A description of dark energy and how it might explain accelerating universe expansion and a simple derivation of the Friedman, Robertson, Walker equation
DrPhysicsA...I just wanted to tell you how helpful your videos are. I am a mother of a 4 year old and a big time space geek. I do a lot of things like QM, relativity, astrophysics etc..in my spare time (its been a passion ever since i was 13). A few days back I was doing a cosmology online course in which the professor was deriving the Friedman Robertson Walker equation. I just couldnt understand a thing what was being taught. And then I remembered you...since I have already subscribed to your videos, it was easy for me to find a video on the derivation that you made. It was marvelous!! Thank you so much for all the efforts and time you put in your videos...especially when you explain each and every step of the calculations. I just love it. Please do carry on with the same style. Thank you thank you thank you.... Cheers from India.
+DrPhysicsA First of all thank you for the lectures. They are great. Considering that i have a good command on Bachelor level physics, could you please guide me on how to proceed towards string theory and what additional subjects do i need to pre-read to basically understand the mathematics of String Theory....
This video was brilliant. I don't know what else to say at the moment, since I just finished it and am still in awe. From a math major to a physics doctor, thank you.
Thanks for your kind comments. Cosmic inflation is said by some to have happened at a very early stage of the universe (ie at about 10**-36 secs after the Big Bang till about 10**-32 secs. During that very short time period the universe expanded at an enormous rate (by a factor of 10**78 or so) thought also to be due to vacuum or dark energy and then continued to expand more slowly.
it is a remarkable quality - to be a great physicist, but at the same time as down to Earth as you are. this helps us in your lectures a lot! thank you.
I am currently in the fourth and final module of an Astrophysics MOOC. In general it has been excellent, but I have struggled a bit with what the Friedman equation represents. This video has provided a clear and easy to follow insight. Thank you very much.
The assumption is that the universe is homogenous and isotropic (at the level of groups of galaxies). That is that no part is more dense than another and that the universe looks the same whichever direction you look.
The Hubble formula V=HD (where H is Hubble's constant) tells us that V increases as D increases. Hence, the further away, the faster it travels. But that doesn't tell us anything about whether the expansion is accelerating or not. Observations of t1 supernova provide evidence of expansion. They are assumed to have the same absolute magnitude so by measuring their magnitude and comparing it with distance (determined by red-shift) gives an indication of expansion.
I don't think that the universe 'works' where (work = Force x distance) And what makes you think the universe uses math to create us? All these formulas are hokey pokey tautologies. Factor in quantum probability and none of this is sound mathematics. But I enjoy these videos, because he's so sure he's right. Good cosmology salesman.
The full answer comes from very complex general relativity. But in essence the concept of energy conservations is only true in a common reference frame. For example, suppose I roll a 1kg ball along the floor at 5km/sec. Its KE = 12.5 Joules (1/2 mv2). But if I happen to be on a train traveling at 5km.sec in same direction, an observer on a platform sees the ball moving at 10km/sec and with KE = 50 Joules. There is no energy conservation violation. Its just that there are 2 frames of ref.
Well no-one knows for sure, but theories can be developed based on what we learn from high energy physics experiments which recreate conditions within the first fraction of a second after the big bang.
Good questions. Not sure anyone really has answers yet. Dark Energy is largely a mathematical solution to explain accelerating universe expansion. We need to understand exactly what it is to find out where it came from and how it has the unchanging effect ascribed to it.
I really appreciate your time and effort in making these sophisticated concepts simple and elegant enough for us to understand. I shall make it a point to go through all of your lectures and would be waiting for more of your lectures. Above all I would like to Thank You as these lectures have significantly helped me to refine my project and get a better picture of reality.
Essentially the atom is ionised. Its the principle of the photoelectric effect. Photons of sufficient energy collide with and transfer their energy to an electron and give that electron more energy than the Binding Energy or Work Function of the electron. So it is able to escape from the atom's Coulomb force which is binding it to the atom.
