What is the Cosmic Microwave Background Radiation? And what does it mean?

This video provides an overview of the accidental discovery and explanation of the cosmic microwave background radiation, the afterglow of the big bang, and follows the narrative of Steven Weinber'gs fantastic book: The First Three minutes. After reviewing the initial experimental work of Penzias and Wilson, a detailed account of the theoretical interpretation is presented, including a discussion of the thermodynamic legacy of the big bang, the Planck radiation law, recombination, and galaxy formation.
References:
The First Three Minutes - Steven Weinberg
Cosmology - Steven Weinberg
The Inflationary Universe - Alan Guth
Introduction to Cosmology - Matts Roos
An Introduction to Cosmology - P. OLESEN
An Introduction to Modern Cosmology - Andrew Liddle
Introduction to Cosmology - Barbara Ryden
You can help support this channel via the Physics Explained Patreon account: / physicsexplained
You can follow me on instagram: / physics_explained_ig
You can follow me on Twitter: / physicsexplain1

[@gianni2k]

Hi Andrew, it’s Gianni here from our PhD days. Just massive congratulations on your videos, I’m happy you stayed in contact with all this fascinating stuff. I’m watching all of them and steal some ideas and explanations here and there for my students, hope you don’t mind. Hope all is well, best.

[@PhysicsExplainedVideos]

Hey Gianni! It is so good to hear from you :-) Thank you for your very kind words, they mean a lot. Seeing your message brought a massive smile to my face and transported me back in time - we had some wonderful conversations. Are you still in Argentina? Would love to catch up

[@gianni2k]

@@PhysicsExplainedVideos I got a permanent position in Santiago, Chile, where I’ve been living with my wife, a dog and 3 cats for 7 years now. How about a zoom call one of these days? I speak of you often with my wife, just a fantastic, incredibly bright and interesting human being. Some real happy memories of you in a tough moment of my life. Would love a chat again.

[@mg7509]

@@PhysicsExplainedVideos huge fan of your videos. Love, from Argentina. ;)

[@tonib5899]

He will be flattered your sharing his ideas.your students also benefit.As long as it’s not plagiarism the point of ideas is to share. Hope all is well.

[@kevincleary627]

It's Andrew? I could have sworn you were Brian Cox! You sound just like him and explain things just as well. Best physics videos on KZbin! I watch and rewatch them all.

[@toxxikanshul]

This is a GEM. I am a Phd research scholar with my thesis on CMB. And this video is must watch for anyone to begin research in this field.

[@PhysicsExplainedVideos]

Cheers for the kind words, much appreciated. Good luck with the PhD!

[@toxxikanshul]

@@PhysicsExplainedVideos thanx and can i have your email bcuz i tried to search in “about” section but its not there.

[@prateekgupta2408]

@@toxxikanshul you're lying that you're a PhD student

[@toxxikanshul]

@@prateekgupta2408 oh lol okay bro. Im surely not gonna pleasure u with proof. Blessings for u.

[@Shadowless_Kick]

@@PhysicsExplainedVideos I think it would be nice if you emphasized why the background microwave can be detected in any direction -- of course, the reason is that the point where we were was INSIDE the universe then and we are still inside the universe now, but this explanation could be hard for most viewers to figure out by themselves.

[@kaanasker4914]

Thank you, this channel is simply the "best" physics channel.

[@PhysicsExplainedVideos]

Thanks!

[@CraftyF0X]

@@PhysicsExplainedVideos Um, forgive me this naively stupid question but I rly don't know who to ask about it. So if one does learn about Rindler horizons and Unruh radiation one may come up with the probably stupid question that how their effects (if they are present at all) are seperated from the CMB ? Let me explain a bit, and you correct me where I went wrong, so our reference frame can be thought as an accelerating one relative to certain distant parts of the universe due to the expansion. If that is true then this would mean that from our point of view the empty space in those regions would have black body radiation which should look like smooth thermal equilibrium. Now the question is that could this be really similar to the CMB itself ? I mean ofc the CMB has tiny temperature fluctuations, but is it possible that the Unruh effect modfies somehow the data ?

