Your Daily Equation #31: BLACK HOLES: And Why Time Slows Down When You Are Near One
Вставка
- Опубліковано 25 тра 2020
- Episode 31 #YourDailyEquation: Shortly after Einstein wrote down his new equations for gravity--his general theory of relativity--a German mathematician found the first exact solution. And within that solution physicists realized that a strange new entity was lurking: black holes. Join Brian Greene for a visual exploration of black holes and some of the mathematics that underlies them.
Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.
The World Science Festival (WSF) is an innovative multi-media organization that produces original live and digital content straddling the arenas of science, technology, the arts, media, performance and education. With the goal of radically transforming public perceptions of science, WSF creates world-class programming, both live on stage and televised, featuring inspired collaborations, outstanding talent and novel production techniques that bring scientific discovery, insight and perspective to a broad general audience.
Official Site: www.worldsciencefestival.com
Twitter: / worldscifest
Facebook: / worldsciencefestival
Instagram: / worldscifest
Subscribe: / worldsciencefestival - Наука та технологія
Here I am having zero experience with such equations yet watched the entire video in awe. Thank you!
I see a lot of space videos but only Prof Greene breaks down complex math and phy for me with simple visuals. Thank you for being a great educator Prof.
Daily equation idea: i^2=j^2=k^2=ijk=-1.
Btw Brian, these 'intermediate' level math/physics videos are a uniquely precious resource! it is a pleasure to hear ur perspectives! Thank you!
Hi Brian,
My name is Luthando Mayatula and I am an aeronautical engineering student at the University of the Witwatersrand, Johannesburg. I have been studying for so long that I thought I would never touch another book after I graduate at the end of 2024. I am happy to tell you that your videos and lectures have inspired me to go further still. I am now so inspired to go into the study of nuclear physics that it is almost a guaranteed next step after I graduate engineering.
Thank you so much for all the hard work you do!!
Thanks for the class Brian !! Fantastic!
Does anyone see his enthusiasm.
Amazing
always
I could listen to Brian Greene for hours. His ability to provide intuitive images that roughly approximate complex phenomena is amazing. As a fellow professor (psychology for me), I can do nothing else but tip my hat to him. I'm sure going to miss these daily equations when we all go back into the classroom.
Omg I'm so excited!!! Been waiting for this one for a while!!! Thank you professor Greene!!
Love it! Thanks so much for the rigorous explanation.
🤯 Awesome video Dr. Greene, thank you!
This was an incredibly important and informative lecture!! Many things become much clear.
Professor Greene.... you're an absolute Genius! Thanks a lot for this mathematical preliminary on black holes.
This is awesome it's exactly what I was looking for thank you Brian!
Hi Prof. Greene, thanks for another great episode of Your Daily Equation.
Take Care & Stay Safe.
Best wishes from West Wales. Thanks Prof. Paul C.
Absolutely mesmerizing lectures Dr Greene! Please keep making more awe-inspiring videos such as these lectures. So mentally captivating! Wonderful!
Thank you Prof. Greene - I find ALL of your Daily Equation videos SO fascinating! I am SUCH a fan of black hole theory; however, I have so many questions (in no particular order):
1. What are the physical properties of a black hole after its collapse (ie: what is it "eventually" made of)?
Does it change over time, and if so, what effect does that have?
2. Since protons are mass-less, what do black holes "work-on" to change their trajectory? (I'm assuming that the answer is, "they don't work on the mass of the proton - they bend space-time around them - which then becomes their trajectory" .. but I want to be sure...
3. Black holes are often portrayed in 2-dimensions (like a funnel); however, in reality, they have a 3-dimensional effect on everything around them in all 3-dimensions). Is this to say that the event horizon is at a given circumference at a given distance around the black hole? If so, how is the event horizon distance calculated? Does it vary? If so, why? (if I missed this, please forgive me in advance...)
4. Gravity is considered a "weak force"; however, in the case of a black hole, the gravitational force can be so strong that it bends spacetime. Doesn't this conflict with the idea of it being a "weak force"?