Einstein's rules apply only to objects travelling through space. They don't apply where objects are carried along (at whatever speed) as part of expanding space.
Well spotted. I probably conflated too much. I was trying to get across the idea that a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero.
u r the best science teacher on u tube... I really love ur vedios.... plz make more and lot of vedios.... On PhD. level Physics and maths. I want to be a physicist. thank you
Lectures are excellent. Physicists are explaining Universe visible and invisible in Calculas for us to understand . Human imaginations , observations are put in mathematical physics which was unimaginalable once for us. We can thank the Professor for his excellent detivation and deliberation which I found quiet correct as a man science .Professor made his derivation very simple and understandable . I wish good health and long life of the Professor.
I assume you mean dimensional analysis. The idea is that each side of an equation must preserve the fundamental dimensions. In this case they are mass, time and length. There are others eg charge which are not relevant here. So we reduce all terms (eg newtons, joules etc) to their basic MLT dimensions and then require dimensional equivalence. Since G and M dont have time dimensions they can be ignored when doing time dimension equivalence.
As a non scientist ordinary bloke I could follow your show in broad outline only but I am always amazed how you manage to reduce almost everything to equations , proportions, and other relationships , and tie them up in order to produce new insights . I like this approach even though our knowledge of the uni verse is incomplete .
It's a difficult concept but space doesn't expand into anything. Space itself expands. So yes there was a starting point and that point has expanded into the universe of today. The whole universe is the expanded point. On your second point I know it seems that the rule of special relativity (nothing can exceed the speed of light) has been violated. But actually there is nothing to stop space expanding at any speed (including >c) and carrying its contents with it.
I like to turn on auto-generated subtitles just to see how accurate they are in Bob's videos. His pronounciation is flawless. He should make audiobooks.
I'd put it like this but open to other explanations. Space expansion carries material objects (eg galaxies) with it but it doesn't actually stretch the objects themselves because the atomic/ molecular forces holding the object together far exceed the force of expansion. So the rulers themselves wouldn't expand but they would all move away from each other.
I think I would have MIT and Princeton and Harvard begging me to work there if I had met this man when I was a sophomore or junior in high school. As it is, I appreciate it now I can't wait to watch every single video.
I listen to your lectures at work often. I absolutely love that you crunch the numbers and do the mathematics. Such fascinating subjects to see and experience the rooted mathematics. Thank you for producing these, they clearly require a lot of your time and they do not go to waste.
Your videos are so good, you teach in a very good and understandable manner and gave me a new understanding of physics as a whole, your videos have been very helpful and until now they are, thank you so much for the effort!!!
I have been afraid of mathematics my whole life - i was tought numbers that meant nothing - while i might fully understand this the more times i watch it I am able to understand algebra and log and stuff that bombarded me - i have no idea how i got an econ degree - but the way you teach a very complex discipline has allowed me to actually learn beyond a conceptual level and apply it to lesser complicated concentrations. its changed the way i view everything essentially.
Excelent video! All your videos are fantastic and of a great quality and clarity. Just one thing thing that I could not help but notice, the function t^(2/3) does not have an upper limit as t goes to infinity, and thus, does not have an asymptotic growth, the rate of expansion would be forever reduced, but the universe would not have a limit size.
The rubber band example is a simple one. But the point about the balloon example is that space is represented by the surface of the balloon. And the surface has no centre. As the balloon expands, every dot expands away from every other dot.
Thank you for your quick response DrPhysicsA, your video was a joy to watch. It was very enlightening to "see" the future of our universe through the beauty of mathematics. Keep up the awesome work!
Technically it becomes a black hole when the escape velocity from its surface exceeds the speed of light. This means that even light cannot escape from its surface and hence the object is black. For the start of universe, you might want to look at my "Cosmology" playlist - especially the video on "From Big Bang to Now"
Although what I am about to say is a bad analogy for the Big Bang it will hopefully serve to explain your point. Imagine an explosion in the middle of a room. You take a series of photos only milliseconds apart which show the material moving away from the site of the explosion. Now consider the material which is furthest away from the explosion site. To reach that point is must have been travelling faster than the material which is still close to the explosion point.
