Deriving Hawking's most famous equation: What is the temperature of a black hole?
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- Опубликовано: 17 июл 2024
- Black holes are perhaps the most enigmatic objects in the universe. Popularised in movies and science fiction, they evoke the magic and mystery of our universe and provide inspiration for those looking to make their mark in the world of academic physics. But what exactly is a black hole? And how can we study them?
According to Einstein’ theory of general relativity, a black hole is a region of spacetime where gravity is so strong that nothing, not even light can escape. The boundary of this region is known as the event horizon of the black hole, and according to classical relativity, once an object has passed the event horizon, it will never be able to escape the clutches of the black hole. However, when you throw quantum mechanics into the mix, as is often the case, the situation becomes a bit more subtle. In fact, in 1974 Stephen Hawking demonstrated that by combining certain elements of quantum field theory with General relativity, it was possible to show that Black holes do in fact radiate, causing them to slowly evaporate, and eventually disappear.
Now I don’t know about you, but when I first read about black holes as a child I was instantly hooked and desperately wanted to find out more. The only problem is that the physics of black holes, and in particular Hawking’s work, is notoriously difficult and requires an advanced knowledge of Einstein’s theory of general relativity as well as quantum field theory. But is it possible to determine the most exciting and mysterious properties of black holes using only advanced high school mathematics? Well, it turns out the answer is yes, and in this short video I would like to show you how.
References:
Black Holes and Time Warps - Kip Thorne
Dimensional Analysis and Black Holes - David Wakeham (hapax.github.io/assets/dimens...)
Some Simple Black Hole Thermodynamics - Michael LoPreso (pubs.aip.org/aapt/pte/article...)
Gravity from the ground up - Shutz
Black Hole Math - Nasa Resource (www.nasa.gov/sites/default/fi...)
Hawking for beginners: A dimensional analysis activity to perform in the classroom - Pinochet (iopscience.iop.org/article/10...)
The Holographic principle - Jean-Pierre Luminet (arxiv.org/pdf/1602.07258.pdf)
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iopscience.iop.org/article/10...
iopscience.iop.org/article/10...
I am 60 years old and I was able to enroll in any university in my country as an engineer. However, at the time, I didn't think I was smart enough to understand the math and physics needed to complete the degree, so I chose to become a Technician instead. After watching three of your videos, you have helped me to remember some of the math concepts I learned 40 years ago. If I had a teacher with even half your ability in high school, I would have pursued a degree in engineering. Your ability to explain complex concepts using only high school math is truly remarkable.
@@Bopplesyou can do it!!! wishing you lots of success 🫶
@@BopplesI hope you are successful! Praying for you!
@@BopplesI believe in you. You’re never too old to change the world. Keep going you’re doing great!!
But how did you know you would not have a good teacher, if you went on to study this in college?
The video is improved, the graphic representation of Hawking radiation is removed, which was used by Hawking himself but was ultimately just incorrect. Such a good video! This subject is popular with more sophisticated physics learners, but ultimately purely mathematical and not intuitive and our “mental picture” of what we think is happening is unlikely to be real. All my opinions, of course.
Yep. What is interesting is that, as he says, we can do these calculations with nothing more (OK, with some measured actual physical quantities thrown in) than dimensional analysis. i.e without proposing an actual mechanism for the process of Hawking radiation. And yes, the "Virtual particle pair separation" model is wrong, insofar as it is NOT the mechanism that Hawking proposed, but has been used, somewhat inaccurately to describe the process (even by Hawking himself, i believe?) as a sort of "easier" explanation than the full reasoning behind his prediction. Would be good to see a video here on the actual mechanism proposed by Hawking. PBS Space time have done a good basic video on this, but would love to see a more detailed mathematical look, here on this excellent channel.
Over to Physics Explained?? 😉
Sometimes an imperfect diagram is still the key to the first-time hearer "getting" it.
@R C So how many of you are there in your mental picture of your self? I take it you all live in fascist mental state.