[@alfredobeltran611]

Agree 100%. Thanks for doing this kind of videos

[@prakashraj4519]

I'm watching every video of yours, they are enlightening me.

[@PhysicsExplainedVideos]

Glad to hear it!

[@emilianocorcino4146]

Same

[@ahitler5592]

I watch chess games and it enlightening me

[@lewgiere2823]

As a retired EE (30+ years of RF/MW engineering, in both military and commercial electronics arenas) I've found your physics videos to be very delightful to watch. I've covered a lot of material over the decades and appreciate your illustrative depth of the derivations and meticulous treatment of the physics principles. This is technical pleasure-reading at its best. I particularly enjoyed your eight-part series on the maths of general relativity, the Bohr model of the atom, and of course this microwave background study. I very much look forward to seeing more.

[@PhysicsExplainedVideos]

Thanks for the feedback, much appreciated!

[@Shadowless_Kick]

@@PhysicsExplainedVideosMany articles say that the microwave radiation distribution corresponds to ~3K temperature because universe expansion has caused the temperature to “cool down” from 3000K at the recombination time. I think “cool down” is very misleading, 3K is not actual temperature, it is the apparent temperature due to Doppler shift effect. 3K implied by the microwave radiation distribution we detect today actually corresponds to the 3000K universe temperature 14 billion years ago. Can you kindly confirm this? Thanks

[@craigwall9536]

I met Penzias shortly after he and Wilson had been awarded the Nobel Prize; for some reason he gave a lecture at a Unitarian Church in Tulsa, Oklahoma, to an audience of about 30 people. I felt so bad for him- he was led to believe that they were interested in Cosmology. In fact, they were using him as a status symbol in a rivalry between two Unitarian "ministers" engaged in "one-upsmanship". When he took questions after the talk it became quite apparent that the audience was trying to use leading questions to put words in his mouth and he got pretty indignant. As the meeting broke up I tried to offer some condolences about how they had used him, but he was pretty terse and got out of there as fast as he could. I couldn't blame him. I myself, though an electronic technician doing avionics but with an interest in physics, had not been aware of this topic in cosmology and attended on a whim; if I had been up to speed on the subject I'd have asked a real question of two. As it was, I'm sure he left with a very bad taste in his mouth regarding the level of intellect in Oklahoma.

[@PhysicsExplainedVideos]

Fascinating story, thanks for sharing!

[@primenumberbuster404]

Oklahoma's average IQ is below the planck scale.

[@musicmakelightning]

Brilliant work. I will add that as a child I lived in New Jersey within a bike ride of the Penzias/Wilson antenna and I rode past it many times. I had no clue what it was, and neither did my parents. It was only much later when I got into university that I learned what it was, and how Penzias won the Nobel Prize using it. Penzias gave the speech at my graduation and I was a rabid physics fan, so it was an experience I will always remember.

[@PhysicsExplainedVideos]

Very cool!

[@thorntontarr2894]

You are to be commended for NOT making it so simple that the message is not presented. This video would have been so helpful during undergraduate days, about the time Wilson, Penzias & Pebbles were doing their work. Yes, I am old. Along with your Vacuum Catastrophe Video this is the best I have ever seen on these topics. Your work is very important; I thank you for your energy.

[@PhysicsExplainedVideos]

My pleasure, thanks for the kind feedback

[@pyrokinetikrlz]

One thing that is almost never mentioned is that the CMB irregularities are extremely small and that lovely multicolor graph is a very exaggerated representation of the real thing

[@pyrokinetikrlz]

1 part in 100 thousand, as said in this video

[@ozzymandius666]

Congrats on breaking 50K subscribers. You earned it, as a matter of fact, you've earned a million in my books, you just haven't received the cheque yet.

[@PhysicsExplainedVideos]

Thank you, I really appreciate your continued support!

[@awolgeordie9926]

Another masterpiece. What I love about your videos is that anyone with A level maths can follow the working. For me though, this will require a second viewing. Thanks man.