Yes. There were three scenarios. a) universe expands - gravity slows the expansion -- expansion stops - gravity causes contraction - big crunch. b) universe expands - gravity slows expansion - but expansion is asymptotic - it gets slower but never stops c) universe expands continuously. b) was the favoured option. If Dark Energy is right then universe will accelerate in its expansion and will never stop.
Fourth scenario is more probable. Universe is quasi stationnaire. When in some place is too dense stars explode and this part starts expanding. When happens too expanded starts shrinks. So we have local oscillations of density.
Well Dark Energy constitutes about 70% of all the mass/energy of the universe; dark matter about 26% and ordinary matter about 4%. That ordinary matter is becoming less dense as space expands and will continue to do so.
DrPhysicsA I made a theory that talks about dark energy as a whole first you have to understand gravity by using Einstein’s field equation it talks about gravity but to understand anti gravity first you should think about the opposite of force which is dark force (f=ma where m=p and a=c for photons) and also you can think about the slowest thing 1/c =p/E and by substituting f=p(p/E) equals (mv)^2/(E=mc2) therefore if we differentiate we will get that dark force =2
Dr physicsA before differentiation you will get that f=(KE)^2/mc^2 now differentiate to get that dark force=2PE/mc^2 now substitute PE to get 2mgh/mc^2 now cancel m to get 2gh/c^2(some dark energy the unit I call w, and for us to get a new idea that gh= hiet basically height becomes smaller when you get smaller to dark energy like a photon approaching dark energy it’s wavelength is going to decrease as it approaches dark energy before it becomes in contact with dark energy it releases all the stored energy and scatters through space but I also have other equations dark force= 2hiet/dark constant(c^2) where dark constant is the amount of (dark energy/speed of light ) please let me know if you’re interested in more equations from las to Dr physics A
you have an awesome talent explaining things! I've watched several different vids about black holes, DM en DE but you're explanation is so clear and simple! Brilliant! Thanks very much. I know it's a simplification you do, but anyhow, very interesting!
DrPhysicsA you have helped me alot im a 14 year old and i live in a place where the education isnt as good and your videos really help me and I hope I could really meet you someday
thank you very much for the great courses. It would be nice to see some notes such as a table of contents, an index, variable definition and cross refrence to other videos organized into possibly a hyperlinked list. your great work would be more useable and easier to use as refrence!
Excellent video. Thank you. The only bits that are unclear are from 54:30 to 55:06 (where you treat ro and V as functions) and from 56:25 to 56:41 the steps where you jump from (d ro / ro) to d log ro Sure would like some clarification on those two parts. Keep up the good work.
No. All it means is that one part of space is travelling at a speed faster than the speed of light with respect to another part of space and carrying its content with it. So we are moving away at greater than the speed of light with respect to a point beyond the edge of the observable universe. The key is that special relativity prevents anything travelling thro space at >c. But space can expand at any speed it likes.
Thank you for great videos! Please keep it up! From your video I learned that matter-dominated expansion is about to give way to dark energy-dominated expansion that is accelerating its pace now. What is the difference between current exponential phase of expansion and the (conjectured) cosmic inflation? Do they have fundamentally different mechanisms or are these phases of expansion just manifestations of the same underlying laws?
Some parts of the universe are already moving in space relative to us at >c. Space can expand at any speed it likes. But light from such parts can never reach us.
Thank you, teacher ! I've always wanted to study astronomy but i ended up being a computer engineer. Luckly, i could understand you well. Thanks to my Physics 101 and 102 classes :)
It's now 2022. I find the occasional errors in notation helpful - because they are apparent, before inevitable correction. It is just remarkable how all this is engraved in marks on paper, a step away from a stick in sand. Thanks..
