Deriving Hawking's most famous equation: What is the temperature of a black hole?

[@Phillip-ey3dp]

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.

[@d.3578]

@@Bopplesyou can do it!!! wishing you lots of success 🫶

[@samheard7849]

​@@BopplesI hope you are successful! Praying for you!

[@AA-gl1dr]

@@BopplesI believe in you. You’re never too old to change the world. Keep going you’re doing great!!

[@brownj2]

But how did you know you would not have a good teacher, if you went on to study this in college?

[@WilliamDye-willdye]

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.

[@alanzyoutube]

I noticed the original video had been deleted before I could watch it, what happened?

[@WilliamDye-willdye]

@@alanzyoutube Enough errors were found that the author decided to issue a corrected version. Unfortunately KZbin currently does not allow revisions, just overlays or re-uploads.

[@tim40gabby25]

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 :)

[@WilliamDye-willdye]

@@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.

[@tim40gabby25]

@@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 :)

[@sphakamisozondi]

This channel is a goldmine for abstract knowledge.

[@jodscience3741]

There is a difference between abstract knowledge and abstract nonsense

[@edwardjcoad]

I would argue that this is the complete opposite of abstract....whatever that maybe.

[@KnufWons]

@@edwardjcoad many use “concrete” as the opposite of abstract

[@radwizard]

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.

[@IrelandVonVicious]

It's a gold mine for unicorn farts. It's all made up, no evidence and wrong.

[@adberg1067]

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!

[@justingreen2432]

You are one of the few smart 17 year Olds! Don't forgot it!

[@rc5989]

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.

[@timbeaton5045]

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?? 😉

[@jimwinchester339]

Sometimes an imperfect diagram is still the key to the first-time hearer "getting" it.

[@Number6_]

@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.

[@chimkim]

​@@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

[@Gizzeit]

​@@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.

[@kendallknight3249]

I've always wondered how all this stuff was connected and how people came up with these relations. Please keep it up

[@PhysicsExplainedVideos]

Cheers, will do

[@20IA]

Hello its only 4 comments but what went wrong here

[@jameszhang9326]

By delving into physics mode of thinking and extreme applied math. 😅😅

[@hOREP245]

@@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.

[@bloodjunkie1919]

@@frankdimeglio8216 how about going to a scientific body with this information (formatted in a way that doesn't hurt to look at, that is)

[@jadegrace1312]

After watching this, I don't get how anyone could find anything more beautiful than physics.

[@PhysicsExplainedVideos]

Couldn't agree more!

[@bryan3dguitar]

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?

[@douglasperry8211]

Wait until you got to do the math. Then, physics becomes a more dynamic, downward trending, and taxing labor further defined as unforgiving, tedious, mundane, and redundant experience where other chores like pounding sand up your ass is a order of magnitude more "engaging" than is physics.

[@jadegrace1312]

@@douglasperry8211 I have a math degree

[@JoimFormula]

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..

[@RizkyMaulanaNugraha]

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.

[@ddognine]

@@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.

[@ibanix2]

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 :-)

[@PhysicsExplainedVideos]

Glad you like them! And thanks for taking the time to leave a comment.

[@devincarlson8866]

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!!

[@PhysicsExplainedVideos]

Glad you like them! Cheers for the feedback, much appreciated

[@masternobody1896]

@@PhysicsExplainedVideos what is dark matter and plank scale

[@masternobody1896]

@@PhysicsExplainedVideos is it possible to go smaller then plank scale

[@obst3085]

@@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

[@twt2718]

@Sean g 137 coo-coo 🤪

[@junkmail4613]

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!!!

[@danimyte3021]

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.

[@Joeleon2]

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.

[@narfwhals7843]

"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.

[@farhadmodaresi4182]

He is better than feynman

[@PhysicsExplainedVideos]

Cheers!

[@littlemissmisses2981]

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”. :)

[@PhysicsExplainedVideos]

Very glad to hear it! Thanks for the kind words :-)

[@Richard.Holmquist]

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.

[@varunahlawat9013]

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!

[@tylerdavis3]

Were you manic or are you on something lmao

[@VintageTechFan]

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.

[@andredavis4657]

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.

[@pengwei8635]

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

[@gimmehendrix]

Probably the best explanation of physics on youtube. Keep em coming!

[@Evenfiber1068]

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.

[@hugonelsson9114]

About to start physics at college this fall. I hope the lectures are even half as interesting as these videos.

[@PhysicsExplainedVideos]

Good luck at uni!

[@hugonelsson9114]

@@PhysicsExplainedVideos thank you!

