Where do particles come from? - Sixty Symbols
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- เผยแพร่เมื่อ 20 พ.ย. 2024
- Professor Ed Copeland discusses the origin of particles - including talk about inflation, re-heating, the Big Bang, and oscillons. More links and info below ↓ ↓ ↓
New paper by Ed and collaborators...
Formation and decay of oscillons after inflation in the presence of an external coupling, Part-I: Lattice simulations: arxiv.org/abs/...
More Ed on Sixty Symbols: • Ed Copeland - Sixty Sy...
Ed's trilogy on the sofa: • Ed Copeland Longer Int...
Ed discusses his career on the Numberphile Podcast: • An A-Class Reject (wit...
Reheating after Inflation by Kofman, Linde and Starobinsky: arxiv.org/abs/...
Oscillons: Resonant Configurations During Bubble Collapse: arxiv.org/abs/...
Patreon: / sixtysymbols
The University of Nottingham physics: bit.ly/NottsPhy...
Sixty Symbols videos by Brady Haran
Animation by Pete McPartlan
www.bradyharanb...
Email list: eepurl.com/YdjL9
More Ed on Sixty Symbols: th-cam.com/play/PLcUY9vudNKBNtF1y-sneLuyCTE-Mda561.html
Can you ask professor to explain the "flat" universe bit? I didn't understand most of what he was saying, but that part wasn't logical at all to me.
@@conanobrien1 curvature of space can be measured by measuring angles. Say you have laser beam and direct it with mirrors in such a way that the beam makes a complete triangle. In a flat space the sum of angles in such triangle would be 180 degrees, same what is used in Euclidean geometry. If the space has a negative or positive curvature, the sum of the angles in such triangle could be larger or smaller than 180 degrees
Have you changed microphones for recording or changed compressor, audio sound to polished and weird. Ed´s voice sounds different.
@@jormam69 Would that be the same (similar) as when they say big objects (black holes or galaxies) curve space-time?
We need more Prof Copeland on the whiteboard.
Love hearing Brady's questions - it's like having a representative for physics interested amateurs like me - but asking the right key questions. amazing video as ever...
It’s the opposite of political interviews, when the journalists always seem to be half asleep and never ask the most obvious questions.
Professor copeland is the professor we never had in uni/school but one we always wanted. Great to see him again on 60 symbols
This is the best condensed explanation of the inflation model I've heard. Great science communication.
Yeah, most understandable of all I heard too.
Incidentally, the only one also.
My favourite Sixty Symbols professor :)
I do like his delivery
Ye, mine too.
His disposition is just so different from the image I have in my mind when someone says "physics professor," and it is wonderful.
yes
All the presenters are excellent, but i must say he is my favorite too (Tied with Sir Martyn I suppose)
I love how he talked so enthusiastically about those ocelots.
Yes, they love to vibrate when they purr.
@@jacobscrackers98 THIS! YES! 🤣😂🤣😅
Baboo...?
Yes, like a new David Attenborough
ocelots give me the shits
Maybe call the initiation of inflation "The Cold Open".
That’s brilliant!
In Universe Res?
If it's within an eternal inflation model, call it the "quick stop."
Naaah, I suggest The Blow Out.
@@aretorta prolapsed singularity?
Well then.
I've been following physics with a rather close layman's interest for about 45 years and this is the first time I've heard that the "hot big bang" came _after_ inflation.
Quite a revelation for me and it makes me want to see an episode of Sixty Symbols or Numberphile where someone with the level of knowledge of Dr Copeland is in the middle of this sort of explanation and suddenly stops, gets a blank, mildly puzzled look on his face, says, "I've just thought of something I hadn't before," and goes into some furious computation which results in the solution to a heretofore unsolved physics/mathematics problem, yielding a massive breakthrough in the field.
So let's get crackin' guys!
You're got roughly a one hour in 60 years chance of that happening 😅
HBB is not equal to BB. BB was BEFORE inflation, HBB is just a new fancy term for saying "after inflation".
@@schawo2 Hm. I must have misinterpreted what the video was saying. I'll give it another look.