@@jimwinchester339yeah, if they tried to teach fifth graders about atoms its a lot easier to think of electrons as tiny balls even if that's not *really* what they are
@@chimkim My second-grade daughter actually IS learning atom structure at school. Yes, protons and neutrons are abstract "balls", and I don't know how electron clouds are explained in their books - thankfully they mostly study without parental intervention ;)
(sure sometimes help is needed, and I'm not abandoning my child, just saying she does good on her own most of the time)
Ukraine.
The fact that you made a video in which you explained this all using physics that a 17 year old school student was able to understand (me) is astounding keep it up!
You are one of the few smart 17 year Olds! Don't forgot it!
This channel is a goldmine for abstract knowledge.
There is a difference between abstract knowledge and abstract nonsense
I would argue that this is the complete opposite of abstract....whatever that maybe.
@@edwardjcoad many use “concrete” as the opposite of abstract
You should check out the other videos that have non-abstract knowledge. You quickly learn it is an amazing channel for a survey and quick review of real concepts we use in physics.
It's a gold mine for unicorn farts. It's all made up, no evidence and wrong.
I love that the audience here carefully scrutinizes each video for errors. It's basically peer review, complete with occasional re-uploads. It's a shame we lose all the comments on the original video. Sometimes people put a lot of time into comments, but re-uploads are still the right thing to do.
I noticed the original video had been deleted before I could watch it, what happened?
@@alanzyoutube Enough errors were found that the author decided to issue a corrected version. Unfortunately RUclips currently does not allow revisions, just overlays or re-uploads.
Any developers out there, as a 'comnent capture' app has a role, allowing the reporter to 'pin' them as a group so they are not lost - and a lot of thought goes into some comments. Just a thought from an old uk duffer :)
@@tim40gabby25 A quick search turned up an existing commercial service (exportcomments dot com), and there may already be open source code available. Despite being a programmer, I usually just take a screenshot of my comments, and shrug off the times when things are lost.
@@WilliamDye-willdye Thankyou. It's so hard to have a novel thought these days. How lovely for you to take the time to let me know :)
I've always wondered how all this stuff was connected and how people came up with these relations. Please keep it up
Cheers, will do
Hello its only 4 comments but what went wrong here
By delving into physics mode of thinking and extreme applied math. 😅😅
@@frankdimeglio8216 this crank has been posting for 12 years apparently. I found some old posts on FQXi where he's saying the exact same things lol.
@@frankdimeglio8216 how about going to a scientific body with this information (formatted in a way that doesn't hurt to look at, that is)
72, Retired Electrical Engineer, Remembered "Dimensional Analysis" for some of the practical engineering calculations, (as a checking system) and remember professors alluding that it was potentially a powerful tool, (and to maybe study up on it after graduation), BUT now I see, Doing simultaneous equations on the exponents of the various dimensions involved! I'm now just stunned! I just subbed. (Mind blown) no recovery insight. I just need MORE!!!
I see at this moment there are 17 videos, having accumulated 3.6 million views Wow. QUALITY WORK!!!
There are some special YT's I enjoy following, and so have a pretty full schedule, but I'm just going to have to nestle yours in among the others. I am going to SAVOR yours like a sweet dessert after a fine meal. Thanks for your great efforts!!!
Here's a fun historical fact about dimensional analysis. Back in 1945, USA did it's first test explosion of an atomic bomb. They then released some pictures of the explosion together with the time they were taken at. Using only these photos, the British physicist T. B. Taylor, managed to pretty accurately estimate the power released by the explosion using dimensional analysis. The power of the explosion was at the time a governmental secret.
After watching this, I don't get how anyone could find anything more beautiful than physics.
Couldn't agree more!
So, you don't think that life is more beautiful (and probably really unlikely, but obviously true) than burning balls of gas and rocks flying thru space?
Loving these videos, as an undergrad physics major. Keep it up. I also firmly agree with your assessment of dimensional analysis. On my last exam (Modern Physics), I used it to show the professor wrote the question wrong. Whole class got to skip that problem :-)
Glad you like them! And thanks for taking the time to leave a comment.