[@KizaruB]

I’m in physics rn. It’s way more vapid than this so far ☹️

[@chemicalnamesargon]

​@@hugonelsson9114 how has it been? :)

[@Stirlingsays]

Whenever I get arrogant over my self regard and intelligence, I just watch this channel.

[@kfawell]

There are so many wonderful channels on KZbin. 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.

[@PhysicsExplainedVideos]

Wow, thank you!

[@adogonasidecar1262]

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

[@anishsharma6702]

This vid is criminally underrated.

[@alexandreolle2340]

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 !

[@jannegrey]

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! ;)

[@PhysicsExplainedVideos]

Cheers for the kind words, much appreciated

[@jannegrey]

@@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 KZbin 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 KZbin when it comes to deep analysis of problems. Something similar to what 3Blue1Brown is for Mathematics - which is a very favorable comparison. Good Luck!

[@None-zc5vg]

Dyslexia

[@christopherdevers2836]

These videos unironically made me reenroll in college.

[@narfwhals7843]

That is unironically awesome!

[@crookedhead3075]

Ha! What a good story!

[@greengirl4985]

Wow!! That’s awesome

[@aidenstern5254]

Hows college going

[@christopherdevers2836]

@@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.

[@Pooksy]

One of the best channels out there

[@EMWave]

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.

[@stevemonkey6666]

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. ..

[@Bundesverfassungsgehirn]

Very underappreciated channel. Hope you get the subscribers you deserve good sir, great videos.

[@PhysicsExplainedVideos]

I appreciate that!

[@chrislp4465]

I Love your Videos they are so well structured and with so much Content keep it up bro

[@omegapoint1258]

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!

[@chimkim]

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.

[@joelmayer1018]

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

[@PhysicsExplainedVideos]

Thank you very much!

[@eskmob1960]

This channel is a universe of abstract information

[@mrpyfisher1995]

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

[@mrpyfisher1995]

@Michael Bishop Thanks for the explanation :D

[@k_dankov]

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!

[@Peringon]

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 ❤️💕💕

[@PhysicsExplainedVideos]

Great to hear!

[@nexus3112]

Wow! We just analyzed Black holes

[@georgelafner8760]

Definitely my favourite physics channel, and I love a lot of physics channels. Thank you for all your work!!

[@PhysicsExplainedVideos]

Glad you like them! Thanks for the feedback

[@_..---]

Yay you fixed it, this channel is amazing.

[@ivanleon6164]

the part of the planck area blew my mind, awesome!

[@AA-gl1dr]

Commenting for the algorithm. Absolutely exceptional. I’m in awe of how wonderfully explained all of this was. Thank you so very much.

[@Anthony-ym6iz]

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!

[@anmolmehrotra923]

Comment for engagement

[@sudokode]

What do I do for engrossment? 🤔

[@SSMLivingPictures]

​@@sudokodeForm an unhealthy addiction

[@bradley1995]

​@@SSMLivingPicturesdone, what next?

[@SSMLivingPictures]

@@bradley1995 Allow Hawkins Radiation to destroy all your relationships, I guess

[@davidr.603]

Same

[@sayantansaha2264]

This man makes you rediscover the thesis of physicists. This is the best method to understand physics and math. Thank you my friend❤❤❤

[@shannonmcdonald7584]

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.

[@RizkyMaulanaNugraha]

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.

[@jamessmith2403]

I was really missing your video 😛and thankfully you uploaded a new video 😍😘 Great 😘😘😘🥰Thank you ...

[@onebronx]

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).

[@generalripper4349]

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.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@tuananhnguyen8998]

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.

[@zeweichu550]

Just based on the title, I will definitely love this video.

[@kentonevans]

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.

[@ProfessorBeautiful]

This answered some questions puzzling me for a long time. Thank you!

[@junkbucket50]

Good video, I'll share it around

[@Slayerzard]

Referring equations as how properties are related to each other really helped me understand what was going on

[@lukasz1128]

Dziękujemy. Thank You. Your explanations of modern physics are brilliant !

[@jamesdavison6290]

As you explained earlier, Planck's constant has units of "flux" . . . matter moving across a surface per second. There is a finite amount of information that can be contained within a specific volume, and as objects falling into a black hole are compressed into two-dimensional wavefronts frozen in time with respect to outside observers. If you have not read John Archibald Wheeler's autobiography I hope you will give it a try! I am always looking for ways to make these incredible concepts more accessible to my mind, and your videos are an incredible resource. Yet is is hard for me to imagine black holes releasing information in any coherent form. I don't see microscopic black holes spitting out spacecraft! I also wonder about what the expected density of "mini" black holes might have been in the early universe to give us an idea of how often we should be seeing those large gamma ray events when they finally decay! Also, you mention the amount of energy decaying in a second, but the real signature of a decaying black hole would be very complex. Necessarily it should contain all the stuff that fell into it . . .