Thanks.
It's because the whole thing is still conjecture and we really don't know whether there even was a beginning
@@dan.j.boydzkreationz a "beginning" makes no sense for the universe.
i always love Professor Copeland and his giddy excitement explaining the fine details in the maths leading to the speculative conclusions and especially his recognition of their benefits and flaws. he's always ready to answer Brady's harder questions and can point immediately to the maths for any given wonderment. its stuff like this that inspires me to further pursue astrophysics as a career
"you need a better term for the start of inflation"
I feel like this is a good point to incorporate the term Horrendous Space Kablooie, introduced by the Watterson-Calvin-Hobbes paper.
Excellent video! 🎉 Many thanks for the kind reference to our work (and our new paper at the end). Ed and Brady rock !! Will think of a new term for the start of inflation in our next paper :-)
I'm just going to give a second plug for my suggestion "The Cold Open", like the pre-credit scene in movies or shows. ^_^
If something hasn't yet inflated it must be a period of flacidity? ;)
Without a doubt. Ed is just one big cuddly hug of physics.
I'll nominate "The Big Breath", such as one would take before inflating a balloon. It would make the creationists happy and maybe they'd shut up for awhile.
is there a name for the sound you make right before you blow up a balloon? like ya know, the gulp of air you take as you lean back slightly and tilt your head up in preparation for blowing it up. Insufflation is the only word that comes to mind. though that's an imperfect fit.
WOW!!! That was by far THE Single BEST video this channel has produced in the last 13 years! It was deep, didn't dumb it down, explained it beautifully and filled a bloody big hole in my understanding of cosmology! I can't thank you enough! I can't wait to see what happens to the expansion rate of 1/H as Dark Energy becomes better understood; assuming I'm still here! BIG *_Thankyou!_*
"...where we think these particles come from." Such an important and wise phrasing... and then there're articles and documentaries stating these hypotheses as fact. I wish more educators were like Prof. Copeland.
We need way more Ed Copeland on this channel!
I love your drive to name things, scientists are spending all their energy on doing science and leaving none left for the creativity of naming things.
When we let physicists name things, we get “quarks” which have “flavors” like “charm” and “strange”
@@AdamKlingenberger They need a branding manager, stat. =:o}
This is complicated.
That's why it's fun!
Fun is measured by the size of the aneurysm 😂
Favourite Professor, calm, focused, competent
The curvature of space thing is better illustrated by talking about the principles of Euclidean geometry. There are a few ways to approach it, but for me what comes to mind first is stuff about infinite parallel lines. In a flat space, parallel lines remain parallel forever; in a positively curved space, parallel lines will converge, and in a negatively curved space, parallel lines will diverge. This works the same if you're talking about a 2d surface (the ball and saddle visuals there) as well as 3d space. Gravity introduces positive curvature, and Dark Energy introduces negative curvature, and it turns out it all seems to balance out at larger scales making the Universe as a whole "flat" in all ways that have been attempted to measure it (IIRC, in general the margin of error is so small in most circumstances the curvature is treated as just being perfectly zero).
Professor Copeland, it's always very nice to listen to this gentleman.
There ought to be more content with him on youtube.
cannot go wrong with an Professor Copeland video :)
prof copeland is not only very nice, but always very insightful
So if I understand, we now differentiate between some initial singularity and a "hot" big bang ? Wasn't aware of that.
Seems everything starts and ends with scalar fields, while everything else is just a consiquence.
Can't be easy to present such complex ideas in a simplified way for others to be able to grasp, great team work by Prof. Ed Coperland & Brady.
My 10 year subscription and I’m so excited to see a rare Ed new video dropped Thanks guy!
Thanks for your loyalty.
@@sixtysymbols
1) When was space-time born?
2) Where the initial insane amount of Potential Energy comes from?
3) If mass is created by interaction with Higgs and that interaction bends space then is gravity the interaction with Higgs?
FreeCourseWare from TH-cam here in the states has been incredible, with that said your channel and specific content is the cherry on top. Thank you sincerely Sixty Symbols I always recommend the channel to others.