Like this content very much!
Add one, Sir.. ;)
1. Include c, when things are fast
2. Include G, when things are massive
3. Include h, when things are quantum
4. Include k, when things are hot
5. Include pi, when things are spherical/circular
Thanks for the nice sharing..
Pi is a dimensionless unit, so it is difficult to include it in dimensional analysis. Or, you can define an angular unit called radians, so you can include it in the analysis.
However, most physical observables doesn’t include radians, so you can’t assign dimension on it. Unless you know it is related with angles. For example, angular kinetic energy has the same dimensions like a translational kinetic energy. It’s just that the radian unit is hidden. This is because a radian unit is a constant produced by geometric proportionality between an arc-length divided by a straight length.
@@RizkyMaulanaNugraha I was going to say the same thing. How would one even know where pi shows up? The numerator? The denominator? Square-root? Cubed? Could literally be anything given it is dimensionless.
These videos are absolutely incredible. I don’t know how you’ve been able to churn them out so fast and consistently without any drop in production value or content quality. Keep them coming! My new favorite physics channel!!
Glad you like them! Cheers for the feedback, much appreciated
@@PhysicsExplainedVideos what is dark matter and plank scale
@@PhysicsExplainedVideos is it possible to go smaller then plank scale
@@masternobody1896 I think he has a video mentioning that it just doesn't make sense in the term of "physics" to go smaller. Technically nothing prevents it, but there's no value to be gained from anything smaller
@Sean g 137 coo-coo 🤪
Thank you for being this long-awaited but high quality link between us, amateur physicists and the beautiful but complex physics we desperatly want to understand :)
Outstanding work with crystal clear explanations as always.
Keep it up ! And thank you again !
"a topic which I hope to return to in a future video" is a much better shortcut than the unclear pair creation. And it gives us something to look forward to! Good work.
He is better than feynman
Cheers!
Just found this channel, and I am amazed. Explaining stuff I heard off but never totally got due to complicated explainations in a extremely clear way.
It’s incredible how I’ve learned a lot of what was mentioned here, dimensional analysis, equations of gravity and energy, thermodynamics and enthalpy/entropy, and all of it I was half asleep for. Now I’m presented with a 40min video using it and willingly watch, crazy how different it is learning for a class against learning for yourself.
I have just finished all the videos from your channel and know there is a new one :D Amazing work you do, keep it up
Thank you very much!
While I saw it yesterday (and there were few errors - minor ones, like 15360/3 being 5210 - unless I missed something or mistaken) - I'll gladly watch it again.
I just don't know which mistake was so big that you had to re-upload.
Regardless - thank you again. Keep making these - they are fantastic videos that look more in-depth than most channels. And while I trip up on mathematics sometimes - well it encourages me to remind myself of how to use it (I'm a person that last time used calculus 15 years ago and almost never professionally).
As your catchphrase says: NEXT! ;)
Cheers for the kind words, much appreciated
@@PhysicsExplainedVideos No problem - it is a pleasure to watch your videos. I hope that in the future (doing it now probably lacks enough foundation in QFT and QED) you'll release a video on Quantum Chromo Dynamics. On RUclips there are only few videos that deal with this subject - and those are couple minutes long and don't go in-depth.
Also do you have a Discord?
Regardless - I love your videos - my favorite being the one on Ultraviolet Catastrophe. While I knew the subject relatively well - at least as much as can be by someone who never studied physics but loves it as hobby - I never truly understood the details that led to birth of Quantum Theory - I only knew that it was to counter infinities. Seeing it unfold in Mathematics and "tricks" used to extract this information was crucial for me to finally begin to understand the subject. I'm not saying that I understand Quantum Mechanics very well - but I spent couple of hours trying to solve equations that you provided. Which increased my understanding of the subject.
Again - Thank You! You're well on your way to becoming the best Physics channel on RUclips when it comes to deep analysis of problems. Something similar to what 3Blue1Brown is for Mathematics - which is a very favorable comparison. Good Luck!