Great video again, but one question, I one hour you brought up the "what if" w=-1, and then proceeded to assume it was true. Where did we derive that negative 1 value for W?
You are right. I didn't actually derive it. In keeping with my general principle of trying to keep things simple I simply asserted it and demonstrated the consequences of it.
Awesome series that I just watched. And I will watch it again ;) There is one thing I did not understand and that's the dimensionality of the t^2/3 and t^1/2 that you arrived at. I have the feeling my basic calculus from 25 years ago may have failed me. ^^
Space expansion does not expand everything. For example the ruler on your desk is not expanding as the universe expands because the molecular forces holding the ruler together are much greater than the impact of space expansion. So the rulers don't expand.
I can't believe I'm learning the basic math behind the amazing concepts I watch in documentaries! Your channel, Sir, is AMAZING!!! Here's a great topic to cover next: High energy physics and the big bang! I was wondering: How do scientists know that x happened at 10^-23 (or whatever) seconds after the big bang? It's not the"x" part that I find puzzling, which AFAIK, scientists cover doing HEP exp., but about the exact timing that correspond to a certain energy-density level or content of the U.
Dr.Physics, have you ever heard of a rotating wave (classical rotation or spin) and could it be a possible reason for the expansion of the universe (as we know it). The classical rotation which also inherently explains relativity and gravity, must some how be brought into rotation by a binding energy. That binding energy is given up when an incidental light wave passes by and bends. Could that binding energy thus explain what dark energy is? I suspect so, but there may be more. Wonderful lecture as always, Bill Christie
Around 48:30, when you are finding the pressure a photon exerts on a wall while traveling one-dimensionally, i understand that Force is the time-derivative of monemtu, but while finding the time-derivative, why is the "dt" part equal to the time the photon travels the entire length of the track twice? Shouldn't the dt equal the time it takes to bounce off the wall? Thanks!
A black hole typically arises when a massive star collapses at the end of its life. The nuclear fusion which up to that point has held of the gravitational force stops. For smaller stars the collapse is halted by Pauli's exclusion principle (either at the electron of nucleon level). But for massive stars the gravitational collapse is too powerful. There is then no known force to stop the collapse to a point of infinite density.
Space probably only expands on a intra galactic scale. Even space within galaxies probably doesn't expand because the forces which hold galaxies together overcome any space expansion factor. That's even more the case when you consider forces operating in atoms.
Space itself is our point of reference for every position and distance. So, if space stretches, our coordinate system is stretching, which makes our units of measure stretch with it. Where can we find a coordinate system independent of space and time that we can use to measure space against, so that we can tell it's stretching? In your example with the rubber band, it's like having coordinates drawn (as you have them) in the rubber band, and two dots that measure distance X (in rubber band coordinate units); after you stretch the rubber band, the two dots will still measure distance X, even if that distance looks larger to us who live outside of (and are unaffected by) the rubber band coordinate system.
Thank you very much for the great courses. But I would like to pose question: who was more wrong? 1. Columbus' sailors who thought the Earth was flat surface; 2. The autor of the video who says that the universe is a sphere.
20:15 Your left-hand side is basically the square of Hubble's constant, which will never be less than zero (the square of any number must be positive, unless we're talking imaginary numbers), so how can you make the argument that the "-k" term to the right of the potential energy part of the formula could ever get bigger than the potential energy term?
When the universe stretches and the energy of each photon is reduced, where does that "surplus" energy go? Thinking in terms of energy conservation? Ignoring photons hitting planets and such, most of the photons from the transition from opaque to transparent universe, should be intact and the same in number (at least not increasing), but each of them now has a lot lower energy than they once did - so where is the energy lost?
Its a rough and ready calculation and assumes that electrons combine with protons to form atoms at about 3000K. So time from Big Bang to time when Temp has fallen to about 3000K is about 300,000 years.