Sincerely.
@@sixtysymbols So he says the system of equations is nonlinear 21:00, right? So I assume whatever system of nonlinear equations he is talking about are PDEs (partial differential equations) or even combinations of PDEs and functional and integral equations.
That's what we differential algebraists work on. We work on finding exact solutions. I own three large handbooks by Soviet authors on differential equationd, the largest of which is the 2nd edition of "Handbook of Nonlinear Partial Differential Equations" by Andrei D Polyanin and Valentin F Zaitsev, followed by 2nd edition of "Handbook of Linear Partial Differential Equations for Engineers and Scientists" by Andrei D Polyanin and Vladimir E Nazaikinskii, and 2nd edition of "Handbook of Exact Solutions for Ordinary Differential Equations". The ODE book is especially full of exact solutions of different types of nonlinear ODEs.
All of the solutions are obtained by looking at differential symmetries of the ODEs. I still do not understand quite how they are getting these symmetries. The ODE book, but especially the nonlinear PDE book, have excellent sections on the general theory of differential symmetries. But, I cannot match that general theory up with the many many examples of exact solutions they find.
I would really LOVE to sit down with somebody to help me work that out together.
Nevertheless, one very general pattern that arises from these solutions is that ALL of them can be expressed, parametrically, by a finite tower of intermediate variables, where one variable in this tower satisfies a linear ODE over the differential ring generated by the variable below it. i.e. given G(x,y,dy/dx)=0 there exists a tower v1, v2, v3,..., v(m), t and another tower w1, w2, w3,..., w(n), t and some final common variable, t, below it, such that x satisfies a linear ODE w.r.t. t over Z{v1} = differential ring generated by v1=v1(t) over the integers, Z, with derivation D such that Dt=1, and v1 satisfies a linear ODE w.r.t. t over Z{v2} and so on until v(m) satisfies linear ODE over Z[t].
Similarly, y satisfies a linear ODE w.r.t. t over Z{w1} = differential ring generated by w1=w1(t) over the integers, Z, with derivation D such that Dt=1, and w1 satisfies a linear ODE w.r.t. t over Z{w2} and so on until w(n) satisfies linear ODE over Z[t].
I’ve been watching this channel for a long time since I was in high school. I love that I keep learning new things now that I am finishing my bachelor’s degree and starting my master’s soon. I absolutely loved this episode as early universe cosmology is an area I really fell in love with. My thesis work was on multi-field inflation, and I got to explore the many interesting effects of perturbations during these inflationary scenarios as well as how inflation ends in these cases. Additionally, I met Dr. Fernando Quevedo earlier this year, who told me a great deal about oscillons from his work of string phenomenology. So I absolutely loved this episode and I am eager to learn more about this line of research.
The joy this guy eminates is incredible :) I am so glad we pay him to do this kind of stuff.
Wow I have been studying physics and cosmology on my own since 13 years old now I am 52 . That Professor explained the Hot Big Bang and inflation better than anything I have ever heard or read . He should write a book on it I never heard anything close to that simple of an explanation without hardcore math involved.
Any day with a new video from Ed is literally the best day of the year.
I had been wondering what Dr. Copeland was up to. I don’t understand it, but it’s good to hear from him anyway
I love this channel so much, and Professor Copeland has a true gift for explaining what I'm sure are immensely difficult topics. Thank you from California for all the great work!
The part about the oscillons' role in cosmological phase transition made me think of an emulsion that arises during a chemical phase transition.
Phase separation can occur in a solution when a change to its physical or chemical properties means that the lowest energy state will now be achieved when one component becomes a separate phase instead of part of the solution. Sometimes this occurs rapidly, but sometimes an emulsion forms, in which the phases form intermixed bubbles or particles. These bubbles are inherently unstable, since the lowest energy state is for the phases to be completely separate. But they can sometimes take an extremely long time to gradually disappear.
it feels like seeing the professor after 100yrs
I eagerly await the Ed Copeland workout video.
While this was a higher level video, I truly enjoyed watching this one. Really opened my mind about the nature of what we think of as the start of everything. Thank you Brady and Mr. Copeland!