Dyslexia
About to start physics at college this fall. I hope the lectures are even half as interesting as these videos.
Good luck at uni!
@@PhysicsExplainedVideos thank you!
I’m in physics rn. It’s way more vapid than this so far ☹️
Mind blowing content. Such a standout format among science videos. Never thought that the “complicated math” that gets abstracted away actually makes things easier to understand
I’d just like to extend a huge thank you to you for this incredible content. I failed maths gcse 21 years ago, but I am now enrolled at college to retake it, thanks to you. We all learn in different ways, and this channel (despite maths I barely understand) has made these concepts easy for me to understand, and genuinely curious to see how far I can now push myself with mathematics. When people ask me why (because I don’t technically ‘need’ it for any reason), I reply with “my brain is hungry”. :)
Very glad to hear it! Thanks for the kind words :-)
Probably the best explanation of physics on youtube. Keep em coming!
Some of the most important results in vector calculus, complex analysis, and differential geometry fall out of Stokes' theorem on manifolds. It's incredible to see the same key insight revolutionize physics in real time.
Man you've no idea what you've inspired in me. I haven't slept during night for two days now, just this video. I followed along every second again and again and again until I absolutely get it. My love for physics just increased many folds.
Please upload such beautiful lectures. I cannot wait to learn the depths of Physics through this channel!
Were you manic or are you on something lmao
No doubt, you are the one of great explainer of complicated subjects in simple way. It is always a delight to watch your video. I wish your video never ends. It is like watching suspense movie and you are on edge of your seat.
I am just starting to watch this video. This is a subject I really want to understand better and having seen all your other videos I'm quite excited. ..
Definitely my favourite physics channel, and I love a lot of physics channels. Thank you for all your work!!
Glad you like them! Thanks for the feedback
Saying thank you wouldn’t be enough for this video. If there’s anything more than thank you, I’m giving that to you. Simply immaculate!
These videos unironically made me reenroll in college.
That is unironically awesome!
Ha! What a good story!
Wow!! That’s awesome
Hows college going
@@aidenstern5254 Pretty good, I had to retake a few courses that I had dropped - but I'm onto the actual core subjects for a general physics. Grades are keeping up thanks for asking.
I Love your Videos they are so well structured and with so much Content keep it up bro
There are so many wonderful channels on RUclips. I enjoy them tremendously. And now as for the past several months one of them that I look forward to the most is yours. You cover topics that I already knew something about but I learned so much each time and the presentation style is fantastic and clear and the animation helps so much and the clarity makes me feel some joy. Thank you very much.
Wow, thank you!
I love the content, it's interesting yet filled with mathematics, it doesn't "dumb down" the audiences, keep it up :)
Always looking forward to videos from this channel.
Glad you like them!
I don't understand most of the math or physics, but I still enjoy listening/watching your explanations. As a matter of fact, I would say that your channel alone has greatly increased my passion (and of many others) for physics. Thank you so very much, I hope there will be many more videos to come! :D
On a separate note, couldn't one say that no information is lost? Assuming that a. the current micro-state of the black hole depends off of all the matter/energy that has entered the black hole & b. all the energy that is radiated away directly depends off of the current micro-state of the black hole, that is to say, the photons direction, amplitude, wavelength, and (I'm not sure if what I'm saying makes sense) the "height" at which the photon finds itself relative to its own amplitude upon leaving event horizon. In such a sense, all the information is conserved, no? Are my premises wrong? Is there a missing premise? Or is my conclusion incorrect? Or all of the above?
Well, once again, thank you ;D
You are correct, in essence. Stephen Hawking made the error of believing that all the matter was crushed into the singularity before be re-radiated, but the fact is, from the POV of anyone outside, it only gets thermalized at the horizon, and is then re-radiated.
@@ozzymandius666 Thanks for the explanation :D
This has quite possibly become my favorite math/physics video on the internet. I learned about buckingham pi not long ago, and seeing how a similar idea can be used is phenomenal.