The binding energy of an electron to a proton (Hydrogen) is 13.6eV. This corresponds to a temperature of approximately 163,000K. However, the black-body radiation curve shows that you need to drop down to a temperature of approximately 3000K in order to not have enough high energy photons at that 13.6ev to ionize Hydrogen atoms. Hence, the Universe had to cool well below 163,000K in order to allow all the hydrogen to be stable.
i watch these videos for pure entertainment I have no idea what he's saying and I can't even begin to say I understand the origins of these ideas. I swear man I have no idea whats going on.
plz Dr Physics !!! m very week in mathematics but i like Physics soo Much , i wanna study space-time as i want , like space curvature , vortex in spacetime caused by massive rotational objects like sprial Galaxy !! how to study that kind of Physics in Mathematics , which maths are needed for this ???? plz make video on it Thanks :)
You misunderstood me, I think. Here's what I don't get: How to set the time scale, when there's increasing uncertainty when we approach the big bang. Suppose we are pretty sure, from what we know from high energy physics, that x and y event happened more or less in this way and that there's has to be this interval between them (10^-10 seconds of separation). That I get, but how can we know the exact timing of the first event: if it was for instance 10^-14 or of 10^-6, etc. after the BB?
Understand you could keep the "DE" term on the left-hand side of the Einstein field equations, and interpret the Cosmological constant term as an "intrinsic curvature" within the "fabric" of space-time, even in the absence of mass-energy, vaguely like the intrinsic curvature in a bow or a flatbed trailer, which "bow upwards" against applied loads -- does not have to be interpreted as an exotic energy field on the RHS of the eqtn
I totally agree whith you, rfoshaug (nice name). The stretching of the foton wavelenght is a real effect, independent of a reference frame that is standing stil relative to space. The cbr consists of fotons with a wavelenght in the radio region and is the same in every direction. If you traveling in a spaceship with great speed through space (change in reference frame) the fotons on the front of your spaceschip appear to have a smaller wavelenght, on the back smaller. A new kind of ether!
wow you just went through the entire Friedmann solution! excellent video!! I was wondering the other day, if λ expands space, and exists within our universe then how it can remain a constant whilst space is altered? isn't that violating the laws of thermodynamics? is DE created from nothing? could it be a relationship between ρ and λ? what is your opinion on Roger Penrose alternative big-bang theory, he replaces inflation with black hole entropy expansion and replaces λ with leftover g radiation
And on related note, does this mean that by jumping up you travel slightly smaller distance than by going down and therefore the potential energy at your highest point is just slightly higher than the kinetic energy used to jump?
In the equation p^2/t^2 = 8πG/3c^3t^3p you concluded that p= 2/3 so that it would be dimensionally correct, but why didn't you consider the gravitational constant G, which has the units kg*m2*s-2 ? I got convinced in the end of the video when you got the same results by other methods, but this part especifically seemed strange.
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I remember watching your videos 6 years ago when I was still a high schooler. I am now graduating with my undergrad in physics studying cosmology :)
Congrats Nihar!!
Good for you, that’s wonderful!
Hey, can u tell me how to get the degree of theoretical physics after 12th STD ???
DrPhysicsA...I just wanted to tell you how helpful your videos are. I am a mother of a 4 year old and a big time space geek. I do a lot of things like QM, relativity, astrophysics etc..in my spare time (its been a passion ever since i was 13). A few days back I was doing a cosmology online course in which the professor was deriving the Friedman Robertson Walker equation. I just couldnt understand a thing what was being taught. And then I remembered you...since I have already subscribed to your videos, it was easy for me to find a video on the derivation that you made. It was marvelous!! Thank you so much for all the efforts and time you put in your videos...especially when you explain each and every step of the calculations. I just love it. Please do carry on with the same style. Thank you thank you thank you.... Cheers from India.
Thank you. Very kind of you to take the time and trouble to say so. Kind regards.