The best explanation of Inflation. Period.
You really have to appreciate how prof Copeland can stay true to the theory and explain it so a bar maid (or ave yuts watching TH-cam) can understand it.
Great video. He always makes these complex concepts understandable.
More maths on sixty symbols!! This was incredible. We need more of this! There is no accessible physics that show maths!! Please Brady!
Mr Copeland seems like the kind of guy who I could find at a pub and still learn from after I've had a few drinks
I love Professor Copeland's amusement. He obviously enjoys what he is doing.
Did the inflaton field vanish completely (from the Lagrangian?) or is it like the top quark field whose particle can still be accessed at the right conditions? Does it contribute to the universe's vacuum energy density?
Great collaboration between Brady and Ed. Very educational.
Flatness is best described with triangles.
Triangles made in flat space are 3 angles that add up to 180 degrees.
Very very large triangles measured across the observable universe likewise would have 3 angles adding up to 180 degrees.
Brady coming in hot with the banger questions again. Always a pleasure to watch
original big bang is when the singularity start to expand
inflation (which should be considered a bigger bang) is when the expansion rate is very fast
'hot big bang' (which doesn't have any bang) is when the energy turns into mass
Love Ed he's one of the best, you can always feel his enthusiasm and it's contagious.
Ed Copeland is such a likeable chap. I have no idea of what he's talking about, and I have an undergraduate understanding of physics with an engineering degree. Usually, when I hear these crazy ideas of theoretical scientists, I have no patience for them, but Ed is such a likeable guy.
Thanks Brady. You've built a great library of videos, all through the sciences. Have you no engineers in Nottingham?
🧙🏼♂️🇺🇲
Very informative. I am none the wiser but I really enjoyed listening.
Would be cool if there were a 3D simulation of curved space and objects in it, so we can experience it more vividly
Excellent material guys. I have been digging on INFLATION for a long time and you guys provided lots of new info. I love it. Thanks.
The idea of the universe being flat must be one of the most misunderstood concepts in physics. I can't count the number of times I've talked to laypeople who have heard this and think it means the universe is a flat plane. Unfortunately I don't think the professor's answer to your question innthis video helped that cause.
Maybe this warrants a special video in the style of your old "does light slow down in glass" video, to set the record straight.
in all fairness its not a very intuitive concept and it can be difficult to explain to people that you might call a layperson. I get the ideas needed and its still sometimes hard to wrap my mind around the idea of it.
@@1104Tea Yeah, I've tried to explain large scale spatial curvature to a few different people with mixed success. The classic analogy people always use is the surface of the earth, but extending to 3 dimensions is tricky. One guy didn't even believe me when I said parallel trajectories on earth come together. Plus there's the distinction between intrinsic and extrinsic curvature...
I think i got a better appreciation of "the metric of spacetime" by playing around with simpler metrics. With chess distance one diagonal step has the same length as one axis-aligned step, meaning that a circle (i.e. constant distance from the center) has the shape of a square. With manhattan/taxicab distance one diagonal step is two axis-aligned steps, meaning a circle has the shape of a rhombus. Understanding that the very notion of "distance" depends on how/what we measure felt like a revelation.
But curvature is about direction rather than distance (i think). I still don't really understand what the heck intrinsic curvature means. Maybe the best analogy is still the Asteroids video game. It takes place on a flat surface but the edges are connected making it topologically a torus 🤷♂️
@@mxlexrd Try going with "Stand on the equator; we'll all walk due north on parallel paths. And it then gets crowded by the time you reach Canada." ;)
It's a really simple concept. Just tell them that 'flat' means all lines on a 3D grid are parallel and straight!
Ed is a top presenter. great guy.
Unrelated but I always loved instructors that use “We” and “our” taking about science. “When we are looking”, “We could be living on a sphere” etc
I feel like we just got let in on some physics secrets. A fascinating glimpse of how these scientist really think and view things. Thanks Brady and Dr. Copeland! :)
this is definitely the most confusing lesson. It's awesome but posing so many questions, like why does the process when the particles got diluted by the inflaton field stop? It's because the potential energy of the field reached a certain frequency at that point. I really need more explanation on the energy, frequency parts, like some example maybe. Thanks Sixty Symbol and Professor Ed a lot for this amazing video.