5. We can measure LARGE gravitational waves (as experienced a few years ago with LIGO) - leading you conclude that gravity is a wave... so can we measure SMALL gravitational waves? If so, to what level? Why are we unable to find/identify a particle (ie: graviton) in play?
6. Assuming the universal speed limit (aka: the speed of light), wouldn't you expect protons to "pick-up-speed" after crossing the event horizon and heading towards the singularity? (this "might" go back to my question #2...)
7. What are your thoughts on the "completeness" of Einstein's General Relativity? I've always felt that it's missing something, but I'm not savvy enough to pinpoint why...
Thanks, and I look forward to future videos!
In case you're interested, I think I can answer some of your questions, to the best of my ability:
2. Basically what you thought the answer is. Photons (protons aren't massless but I think you meant photons) follow geodesics in spacetime, and near large mass/energy those geodesics are curved.
3. Yes, the event horizon is a sphere around the black hole, and the distance is the r_s that Prof. Greene talked about in the video.
4. Gravity _always_ bends spacetime, that's what it _is_. Even the Newtonian approximation is only an approximation. As for weak, it's weak in the sense that the strength of gravity of a single particle (say an electron) is many many orders of magnitude less than the strength of its electric field. Individual particles have very weak gravitational fields, but strong electric fields (and those that experience the weak force or strong force are coupled even more strongly to those interactions). But if you get enough of them together, the gravitational force, being always positive, can add up to a very strong force indeed.
5. This is related to the last question. Because particles interact so weakly with the gravitational field, detecting the influence of individual gravitons will be very difficult. As for gravity being a wave, this is something that we knew (from Einstein) before LIGO, but it did confirm that prediction of the theory. It should be noted that there's no contradiction between gravitational waves and gravitons, any more than there is a contradiction between electromagnetic waves and photons.
6. In some sense things will travel faster than the speed of light (their coordinate velocity goes higher than c) inside of a black hole. If you think about the waterfall analogy mentioned in the lecture, it's as though space itself is falling inward faster than the speed of light. This way of thinking can also make clear why you can't get out: you're limited to c, but the space you're in is falling inward faster than c, and carrying you with it. This may not be the best picture of the interior of a black hole, but it does have some use. This doesn't break the "speed limit" though, as that applies to things traveling through spacetime, not spacetime itself.
@@ReddooryogaSH Great answers! Thank you!
@@ReddooryogaSH you answered questions I didn't even know I wanted the answers to lol thank you!
I shall surely wait for him to give you the answers. Some interesting questions.
I suspect some answers done and dusted here.
Thanks Dr. Greene for such a wonderful lecture on Black Holes.
Wow, amazing again! Thank you!
What an excellent episode! Way back at the beginning of YDE, I asked you to show where in GR could be found the prediction of black holes. And there you did it. It’s very clear. And as you explained in the historical part at the beginning, how extraordinary that a prediction can be extracted from a mathematical equation and 100 years later, we can have observational evidence of the existence of the predicted object. Bravo.
That black hole photo is one of my favourite screensavers. Such an intellectual and technical achievement.From Schwartzchild to Hawking to Shep Doleman and the rest of the EHT Team. Mathematics really does provide humans with a perspective that is as big as the universe.
The advantage of channels like this is that we can thank our professor for the many times he was on TV shows and UA-cam videos like with Janna Levin and the very nice talk on the Commonwealth Club channel two months ago for example.
Thank you professor Greene.
agreed whole heartedly, thank you professor, you have expanded the brains of roughly 20,000 of us or more every episode of your daily equation, thank you!
Thankyou professor for such simple explanation of such great topic.
Awesome series.. Thank you professor Brian greene..
I will say this about professor Greene, he has some of the neatest handwriting I've ever seen in a professional scientist.
For some reason it reminds me of the Disney logo
Awesome! Thank you Dr. Greeen.
This was sooo helpful for my uni course. Thanks loads!
Thanks for these great videos, Brian. I really appreciate you taking the time to explain these physics and mathematical concepts to the layman. Your book, The Elegant Universe, piqued my interest and was the gateway for me wanting to learn more about theoretical physics.
