Amazing how Sean Carroll can cover such deep, technical discussions in an understandable way. A great teacher, educator and of course genius! Thank you...
21:55 I like the explanation very much for small dimensions. Another example would be a very thin wire, which for us big things is practically a 1D thing, a single line, but a tiny insect would see 2D because it can go around it.
I rarely comment but I just wanted to say thanks a bunch for these videos Sean, they’re great! You’re a great educator; wish I could same the same about more of my professors.
Thank you, Professor. These Q&A videos are fantastic and this series of videos is the very best content for me during the current events. I appreciate the effort and time you have devoted, it is like a free gift for us all.
Professor Carrol, there are no words to describe our gratitude to your great efforts! Think about how many people would love this subject, at least change their minds about it, and many would like to pursue it to become our future great scientists, as yourself, and they will carry on the torch of science further!
Oh boy. Just when I think the last video you did in the series was really good, you go ahead and produce one that's even better!!!!! I especially enjoyed the way you tied the concept of the Hamiltonian with ways to explore deeper insights into nature and reality. I am now officially addicted to this video series. Long live the Biggest Ideas !!!!!!
Fantastic series. I've not seen this amount of accessible description of arcane concepts like Hamiltonians and extra dimensions. You are really making a series for those that half understand mathematics and physics but were previously unable to relate all the concepts. Thank you.
In quantum mechanics, the position and momentum together is, in some sense, a single thing that can have different classical aspects revealed. (position and momentum are conjugate variables, thus the uncertainty principle that the combined knowledge of both is limited by Planck's constant) So, x and p are different shadows on Plato's Cave wall, of a singular true reality. The difference in nature between x and p are keyed with the difference between space-like and time-like dimensions. Look at how you apply operators to the wave function to obtain them.
Thank you Sean for the amazing series! Neither Laplace nor Leibniz invented ∂ (curly d; del). There are many "L-men" in the history of mathematics and curly d is attributed to Legendre. In fact, it was Condorcet who used it first and Jacobi (after Legendre) who made it popular (hence sometimes called Jacobi delta).
I believe in regards to the entropy of the black hole violating the hamiltonian and Laplace deamon of where the energy goes it may very well be that 3 dimensional space simply doesn't exist in a black hole and instead those extra tiny dimensions that are so small are allowed to form and suck up that energy and retain it for some time; like a periodic table of dimensions would form and there could be more than the posterized based limit of 10 or 11 that could support the symmety in supermassive black holes like Matthias Kluge
Sean - there's nothing else like this series on the web. These are wonderful! I know it's probably a little obscure but I'd love to understand more the concepts behind the theory Lee Smolin discussed a few years ago about time being fundamental and space being emergent and dependent on a multi-dimensional network or graph - the implications of this seem to me to be quite significant at a foundational level. - Thanks, Alex
Professor will be great if you do a video explaining your paper on the compactification of dimension. I have tried to read it but it is still difficult as a student to understand some parts. Thank you!!
it's past 2am, I've been programming a random map generator for a video game I'm starting designing. about to go to bed cause I'm making mistakes Sean Carroll uploads something Well, looks like I'll be up for a bit longer
Reflective Layer randomly generated metroidvania. I’ve made one before (search “Birth of a Hunter” on steam if interested, it’s free), but I thought of a (possibly) better algorithm for making more complicated maps (that are more like normal metroidvanias). Not sure if it will turn into anything, this is just a fun little idea I had and wanted to see if I could get just this part to work.
notability has a red-dot (laser point) feature, i like to use it to highlight when i'm talking to class. It's the rightmost icon of the group of drawing options at the top.
Another way to have undectable extra dimensions of space: they might be big, but movements through them might be so slow or so inertial (i.e., constant velocity) that we haven't ever developed any senses to detect them. This is to mean p vectors mightn't sway enough in such directions or their components in such directions mightn't vary fast enough to be of any use to animal survival. Would you sense a speed of a metre per millenium? Would you have muscles that would take ages to move anything in such dimensions?
