5 min physics: A mathematical appendix

Warning: This video is for those who are comfortable with calculus, and have some physics background.. namely physics students among others. I show mathematically how the 'equation of state' can be derived for matter, radiation, and dark energy and how this determines their evolution in an expanding universe... in 7 minutes! (I forgot to mention at the end that once we show p=-rho, then plugging it in the initial equation I derived, shows that the energy density remains constant for dark energy

[EEVblog]

You win the 2020 social isolation tutorial video of the year award. Your golden toilet roll award will be santised and mailed to you.

[joshua]

It' amazing how some letters with a specific meaning and numbers rearranged around can show you the workings of something as grand as the universe

[muhammadhadi]

Dr Krauss, you make it look so simple and understandable. More of contents like these please.

[mauriceguymoi]

Like my physics professor used to say jokingly; "The slower you go, the faster your speed decreases". Other definition of deceleration.

[CyberSystemOverload]

Why do people dislike such videos? Just because THEY dont understand it? Learning and spreading knowledge is so important. Excellent video as always!!

[danielstandley-Physicist]

Thanks for this as a mature age student work towards my physics degree I aim to have a deep understanding of this soon

Keep up the great work

[sandydl]

Can't wait for the something from nothing videos 5 Min Physics videos. These have been fun to watch.

[cnsaw]

Love these videos Laurence, keep them coming please... please visit Ireland for a talk sometime 👍

[marshalljman]

This is absolutely awesome even though it gives me flashbacks to thermodynamics

[ThomasLahn]

Great explanation, but you lost me a bit on the calculation of the radiation energy density (rho): If p = 1/3 in natural units (c = 1), why is rho = 1 so that we get -3 (p + rho) = -3 (1/3 + 1) = -3 * 4/3 = -4?

[traetuusplays]

As a person from a small town who dreamed of being a Nuclear Engineer, and possibly a physicist when they grew up was shattered by the constraints of the public education system, and religious radicals as my science teachers, I deeply appreciate these videos. I'm near age 30 now, and my thirst for knowledge became merely a hobby when real life took hold. Is it at all possible for a person to become something more in this regard, and have a future, or have I simply missed my departure time?

I was solving Einsteins equation in 6th grade, for every star I knew the size, and name of, and would always get told to put that work away to do some seriously remedial at best worksheet. I felt my teachers failed my advancement to becoming the best intellect I could be, and now at my age, I wonder if simply paying bills is my future. It seems such a waste, but with these videos I get a slight bit of resolve with each one knowing someone out there is educating those who want to listen.

I never made it into calculus as a student. Simply because my highschool didn't offer anything past trigonometry, but even without a day inside that caliber of a class room, I understand what you teach, and want to dive further. I know I post this under an arbitrary internet alias, and really should have not taken "no" for an answer in those days as a kid growing up. Thanks for your knowledge, and sharing of this. I cannot wait to see the next iteration of your teachings. I apologize if this was to long a comment, but I felt if anyone could understand it would be you.

Thank you again Dr. Krauss. Happy quarantine time.

[deathpenguin]

Wow that was awesome. My knowledge of theory helped me follow some of the reasoning behind what you were doing but yeah mathematically. No. But you did say not for general public haha.

[Firstvgd]

Mr. Krauss, please give us some explanation on the energy created with the big bang, are we all part of it, does it dissipate with the time?

[kanabellhitoshi]

How are you able to work out a math problem that has little to no numbers in it? That's like magic to a simple layman.

Edit: l just remembered, this is for math majors, and not for simple common folk. My bad. XD

[Petrov]

Once more since it preoccupies me: Dear Prof. Krauss -- can you comment on Prof. Penrose’s CCC (Conformal Cyclic Cosmology) hypothesis, his utter disbelief/rejection of "inflation" in trillionths of second after Big Bang and the contradiction of entropy that his hypothesis addresses/solves.
Many thanks in advance.

PS: So far I know of only one of your colleagues theoretical physicists who is on record of doubting the "inflation" -- Sean Carroll who gave it only 50% chance of being correct... (when interviewing Roger Penrose) ;-))

[Ihab.A]

Prof, please use a larger black marker, it is hard to see what is written on the white paper

[skepticsapiens]

Hi sir krauss I am 13 years old which books should I read for being a cosmologist like you.

[anitabanik]

Sir can you please show us wave function...

[markmd]

Does I know correctly that several billions years ago the universe expansion was decelerating then suddenly picked up speed and began to expand with acceleration?

[bhanutejadasari]

Hi Lawrence! Could you please explain some complex mathematical concepts like calculus and why it's so important in an long simplistic way? Also, the very fundamentals like what electrons and other similar particles are, what they actually do, how they exist in an atom and what existing as a wave actually mean. I tried to learn about them in so many ways. But in every case I felt that I kind of almost get it but not quite. There was always something missing in totally understanding calculus and especially atoms. I've got no idea where else to get the missing information from if not from a very good scientist. The feeling of not sufficiently understanding something as fundamental as that has always been a hindrance in properly learning advanced concepts. If you at all decided to make a video on that, I urge you to take a little more time than you normally would and decode every practicably decodable term. If it is practically not possible or you don't have the time for it, please suggest a book or two that you think can help with it. Thanks so much. For all the things you've done for the human kind.