This answered some questions puzzling me for a long time. Thank you!
One of the best videos I have seen on black holes and the only one that actually includes a discussion on the CMB which no one else seems to do! Excellent video, just excellent!
This might just be the most informative video about physics ive ever seen.
Thanks maaan, rlly learned a lot!
Excellent video ...Dimensional analysis is such a powerful tool. And paired with thermodynamics, it's fascinating how many problems can be tackled with this approach. I remember it well from my physics education.
Glad you enjoyed it!
Thank you so much! I really wanted to grasp this in a comprehensive and also in an intuitive manner. You hit the nail on the head for me with this video.
Bro, I swear this channel has taught me lots of things in simple ways, plss keep it up! I really like how you explain everything with numbers!
And I didn't quit understand the idea of radiation and that stuff of blackholes. Thank u so much!!
Great job with the video. Didn’t expect that you will also cover holographic principle.
Recently there are also some approach that tries to recover Newtonian gravity using holographic principle as the first principle. Of course it is just a conjecture at the moment because we can’t really test it yet. What I find really interesting is the derivation is backwards. Start by assuming information entropy is preserved, we can “deduce” that we are experiencing gravity because we are receiving “information” from somewhere in the form of physical entropy. Since entropy should always increased, there is no way to consume this information, other than being attracted to the source of the information, which in this case, encoded in the surface area.
By simple rules of flux, gravity then will have to be written in the form of inverse square law, simply because the amount of information encoded in the surface diminishes by a factor of inverse square distance from the source.
These videos are always so calm and relaxing with information presented in such a wonderful style, it’s relaxing, and puts me to sleep in the best way at night, while making for the most engaging RUclips lectures during the day.
One of the best channels out there
Yet another brilliant presentation. It reminds me of what I thought was a paradox after covering general relativity (and touching on black holes) in 1973 as a first year undergraduate. The reasoning was as follows : As black holes do not radiate, their temperature must be very low. As matter from a very hot accretion disk falls into the back hole it must heat up to very high temperatures. So I wondered what is the temperature of a black hole.
As I was a lazy student I went no further but I later thought that the resolution of my quandary might lie in considering entropy, but never bothered going any further.
Thank you so much for answering my 50 year old question.
22:50 and 23:40 ish. And then 37:50 ish. And of course 41:00. That's where I cycled the most. Listened and thought for at least 10 min. Maybe a minute of recording. Mileage may vary but to me this should have been much slower, and the equation work quite a bit faster. All hail to the ahah moments!
Thank you, incredibly fascinating
These are the exact kind of walkthroughs of the math of advanced physics that I crave. Also you have a very good voice for this stuff, it's seriously like math/physics ASMR
Although I don't get "tingles" from even normal ASMR stuff, I just mean it's generally pleasant and relaxing but also engaging cuz I'm learning stuff that interests me
Glad you enjoyed it!
By the time the holographic principle comes up, I move my mouse to the progression bar in hope that the there will be more time left of the video. If this isn't the proof of how good your work, I don't know what is. Thank you for all the hard work to make those amazing contents.
This is excellent stuff! Of course, dim. analysis is rarely used to generate formulae, and they would not constitute a theory by themselves. The only well-known instance of this that I can recall might be Dirac's equation, but even that is probably being presumptuous. Developing an extension of an established theory by adding an idea, guided by instinct, is a more orthodox approach.
Wow! Brilliant as always. Just love, love, love your videos.
Just came across your work Sir, thank you, excellent material, William
This is about the coolest video I've seen on the physics of black holes!
3 months ago i could not have followed this. But finally, after 6hrs a day of algebra and physics videos... it makes sense. And now that i get it, wow. Great video.
Commenting for the algorithm.
Absolutely exceptional. I’m in awe of how wonderfully explained all of this was. Thank you so very much.
