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The Biggest Ideas in the Universe | 4. Space 

Sean Carroll
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The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody.
This is Idea #4, "Space." We talk about what is meant by three-dimensional space, why it might be three-dimensional, and why space exists at all. Why do we live in position space, rather than in momentum space, anyway? And what's so important about "locality"?
My web page: www.preposterousuniverse.com/
My RU-vid channel: / seancarroll
Mindscape podcast: www.preposterousuniverse.com/p...
The Biggest Ideas playlist: • The Biggest Ideas in t...
Blog posts for the series: www.preposterousuniverse.com/b...
Background image: wallpapercave.com/w/Pr9hNhy
#science #physics #ideas #universe #learning #cosmology #philosophy #math #space #locality #dimensions

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30 июн 2024

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Комментарии : 437   
@hero227
@hero227 4 года назад
Thanks Sean, for putting out these videos. We often take for granted how the internet grants us a wealth of knowledge at our fingertips, but it's like you're literally giving us a 1-on-1 lesson on these topics from the comfort of our homes. I find them incredibly interesting & informative.
@avrenna
@avrenna 4 года назад
This comment made me pause and reflect for a moment on how incredible it is that we have this ability. "Any sufficiently advanced technology is indistinguishable from magic."
@CMDRunematti
@CMDRunematti 3 года назад
1-on-1 lol... i was asking "yeah but why..." and he actually started explaining what i asked from the video XD
@CMDRunematti
@CMDRunematti 3 года назад
@@avrenna or otherwise: anything that looks magical is probably some fancy tech. knowing this saves you from a lot of woo
@vansdan.
@vansdan. 4 года назад
These videos are exactly what I need. I could listen to you talking about science for hours, and you're granting me that ability; thank you!
@shikulli
@shikulli 4 года назад
FACTS
@avrenna
@avrenna 4 года назад
I love how relaxed and friendly these are. Check out the phenomenal sound effects at 16:43. :)
@beenaplumber8379
@beenaplumber8379 3 года назад
Totally! If my uncle were a physics professor and I asked him to explain all that crazy technical crap to me, he might smile and say sure! Easy! Then we'd sit down over a coffee and this is what would happen. This format helps me learn so much better than lectures. We're just chatting. He knows how much I don't know, but he also knows I have a brain. He just helps me to discover it and explore it. It's bigger than physics. There's a lot of "how to think" in these videos.
@veroosh
@veroosh 4 года назад
I showed this to my dad and it turns out he's a fan too. His words, "he's a really great teacher." I agree.
@harshvardhan4766
@harshvardhan4766 2 года назад
yeah and look at you doing shit like horoscope
@pierfrancescopeperoni
@pierfrancescopeperoni 2 года назад
@@harshvardhan4766 Well said.
@ScattMatt3000
@ScattMatt3000 2 года назад
Tell your dad you love him for me 😞💪… greatest teacher you’ll never truly appreciate.
@hifibrony
@hifibrony 2 года назад
Both Sean and Brian Greene have a remarkable ability to clearly explain highly abstract and complex physics to intelligent and interested non-physicists. Two of my favorite science communicators, along with Jim al-Khalili and Brian Cox.
@soulremoval
@soulremoval 4 года назад
so grateful the internet exists, letting people like Dr. Carroll and Dr. Greene give these amazing lessons.
@321rafwaf123
@321rafwaf123 4 года назад
Jessy Nemati dr greene can u share his channel? thxx
@frede1905
@frede1905 4 года назад
@@321rafwaf123 He has a series called "Your daily equation" on the World Science Festival channel.
@sandrasandra7593
@sandrasandra7593 4 года назад
Thank you dr Carroll, great lessons! High school made me hate physics, now I love it! Thank you for using your intelligence, your knowledge and skills to make the world a better place
@johnphil2006
@johnphil2006 4 года назад
Can we expect your next book: "The Biggest Ideas in the Universe". Much deserved one.
@beenaplumber8379
@beenaplumber8379 3 года назад
It would have to be a coffee table book or something informal like that. Nothing resembling a textbook. What about a big, thick comic book starring Alice & Bob?
@christopher6971
@christopher6971 4 года назад
Sean, the production quality paired with your concise communication style makes this series an invaluable asset to the physics/cosmology community. We sincerely appreciate the time, effort, and thought you invest in these learning tools. All the best to you, Mr. Carroll.