This specific area is worthy of at least a dozen more videos, perhaps with collaborators, such as other channels in the "Bradyverse", and Matt at PBS Space Time. Or perhaps start with a master playlist of the best videos in this area, with new content only to fill gaps and/or generalize the whole.
The Hot Big Bang starts with the unification of almost all fields, where at increasing energy levels the electromagnetic and weak fields unify into the electroweak field, and the other fields unify at ever higher energies until all are unified into a single "grand" field. It is thought the Higgs is the second field to separate, preceded only by the inflaton, with the others following in short order. The "Cold" Big Bang creates (or is created with) the unified field (that also includes the inflaton), and it is the separation of the inflaton field that drives the HBB.
Or at least that's what I gather to be the case. I've not kept up well with research in this area.
As the temperature of the universe continues to drop, each combined field separates in turn, excitations in that field create both the specific force-carrying particles and the particles upon which they act, such as the photon being the force carrier between charged particles for the electromagnetic field, and gluons being the force particles between quarks in the strong field. With other fields for the quark colors and flavors.
However, the photons in the plasma presumed to be present in the electromagnetic field when it separates is NOT what we see as the CMB! The CMB was generated much later, by a different mechanism.
What determines the temperature at which each field will separate (with cooling) or will unify (with heating)? What determines what happens within each field as it separates? (The Higgs in an especially delicious example.)
Professor Copeland shows that even superficial exposure to the math can yield fascinating diagrams that in turn can motivate high-level discussion in a generally comprehensible manner. I had not previously heard of "oscillons", yet quickly comprehended how they fit into the overall picture.
More please!
Excellent video ! And this did remind me of my 9th grade research paper and oral presentation in 1994 on this topic. I think that I only had less than 5 minutes, and the chalk was flying all over the place as I tried to demonstrate the various epochs. I do believe that the rough draft of this must be stored in a box somewhere, but alas I have not found it yet.
On a side note, something is off with Ed's audio signal there is a strange modulation and/or reverb that is occurring. Please take a look at this in post production, as it was slightly distracting.
So interesting and intriguing. I was just thinking about where particles come from yesterday and then this video appeared! Yay!
Fascinating! Nice delivery from Professor Copeland.
Always love Professor Copelands videos! Especially the one on cosmic superstrings.
Ironically, flat universe might be the way to talk sense into the flat earthers. We just have to frame it like they were so close. They weren’t wrong, just wrong scale. They were “right all along” and don’t have to “feel bad.”
I'm always fascinated by how much effort the simulation puts into its hand waving and pseudo world building.
Great video. Please make more advanced videos like that!
I love that Brady is always thinking about names for things, it's gotta have a snappy name!
so glad to see this channel still going 👍👍👍
Its always a great day when the new video its with professor Copeland
I'd love more videos of the good Dr. Copeland explaining the mathematical side.
A reference to a Brazilian scientist, Marcelo Gleiser. Let's go 🇧🇷
This was soo interesting! Ed should DEFINITELY write a book about this stuff!!!
Hey David quick question do whales become more communist if we leave them in an elliptical low earth orbit?
@@evanm6739 yes
“We’re currently inflated and we’re like a melon…” Brady, you crack me up! 😂😂😂
Yesssss this is right up my alley, can't wait to hear Prof Ed speak on this
Please more with Professor Copeland.
This is profound - one of the first bit of theoretical physics that seems both grounded and groundbreaking. There are so many ideas here I've never heard of - is this an established area of research, or is Prof Copeland giving the pre-amble to a massive publication from his team?
The idea of inflation (slow roll and eternal) has been around since the 1980's.
The real mystery is how does that last bit of toothpaste seem to last longer than the rest of the tube did?
I was thinking the same thing
This was mind blowing and enlightening to me!