[@PhysicsExplainedVideos]

Thanks for the kind feedback, it means a lot

[@misterschifano]

Your videos are exactly what I need as I prepare to make the transition from being a lifelong chemistry and physics teacher to a second career as an actual physicist. I watch once all the way through for conceptual flow, then again stopping them until I can do the maths shown at each step. The single fastest improvement in my rigorous understanding.

[@PhysicsExplainedVideos]

This makes me happy :-)

[@chacmool2581]

I am an EE graduate who once considered switching to Physics. To this day I remain fascinated by these topics. These are brilliant videos.

[@mattkerle81]

Straight up in my top three physics channels for accessibility and making complex topics available for under grads, thanks!

[@Mr._Wizard]

Former physics undergrad here, have been out of school for some years now. This content is incredible. Makes me feel like I'm able to apply myself to thinking about this stuff again. Really hope you keep making videos

[@srinivasatr1395]

Really appreciate your in depth understanding of the subject you are presenting and doubly appreciate the meticulous nature of your explanation. Great work. Keep it up.

[@PhysicsExplainedVideos]

Wow, thank you! I really appreciate the kind words and feedback

[@emmettgriner6345]

Awe-inspiring, as usual. You assemble the pieces of the story without getting bogged down in the details but disclose the details in boxed digressions. It was good to see how this video built on your video about the ultraviolet catastrophe. Also as usual, you've given me a few days worth of homework. Thank you and please keep up the good work.

[@PhysicsExplainedVideos]

Thanks for the kind words and continued support, I really appreciate it!

[@rakeshkumar-db7qh]

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[@rakeshkumar-db7qh]

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[@rakeshkumar-db7qh]

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[@rakeshkumar-db7qh]

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[@johnopalko5223]

Very nice and informative video. Arno Penzias was quite the character. He probably still is, at age 87. About 25 years ago I worked for a startup company of which Arno was one of the chief instigators. One day my boss and I were talking and he allowed as to how sometimes, when investors, etc., were giving them problems, they had to "wield Arno." The two of us decided that Arno was a +5 Nobel Laureate of Influence.

[@PhysicsExplainedVideos]

Thanks for the info! Very interesting :-)

[@georgefan2977]

This is some incredible work. Also I love the dark theme, super friendly for our eyes

[@PhysicsExplainedVideos]

Glad you like it! Thanks for the feedback :-)

[@mostinho7]

The first time I understand what all the pop science channels mean when saying the universe was opaque before it cooled down 13:45

[@acedia4454]

Got 0 (out of 15) points in circular motions & harmonic oscillators and 1 (out of 15) points in mechanical waves - why am I watching this? Im literally incapeable of understanding physics lol. Still enjoy your videos a lot. Your voice is so comforting.

[@Moral-insights]

You just have to continue to produce these videos. I have never really come across physics videos that I can listen to for more than ten minutes. Your work is great and it's so great that I had to come out and actually comment on a KZbin video which I don't do much at all. I am here to encourage you to continue producing these great works, I am hungry for this stuff and I am far from being satiated.

[@PhysicsExplainedVideos]

Thank you very much for your kind words of encouragement, they mean a lot! I have plenty more videos on the way!

[@tiaraguy7705]

I'm very much your average Joe who works a normal job and has a GED but I've come to realize in these last couple years I always seem to enjoying watching videos regarding science or reading about the history of math. I even enjoy videos like these when it's so far out of my pay grade but I still feel like it can teach me so much even from a conceptual standpoint. It helps me feel like I have a slightly better grasp of something that's still very foggy to me. Hopefully I will be able to understand this from a purely mathematical view someday too.