[@petar807]

Best physics channel on youtube

[@phths]

Amazing explanation of dimensional analysis… I wish I watched this before I took fluid mechanics though 😅

[@alexpotzel8853]

This might just be the most informative video about physics ive ever seen. Thanks maaan, rlly learned a lot!

[@shameemmodu]

This is extraordinary, i am doing my bachelor in physics.This is the best explanation I've ever seen with mathematics regarding black hole. It is 3 am, i am watching this.

[@elliottdickens1797]

This is incredibly well produced

[@randycarstens1100]

Excellent presentation. I followed you to my astonishment!

[@Flacopro40]

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.

[@hughbishopnh]

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.

[@avr8844]

Fantastic videos, thank you. I can't really follow the maths, but you manage to make the subjects understandable regardless.

[@radwizard]

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.

[@craigfowler7098]

I studied degree in Physics 30 years ago, so able to follow the Maths and Physics. Very interesting stuff.

[@Draginx]

This is hands down the best physics videos i have ever watched in my entire life.

[@wardieleppan8443]

Wow! Brilliant as always. Just love, love, love your videos.

[@katenpp]

Thank you for your incredible work!

[@PhysicsExplainedVideos]

Glad you enjoy it!

[@ltloxa1159]

Might need to rewatch to understand it all, but still waaay easier than I thought it could be explained.

[@thisaccountisdead9060]

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.

[@leisulin]

This is about the coolest video I've seen on the physics of black holes!

[@lostson1st]

I have a diploma from the University of Technology and I think that the way of presenting complex mathematical and physical analyzes here is brilliant.

[@bryanb2653]

he can explain it in a high school level, I jump for joy

[@AashishKumar1]

Always looking forward to videos from this channel.

[@PhysicsExplainedVideos]

Glad you like them!

[@soulesswanderer2452]

I love the content, it's interesting yet filled with mathematics, it doesn't "dumb down" the audiences, keep it up :)

[@AZ-vy4gl]

I always appreciate videos that make me think. Thank you

[@PhysicsExplainedVideos]

Glad to hear that!

[@nickbarton3191]

Brilliant video. I assume that Hawking wasn't awarded a Nobel prize because his theory wasn't confirmed experimentally? The idea of holographic memory chips with microscopic Black holes with Planck area sized bits is tantalising. When the universe is in the last phase of heat-death, the last remaining Black holes will evaporate the energy of whatever mass is left of them in a fraction of a second. The photons will bounce around for a long long time but finally, after collisions, loose momentum until there is no longer even quantum energy/mass. Photons are mass-less in of themselves so the whole universe will be mass-less? So where did all the energy go assuming a finite universe? It implies that it will never cool to absolute zero, ever. Just have incredibly high entropy with a lot of very lonely protons.

[@jeancorriveau8686]

This video allowed me to understand concepts I was unable to grasp before. Well done!

[@haneen3731]

This is beautiful, thanks for sharing your knowledge!

[@WildGamez]

Wow. You are a great teacher and presenter. And obviously very smart.

[@randymartin5500]

Wonderful mathematical analysis ...better than the layman Nova and Discovery shows and not as complex as 25hr long Lenny Susskind lectures . Thank you so much!

[@PhysicsExplainedVideos]

Glad you liked it!

[@timewalker6654]

Finally, a video. Your last 3 videos were awesome.

[@timewalker6654]

Actually all of them, but i have only seen last 3.

[@PhysicsExplainedVideos]

Glad you like them! Thanks for the feedback

[@lkrdp9463]

wow i understood it so far until the 23 min mark (i had to pause), what a great teacher you are

[@wolfrowell9435]

Wow!! One of the best explanations I have ever seen in my life!! Congratulations pretty awesome didactics!! 👏🏻👏🏻👏🏻

[@TheGoodMorty]

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

[@TheGoodMorty]

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

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@willygreg3489]

Just came across your work Sir, thank you, excellent material, William

[@mr_hxid]

"We should include Planck's constant, when things are quantum." This single sentence pretty much sums up the entirety of quantum mechanics, i love it.

[@vaels5682]

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.

[@jimtwisted1984]

I have never seen a black hole described like this.Thank you.

[@brendonwest-m1n]

Your work is just so bloody good. Thank you.

[@PhysicsExplainedVideos]

Glad you enjoy it!

[@edwardjcoad]

So good but give us the charged and rotating version!! Dimensional analysis was always the way to deduce correct derivation from first principles. Sadly this powerful tool which is so simple is no longer taught in schools.

[@ganeshg8946]

Mind blowing video..thanks 🙏