Well explained and intuitively taught
So he says the system of equations is nonlinear 21:00, right? So I assume whatever system of nonlinear equations he is talking about are PDEs (partial differential equations) or even combinations of PDEs and functional and integral equations.
That's what we differential algebraists work on. We work on finding exact solutions. I own three large handbooks by Soviet authors on differential equationd, the largest of which is the 2nd edition of "Handbook of Nonlinear Partial Differential Equations" by Andrei D Polyanin and Valentin F Zaitsev, followed by 2nd edition of "Handbook of Linear Partial Differential Equations for Engineers and Scientists" by Andrei D Polyanin and Vladimir E Nazaikinskii, and 2nd edition of "Handbook of Exact Solutions for Ordinary Differential Equations". The ODE book is especially full of exact solutions of different types of nonlinear ODEs.
All of the solutions are obtained by looking at differential symmetries of the ODEs. I still do not understand quite how they are getting these symmetries. The ODE book, but especially the nonlinear PDE book, have excellent sections on the general theory of differential symmetries. But, I cannot match that general theory up with the many many examples of exact solutions they find.
I would really LOVE to sit down with somebody to help me work that out together.
Nevertheless, one very general pattern that arises from these solutions is that ALL of them can be expressed, parametrically, by a finite tower of intermediate variables, where one variable in this tower satisfies a linear ODE over the differential ring generated by the variable below it. i.e. given G(x,y,dy/dx)=0 there exists a tower v1, v2, v3,..., v(m), t and another tower w1, w2, w3,..., w(n), t and some final common variable, t, below it, such that x satisfies a linear ODE w.r.t. t over Z{v1} = differential ring generated by v1=v1(t) over the integers, Z, with derivation D such that Dt=1, and v1 satisfies a linear ODE w.r.t. t over Z{v2} and so on until v(m) satisfies linear ODE over Z[t].
Similarly, y satisfies a linear ODE w.r.t. t over Z{w1} = differential ring generated by w1=w1(t) over the integers, Z, with derivation D such that Dt=1, and w1 satisfies a linear ODE w.r.t. t over Z{w2} and so on until w(n) satisfies linear ODE over Z[t].
I really like to learn from Prof. Ed Copeland.
Okay, we're having this conversation. So...when a mommy particle and a daddy particle love each other very much....
Cant daddy particle love another daddy particle?
Too funny! I came down to suggest the name "Conception".
@beebhaz as long as they they're both positive (or both negative) they should get along quite well
This is like an early Christmas present i adore Sixty Symbols (10 years goes by Fast!)
…a stork particle brings them a baby particle, and that’s how you create a family…i mean, hadron.
No idea how I wasn't aware of Ed being from Nottingham. I just visited from Australia a few months ago. Oh well.
This channel remains a true gem.💙
This Copeland guy is fantastic! cheers from Spain!
I wish Professor Ed had his own podcast or something
After all this time, Brady just learned that a dot above a dependent variable means take the time derivative. Yet he follows the mathematical story told by Prof. Copeland very well.
Thank you so much!
Very interesting.
Glad you enjoyed it!
I can feel my brain melting and slowly dripping out of my ear.
Ed Copeland. I've never clicked faster to watch a vid.
Is there some sort of effect or compression on Ed's voice in this particular video? It almost sounds like his audio is clipping or he's been autotuned.
Yeah! I was looking for this. Sounds like it been pitched down or he's got a cold or something
I'm not complaining or trying to be rude!
Glad I wasn't alone in this thought. Feels like there may be distortion from any audio level normalization is my guess, since Ed isn't wearing a microphone and his distance from the mic probably isn't constant
Mic broke, so we had to fix up the camera audio the best we could
An absolutely flat universe is exactly what would be expected if the total energy content of the universe equals zero. Then again there could be a false vacuum (but that's something that would need an additional explanation).
Any recommended book about this reheating phase of universe?
I love this corner of youtube!
Professor Copeland. My favourite. Thanks for a very nice video
Its been too long since Ive seen a Prof Copeland vid.
One thing I can't wrap my head around is the idea of anything happening "in a few 10^(27) seconds" BEFORE time exists.