Thank you so much for this series from UK
Thank you Professor Greene (btw greetings from Italy). Thanks for all the effort you do to clarify these wonderful concepts, I really appreciate it. About black holes, could you please explain (maybe in the next Q&A session) what underlies in the "information paradox" of black holes? Because I didn't understand where is the paradox....thank you very much, Sir.
Take care
@@chriswarburton4296 Thanks for your very interesting view, Chris. But I've been lucky! Because my question has been answered by Prof. Greene in the beginning of the last Q&A session (May 29th). In case you missed it, I suggest you to watch it. Sorry for my English, I'm an italian guy with a passion for physics :-) Bye
Thanks u professor.. u r really one of the smartest man on earth
Thank you Dr. Greene, watched you on tv since I was a little, watching this fills my void of curiosity about the universe. Also, the unknown about the universe makes me smile 😊 I see it as a cyclical balance.
That was pretty good. I didn't totally understand it but I like how you presented it and wrapped it up in the end. Thanks! I couldn't help but think of a Simpson episode though where Homer put his head in a black hole and it stretched and he finally went in and he was in a 3D world. Keep 'em coming, love the Daily Equation.
I don’t know the equations but I find the concepts incredibly fascinating
This is as good as it gets for the non-experts. These your daily equation videos should get millions of views from the public. But if one wants to have real understanding of these ideas, I think one should have a good grasp of differential geometry, which I find very difficult.
So thankful for your existence professor, want to meet you one day
Wonderful. All these are absolutely delicious. Just amazing, how you explain all of it.❤️
This guy’s explanations are amazing, a separate skill from the actual math.
Your Bidiurnal Equation, perhaps? But the fact that you do these, Brian, is fantastic and you are an excellent communicator.
THANKS SIR
Our teacher showed us, we can get correct schwarschield radius using newtonian gravity as radius where escape velocity is c
(wrong procedure, correct result)
This is amazing
This is great thank you. Will you show us how to get to the Kerr metric solution for a rotating black hole and the implications thereof? That would be great. Thanks
Thanks, Brian.
Many Thanks
Does the stars core collapse initially do to the core cooling rapidly? Fun to follow even a glimpse of gleaning the meaning! Thanks Doctor
Excellent explanation of black holes for those maths dumbos like me . From this I gather that closer to a black hole you get your future is directed to the singularity until you can’t escape is that correct Brian?
Love the channel. Only writing to Express my dismay at the accelerated writing of equations. When 'you' write them, you seem to give them more context during the writing of them. I would ask you to return to your former method. Thanks for the priceless knowledge you pass along so well.
Thank you professor. What is your opinion regarding the idea that the whole universe can be inside a black hole from the point of view of these solutions?
This is what Your Daily Equations is all about: esp in this subject it is the details from the equations that show why the amazing corollaries we armchair physicists all know about black holes, are real.
Brian Greene - Brilliant Guy. The test of a brilliant guy is the ability to make everything as simple as possible; but no simpler...as Einstein himself would say!
Love your vids!!! Is there a equation explaining why a BH doesn’t form from a nebula ( matter collapsing since the beginning) or why is it necessary a star before a BH is born? Thx!
Thank you
Excellent
Daily equations VS Big ideas. Great 🙏🎉🎉
thank you so much
Hi, I have a question which is making my brain go around.
So, the attraction between earth and the sun ( for example) depends on both their masses, and the distance. However if that attraction comes from space time curvature then say if the sun was bigger smaller but much more dense ( the mass would stay the same) wouldn’t the space time be curved in a different way? And therefore gravitacional force would depend not only on the mass and distance as newton shows in the equation right?
The metric g only depends on the mass M (no dependence on the sun's radius) 23:20, just like the Riemann tensor because it's calculated from g.
This is another example of the fact that the representation as a rubber sheet (which you are probably thinking of) is misleading.
But, Volume in this case is a function of radius itself?
Space and time flipping is fascinating! The parallels between being unable to go back in time and being unable to leave a black hole🤯 It seems like we're pulled into the future, right now in the Universe at large, as if into the centre of a black hole! I feel there are strong connections here with the arrow of time in general and entropy?
Enjoying your lectures....we are so lucky that corona seems to have you with us -a very real silver lining! So.... my question....Is gravity emergent and if so can it be manipulated by affecting entropy in a particular volume of space or specifically here on Earth?