38:45 PLEASE prof explain further, this is the only thing in the universe I don't understand (ignorance is bliss..), how can something with a gravity that lets nothing escape, even light, let radiation (light) to escape? I saw a PBS space time episode and I guess either I cant remember or I still did not understand after their attempts to explain.. Thanks for these videos 💖💪👍👍
Reminder : Hamiltonian / Phase space discussed + example. SHO. Calculus, D, delta & del. Xtra dimensions, Locality, Holographic Principle. All in 48 mins !!
The particle position is written in terms of the probability of fluctuation of space-time. It does not displace anything. Space isn't like a fluid and particles are not displacing any space while they move in space-time.
Ok. but then what is actually fluctuating - not the probability, surely? The particle must have an actual position, and the probability is only a measure of our uncertainty of where it actually is via Heisenberg. If space is distort-able, is the particle distorted, too, by its ability to distort space if it is 'in' space'? I'm honestly asking, not proposing anything - I know I don't know enough about it.
I'm not sure I agree with common common. I think perhaps "displace" isn't quite the verb you meant to use, based on the description of an object "moving". I can't think of a better word for it at the moment, but if it is what I think you're asking, then actually the answer is probably "yes". I mean this in the sense that a spinning object drags spacetime around with it in the (experimentally verified) phenomenon of frame dragging. Likewise, objects moving with a very high delta of momentum, such as two black holes spiraling in toward a merger, causes ripples in spacetime that propogate outward as gravitational waves. In neither case does any probability enter into anything; this is explicitly not a QM question. Heisenberg does not apply because it's classical physics. For your later question of, essentially, "Is an object distorted by its own distortion of spacetime?" if I understood you correctly? Absolutely, yes. As Dr. Carroll has said, "Mass tells spacetime how to curve; spacetime tells mass how to move". This is very literal, and yes, it goes both directions at once, and yes, that absolutely does make the math a giant nightmare, and yes, that is precisely why we have yet to unify gravity with the Standard Model... though Dr. Carroll and some others seem to be getting closer than anyone else has thus far, as you can read about in his book, Something Deeply Hidden. ;) If you meant literally "displace", however, in the sense in which a ship displaces water to float... then no. It's actually rather spectacularly and mind-meltingly the opposite. A large object's gravity can be quite literally thought of as space-time flowing into it, continuously and without end.
Thanks for this series - definitely a silver lining in these strange times. At the risk of using terminology I don't fully understand, can the extra curled up dimensions be thought of as a fibre bundle?
I'm with you in the struggle to grasp this, but my understanding is exactly that. A 2D surface curled in on itself and viewed from a great distance would appear to be a fiber approaching zero width but still infinite in length (unless it is also curled in on itself, in which case *I think* it would be a torus). In the main video he talked about a tube (I think he should have said it was infinite in length) that would look narrower and narrower as you step farther away from it, or as you increase in size. What he's talking about here is a fiber that appears so small we can't even see it, but it would still be 2 dimensions. One thing - you mentioned a fiber bundle. This model only represents a single fiber with 2 dimensions, not a bundle of them, but why not?
As a matter of fact the symbol of partial derivative is indeed a letter in "some language" and that language would be Greek ;) It's a small (as in non-capital) theta. Not that it is of any significance at all but just mentioning it. What is of a major significance though is that you are doing a spectacular job something that makes me (and i am sure many- many others) deeply grateful for. And i am not referring just to this project alone but in general; As I've been following your lectures and books for quite sometime now. Consider even, that you have me "almost" convinced that the "Many Worlds" - an idea that i was holding as one of the most absurd things i had ever been exposed to - might actually be the way to go :P
Hey Sean, what are your thoughts on guys like Eric Weinstein and Stephen Wolfram each developing their own version of a "Theory of Everything"? Do you think they have any chance of succeeding? They're both highly capable individuals.
The Hamiltonian bit was great. I'm curious to learn more about that formulation of mechanics. I'm still working my way through introductory Newtonian mechanics so it will be a while perhaps.
Thank you so much for this series, it's fantastic! Question: If we postulate that space is quantized and nothing can be smaller than a Planck Length, does that solve the problem of gravity and quantum mechanics clashing in singularities and producing nonsense numbers? If so, do we still need string theory to unite gravity with the Standard Model, or is quantized space sufficient?