@archaicentity38
@archaicentity38 4 года назад
This is genuinely one of the biggest ideas in the universe: "Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space." - Douglas Adams
@archaicentity38
@archaicentity38 4 года назад
@Vendicar Kahn I'll answer that on the next conformal cycle.
@PazLeBon
@PazLeBon 4 года назад
its not very far from here so his logic was wrong. Also peanuts ? I dispute that too, it's more pistachio, def from a tree; he also prob thought a tomato was a vegetable ;)
@agimasoschandir
@agimasoschandir 3 года назад
@@PazLeBon Adams logic is a mixture of sarcasm and wit, and sort of an anti-logic. Most of the books after all are during the use of the improbability drive, which you program by bistromatics. In a sense, it is the use of the drive that probably cause the improbable reconstruction of the Earth after it was destroyed. Not sure why the nut has to be from a tree, people are familiar with sayings such as "I worked all day and all the boss paid me was peanuts"
@PazLeBon
@PazLeBon 3 года назад
@@agimasoschandir I think peanuts grow in the ground ;)
@agimasoschandir
@agimasoschandir 3 года назад
@@PazLeBon Correct. If you are implying it isn't a true nut, you would be correct as well if using the botanical definition, but not the culinary definition. Bit like the fruit tomato is classified as a vegetable
@TheJonlamb12
@TheJonlamb12 4 года назад
I’m trying to “wrap” my head around thinking in four dimensions, but the idea seems to pass right by. Oh wait... Great video! Thanks for making this quarantine interesting.
@veroosh
@veroosh 4 года назад
This is brain candy - just in the first five minutes you've explained several concepts in a totally unique way I have never heard them explained before.
@veroosh
@veroosh 4 года назад
Listen, I think you SHOULD teach us. Yes the delivery is super approachable, as is all your content I've encountered, but I don't think you should downplay the benefit these "sessions" ;) offer to anyone who wants to expand their understanding of physics. In some ways this is a topper to a course, and I hope you really get into this and make 1000 of these.
@PavaniGanga
@PavaniGanga 4 года назад
Thank you! Only one physics course decades ago. It took me twelve hours, reduced playback speed, pausing the subtitles, multiple repetitions, and so much scratching my head, mulling my notes, and wrinkling my math-challenged brow. But I finally pulled through. I a 73 yo retired nurse was motivated, because you make the subject so interesting! (The other videos were much easier for me, but for some reason the Hamiltonian was tough.)
@Peterskovtvermoes
@Peterskovtvermoes 3 месяца назад
This is truely a gift. I tried to push it to my daughter and her Tik Tok infected friends. Asking for defeat, I know but I was too excited to realize. Thanks Sean for donating your time and invite us to your realm of physics👏
@raf69777
@raf69777 4 года назад
This is so incredibly fun, thank you Sean.
@dazecm
@dazecm 4 года назад
Can I just say thanks for a great book (Something Deeply Hidden), a great podcast (Mindscape) and these great videos. You are single-handedly keeping me sane and entertained throughout this infuriating virus lockdown.
@peterpackiam
@peterpackiam 4 года назад
Thanks, Sean for sharing your Precious Time & Services, most appreciated Cheers.
@edmeko3262
@edmeko3262 3 года назад
Sean, what you are trying to do here for all of us trying to learn about this Universe is really fantastic. Each episode gives me another small window into what is happening around me every day. Knowledge of the immense space in which I am swimming. Thank You so much. I also enjoy many of the episodes in Mindscape.
@jcliggett53
@jcliggett53 4 года назад
Great series! I love that you bring up questions to which you don't have an answer, and even say "maybe one of you knows the answer". Great way to entice budding physicists to explore the ideas that interest them!
@danstrtelagergren6389
@danstrtelagergren6389 4 года назад
You are making the lockdown bearable, and through this video series reaching people all over the world. Sean, keep spreading knowledge to the world! It’s your gift! Thanks from Norway!
@TontoBongRonto
@TontoBongRonto 4 года назад
If it's unbearable why do you accept it ? If you really beleive it is warranted it wouldnt be unbearable
@BishopNE1
@BishopNE1 4 года назад
Sean, thank you SO MUCH for the free education. You are my favorite professor. We loved you on Joe Rogan as well. I wish you and your family the best!