This was a really great video. Simply a pleasure to watch. I'm not an expert in physics, but I know enough to be sceptical of the holographic principle - having looked into Ads/CFT Correspondence. I'm as sceptical of the 'scale free' aspect of Ads/CFT Correspondence as I am of 'scale free' models of network relations in society being an adequate explanation of the current state things. I'm not one of these people who rejects it as just 'cartesian dualism' - sadly, many people mis-understand dualism.
This video allowed me to understand concepts I was unable to grasp before. Well done!
Thank you for covering this. This is one of the most interesting and simultaneously one of the most difficult concepts in I've found in physics.
Fantastic videos, thank you. I can't really follow the maths, but you manage to make the subjects understandable regardless.
Another great video, as usual. I gather from the comments that a previous version covered the mechanism of Hawking radiation, but was removed due to inaccuracies. Would love to see something on this in future -- I vaguely get the idea of Unruh radiation and that we'll see something equivalent in highly curved regions of space, but no idea of the details. I'm also really clueless on how the black hole information paradox stems from considerations of unitarity, although I've seen it said many times. In classical thermodynamics we don't complain when, say, information about the initial state of a box of gas with hot and cold sides is lost when when it's allowed go to thermal equilibrium.
And finally, the evaporation time for a 3 solar mass BH ignored the extra time needed for the universe to cool below the black hole temperature. I was wondering if that was significant. A quick mental calculation based on CMB temperature in a uniformly expanding universe proportional to age^(-2/3) suggests a "mere" 10^35 years or so to get down to the temperature of the 3 solar mass BH. So I see why it's ignorable ... it's utterly negligible compared to the evaporation time. I guess it would be even shorter in a dark energy dominated universe.
This video is great! Not only I learned the abstract information but I also learned about using dimensions for building up formulas this will really help me out as a high school student since some topics and formulas are shown without any proof (they are basically saying calculate this and that) so I need to memorize formulas to be able to solve questions but now I may able to use dimensional analysis for building up basic formulas instead of memorizing them just to forget it later on...
I was really missing your video 😛and thankfully you uploaded a new video 😍😘
Great 😘😘😘🥰Thank you ...
This is beautiful, thanks for sharing your knowledge!
This is hands down the best physics videos i have ever watched in my entire life.
How exactly are you getting those numbers from the exponents?
By the way this video is amazing and I never imagined you could do things like this.
This vid is criminally underrated.
Whenever I get arrogant over my self regard and intelligence, I just watch this channel.
I always appreciate videos that make me think. Thank you
Glad to hear that!
Interesting approach simplifying all those complex formulas, big props
Is this a reupload? Didn't I see this yesterday? :D
There was one error at 15 minute mark
This is exactly what I thought as I saw the notification…
I shouldn’t have teased him about it!
I have to admit that I don't fully understand everything that's presented here (I'm awful at math), but I just love that this channel exists 💕💕❤️ it's so inspiring ❤️💕💕
Great to hear!
Were you teaching high school, an AP physics student might think he/she had fallen into heaven: finally a teacher who communicates the interconnectedness of not just the ideas, but making it concrete through basic mathematics. The value of dimensional analysis is too seldom taught.
Please keep up ur great content, can’t wait to see you deriving other equations like Newton… etc
Thank you for your incredible work!
Glad you enjoy it!
Finally, a video. Your last 3 videos were awesome.
Actually all of them, but i have only seen last 3.
Glad you like them! Thanks for the feedback
Yay you fixed it, this channel is amazing.
Fantastic presentation. All of it made so much sense. A bit of an "ah-ha" moment for me when I realized that larger temperature of a small black hole would coincide with a tiny, transient black hole created by hyper dense energy, as in the case of attempting to make sub plank-scale observations. Thus this fits with the Heisenberg uncertainty principle.
One thing I wonder about in regards to the holographic principle for black holes:
Since the Schwartzchild radius is increases in size with more mass crossing the event horizon, wouldn't that mean that the information which was sitting on event horizon of the previous state of the black hole would be subsumed in the new, larger black hole. Thus the old information would not no longer exist and the surface would not successfully persist all the information as the black hole grows? Perhaps this is solved by virtual particles.
very well explained for someone profane with some knowledge of physics, thermodynamics and also dimensional analysis Thanks for your time to educate us!