No. In fact, that is the exact line of thinking that *leads* to the discovery of the fundamental incompatibility between the two, much more than the singularity problem. The latter is often just a matter of coordinate choice, but trying to quantize spacetime leads to math that just doesn't math, as I understand it.
probably too late to ask a question now 😢 but is it conceivable that there are giant macro dimensions that dwarf the 3 macro dimensions we inhabit in a similar proportion than our macro dimensions dwarf the hypothesised micro dimensions of string theory? I don’t know whether this question is ‘interesting’, ie I don’t know whether an assumption that they exist would be of help in answering some other question - I just thought I’d mention the thought.
We talk about hiding dimensions in smaller scales, but shouldn't the inverse be true? What if our 3D space is like that 2D tube that vanishes to a fiber as we move away from it. If we can move away from a 2D tube and make it look 1D, might we be on a 3D space that is seen as a 2D surface to a 4D observer at a great distance? Or maybe all of our dimensions are small to a large enough observer living in large space? Is there anythi9ng wrong with that?
Is "mass" considered a dimension in the extra dimension that is mentioned here?? Even in Newtonian mechanics why isn't "mass" considered as an parameter to describe where as momentum does.
@@michaelsommers2356 it is also a possibility that, mass can be derived from momentum and that is easier to use for determining other factors like energy.. However still mass is property which could be used as a dimension (my opinion)
@@michaelsommers2356 I just raised a doubt, and your reply doesn't seem to give a proper answer. mass=momentum/velocity (Newton Mechanics) so in this sense if i know the momentum, I know the mass given I know the rate of change in x,y&z coordinates Well Photons carry energy, and energy and mass are the same (E=mc^2). So photons have momentum, energy and mass however you may look at and depends on the application.
@@michaelsommers2356 , maybe " photons have no rest mass" is more accurate. I would really hope my doubt is cleared by Sir Sean Carroll. I was just talking about Newtonian domain. The Photon part is better understood in the relativity and space-time physics
Math is the law of science written down, the thought we can use math presumptuously by itself to make sciences like quantum mechanics is totally preposterous because the laws of nature are already set. The fact they are unchanging allows us to do science.
Thank you for the series. You've piqued my curiousity now that you mention 10 or 11 dimensions. Knowing that we traditionally have time as one dimension plus 3 dimensions of space making the 4D universe. In these extra dimensions that you mention could there be extra dimensions of time or is that always restricted to the one?
@@michaelsommers2356 Indeed. But is there a time when the cat is not in the box to be determined as either been dead or alive? Could it have gone through some sort of temporal phase transition and gone for a stroll around the neighbourhood before or after? I'm just curious to know if it has many worlds to Interpretate.
@@michaelsommers2356 Well in the double slit experiment the atom when a detector is present is detected 50% of the time going through the top slit. The assumption being the other 50% of the time going through the lower slit. Sure enough the results show two lines of position for atoms ending up. When the detector is not present then the results give a completely different set of results as if the atoms have acted like waves instead. Maybe there is a temporal phase transition going on? I only ask the question and don't know either.
I would be interested in more on the Hamiltonian formulation... specifically how the Hamiltonian for simple harmonic oscillation leads to trigonometric functions. I suspect the actual movement over time has something to do with the integral of the hamiltonian rather than the derivative, and that an i comes into it at some point and then gets used as an exponent in an e^i(something)? Or at least a "something^i(something)" that then gets normalized to e? Actually, I'm getting hazy memories of this maybe having been done in college...
IT&T - imagine this and that theory :) I so want us to prove anything new "soon", let's hope the major construction of any future supercolliders won't be halted and hindered. Get well, America!
Once Sean gets into the stringy stuff. Physics is getting funky somehow. Likes its moving away from reason and knowing to an unknowing madness. The more we open the intricate clock. The more it confounds us but just keeps us interested enough to stay in the maddening game. The answer will never be what we expect. The future is gonna seem crazy if we knew it. But it will overall over time be good. Heart somehow trumps head. Even in physics for me.
Suggestion: maybe you could use the screenspace in the video more efficiently. For example extending the part where you write towards the bottom of the screen. Or using the space above your head, maybe with a second screen for short notes, however that would maybe be overkill. Great series btw !