@tonib5899
@tonib5899 4 года назад
Thankyou Professor Carroll, not just for the maths but for also being a decent person exactly when we need it. T.B from the U.K.
@dizy3513
@dizy3513 4 года назад
Sean what you dont get is this is extremely important... you do these to educate and expand minds .... even if only 500 ppl watch these ... idk man I've spent years reading physics books ...what you are doing breaking it down and keeping it real ... is massive ... if I had these 20 years ago ... my life would be different... thank you is all I can say
@_Messiii
@_Messiii 4 года назад
Thank you Sean, these videos are gems!
@KieranGarland
@KieranGarland 4 года назад
I'd been meaning to bug you with a question about Lagrangians and Hamiltonians, and here you've beaten me to the asking of it. This is all really great, like a Theoretical Minimum for the layman. Thanks again.
@ritemolawbks8012
@ritemolawbks8012 Год назад
I know it's an understatement, but has anyone else noticed how smart this guy is?
@0endofsilence
@0endofsilence 4 года назад
Sean, you are one of the best educators on physics out there. I always hated physics and math but after seeing you on JRE I am now fascinated by it and want to know more. I'm in the middle of Susskind's Cosmic Landscape and im binging your podcast and the PBS Space-Time. Thanks for making me realize how awesome the universe is.
@supersleeper8545
@supersleeper8545 4 года назад
The quality of content here and your podcasts are a massive contribution to science education. Thank you. May God bless you with a long and healthy life. It is a privilege to be alive in a time when access to this knowledge from such a deep knowing perspective is accessible.
@michaeljehlik5393
@michaeljehlik5393 3 года назад
Thanks a million Sean it's really great that you are teaching and sharing your ideas about physics on RU-vid! You are such a great teacher! Your videos and presentation style are top notch. You teach advanced concepts in comfortable inspiring way that helps me postulate and want to dig in.
@Rich-rp9xy
@Rich-rp9xy 4 года назад
Hello Sean Carroll, thank you for these videos! you and other physicists that post videos on youtube made me love to learn about physics. I used to hate physics in my school because we had a teacher who made it impossible to understand it for most of us, and back then with no internet, there was no one other to explain it.
@minaghavimi4843
@minaghavimi4843 4 года назад
Thank you so much for taking the time to prepare these fantastic sessions to explain physics to the public.
@ankiesiii
@ankiesiii 4 года назад
Absolutely amazing, and so well communicated.
@chromabotia
@chromabotia 4 года назад
That was great, a little more freewheeling, but fun and intriguing! Thank you Dr. Carroll.
@Cemselvi1988
@Cemselvi1988 4 года назад
I am doing an astrophysics PhD and I enjoy this very much
@DCardinell1207
@DCardinell1207 4 года назад
Thanks for your time and energy sir. These videos are great.
@user-gj7vp6wk3e
@user-gj7vp6wk3e 3 месяца назад
I AGREE. AS FAR AS SPACE GOES, CLASSICAL PHYSICS IS PERFECT.❤
@drwaynebuck
@drwaynebuck 4 года назад
To sum up - space is the thing that enables stuff to bump into other stuff. So without space we wouldn't have to social distance!
@brendonhammer6108
@brendonhammer6108 3 года назад
I loved the cool way you made "dimensions" (literally the word) disappear, in a time reversed kinda way, from 19.25 to 19.45 min ;) Meanwhile, just such a great series. Thank you so much.
@iuliandoroftei5088
@iuliandoroftei5088 4 года назад
I am a huge fan of Physics and you are my new hero! I have never watched something more engaging. What can I do to contribute to you continuing these lectures? Life has taken me to other endeavors but science will always be my number one reason to excitement and inspiration. One day soon, I will finance one of your projects, Sean!
@galleoboutique1852
@galleoboutique1852 4 года назад
Love your talks & have much respect for what you guys do. Im a true physicist at heart. Thanks Sean, very interesting.