[@LetsFindOut1]

i forget if ive commented before, but just want to give a little encouragement along with the rest of the commenters here. I'm reading up on JWST and am trying to grasp the general consensus about the LCDM model and obviously the CMB is a huge part of what any model of the universe must fit into. So I just want to say thanks for making such articulate and precise explanations in easily digestible video form. (your graphics are amazing too btw) Your channel is one of the few that find a great balance between understandable-but-too-simple and accurate-but-too-complex-to-follow. I walk away feeling like Ive understood a majority of the maths and (equally importantly) the history of how theorists arrived at our current understanding. Too many popular explanations of the CMB in particular fail to explain blackbody radiation, Dicke and Peeble's prediction of the recombination epic, and useful historical tid-bits like that Penzias and Wilson were originally looking for 21-cm lines and even pointed their telescope at Andromeda to rule out Milky Way origins for the unexpected microwaves. Sorry for the ramble. No need to respond, just keep up the great work. This channel will undoubtedly be used in the classroom for generations to come. It's just way too insightful not to. (I can only hope you get compensated appropriately for your excellent work).

[@ahamadullahkhan4896]

This is the best physics related KZbin channel explaining concepts in detail…..thanks a lot sir…….

[@PhysicsExplainedVideos]

You are most welcome

[@jamesgreen-armytage9927]

I love how much of this stuff actually got started in New Jersey, which most people think of one of the most prosaic and least "cosmic" places around.

[@_abdul]

We all have had our fair share of "White Dielectric Material"

[@pipertripp]

I was spewing it liberally all over the disc golf course just this afternoon.

[@duncanbrown7082]

Apparently it’s good luck to be struck by it.

[@kulhman]

Your videos are so in depth. I'm glad the algorithm brought you to my attention. Keep up the great work!

[@PhysicsExplainedVideos]

Thank you!

[@Briantreeu123]

Great video great channel thank u for these videos and the explanations that come with it. Maybe a video on Gravitational wave background

[@PhysicsExplainedVideos]

Great suggestion! One for the future

[@beardog6569]

Hi Andrew, I'm a stem cell biologist watching your videos for... fun. They are so good. I'm writing a lecture series and I'm so impressed with your style that I'm going to use some of it in my own delivery. Thank you

[@PhysicsExplainedVideos]

Sounds great!

[@pipertripp]

Another excellent programme. One of my favourite things about the history of Planck's radiation law is that Wien had found this relationship empirically in 1896, 4 years before Planck's solution to the ultraviolet catastrophe. Then, as you show, Wien's law just falls right out of Planck's work.

[@arniepatel9841]

I did my PhD in physical/quantum chemistry and im eternally grateful for your videos. They effectively clear up all the missing links in my knowledge. Incredible work!

[@mpicos100]

Fantastic videos. Historical background, physical explanations (really good and insightful), some mathematical formulas to show how works the numbers, and great presentations with graphics and so on. Thanks for this, keep working on it, great material.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@ReynaSingh]

Keep up the good content 🙏

[@PhysicsExplainedVideos]

Thanks!

[@borisdorofeev5602]

Already in the very beginning of the video is probably the best explanation of the 21cm hydrogen emission on KZbin. I'm not knocking other channels but most just say its a wavelength at which hydrogen emits a photon without this deeper understanding. It was very well explained in this video.

[@PhysicsExplainedVideos]

Cheers, thanks for the feedback!

[@ColeCoug]

I love well done physics videos that aren't scared of explaining the math!! New favourite channel

[@PhysicsExplainedVideos]

Cheers, glad you enjoyed the video

[@awkweird_panda]

Found your channel yesterday, going to binge watch all your videos now💯

[@PhysicsExplainedVideos]

Hope you enjoy!

[@marlonwood6529]

Always makes me happy to see a new video of yours :)

[@PhysicsExplainedVideos]

Happy to hear that!

[@adogonasidecar1262]

Beautiful video. Thank you. I find myself struggling at times with transitions you make and having to pause, rewind and listen many times... Even with such great videos, this is no easy stuff!

[@PhysicsExplainedVideos]

Thanks for the comment and feedback. You are right, there is a lot of content squeezed into a short amount of time, so I think it makes sense to pause and process all the information. Good effort!

[@bennyloodts5497]

Thank you for making! Never understoot it like this good.... A video that explains in good detail and keeps overview... Great work, my compliments!

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@_..---]

Thank you youtube for recommending this video.

[@acommunistdwarf]

Thanks man, have binge watched a bunch of your videos lately and they are all great with very detailed but approachable information.