Is a black hole a thing, or the absence of something? They appear to hold a spherical shape. Yet to my knowledge they aren't comprised of something, if they were, shouldn't those 'somethings' experience instant spaghettification? Thereby vanishing from existence entirely and instantaneously? So why do they have the appearance of a shape? Larger/heavier bodies are spherical due to their relationship with gravity. That force is equally applied evenly to the entire surface-area of said object, resulting in a spherical shape. Black holes don't have surfaces, right? When I think about a star collapsing into an anti-star (BH), shouldn't the near infinite gravity just pull the remaining material into oblivion instantaneously? How could a field of any kind remain after the collapse? Anti-stars shouldn't leave anything behind, let alone a light consuming spherical field that decimates matter. Just the fact that anything remains after such a collapse doesn't make sense to me. My conjecture: Unless these anti-stars are actually antimatter fields, whereby matter that gravitates too close to the field are annihilated upon contact. The Hawking Radiation could be matter converted into out-gas after making contact with said event.
@Sean - Your Partial Derivative "funny d" symbol looks a lot like the the letter "d" used in English Lute Tablature in the very famous 1610 publication of the "Varietie of Lute Lesssons" by Robert Dowland. Here's an example: walterbitner.files.wordpress.com/2015/09/earleofessexgalliard.png There are a couple in the first measure (an elsewhere), and indicate the the 3rd fret for a particular string. I so know you play music, so I thought you might find this trivia interesting.
Flying through space surrounded by dweeble brands reminds of a story I wrote in sixth grade must of had old physics books available somewhere about 37 years ago
If the information in the book is written in Chinese, for me me is zero information because I don't know Chines language, so this paradox might be false. The information written in Chines carries zero energy for me, so wouldn't radiate from the black hole.
A dabble of math might answer the 'is this entangled?' questions better -- talking about whether you can factor things isn't too much, I think, for this audience.
THE EQUATIONS HELP ME! THANK YOU, PROFFESSOR SEAN CAROL!👋🤚✌🏼🖖👌🤙👍
Amazing how Sean Carroll can cover such deep, technical discussions in an understandable way. A great teacher, educator and of course genius! Thank you...
I love it, even though it is way over my knowledge. Great masters know how to present complex topics.
21:55 I like the explanation very much for small dimensions.
Another example would be a very thin wire, which for us big things is practically a 1D thing, a single line, but a tiny insect would see 2D because it can go around it.
I rarely comment but I just wanted to say thanks a bunch for these videos Sean, they’re great! You’re a great educator; wish I could same the same about more of my professors.
I would like to be as genuinely patient as Sean Carroll.
Thanks Sean. I've been trying tu understand partial derivatives and Hamiltonians for years and you nailed it in the first ten minutes of this Q&A!
Thank you, Professor. These Q&A videos are fantastic and this series of videos is the very best content for me during the current events. I appreciate the effort and time you have devoted, it is like a free gift for us all.
All made possible by the percentage of people that are sensitive to ads
Thank you so much for this amazing series ! Absolutely amazing
Before sleep i watch this brilliant lectures. Dr. Carroll is such a great teacher.
Professor Carrol, there are no words to describe our gratitude to your great efforts! Think about how many people would love this subject, at least change their minds about it, and many would like to pursue it to become our future great scientists, as yourself, and they will carry on the torch of science further!
Oh boy. Just when I think the last video you did in the series was really good, you go ahead and produce one that's even better!!!!! I especially enjoyed the way you tied the concept of the Hamiltonian with ways to explore deeper insights into nature and reality. I am now officially addicted to this video series. Long live the Biggest Ideas !!!!!!
Fantastic series. I've not seen this amount of accessible description of arcane concepts like Hamiltonians and extra dimensions. You are really making a series for those that half understand mathematics and physics but were previously unable to relate all the concepts. Thank you.
In quantum mechanics, the position and momentum together is, in some sense, a single thing that can have different classical aspects revealed. (position and momentum are conjugate variables, thus the uncertainty principle that the combined knowledge of both is limited by Planck's constant)
So, x and p are different shadows on Plato's Cave wall, of a singular true reality.
The difference in nature between x and p are keyed with the difference between space-like and time-like dimensions. Look at how you apply operators to the wave function to obtain them.