Thank you so much Prof Greene. But there's something I just can't wrap my head around. Once you cross the R S boundary then time and space invert. If space becomes extremely distorted and together with extreme time dilation how is the speed of light conserved? And so, essentially photon is travelling mostly through time towards singularity. How is it possible to travel through time and not through space, if, as we've seen the space is there and it's stretched, or is the stretched shape only a stretch in time ie time dilation. Is it same concept of a worm hole? Sorry, a little confused. Please explain during Q&A.
Awesome! I'm glad you are doing these videos, your books are what initially got me beyond the mere interest into the obsession of physics.
I think it is very necessary for these concepts to be shown to people to generate and keep the interest alive. Lots of physicists and only a few who want to explain it to us so thank you!
After years, i now understand most of it to a very good conceptual degree and want to start getting into the math, you are making it as accessible as such complicated math can get.
Thank you prof. Brian! I enjoyed the video. I have a question that if we pass a light beam between two black holes of same mass which direction will it go?
) + ( = |
straight ahead i guess
except that all black holes rotate really fast. Which ever one drags things more I think the light will curve round that 1
29.45 new word, thanks.
Thank you for showing the Schwartz child radius solution. Very cool.
So what does having 0 mass (photon) mean when you pass the event horizon, when the spatial and time coordinates swap?
And what would it do if the spatial and time coordinates didn't swap, could light escape that kind of anomaly?
Thanks Brian for explaining the black hole equation. Using the mass of the Universe the Schwarzschild radius is within the observable Universe. Is it because of the density of the Universe is defused and crossing the horizon would be much less than the speed of light? Between the Big Bang and about 3 BLY after the Big Bang the Schwarzschild radius is bigger than Universe radius then what is your idea about the conditions that kept the Universe from collapsing into a singularity? Thanks for your reply?
Those animations are amazing. Were they made by your team or is it stock footage?
Master of sciences
For those of us who attend his lectures via UA-cam, does that officially make us his students? Or not quite?
Love from Nepal
With gravitational time dilation, when we sync two clocks, send one somewhere into space, and then have it return; is not the two differences in time a form of time travel, however small that difference may be?
we're all travelling through time dude. Otherwise we wouldn't get to lunchtime
The clock travelling through space, has some of it's motion through the time dimension converted into motion through the space dimensions. Therefore it runs slower than our clocks on Earth i.e. it travels through time less than we do.
Awesome presentation, thank you so much for this series. One question I have is how relativistic mass comes into play in thinking about black holes. Is it possible to make essentially any mass/object appear like a black hole to an outside observer by making that object move fast enough relative to the observer? If so would a real world example of this be possible to see thanks the the accelerating expansion of the universe, in other words would some distant object from earth that is nearly massive enough to be a black hole become one from our perspective simply because it ended up moving fast enough relative to us slow pokes here on earth? The opposite of this idea would be if a black hole (but just barely one) was slowing down for some reason relative to earth and the relativistic mass decreased enough such that from our perspective a black hole would cease to exist and a star or whatever the object was would appear? My guess is I don’t get relativistic mass vs real mass but I thought it would be fun to ask these kind of crazy question, again thanks so much for your talks!
I think the Starship Enterprise doesn't suddenly get a big gravitational field sucking objects into it whenever it goes fast
There's a good video on 'Albert Einstein's Theory of Relativity' by Eugene Khutoryansky
in which he/she talks about relativistic mass increase. Let's say
1) We have 2 balls of equal mass
2) You drive past me in a futuristic car
3) You throw a ball at me
4) i throw a ball at you
5) our balls hit each other
6) Your car's so fast that i see your arm moving slowly due to time dilation
7) Thus i see my ball moving faster than yours
8) Therefore my ball should push your ball back
9) But it doesn't. They both stop & fall to the ground. Therefore your ball seems to have become heavier
However, from your perspective, your car is stationary & it's everything else that's moving. This is the principle of equivalence. So you see ME moving fast. You see MY arm moving slowly due to time dilation. Therefore your perfectly entitled to expect that your ball should push my ball back. & it doesn't therefore I have massive balls
If we looked through a telescope at the Starship Enterprise moving near c we would see the crew running around in slow motion. But Captain Picard would see his crew running about like headless chickens in normal speed. So this whole slow motion time dilation thing that gives rise to the feeling that some people have massive balls bigger than our own balls, I feel maybe we have to take it with a bit of a pinch of salt?