[@PhysicsExplainedVideos]

Glad you like them!

[@tophan5146]

20:50 Hey, I remember integrals that result in a PI from your other video!

[@matrix3509]

For a visible light telescope, its easy to cancel out the noise of the electronics. You just need take an exposure with the camera shutter still closed. The resultant image is pure electronics noise (along with the occasional cosmic ray strike). I'm not a microwave or radio astronomer so I don't know if the procedure is as easy.

[@ironlegnebula]

Thank you very much for keeping quality content going!

[@PhysicsExplainedVideos]

My pleasure!

[@reversethursday4975]

I really love your videos, I look forward to the next fascinating deep dive. Best wishes man 👍

[@PhysicsExplainedVideos]

Thank you very much!

[@AZ-vy4gl]

This is tons better than the usual "they heard extra static" explanation I've heard from everywhere else

[@paulwolf3302]

You find this to be powerful, conclusive evidence?

[@primenumberbuster404]

​@@paulwolf3302 Do you agree that 1+1=2? 😳

[@syte_cloud9829]

i absolutely love these videos

[@diogenes999]

The clearest and most profound presentation I came across! Keep up the good work.

[@PhysicsExplainedVideos]

Thanks for the kind words, much appreciated

[@amityaffliction4848]

Excellent video. Well done

[@PhysicsExplainedVideos]

Thank you very much!

[@TheKyros79]

I always get excited when I see that you have posted a new video. Keep up the great work!

[@PhysicsExplainedVideos]

Thank you!

[@EMWave]

Yet another wonderful explanation of formation in such a lucid way. It makes my day when I watch your videos. It is comforting to know that universe works on a basic laws of physics, yet it looks very complicated when looked at it with bare eyes. Thank You!

[@PhysicsExplainedVideos]

Thank you for the kind feedback, it is very much appreciated :-)

[@Filip-ci3ng]

This is great ! If opinion of a KZbin hobby physics follower matters, I think the best CMB short story so far

[@nathanevans6277]

This is the best description of the CMB I have yet seen. Excellent work. Subscribed

[@PhysicsExplainedVideos]

Thank you very much, I really appreciate the feedback

[@WissenSync]

This is my favorite channel now, keep the nice work!

[@PhysicsExplainedVideos]

Thanks, will do!

[@bernard2735]

I feel as though I have just stumbled across a gem. Thank you for creating this wonderful channel. Liked and subscribed.

[@PhysicsExplainedVideos]

Awesome, thank you!

[@brendanacord2557]

Thanks for such a comprehensive explanation of one of my favorite stories in physics!

[@PhysicsExplainedVideos]

You're very welcome!

[@austist]

my person deep down has an agonizing interest in answering questions i have for this universe. i have yet to fully understand the contents of this video but i will come back when im learned and do understand. thank you for your content

[@supreetsahu1964]

Your channel is everything I ever wanted from KZbin. Hope you skyrocket to a million subscribers soon

[@PhysicsExplainedVideos]

Thanks!

[@NadellaVasishta]

Been a fan of your work and presentation since black body radiation video.. thanks for making productive content for us.. ❤️

[@PhysicsExplainedVideos]

Thanks for the continued support, I really appreciate it

[@kappo8993]

Just amazing! I'm from Brazil and I would probably never find that level of information and detailed content by ordinary ways. Thanks.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@leighcoulson2148]

I can't pretend to understand all of the maths (not that I've really tried to), however I can understand the concepts from your explanation, great.

[@PhysicsExplainedVideos]

Thanks for the feedback! I am glad you were able to follow along - I try to make the videos so that you can follow the main thread even without following all of the mathematical details

[@EASYTIGER10]

This is the clearest explanation of microwave background Radiation I've heard

[@Dogan979]

Saw the video 4 days ago. Knew it would be awesome, so saved it for a quiet night, and enjoyed every single atom of it. Keeps getting better and better...

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@felicityc]

I really like these videos even if I have gone over it all a thousand times. probably the accent

[@MrDaanjanssen]

great. I love these, will watch soon

[@nexus3112]

Your videos make me perceive the concept at the plank level of understanding ... keep it up ... Really appreciate your work!