Wow this is so interesting. Eye opening stuff about physics we were taught in school, that suddenly makes sense
Many thanks professor for this wonderful series. Combined with the Mindscape podcasts you're providing some of the most compelling content extant.
I could listen to Sean all day long thanks for this new series.
Just yesterday discovered this. Immediately subscribed. Thank you, Dr Carroll, for this and for the books.
“And why is it negative? Because trust me.” Thank you for doing these, they are saving me from rotting my brain watching Marvel movie update videos.
Great contents! Absolutely love it!!
In the Q&A videos, I believe more examples would be great!
Thank you again for your work.
Sean thank you for these lectures. As always they are brilliant.
Thank you Sean for the amazing series!
Neither Laplace nor Leibniz invented ∂ (curly d; del). There are many "L-men" in the history of mathematics and curly d is attributed to Legendre. In fact, it was Condorcet who used it first and Jacobi (after Legendre) who made it popular (hence sometimes called Jacobi delta).
I believe in regards to the entropy of the black hole violating the hamiltonian and Laplace deamon of where the energy goes it may very well be that 3 dimensional space simply doesn't exist in a black hole and instead those extra tiny dimensions that are so small are allowed to form and suck up that energy and retain it for some time; like a periodic table of dimensions would form and there could be more than the posterized based limit of 10 or 11 that could support the symmety in supermassive black holes like Matthias Kluge
Sean - there's nothing else like this series on the web. These are wonderful!
I know it's probably a little obscure but I'd love to understand more the concepts behind the theory Lee Smolin discussed a few years ago about time being fundamental and space being emergent and dependent on a multi-dimensional network or graph - the implications of this seem to me to be quite significant at a foundational level. - Thanks, Alex
Professor will be great if you do a video explaining your paper on the compactification of dimension. I have tried to read it but it is still difficult as a student to understand some parts. Thank you!!
Looking forward to watching this video, I have to watch at least twice to grasp the topics.
it's past 2am, I've been programming a random map generator for a video game I'm starting designing.
about to go to bed cause I'm making mistakes
Sean Carroll uploads something
Well, looks like I'll be up for a bit longer
What kind of game are you making?
Reflective Layer randomly generated metroidvania. I’ve made one before (search “Birth of a Hunter” on steam if interested, it’s free), but I thought of a (possibly) better algorithm for making more complicated maps (that are more like normal metroidvanias). Not sure if it will turn into anything, this is just a fun little idea I had and wanted to see if I could get just this part to work.
Thanks for your work
please give the name of application that you use for blackboard on the screen
Thank you keep them coming!!
notability has a red-dot (laser point) feature, i like to use it to highlight when i'm talking to class. It's the rightmost icon of the group of drawing options at the top.
update, i just noticed, this pointer only appears when i'm connected to my macbook using quicktime (i use this to share my ipad screen)
Another way to have undectable extra dimensions of space: they might be big, but movements through them might be so slow or so inertial (i.e., constant velocity) that we haven't ever developed any senses to detect them. This is to mean p vectors mightn't sway enough in such directions or their components in such directions mightn't vary fast enough to be of any use to animal survival. Would you sense a speed of a metre per millenium? Would you have muscles that would take ages to move anything in such dimensions?
38:45 PLEASE prof explain further, this is the only thing in the universe I don't understand (ignorance is bliss..), how can something with a gravity that lets nothing escape, even light, let radiation (light) to escape? I saw a PBS space time episode and I guess either I cant remember or I still did not understand after their attempts to explain.. Thanks for these videos 💖💪👍👍
6:18 I think you meant to say ‘momentum is mass times velocity’, not position
Haven't understood getting the "yellow" equality at 9:35, can anybody explain?
Can we view uncertainty as a feature of and by itself ? A tool just not for quantum mechanics?
Reminder : Hamiltonian / Phase space discussed + example. SHO. Calculus, D, delta & del. Xtra dimensions, Locality, Holographic Principle. All in 48 mins !!
Does an object moving displace space as it distorts it?
The particle position is written in terms of the probability of fluctuation of space-time. It does not displace anything. Space isn't like a fluid and particles are not displacing any space while they move in space-time.