@crisdellani
@crisdellani 4 года назад
Sean makes an apparently dull and mundane topic such as space look incredibly interesting, mysterious and mathematically complex. You're a terrific communicator. Thanks for doing this
@AbyssLMachiine
@AbyssLMachiine 4 года назад
Nothing wrong with a little extra hair! Keep up the great work Sean
@edmundodelagarza4418
@edmundodelagarza4418 4 года назад
Thanks doc Carroll. Your matter-of-fact disposition is most inviting and whets my imagination for more; all the while smoothing the rough edges of uncertainty remaining from school.
@robertgoss4842
@robertgoss4842 7 месяцев назад
Dr. Carroll: Thank you for this superb series. I have seen about 8 or 9 parts of your series and I am just a bohunk boy from Georgia. But I must say that you speak intelligibly on even the most complex topics. I have reaped huge benefit from this series of programs. Thank you again.
@akumar7366
@akumar7366 4 года назад
Thank you Sir for sharing great post.
@BlackHermit
@BlackHermit 4 года назад
Thanks for the free content Sean. You’re the man!
@Wandering_Chemist
@Wandering_Chemist 3 года назад
Just wanted to say thank you for these sir.
4 года назад
7:36 like the "2000 miles long man" (as he stated) in Leonard Susskind's lectures on GR :) OK, different context (there it was about explaining the tidal forces) but still it made me smile :)
@farty555
@farty555 3 года назад
thank you for these videos. I am learning so much.
@alvarorodriguez1592
@alvarorodriguez1592 4 года назад
00:00 Sean Carrol looking like a lovecraftian god. Because why not
@Pycrih
@Pycrih 4 года назад
You are a great teacher! Thank you!
@antoninbesse795
@antoninbesse795 3 года назад
This series is brilliant. Full strop.
@pinball1970
@pinball1970 3 года назад
This is such a good series. I am writing up these notes into a book
@-AndAllThatJazz..
@-AndAllThatJazz.. 4 года назад
extremely grateful for making complexity into simplicity.
@rayguthrie7489
@rayguthrie7489 4 года назад
I'm enjoying your conversations on the biggest ideas in the universe. thank you for sharing your knowledge and invite to the common man such as me.
@nurk_barry
@nurk_barry 4 года назад
Read “the big picture” and it’s one of the most comprehensive theoretical physics books. I’ve read all of Brian green’s work as well as Susskind and Krauss. Sean is among the best physicists /public figures there is when it comes to understanding the laws of nature. So much fun to learn about this stuff.
@ChaineYTXF
@ChaineYTXF 4 года назад
This is a very, very good series. I certainly will spread the word.
@helicalactual
@helicalactual 4 года назад
thank you! that was another amazing video!!!
@jacksontrollinger876
@jacksontrollinger876 4 года назад
This is so great, I appreciate it a lot
@pizzacrusher4632
@pizzacrusher4632 4 года назад
Fantastic, thank you so much!
@appercumstock3017
@appercumstock3017 4 года назад
Innovative approach, cool!
@fatmaoylu5374
@fatmaoylu5374 4 года назад
You are an excellent tutor, thank you.
@rostamr4096
@rostamr4096 4 года назад
Thank you, I really enjoy these lectures.
@chrihipp
@chrihipp 4 года назад
This was fun. Thank you.
@gr500music6
@gr500music6 4 года назад
I am watching a version of you in two dimensions and it seems to be doing just fine !
@shanestrickland5006
@shanestrickland5006 4 года назад
This video was great as always.
@peterb9481
@peterb9481 2 года назад
Good video. Interesting topic and facts put over. Whilst I watch these videos for the physics, it was also interesting to hear about the psychology of time. And very funny at around 38 minutes, when David Eagleman measures time perception by throwing his subjects off buildings. (I know he is a good guy, and he has a good BBC series - and book - on the brain.) I am really loving The Biggest Ideas In The Universe episodes and am learning from them (I have been studying physics for some years).
@brendandarmetko7646
@brendandarmetko7646 4 года назад
the way Sean articulates these complex ideas is parrelled only by people like Neil Tyson and Brian Greene. We live in an amazing time for information.
@Cooldrums777
@Cooldrums777 4 года назад
Well I finally have an understanding of the Hamiltonian. I have read Wikipedia and a few other tutorials on this subject, but I never really understood them. Thank you for the excellent tutorial.