This man makes you rediscover the thesis of physicists. This is the best method to understand physics and math. Thank you my friend❤❤❤
Thank you for the clear explanation. I have always marvelled at the power of dimensional analysis.
Referring equations as how properties are related to each other really helped me understand what was going on
Man I love this channel
Read about this in Leonard Susskind's book "Black Hole Wars". This is by far one of the better Physics channels out there. I have watch a few of them. When my Family and Friends ask me about physics in college, I send them a couple of these videos so they can get a look at the equations and concepts we work with.
Great video!
Note that formula for a BH evaporation rate presented here is valid only for a universe with no CMB. With CMB, the rate will be defined by a temperature difference between BH and CMB at every moment of time, so the formula presented underestimate the time of evaporation (and underestimate size of primordial BHs survived as of now).
This is incredibly well produced
Good video, I'll share it around
Wow, very simple and straightforward explanation. First time I trully understood Hawking radiation and Black Hole entropy. The approach is still a kind of phenomenological but truly enlightening!
Wow. You are a great teacher and presenter. And obviously very smart.
@PhysicsExplained This was terrific. I wish if you could make a video dealing with a no-nonsense explanation of the Hawking radiation using the formalism of QFT in curved spacetime.
Cheers for the kind words. I hope to return to a proper explanation of Hawking radiation in a future video
What a lovely video ❤️
your videos are as beautiful as the identity of Euler. They are nicely clear and well explained!!
your efforts in preparing this video are very grateful. Thanks very much.
Thus, I subscribe, like and share. Good lucks.
Your work is just so bloody good. Thank you.
Glad you enjoy it!
Excellent presentation. I followed you to my astonishment!
Wow!! One of the best explanations I have ever seen in my life!! Congratulations pretty awesome didactics!! 👏🏻👏🏻👏🏻
Very underappreciated channel. Hope you get the subscribers you deserve good sir, great videos.
I appreciate that!
the part of the planck area blew my mind, awesome!
Thank you. Well explained. Apart from the last bit about information being retained on the event horizon of a black hole. Ever looked at the rim of a wood chipper? Doesn't say Oak 6/15/21. I did find one which had some scratches which in binary said "trust Susskind as far as you can throw Hawking" probably put there by Douglas Adams.
Dimensional analysis was something I've always been doing in my high school and Freshman year at uni. It doesn't give you the coefficient, but it at least verifies if the final result makes sense. It was something our physics teacher taught us: "match the units of quantities".
Might need to rewatch to understand it all, but still waaay easier than I thought it could be explained.
This is incredible, I always wondered how people came up with this, in short a lot of critical and logical thinking, but this made a lot of sense, I was just watching the video and not checking any numbers but this mathematical trick called dimensional analysis really made it more simple to understand some of the math behind the ideas of these concepts, I used to watch physics vids a lot like Arvin Ash or PBS Space Time but I've stop since it's only theory and without math its hard to wrap your head around it, but the math is god awfully complicated, but this, was much more simple and everything makes sense how its connected, I never thought that such complicated maths could be possibly simplified, but you my friend proved me wrong! Great content seriously, I finally watched a abstract field of physics without theory only and with simpler math that I can understand, and It all clicked because of it!
Still the absolute reality is far from the reach of these equations 🤡.
@@avg_user-dd2yb yeah no shit 🤣
I have never seen a black hole described like this.Thank you.
You are great at explaining. Thank you for the information. I loved it!
The holographic principle - especially when extended to the entire Universe - is hard to accept but one must recognise that makes a lot of sense.
Hard to accept - I mean, how we could imagine the instant connection between the content of the space volume, and the information presented at the boundary. Obviously, our understanding of the nature of Space need some advancements...
Thank you for the video. Your ability to describe advanced physics is unique.