Ok. but then what is actually fluctuating - not the probability, surely? The particle must have an actual position, and the probability is only a measure of our uncertainty of where it actually is via Heisenberg. If space is distort-able, is the particle distorted, too, by its ability to distort space if it is 'in' space'? I'm honestly asking, not proposing anything - I know I don't know enough about it.
I'm not sure I agree with common common. I think perhaps "displace" isn't quite the verb you meant to use, based on the description of an object "moving". I can't think of a better word for it at the moment, but if it is what I think you're asking, then actually the answer is probably "yes".
I mean this in the sense that a spinning object drags spacetime around with it in the (experimentally verified) phenomenon of frame dragging. Likewise, objects moving with a very high delta of momentum, such as two black holes spiraling in toward a merger, causes ripples in spacetime that propogate outward as gravitational waves.
In neither case does any probability enter into anything; this is explicitly not a QM question. Heisenberg does not apply because it's classical physics.
For your later question of, essentially, "Is an object distorted by its own distortion of spacetime?" if I understood you correctly? Absolutely, yes. As Dr. Carroll has said, "Mass tells spacetime how to curve; spacetime tells mass how to move". This is very literal, and yes, it goes both directions at once, and yes, that absolutely does make the math a giant nightmare, and yes, that is precisely why we have yet to unify gravity with the Standard Model... though Dr. Carroll and some others seem to be getting closer than anyone else has thus far, as you can read about in his book, Something Deeply Hidden. ;)
If you meant literally "displace", however, in the sense in which a ship displaces water to float... then no. It's actually rather spectacularly and mind-meltingly the opposite. A large object's gravity can be quite literally thought of as space-time flowing into it, continuously and without end.
Sean has some legit hockey flow.
Thanks for this series - definitely a silver lining in these strange times. At the risk of using terminology I don't fully understand, can the extra curled up dimensions be thought of as a fibre bundle?
I'm with you in the struggle to grasp this, but my understanding is exactly that. A 2D surface curled in on itself and viewed from a great distance would appear to be a fiber approaching zero width but still infinite in length (unless it is also curled in on itself, in which case *I think* it would be a torus). In the main video he talked about a tube (I think he should have said it was infinite in length) that would look narrower and narrower as you step farther away from it, or as you increase in size. What he's talking about here is a fiber that appears so small we can't even see it, but it would still be 2 dimensions. One thing - you mentioned a fiber bundle. This model only represents a single fiber with 2 dimensions, not a bundle of them, but why not?
As a matter of fact the symbol of partial derivative is indeed a letter in "some language" and that language would be Greek ;) It's a small (as in non-capital) theta. Not that it is of any significance at all but just mentioning it. What is of a major significance though is that you are doing a spectacular job something that makes me (and i am sure many- many others) deeply grateful for. And i am not referring just to this project alone but in general; As I've been following your lectures and books for quite sometime now. Consider even, that you have me "almost" convinced that the "Many Worlds" - an idea that i was holding as one of the most absurd things i had ever been exposed to - might actually be the way to go :P
Thanka!
Hey Sean, what are your thoughts on guys like Eric Weinstein and Stephen Wolfram each developing their own version of a "Theory of Everything"? Do you think they have any chance of succeeding? They're both highly capable individuals.
He thinks they’re full of shit. Tweeted about it yesterday
@@tripp8833 Damn. Really? I had no idea. Need to go check out the tweet..
Not sure if it was my comment about locality or someone else’s you were addressing, but thank you Sean! Your answer helps tremendously
Got left in the dust at branes being related to strings. Phew!
The Hamiltonian bit was great. I'm curious to learn more about that formulation of mechanics. I'm still working my way through introductory Newtonian mechanics so it will be a while perhaps.
Great content
Could other branes' gravity leaking into ours explain, in part or in whole, the effect we currently attribute to dark matter?
...and can we extract info from gravitational waves to illuminate that
This is great stuff
Thank you so much for this series, it's fantastic!
Question: If we postulate that space is quantized and nothing can be smaller than a Planck Length, does that solve the problem of gravity and quantum mechanics clashing in singularities and producing nonsense numbers? If so, do we still need string theory to unite gravity with the Standard Model, or is quantized space sufficient?
No. In fact, that is the exact line of thinking that *leads* to the discovery of the fundamental incompatibility between the two, much more than the singularity problem. The latter is often just a matter of coordinate choice, but trying to quantize spacetime leads to math that just doesn't math, as I understand it.