The mathematical approximation of considering a massive body with a 'point mass', introduces idealize any physical description. Newtons law of gravitation predicts g=0 at the center of the earth, although at the center the pressure is billions of tons. Mass of the BH is not at the center, but at the event horizon (Hartnoll).
Thank you Prof Greene...after two Panadine I see the light, I mean the Blackhole. That's a lot of Greek letters!
Love your videos... xoxo
The achievement of Schwarzschild in the WW I, in the trenches and being bombed, is what anthropologists call "situational logic"...a concrete sense of singularity.
Are the little g in the General Relativity equation represent the metric tensor and not gravitational acceleration? G is the gravitational constant on the right side of the equation but none on the left side? If G is represented by the distortion in the geometry then how is the amount or magnitude represented in the left side of the equation? Can you elaborate on the details including the Tuv energy tensor in another video? Thanks
g(with subscripts u&v) is a metric tensor in Einstein's field Equations and G on the RHS is just a constant which doesn't describe anything about the geometry of space-time, the interesting object in the right hand side is rather an energy tensor!!
Is space itself _really_ flowing or are objects and material travelling or being pulled through space into the black hole?
Brian: Thanks for your great work. Great video. At 2:25 Wouldn't it be more precise to say that compressed mass creates a warp in time, really?
Space doesn't know about time per se, doesn't it? Isn't it that mass gives space its time...
Sorry, but a gain at 8:08 wouldn't it just be allowing spacetime to slow down for that to be happening...?
I wonder what would happend if we set a time from a speed that is way higher then c, but just use it as referense, let say we set time t_ref = 10^-40 s as one unit, so like it would depend on some particle traveling at speed (10^40m/s)/c, even tho nothing can travel faster then speed of light, but this is just a time reference. then our time should still be 0 at event horrison, but t_ref should still be bigger then 0, since it follows an imaginare particle, and used as a time refference, just wondering, I will try something like this out when I learn einsteins Eq, but I am still curious tho :) also love your videos!!
I have no idea what you just said. I love it. H~0=L (E)
I thought I had about what happens in a black hole. The singularity doesn't make sense to me. I think it might be something like an hour glass. Stuff gets crushed down into its smallest part (01010101?), but it can't go beyond that, and then it gets "released" as information.
What happens to spacetime geometry at the Schwartzchild radius which means and implies that it is equal to 2GM/c^2? Do people know or is this just the result of the Schwartzchild math solution.What is the reason for this combination?
What I've always imagined is that Delta T becomes zero at the surface of the singularity. Then, I think that it can't be zero. If it were zero, Hawking radiation wouldn't exist and it would never evaporate. My other question is about the size of the actual singularity. We know the event horizon between a low mass singularity is relatively small and super-massive singularities like at a galactic core will be rather large. Although the masses are dramatically different, does this translate to the actual physical size of the singularities? Intuitively, the physical size of a super-massive singularity would be larger. Does the math break down before we can make this determination? Only so much information can exist within a given volume of space, or is that correct on an intuitive level, but incorrect in the maths? I'm not sure these are even good questions but they've been rattling around my brain for a while. Unfortunately, I left my differential equation calculator in my other brain, so perhaps I could get a little help here?
When last atom collapses-- does it mean that in that atom region : basic masses are changed at it's no longer have all this proper masses to be in our space so everything collapses in that region?
Now I understand why Gargantua turns into time dimension in Interstellar
I wonder what is the schwarzschild radius for the observable universe
I don’t understand the premise of “falling into a black hole” if it’s space which warps when there is mass present, aren’t you falling into the warp the black hole creates? As opposed to the black hole itself?
Edit: Never mind lol, I posted this just as the video began, and Professor Greene explained the exact scenario at 2:41 😁
2nd Edit: Actually, if it is the space which is warped that’s classed as the “black hole”, then where is the mass which is creating the warp in the first place?