@etprecisionmachine2379
@etprecisionmachine2379 4 года назад
Greetings Professor Carroll, I am so happy that you are so driven to teach, Though Science and The Scientific Method (should that be capitalized?) have been important in my life since I was a child I ended up being a Machinist. I am very good at what I do in large part because I use science to achieve the best results. Even though I like machining and all that's involved with complex metalworking, I still seek out a physics education that I missed. Folks like you really help. The math is fine, I struggle through some of it though because I'm an auto didact, and the concepts sometimes elude me. Your videos really help. Not just these latest however, but many previous videos of your lectures have also helped me to understand our universe. Thank you so much for spreading knowledge, you are making an important contribution to general human knowledge. Cheers, Eric
@AltonMoore
@AltonMoore 4 года назад
These are really excellent videos. I still won't be converting to the many-worlds view, but the level of presentation is about right. The hair is looking good, hah!
@paulotheman8734
@paulotheman8734 4 года назад
man, I almost fall from my chair as the video was displayed in my 50" tv. Thanks for the great video.
@TheNORRA100
@TheNORRA100 4 года назад
This is just Great Mister Carrol.Greeting from Northern Europa...
@willtothewong
@willtothewong 4 года назад
Great video!
@kenyo5087
@kenyo5087 3 года назад
Amazing contents!! Thank you!!
@Schneeger-zk3uq
@Schneeger-zk3uq 3 года назад
Very nice series Herr Carroll, keep it up and dont avoid too much mathematics, which is nice to really understand the idea behind the phenomena. Vielen Dank! Liebe Grüße, Leon
@neeznees1181
@neeznees1181 3 года назад
I love watching 👀 your work ... I am now a new fan
@duggydo
@duggydo 4 года назад
I'm here early. Happy times! :)
@benfurstenwerth
@benfurstenwerth 4 года назад
Thank you so much Sean, this series is amazing! Side note, your preferred interpretation of quantum physics solved the devs machine lol... One more episode to see if they screw it up :)
@johnrendle1303
@johnrendle1303 2 года назад
Fabulous!!!
@emilylowrance7930
@emilylowrance7930 4 года назад
the key to growth is the introduction of higher dimensions of consciousness into awareness - Lao Tzu
@Bill_Garthright
@Bill_Garthright 4 года назад
What does that mean? Seriously. I know what each of those words mean, but when put together into a sentence like that, I don't have the slightest idea what the sentence is supposed to mean.
@emilylowrance7930
@emilylowrance7930 4 года назад
@@Bill_Garthright like you can't solve a new problem with the same thinking that created it...that's what it means to me anyway
@Bill_Garthright
@Bill_Garthright 4 года назад
@@emilylowrance7930 _like you can't solve a new problem with the same thinking that created it_ Um,... OK. I can't for the life of me see how you got that meaning out of it, but... OK. :) Thanks for the reply.
@bruceneeley1724
@bruceneeley1724 4 года назад
Great talk!!
@w6wdh
@w6wdh 4 года назад
Lovely video! Two of the weirder aspects of 3D space and bounding surfaces that I’ve heard about: 1. The maximum information content of a volume of space is proportional to the area of its bounding surface, and 2. Logically our 3D space is equivalent to a holographic projection onto a 2D bounding surface. Maybe these things will come out in a future video? In any event, I’m hooked on these videos.
@sachaaustin
@sachaaustin 4 года назад
Awesome!
@kaaregus
@kaaregus 4 года назад
Great video
@raedshaiia3976
@raedshaiia3976 4 года назад
Thank you very much for this fantastic series. I wish if you talk about theories that posit the existence of more than one time dimension :)
@Adrian-me4qz
@Adrian-me4qz 3 года назад
Thatstring wrapping thing is mind blowing
@FergusScotchman
@FergusScotchman 4 года назад
Sean, these are great and welcome during the covid experience. At 8:44 you essentially talk about the energies of different wavelengths. This obviously has relevance to red and blue shifting of stars... moving away shifts the spectrum toward red. - Can you tell me if energy is conserved in the spectrum shifts cast off by celestial objects, since red-shifting must mean a loss of energy. - How much does relativistic space-time have to do with the conservation of such electromagnetic radiation. (I know Einstein wanted to find an eclipse to try to look at these curvatures) Thank you for your service!
@ssshurley
@ssshurley 4 года назад
I hope more people have your view on multiple dimensions, start to treat it as a fact, while moving above and beyond our current understanding.