[@PhysicsExplainedVideos]

Glad to hear that! Thanks for the feedback

[@addy7464]

As a physics undergrad i would like to say these are one of the best if not the best youtube lecture videos on physics.... These are just beautiful.

[@ThumperPruitt]

Excellent video and I appreciate you taking the time to explain things simply vice making it so complex that you can't follow along. I will be using this when tutoring my young students.

[@jay89boy]

really great Videos! watched almost all by now thank you for doing this

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@johnlandrum4649]

One of the most amazing videos I have ever seen. Thank you so much for doing this.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@Jaggerbush]

Thank you. This is so detailed. By far the best explanation of this anywhere.

[@PhysicsExplainedVideos]

Glad it was helpful!

[@hai-duynguyen8429]

Can I ask what is your professional background? You have such a good grasp on topics like these. I wish I received the same process of thinking from uni professors. I keep rewatching some of your videos because I always seem to gain a new perspective on how intimate our world really is. From the cosmos down to the atom, these series beautifully compliment one another. Man what a great time to learn physics.

[@PhysicsExplainedVideos]

Thanks for your comment, much appreciated. In terms of my background, I completed a PhD in theoretical physics (focusing on String Theory), and have been teaching physics for the past ten years.

[@hai-duynguyen8429]

@@PhysicsExplainedVideos that is awesome, 10 years?! Can I also ask why did you started a KZbin series? Your videos have a lot personality to them. They give me vibes that you are really approachable to ask questions about physics.

[@samposyreeni]

@@PhysicsExplainedVideos That teaching background really shows and shines, yet it's importance is often underestimated. The didactic punch really is what produces the prerequisite number and quality in the next generation of science, for someone within it to "stand on the shoulder of giants".

[@marcosfreijeiro8763]

Awesome videos, love your content. Keep them coming👍🏻👍🏻

[@PhysicsExplainedVideos]

Thank you! Will do!

[@JimGobetz]

Much Thanks, absolutely great stuff as all your videos have been.

[@PhysicsExplainedVideos]

Cheers, much appreciated

[@enricolucarelli816]

Wonderful history, wonderfully narrated. This video is a Gem. Thank you very much.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@osoreru4381]

Great work, very well explained!

[@md.hamidulhaque5816]

All of the videos of this channel are simply GEMS.

[@system888776]

Thank you for this superb video! I was wondering whether you have been planning a video on thermodynamics in the future, e.g. statistical thermodynamics explaining Maxwell-Boltzmann speed distribution, Boltzmann entropy and the origins of Boltzmann constant, and equipartition theorem. In any case, I’m looking forward to watching your next video!

[@PhysicsExplainedVideos]

Great suggestions, they are definitely on my 'to do' list!

[@billfeatherstone3018]

Thank you for your videos..They are the clearest I have ever seen .. if I may say , your sentences are beautiful

[@edcoad4930]

Simply wonderful. I cringe when I think how much effort and planning must go into one of these videos so offer my most sincere thanks for your efforts to educate people with an interest in physics. Saying that; more please!!

[@PhysicsExplainedVideos]

Cheers for the kind words, more on their way!

[@kaanasker4914]

Can you make a video about general relativity?

[@coeur8042]

Yes, and all relativity theories!

[@anasroumeih3605]

The king is here

[@dottedrhino]

I hope you will continue making these excellent video's :)

[@PhysicsExplainedVideos]

That's the plan! Thanks for the feedback

[@raphaeldesousaa]

This is honestly my favorite channel on KZbin 😭

[@icyfyer]

I love these videos. Thank you so much.

[@crunchybacon2915]

Just found your channel and subscribed right away, nice work

[@PhysicsExplainedVideos]

Awesome, thank you!

[@pyromen321]

You do such a great job with these videos. I feel like you fill a great niche between introductory, overview videos and complete month-long courses! Keep up the amazing work!