+DrPhysicsA First of all thank you for the lectures. They are great. Considering that i have a good command on Bachelor level physics, could you please guide me on how to proceed towards string theory and what additional subjects do i need to pre-read to basically understand the mathematics of String Theory....
+kusukuttan i am also from India , i also like this lecture , will yu accept my fb friendship ?
bc
we are in a simulation. we are all gods
This video was brilliant. I don't know what else to say at the moment, since I just finished it and am still in awe. From a math major to a physics doctor, thank you.
Lately you are all a listen to. i sofrer with chronic pain and you seem to keep me mind of it.THANK YOU PROFESSOR.💜☀️🌻
Thanks for your kind comments. Cosmic inflation is said by some to have happened at a very early stage of the universe (ie at about 10**-36 secs after the Big Bang till about 10**-32 secs. During that very short time period the universe expanded at an enormous rate (by a factor of 10**78 or so) thought also to be due to vacuum or dark energy and then continued to expand more slowly.
it is a remarkable quality - to be a great physicist, but at the same time as down to Earth as you are. this helps us in your lectures a lot! thank you.
I am currently in the fourth and final module of an Astrophysics MOOC. In general it has been excellent, but I have struggled a bit with what the Friedman equation represents. This video has provided a clear and easy to follow insight. Thank you very much.
The assumption is that the universe is homogenous and isotropic (at the level of groups of galaxies). That is that no part is more dense than another and that the universe looks the same whichever direction you look.
The Hubble formula V=HD (where H is Hubble's constant) tells us that V increases as D increases. Hence, the further away, the faster it travels. But that doesn't tell us anything about whether the expansion is accelerating or not. Observations of t1 supernova provide evidence of expansion. They are assumed to have the same absolute magnitude so by measuring their magnitude and comparing it with distance (determined by red-shift) gives an indication of expansion.
your pure clear lectures are great, and you are Vgood teacher
I don't think that the universe 'works' where (work = Force x distance) And what makes you think the universe uses math to create us? All these formulas are hokey pokey tautologies. Factor in quantum probability and none of this is sound mathematics. But I enjoy these videos, because he's so sure he's right. Good cosmology salesman.
The full answer comes from very complex general relativity. But in essence the concept of energy conservations is only true in a common reference frame. For example, suppose I roll a 1kg ball along the floor at 5km/sec. Its KE = 12.5 Joules (1/2 mv2). But if I happen to be on a train traveling at 5km.sec in same direction, an observer on a platform sees the ball moving at 10km/sec and with KE = 50 Joules. There is no energy conservation violation. Its just that there are 2 frames of ref.
That's very kind. Thanks.
Please return !!😭 Do more lectures . Would love it
Well no-one knows for sure, but theories can be developed based on what we learn from high energy physics experiments which recreate conditions within the first fraction of a second after the big bang.
Good questions. Not sure anyone really has answers yet. Dark Energy is largely a mathematical solution to explain accelerating universe expansion. We need to understand exactly what it is to find out where it came from and how it has the unchanging effect ascribed to it.
I really appreciate your time and effort in making these sophisticated concepts simple and elegant enough for us to understand. I shall make it a point to go through all of your lectures and would be waiting for more of your lectures.
Above all I would like to Thank You as these lectures have significantly helped me to refine my project and get a better picture of reality.
You have a crystal clear way in explaining stuff. Thank you DrPhysicsA
Essentially the atom is ionised. Its the principle of the photoelectric effect. Photons of sufficient energy collide with and transfer their energy to an electron and give that electron more energy than the Binding Energy or Work Function of the electron. So it is able to escape from the atom's Coulomb force which is binding it to the atom.
Thank you for this video. I have left school for close to a decade. Watching this reignites my interest in science. Keep up the great work!
Einstein's rules apply only to objects travelling through space. They don't apply where objects are carried along (at whatever speed) as part of expanding space.
Well spotted. I probably conflated too much. I was trying to get across the idea that a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero.
u r the best science teacher on u tube... I really love ur vedios.... plz make more and lot of vedios.... On PhD. level Physics and maths. I want to be a physicist. thank you
Lectures are excellent.