I thought the metric is only valid outside of the mass region causing the black hole. Therefore is the singularity not just a reflection of the fact that the solution is not valid at r close to or at 0?
When I imagine a black hole crushing matter so dense that even light cannot escape I think that black holes would also be responsible for the expansion of space and movement of time. If matter is made up of atoms and atoms are made up of mostly space with some particles, compressing matter to the density of a black hole would certainly leave no space between any of the particles and what happens to the space that was normally trapped between the matter that spacetime warps around? What would be the left over product of matter compressed so densely that there isn't any space for any vibrations at all? Dark matter perhaps? If matter is mostly empty space but also warps spacetime then it would seem logical to me. If black holes convert matter to dark matter and in doing so release the space that is normally trapped between the particles of matter wouldn't the space itself be able to escape the black hole by mere fact that it doesn't interact with matter? On a side note if matter is converted to dark matter and we imagine time stops inside a black hole maybe that's because once you release the space it helps with expansion and it also pushes time forward in that sense. I don't have the mathematical education to put that idea into an equation but I wonder what they would look like. One last thought if the above were to be reality wouldn't matter be giving back it's space to spacetime fueling expansion of space and movement of time. Basic particles are restless because they have no mass, by mass we really mean how much space can be trapped between particles because it's the trapped space that moves us through spacetime, as spacetime expands the space between our particles gets pushed like a sail which is how matter can be seen moving apart faster then the speed of light. Dark energy is just the release of space from matter. I try to always keep inside the concept that everything is linked to everything in one way or another anyways I just wanted to put my thoughts out there.
Brian Greene time =41 min to explain, my time to understand properly approaches infinity! :) ...
I tend to believe that the gravity itself has a speed of expansion wich can be superior of the light speed!!
Particle wave duality to projection of mass energy state, that uses space mechanically. Gravity induction at it's finest, currently accepted methods and means of technological understanding beyond nuclear. Dare we manufacture greater technology?
Sir, how to access your course on general theory of relativity?
I believe its on the world science festival web page
Sir please make a video on quantum gravity
Go to WSF....plenty of thrills.
He haven't covered Quantum field theory yet, which is prerequisite of QG.
5 min in ..... i'm lost in the equation still trying to understand. Yet i see explanation in a 2 dimensional way somehow. 3 d or better yet (very difficult) 4 d ( above, underneath, dept and diagonal) how you see the"hole" if it's not a black hole ??? i still believe it's an orb as i have not seen from another perspective view then the "event horizon"
Of course you can go back in time, just go faster than the speed of light!
When the star explode and the core remain and then turn into a blackhole maybe the core is still there but it is so massive that it warps space fabric so much that light can't get out and you can't see that core
yeah but it has to be smaller than the Schwarzchild radius eg Earth squashed to 1 cm = a black hole. So the process is big star runs out of fuel, supernova, loads of matter thrown into space, the rest collapses in on itself due to gravity so strongly that there's no force that can stop it contracting into a dot. If you have a star that is still big then it's not going to suck that hard. It has to be small to become a black hole. This is because gravity is a 1/r^2 force, thus small r = very big gravity
btw i'm not sure if all go supernova actually
Can anyone explain why speed of light does not experience relative motion? Just came from the relativistic velocity and by that formulae if 2 objects are moving with speed of light to each other the relative remains c. Why is this so, apart from the formula can someone give a reasoning?
You've heard the talks about the difference in the perceived time at which an event took place when observed by a stationary observer vs an observer on a moving train where the event took place? In a way your perception of the speed of light may appear to be relative, however the actual speed of light is constant and unaffected by the motion of the light source or the observer, as opposed to two observers moving towards each other who are in essence moving in a very real way at a different relative speed than if one were truly stationary relative to the medium through which they are moving. No matter how fast you move through the medium any light you emit will never move faster or slower than c.
Also can you say more about Lambda?
Is it posible when the universe expands faster than the speed of light to rip the black hole?
It was a woman who figured out how to see a black hole i cant remember her name i watched a special on black holes and the advancenent in tech that allowed this mark in history. It was pretty cool.