Thanks for answering my question about "disappearing" dimensions. I originally thought you meant disappearing was literal :) Now I get it.
Merci beaucoup pour votre travail de vulgarisation
Thank you so much!
Can entangled particles be connected by compactified smaller dimensions?
Thank you
Thanks for the math example!
The Simple Harmonic Oscillator is ‘Super famous’. Well it is more famous now for sure!
probably too late to ask a question now 😢 but is it conceivable that there are giant macro dimensions that dwarf the 3 macro dimensions we inhabit in a similar proportion than our macro dimensions dwarf the hypothesised micro dimensions of string theory? I don’t know whether this question is ‘interesting’, ie I don’t know whether an assumption that they exist would be of help in answering some other question - I just thought I’d mention the thought.
Hopefully someday we get to the symplectic structure of phase space :)
Is there a symmetry that preserves locality, in Noether's theorem?
We talk about hiding dimensions in smaller scales, but shouldn't the inverse be true? What if our 3D space is like that 2D tube that vanishes to a fiber as we move away from it. If we can move away from a 2D tube and make it look 1D, might we be on a 3D space that is seen as a 2D surface to a 4D observer at a great distance? Or maybe all of our dimensions are small to a large enough observer living in large space? Is there anythi9ng wrong with that?
Feynman student, You're my professor now!
Is "mass" considered a dimension in the extra dimension that is mentioned here??
Even in Newtonian mechanics why isn't "mass" considered as an parameter to describe where as momentum does.
@@michaelsommers2356 it is also a possibility that, mass can be derived from momentum and that is easier to use for determining other factors like energy..
However still mass is property which could be used as a dimension (my opinion)
@@michaelsommers2356 I just raised a doubt, and your reply doesn't seem to give a proper answer.
mass=momentum/velocity (Newton Mechanics) so in this sense if i know the momentum, I know the mass given I know the rate of change in x,y&z coordinates
Well Photons carry energy, and energy and mass are the same (E=mc^2). So photons have momentum, energy and mass however you may look at and depends on the application.
@@michaelsommers2356 , maybe " photons have no rest mass" is more accurate.
I would really hope my doubt is cleared by Sir Sean Carroll.
I was just talking about Newtonian domain. The Photon part is better understood in the relativity and space-time physics
Math is the law of science written down, the thought we can use math presumptuously by itself to make sciences like quantum mechanics is totally preposterous because the laws of nature are already set. The fact they are unchanging allows us to do science.
Thank you for the series. You've piqued my curiousity now that you mention 10 or 11 dimensions.
Knowing that we traditionally have time as one dimension plus 3 dimensions of space making the 4D universe. In these extra dimensions that you mention could there be extra dimensions of time or is that always restricted to the one?
@@michaelsommers2356 Indeed. But is there a time when the cat is not in the box to be determined as either been dead or alive? Could it have gone through some sort of temporal phase transition and gone for a stroll around the neighbourhood before or after? I'm just curious to know if it has many worlds to Interpretate.
@@michaelsommers2356 Well in the double slit experiment the atom when a detector is present is detected 50% of the time going through the top slit. The assumption being the other 50% of the time going through the lower slit. Sure enough the results show two lines of position for atoms ending up.
When the detector is not present then the results give a completely different set of results as if the atoms have acted like waves instead. Maybe there is a temporal phase transition going on? I only ask the question and don't know either.
I would be interested in more on the Hamiltonian formulation... specifically how the Hamiltonian for simple harmonic oscillation leads to trigonometric functions. I suspect the actual movement over time has something to do with the integral of the hamiltonian rather than the derivative, and that an i comes into it at some point and then gets used as an exponent in an e^i(something)? Or at least a "something^i(something)" that then gets normalized to e?
Actually, I'm getting hazy memories of this maybe having been done in college...
IT&T - imagine this and that theory :) I so want us to prove anything new "soon", let's hope the major construction of any future supercolliders won't be halted and hindered. Get well, America!
Thanks Sean for another good video. I'd like to suggest the next Biggest Idea: universal constants.
nice show - maybe try Rule of thirds - will make show look better
Do you have a discussion about dark matter hidding in extra dimensions?