Physicists are explaining Universe visible and invisible in Calculas for us to understand . Human imaginations , observations are put in mathematical physics which was unimaginalable once for us.
We can thank the Professor for his excellent detivation and deliberation which I found quiet correct as a man science .Professor made his derivation very simple and understandable . I wish good health and long life of the Professor.
I assume you mean dimensional analysis. The idea is that each side of an equation must preserve the fundamental dimensions. In this case they are mass, time and length. There are others eg charge which are not relevant here. So we reduce all terms (eg newtons, joules etc) to their basic MLT dimensions and then require dimensional equivalence. Since G and M dont have time dimensions they can be ignored when doing time dimension equivalence.
As a non scientist ordinary bloke I could follow your show in broad outline only but I am always amazed how you manage to reduce almost everything to equations , proportions, and other relationships , and tie them up in order to produce new insights . I like this approach even though our knowledge of the uni verse is incomplete .
It's a difficult concept but space doesn't expand into anything. Space itself expands. So yes there was a starting point and that point has expanded into the universe of today. The whole universe is the expanded point. On your second point I know it seems that the rule of special relativity (nothing can exceed the speed of light) has been violated. But actually there is nothing to stop space expanding at any speed (including >c) and carrying its contents with it.
I like to turn on auto-generated subtitles just to see how accurate they are in Bob's videos. His pronounciation is flawless. He should make audiobooks.
I'd put it like this but open to other explanations. Space expansion carries material objects (eg galaxies) with it but it doesn't actually stretch the objects themselves because the atomic/ molecular forces holding the object together far exceed the force of expansion. So the rulers themselves wouldn't expand but they would all move away from each other.
I think I would have MIT and Princeton and Harvard begging me to work there if I had met this man when I was a sophomore or junior in high school. As it is, I appreciate it now I can't wait to watch every single video.
There is actually no energy loss. Its just that we observe them from a different reference frame.
Sir you have increased my interest in ASTRONOMY and astrophysics ,that's great ,i am highly greatful to yu all .Happy New Year.
I listen to your lectures at work often. I absolutely love that you crunch the numbers and do the mathematics. Such fascinating subjects to see and experience the rooted mathematics. Thank you for producing these, they clearly require a lot of your time and they do not go to waste.
Your videos are so good, you teach in a very good and understandable manner and gave me a new understanding of physics as a whole, your videos have been very helpful and until now they are, thank you so much for the effort!!!
I think it's largely convention to do so. If k=0 (which it appears to be) then space is flat.
I have been afraid of mathematics my whole life - i was tought numbers that meant nothing - while i might fully understand this the more times i watch it I am able to understand algebra and log and stuff that bombarded me - i have no idea how i got an econ degree - but the way you teach a very complex discipline has allowed me to actually learn beyond a conceptual level and apply it to lesser complicated concentrations. its changed the way i view everything essentially.
Excelent video! All your videos are fantastic and of a great quality and clarity. Just one thing thing that I could not help but notice, the function t^(2/3) does not have an upper limit as t goes to infinity, and thus, does not have an asymptotic growth, the rate of expansion would be forever reduced, but the universe would not have a limit size.
The rubber band example is a simple one. But the point about the balloon example is that space is represented by the surface of the balloon. And the surface has no centre. As the balloon expands, every dot expands away from every other dot.
Thank you for your quick response DrPhysicsA, your video was a joy to watch. It was very enlightening to "see" the future of our universe through the beauty of mathematics. Keep up the awesome work!
Thanks so much for the great videos. You have a unique way of presenting complicated subjects is an easy to understand manner.
Well in essence it is the energy density that reduces but the volume of space increases so overall energy remains the same.