[@PhysicsExplainedVideos]

Thanks for the kind feedback, I really appreciate it

[@3Space1time]

You need not mention radiation as microwave is a type of radiation only 😄 Btw Loved the video 🤩

[@fburton8]

Wonderfully clear exposition of the topic (notwithstanding the ghastly green expression).

[@PhysicsExplainedVideos]

Thanks!

[@ps200306]

Thanks for another great video. Really loving the long format and the way the calculations are provided. I've watched it a couple of times and am really confused on one point. I'm looking at the Stefan-Boltzmann law at the 21:00 mark. When I work out the dimensions it does indeed come out to units of energy per metre cubed, as subsequently used in the video. But in astronomy we regularly use the Stefan-Boltzmann law to compute the total luminous power of a star. The Stefan-Boltzmann law supposedly gives dimensions of power per square metre, and we multiply up by the surface area of the star to get total power. When I look at the law as given in Wikipedia and elsewhere, there is an extra factor of _c_ included. This would explain the different dimensions as energy per metre cubed multiplied by a speed would give power per square metre. But whence these two different formulations? Then when I look back to the version of the Planck Law from which the Stefan-Boltzmann law is integrated, at 16:45 in the video I see that this is also missing the extra factor of _c_ given in other sources. Alright, so it seems there is a version of Planck's Law used here that gives an energy density per unit wavelength instead of the spectral irradiance (power per unit area per unit wavelength) used elsewhere. I'm wondering how to physically understand this? I'm thinking back to the Ultraviolet Catastrophe video and the calculations based on a black box cavity. I'm right in thinking the actual black body in those examples is the hole in one face of the box, rather than the box itself? So the energy density could refer to the "photon gas" (i.e. Planck's quantised version of the Rayleigh-Jeans modes) inside the cavity, while the spectral irradiance would be the power emitted from the hole? Clutching at straws here. Even if my speculation is right, I am then further confused by the video at 24:25 where we calculate the number density of photons. Whatever about freely propagating radiation in a black box cavity, intuition fails me when we are talking about a plasma. Surely photon number does not have to be conserved in scattering interactions in the plasma? So how does it make sense to talk about a photon number density? Is there some sort of statistical conservation principle at work? _(EDIT:_ on reflection, that's a stupid question: of _course_ there are statistically conserved properties, otherwise neither the Planck law nor the Maxwell-Boltzmann distribution would work. The bulk properties of systems in thermal equilibrium are _all about_ statistics. Nevertheless, Maxwell-Boltzmann was all about indestructible atoms, whereas the concept of a conserved number of transient photons boggles my mind. But perhaps no more than energy conservation in general, which seems to require some sort of unseen backroom accounting in Nature's ledger book). Anyway, I've studied some physics before and these questions never arose, so I'm really loving how this video makes me question what I thought I'd understood.

[@ramijraja1867]

Never stop making such awesome videos

[@PhysicsExplainedVideos]

Cheers, plenty more on their way

[@NalitaQubit]

This is a well done video. Thank you.

[@wdavis6814]

I visited the Holmdel Horn Antenna a few years back, it was very sad. There was no signage or anything, just a random service road next to the NJ Parkway led you to this historic site tucked away in the hills. I got there and the only people who were also there were some local engineers on their lunch break. They were eating I'm their cars in front of this historic machine by themselves. I'm happy they still appreciate it.

[@rajarshisen1631]

Your work is simply beautiful 👍

[@PhysicsExplainedVideos]

Thank you so much, that is very kind of you to say

[@JGS2295]

Another excellent video!

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@kentonjones5394]

I appreciate your work.

[@PhysicsExplainedVideos]

Thanks!

[@leonig100]

Thank you for a very well prepared video with enough detail to attract a wide knowledgeable audience. Just one clarification. The main characteristic of the microwave background is that it can be found whatever direction it is measured. When more detailed maps were made of the temperature based on the peak frequency of the radio waves received then clearly in some directions the peak frequency measured was different. This can lead to the conclusion that in those directions one was not measuring the microwave background but maybe something else. How was this problem overcome?

[@justinwinter4908]

Thank you. I love your videos, Well done!

[@PhysicsExplainedVideos]

Thanks for watching!