@marwanelmobader7851
@marwanelmobader7851 2 года назад
this is the best presenter I've seen so far
@mgenthbjpafa6413
@mgenthbjpafa6413 4 года назад
Thank you, better late than never. Eric Weistein is talking about 4+6+4 equals fourteen, Brian Greene is still on it. We thought String theories are zombie like, as in refusing to give up... We, common people, knowing how epistemology and proof theory are really evolving into other emergent paradigms, appreciate your step by step approach .We should be very grateful for your pedagogical capabilities. I am not trying to patronize anyone, since you are above and justifiable so. Congrats, Professor
@pb4520
@pb4520 4 года назад
Wonderful thankyou for this .
@hayden9127
@hayden9127 4 года назад
Q&A. For the spooky action at a distance. Does the entangled particle branch instantly or does the change spread out at the speed of light?
@tommasoforni
@tommasoforni 4 года назад
Instantly, but Bob wouldn't know the result unless he himself performs an experiment or Alice tells Bob with good old-fashioned slower than light communication. In other words when Alice performs an experiment nothing changes for Bob
@BoazRosenan
@BoazRosenan 3 года назад
Thanks for this series. Although I know (some) physics, it's always good to reiterate on the basics. Regarding the claim that 2D space is not sufficient to do anything "interesting", Conways Game of Life is an example of something "interesting" (a Turing-complete computational model) that lives in 2D space + time. Furthermore, Rule 110 is an example for a cellular automaton that does something "interesting" (Turing complete) with 1D space + time. The extra 3rd dimension makes the computational models we can have in our universe much more efficient (e.g., the human brain), but overall, I don't think there is a fundamental difference.
@chrisn.3096
@chrisn.3096 4 года назад
Sean, have you taken a cursory look at Stephen Wolfram's new work and claims about finding a "path to a fundamental theory of physics"? It's making the rounds right now!
@beeble2003
@beeble2003 4 года назад
Self-published books are a huge red flag. Science being published in books rather than papers is a huge red flag.
@barbiecarlyX
@barbiecarlyX 2 года назад
Gawd i love Sean
@milkypelf
@milkypelf 4 года назад
damn i love those videos , thank you so much.
@carldehez3117
@carldehez3117 3 года назад
When Kant says space, time and causality are "a priori" concepts, these have little to do with physics but all the more with our cognitive abilities. We order and interpret reality automatically as we experience it. Visually, we order it in a 3-dimensional space. Even before we see something, we have this ability. Hence, space is an "a priori" concept. It is a condition of our understanding.
@mokopa
@mokopa 4 года назад
15:09 Here's how I visualised it: It's easy to imagine that two strings in 3D space CANNOT pass through each other, but if you add the dimension of time, it's easy to imagine how one string passes first, and then the second string passes. Obviously they do not need to pass through each other because they are separated by time, that is, they are separated in the 4th dimension
@David_Last_Name
@David_Last_Name 4 года назад
Nice, I like that analogy.
@itellyouforfree7238
@itellyouforfree7238 4 года назад
That's more or less the proof, you can make it rigorous. What you get also, is that every knot in 4D is trivial, you can always untie it. In particular, you cannot tie your shoes in 4D.
@tetraedri_1834
@tetraedri_1834 3 года назад
The analogy doesn't quite work, as strings in 3+1 -dimensional space-time are 2-dimensional. Unless I'm misunderstanding something
@crusherolies8195
@crusherolies8195 4 года назад
mr carroll, i saw a lecture or group lecture where spooky action was said a little differently. the two particles are created together, and they have opposite spins. so when you detect one and its spin up, the other is spin down, their pairing is similar to electron/positron pairs released from energy state changes. they still have the no distance issue, as you know one you know the other. personally i believe the opposite spins explanation is better because its isnt as usable for WOO peddlers like deepak chopra, since their spins were determined at their paired creation, its not them communicating in any way. by the way im loving this series. thank you.
@MikhailBarabanovA
@MikhailBarabanovA 4 года назад
Thanks for the video! Finally some understanding of how dimensions could be 'curled'. Could you(or somebody else) recommend some sort of introductory textbook with description of math behind such processes?
@MikhailBarabanovA
@MikhailBarabanovA 4 года назад
@@michaelsommers2356 Thanks!
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