Once Sean gets into the stringy stuff. Physics is getting funky somehow. Likes its moving away from reason and knowing to an unknowing madness.
The more we open the intricate clock. The more it confounds us but just keeps us interested enough to stay in the maddening game. The answer will never be what we expect.
The future is gonna seem crazy if we knew it. But it will overall over time be good. Heart somehow trumps head. Even in physics for me.
Not sure how you can watch videos as clearly laid out and as logical as Sean makes them, and yet come away with "physics is moving away from reason".
Can twins be quantum entangled?
Hey, 130 videos would be great :) I got plenty of time right now.
What about M-theory?
Suggestion: maybe you could use the screenspace in the video more efficiently. For example extending the part where you write towards the bottom of the screen. Or using the space above your head, maybe with a second screen for short notes, however that would maybe be overkill. Great series btw !
If there's one thing Ive learned watching and listening to Sean M Carroll, is that he loves Laplace and his demon.
Thank you Seany boy.
Good example of fase space is attractor of Lorenz
Do you think that multi-dimensional beings would derisively call us "silly three-branes," confusing people who don't know about M-theory?
Is a black hole a thing, or the absence of something?
They appear to hold a spherical shape. Yet to my knowledge they aren't comprised of something, if they were, shouldn't those 'somethings' experience instant
spaghettification? Thereby vanishing from existence entirely and instantaneously?
So why do they have the appearance of a shape?
Larger/heavier bodies are spherical due to their relationship with gravity. That force is equally applied evenly to the entire surface-area of said object, resulting in a spherical shape.
Black holes don't have surfaces, right?
When I think about a star collapsing into an anti-star (BH), shouldn't the
near infinite gravity just pull the remaining material into oblivion
instantaneously?
How could a field of any kind remain after the collapse?
Anti-stars shouldn't leave anything behind, let alone a light consuming spherical field that decimates matter.
Just the fact that anything remains after such a collapse doesn't make sense to me.
My conjecture:
Unless these anti-stars are actually antimatter fields, whereby matter that
gravitates too close to the field are annihilated upon contact. The
Hawking Radiation could be matter converted into out-gas after making
contact with said event.
Space episode was very difficult to follow... ;-(( -- especially Hamiltonian ;-))
wow great video to sleep to
@Sean - Your Partial Derivative "funny d" symbol looks a lot like the the letter "d" used in English Lute Tablature in the very famous 1610 publication of the "Varietie of Lute Lesssons" by Robert Dowland. Here's an example: walterbitner.files.wordpress.com/2015/09/earleofessexgalliard.png
There are a couple in the first measure (an elsewhere), and indicate the the 3rd fret for a particular string.
I so know you play music, so I thought you might find this trivia interesting.
"Take a brain and wrap it around" - I'm trying!
Give the shut-down a few more weeks, and your hair will get as wild as my university calculus professor's hair. (he was also quite good)
Design tip: don't cut your image (body) under your chest ;) :D
Thank you very much for your videos!
Flying through space surrounded by dweeble brands reminds of a story I wrote in sixth grade must of had old physics books available somewhere about 37 years ago
If the information in the book is written in Chinese, for me me is zero information because I don't know Chines language, so this paradox might be false. The information written in Chines carries zero energy for me, so wouldn't radiate from the black hole.
"Particles" whose mass changes over time? That's a rocket that burns its fuel.
No, dels are used in Russian handwriting too.
б is not the same as del. They are mirror images of each other
Branes
A dabble of math might answer the 'is this entangled?' questions better -- talking about whether you can factor things isn't too much, I think, for this audience.
These are wonderful, but getting very ‘mathy’ and not as accessible for the casual listener/watcher.
So, I don't know if this is worth mentioning, but I heard Mike Tyson say it, and tried to figure out what about being massy limited accessibility.
Can you post something special when we reach 100K subscribers legend? You make Carl Sagan look like Arnold Schwarzenegger in Kindergarten Cop.
I loved it when he said funny d 8:40
Your shirt is the same color as background, it looks really weird.
Anyone watching you vids on the Hamiltonian and you have to show how to take a derivative....instant let down!
I used to think i was smart....
Where are you in face space? I’m in the nose.
first