Same here. Time is not supposed to exist without space, that's why Einstein called it spacetime! So where is this exotic oscillating supposed to be taking place?
The universe is believed to be flat, but it also has a finite volume and it’s “borderless”. If you move in one direction, you eventually end up where you started. The way I like to think about it, is like in these old space games where you have to shoot other ships and avoid asteroids. Your space ship is always displayed in the middle, but the space and everything in it moves in the opposite direction that you are moving in. And in the corner of the screen there is a map of the whole universe where you see your space ship moving, but if you leave the map on one side, you come out on the other side.
This game is 2D, but you can easily imagine it in 3D. It’s basically a cube with the opposite sides identified.
Great video! Did anyone else notice this: It felt like Eds voice was sounding somewhat strange sometimes, like if there was some resonance ;-) of another mic or something, that was interfering
The microphone broke, and they had to use the on-camera microphone. (Explained in another comment.)
Ah, the gall of trying to explain inflation to the public like this - what a shameless attempt to condescend ... I mean, everyone in the field knows, that no one out there could grasp it, and then you, prof.Copeland have the audacity to come out here, and in 25 mins accomplish the impossible…
…but seriously, thank you prof. for taking a swing at it, I never heard anyone communicate about it as you - without getting lost (and losing us) in the detailed analytics of it, etc. You are a powerfully gifted communicator, not “just” your rank-and-file incredibly brilliant mind. :-)
Thanks for applying yourself to this for our sakes!
There's a third mode of reheating oscillation called the Big Crunch enhancer, where the sled gets coated with non-nutritive cereal varnish. It's semi-permiable. It's not osmotic. What it does is it coats and seals the flake, prevents the milk from penetrating it.
Fantastic video! This is what I'm here for!
This matter of curvature is one that's often neglected or glossed over, and yet it's fairly intuitive if you look at it from the right perspective.
To set this up, we have the four dimensions of spacetime. If we want to talk about those dimensions being like a kind of grid, it's not hard to imagine that grid being twisted. The video shows some possible shapes, such as spheres or cylinders or saddles.
I always assumed that these shapes would have to exist in higher dimensions. A piece of graph paper or wire mesh itself has basically two dimensions, but if you roll it up into a cylinder, that takes place in three dimensions, right? So it's natural to think that if spacetime is curved, there must be a fifth dimension for it to live in.
Well, yes, that works, and if we had separate evidence of that higher dimension then we'd be justified in saying that it exists. But so far we don't have any such evidence.
Meanwhile, there's another mathematical explanation which takes care of the curvature without adding dimensions. It's called a "manifold" and really it's just a richer way to talk about geometry, curvature in particular. So let's take a little sidebar about that.
The standard way to picture how a manifold works is to think of ourselves as little two-dimensional beings on the surface of a sphere. Because we only experience two dimensions, we think that the surface is flat. But we're about to find out we're wrong. If it were flat, then when we go to survey the surface, we expect to be able to draw a square with four sides of equal length and four right angles. When we draw a small square in this way, it seems to work well. But as the size of the sides becomes much larger, it becomes more obvious that the square doesn't join up properly.
The point is that we never had to go beyond our perception of two dimensions in order to figure out that something isn't adding up. We've detected a curvature. With careful measurement, we could figure out the rules of how to account for that curvature. Those rules define the manifold for our surface.
Sure, to help with the initial visualization I said that we were living on a sphere, which of course involves a higher dimension. But the people on the surface don't know that. They don't even need to think in those terms, because they can use the manifold instead as a complete description.
You won't be able to visualize this next step, but think about it. If they've got the manifold and it works for them, does there even need to be a sphere in reality, or a higher dimension? Strange as it seems, they're in a two-dimensional reality that's "curved" solely by the rules of the manifold, not in some higher dimension.
Q:Whats this thing that cause magnets to attract each other?
A: We dont really know
Q:what happened 13.8b yeara ago?
A:that we know precisly well, Universe apeared out of nothing just like that.
Nope, both answers are "we don't fully know"
When professor Copeland retires, he has an ASMR-artist career waiting for him.