was very interesting. I'd be interested in seeing more videos about Einstein.

[@CaseyJMoore]

more videos with math like this! Love to see it even more in depth.

[@AlphasysNl]

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.

[@jordanweir7187]

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.

[@dante224real1]

here's a tiny little observation in defense of einstein's time in putting this all together: what he was trying to justify in the equation of space time and physical matter was that a(t) would change at an equal rate to the velocity of mass within it, and i could see how he might mistake that for "if one side is static, then the velocity would also remain zero" and he went with that as a means to study energy=mass variants and light speed variants. basically he wanted to say v=0 so he could make the big picture simpler for himself. we know now that its not that simple, but back then he was doing most of this by himself on a chalk board and a set of typewriters. we can't really blame him for it.

[@soulcatch]

Love the excitement at 16:45 on Professor Copeland's face when Brady mentioned getting Einstein into the room.

[@johnpearcey]

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.

[@pypes84]

This is the best numberphile video sixty symbols has ever done.

[@squidcaps4308]

What if.. there is a very very weak repulsive force that gets stronger with distance. So we have never noticed it as in the grand scale we always have about one googolplex stronger gravity.

[@tingla1]

This was fantastic! I would love it if this channel did a seminar or lecture type video on physics with all the mathematics included.

[@unclesam997]

I kind of like having the equations. It's cool to look at them and actually understand that each term actually means something.

[@Grungen1]

Ed should really get into recording audio books.

[@jonathan.gasser]

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...

[@JK03011997]

I very much enjoy this type of video where equations are included but not a lot of detail for deriving them is given

[@danielmachado3848]

16:45 "yes please '' hahahahahaha

[@phil53256]

16:44 every physicists dream. He got a bit excited just by thinking of sitting at a table together with Einstein.

[@karthiknaicker8216]

One of the best Sixty Symbols videos. Thanks for not editing out the equations!!

[@bgoggin88]

They say for each equation you lose half your viewers. If thats true, this video should get -1/12 viewers.

[@commenter4799]

- 1/12? Can we use Euler's constant to calculate how many people hate math? Lol.

[@waynelast1685]

bryangoggin so make two parallel explanations. One with math and one without . You really can’t understand anything without math though. Without math it’s just entertainment.

[@twilightknight123]

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!

[@wyatthess374]

I love how the view count shows how much the info in these videos trumps the subpar video production

[@patrickglieca6431]

I agree with him, entropy is a sad thing. :) Amazing how this one remains me that popping equation from thin air is a sign of mastering... and needs constant work or application.

[@captainrocketblast2529]

Doesn't Relativity have other problems? -Sagnac experiment 1913 -The Clock Paradox ("both can't be slow") - That 2 atomic clocks moving at different speeds have never shown different times?

[@mrsatterthwaite410]

The irony is that Riemann conjectured the form of the universe in his famous doctorate work in front of Gauss, and even he invented the mathematics for the so call Riemann Geometry 70 years before Einstein used it , but Einstein ended winning the glory and Riemann died at the early age of 39... Life is unfair, isnt it ?

[@JK03011997]

I know this is theorethical physics , but if you got "negative pressure" (what ever that might mean in real world terms), you can have a static universe, and probably also a warp-drive

[@parthasarker4650]

Awesome explanation! Copland made it so easy to grasp to a non-physicist like me. Nobody's beyond blunder even if he's Einstein!!!

[@4or871]

I try to combine the cosmological constant and the schrodinger solution on the planck scale. I used planck units. At the end I went back to SI units to compare with the measured vacuum energy density (0.63 10^-9 J/m^3.) Combine: 1) Einstein, cosmological constant 2) Schrödinger solution 3) Planck units Result: - vacuum catastrophe solved? 1)Einstein, cosmological constant Λ = (8π 𝐺 ƐΛ)/(𝑐^4) Planck units: G=1 c=1 Λ (6.1871424 10^34)^-2 = (8π ƐΛ [planckEnergy/planckVolume] 1.1056 10^-52 (6.1871424 10^34)^-2 = 8π ƐΛ 0.001149 10^-120 = ƐΛ 0.1149 10^-122/ ƐΛ = 1 2)Schrödinger solution, n=1 (ℎbar^2 𝑛^2 𝜋^2) / (2𝑚𝐿^2) = E Planck units hbar=1 n=1 m= mplanck =1 L= Lplanck=1 0.5 𝜋^2= E 1= E/0.5 𝜋^2 3)Einstein, Cosmological Constant = Schrödinger solution 0.1149 10^-122/ ƐΛ = 1 = E/0.5 𝜋^2 0.1149 10^-122 0.5 𝜋^2= ƐΛ Eplanck Eplanck =1 0.1149 10^-122 0.5 𝜋^2= ƐΛ 0.567 10^-122 = ƐΛ [planckEnergy/planckVolume] 0.567 10^-122 1.9561 10^9 /(1.61625502 10^-35)^3= ƐΛ [J/m^3] ƐΛ = 2.627 10^-9 [J/m^3] Measured: 0.63 10^-9 [J/m^3] I am looking forward to your response.

[@MichaelEhling]

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.

[@daddsfasdasd]

This is fake they aren't using brown paper! I call they got hacked!

[@Christian.h.]

Brown paper is Numberphile only =)

[@kissassparty]

+Christian Hünnekens and lined stack of paper is for computerphile

[@AMAJAR44]

It is nice to see the maths behind physics once in a while. I think that you guys should show it more frequently

[@karlsykes7710]

I hope you'll opt for explanations like this that are based around maths in the future. On the flip side, the average youtube video probably doesn't have enough time for that in most topics.

[@palvindarchhokar9821]

Thanks so much for this upload! Brilliant video! :D

[@sixtysymbols]

+Palvindar Chhokar you're welcome

[@Erik-yw9kj]

4:06 - he says "c^2 is the speed of light" - doesn't he mean "c^2 is the speed of light squared"?

[@BerkSarikaya]

Yes he means that.

[@VeterannMann]

Dumbass.

[@Azagro]

+VeterannMann Why you so mad? He corrected the man, right?

[@Erik-yw9kj]

VeterannMann Am I the dumbass, or is the professor the dumbass? Or are you just announcing your status so we can all feel free to ignore whatever you say next? Some kind of moron public service announcement?

[@sirbruce1970]

+Erik In cosmological context, physicists commonly set their units so that c = 1, so c^2 is still 1.

[@jorgerangel2390]

I loved the way the equations where explained

[@GFJDean35]

I really wish they used more equations on this channel.

[@andreaorozco9660]

I'm so glad I switched from chemistry to physics! Physics is so fascinating and I want to know more. 😁

[@oleksijm]

Chemistry is also great though.

[@murilotrigo8578]

One of your best videos, Brady. Great work! And kudos to Prof. Copeland as well.

[@psmoyer63]

Professor Copland was able to make the equations speak with great clarity.

[@NoFakerLP]

0:35 He says: "Es ist mir eine Freude und gleichzeitig eine Ehre" That means "It's a pleasure and a great honor at the same time"

[@MatthewSuffidy]

I was thinking that what may be happening is that empty space may have a reverse curvature, and act as anti-gravity between galaxies. If this was the case though, they really shouldn't go faster than the speed of light apart from each other though.

[@PRINCESORH]

Did 14:22 have anyone else in tears laughing? Brady's insistence on Ed's specificity was quite hilarious. Perhaps, this is the wine talking....