Technically it becomes a black hole when the escape velocity from its surface exceeds the speed of light. This means that even light cannot escape from its surface and hence the object is black. For the start of universe, you might want to look at my "Cosmology" playlist - especially the video on "From Big Bang to Now"
Excellent lectures sir, very productive and knowledgeable content....Thankyou very much, God Bless All
Although what I am about to say is a bad analogy for the Big Bang it will hopefully serve to explain your point. Imagine an explosion in the middle of a room. You take a series of photos only milliseconds apart which show the material moving away from the site of the explosion. Now consider the material which is furthest away from the explosion site. To reach that point is must have been travelling faster than the material which is still close to the explosion point.
Yes. There were three scenarios. a) universe expands - gravity slows the expansion -- expansion stops - gravity causes contraction - big crunch. b) universe expands - gravity slows expansion - but expansion is asymptotic - it gets slower but never stops c) universe expands continuously. b) was the favoured option. If Dark Energy is right then universe will accelerate in its expansion and will never stop.
Fourth scenario is more probable. Universe is quasi stationnaire. When in some place is too dense stars explode and this part starts expanding. When happens too expanded starts shrinks. So we have local oscillations of density.
Well Dark Energy constitutes about 70% of all the mass/energy of the universe; dark matter about 26% and ordinary matter about 4%. That ordinary matter is becoming less dense as space expands and will continue to do so.
DrPhysicsA I made a theory that talks about dark energy as a whole first you have to understand gravity by using Einstein’s field equation it talks about gravity but to understand anti gravity first you should think about the opposite of force which is dark force (f=ma where m=p and a=c for photons) and also you can think about the slowest thing 1/c =p/E and by substituting f=p(p/E) equals (mv)^2/(E=mc2) therefore if we differentiate we will get that dark force =2
Dr physicsA before differentiation you will get that f=(KE)^2/mc^2 now differentiate to get that dark force=2PE/mc^2 now substitute PE to get 2mgh/mc^2 now cancel m to get 2gh/c^2(some dark energy the unit I call w, and for us to get a new idea that gh= hiet basically height becomes smaller when you get smaller to dark energy like a photon approaching dark energy it’s wavelength is going to decrease as it approaches dark energy before it becomes in contact with dark energy it releases all the stored energy and scatters through space but I also have other equations dark force= 2hiet/dark constant(c^2) where dark constant is the amount of (dark energy/speed of light ) please let me know if you’re interested in more equations from las to Dr physics A
you have an awesome talent explaining things! I've watched several different vids about black holes, DM en DE but you're explanation is so clear and simple! Brilliant! Thanks very much. I know it's a simplification you do, but anyhow, very interesting!
DrPhysicsA you have helped me alot im a 14 year old and i live in a place where the education isnt as good and your videos really help me and I hope I could really meet you someday
thank you very much for the great courses. It would be nice to see some notes such as a table of contents, an index, variable definition and cross refrence to other videos organized into possibly a hyperlinked list. your great work would be more useable and easier to use as refrence!
Excellent video. Thank you.
The only bits that are unclear are from 54:30 to 55:06 (where you treat ro and V as functions) and from 56:25 to 56:41 the steps where you jump from (d ro / ro) to d log ro
Sure would like some clarification on those two parts.
Keep up the good work.
You are the best teacher I have ever known!
No. All it means is that one part of space is travelling at a speed faster than the speed of light with respect to another part of space and carrying its content with it. So we are moving away at greater than the speed of light with respect to a point beyond the edge of the observable universe. The key is that special relativity prevents anything travelling thro space at >c. But space can expand at any speed it likes.
Thank you for great videos! Please keep it up! From your video I learned that matter-dominated expansion is about to give way to dark energy-dominated expansion that is accelerating its pace now. What is the difference between current exponential phase of expansion and the (conjectured) cosmic inflation? Do they have fundamentally different mechanisms or are these phases of expansion just manifestations of the same underlying laws?
Some parts of the universe are already moving in space relative to us at >c. Space can expand at any speed it likes. But light from such parts can never reach us.
I don't think I have assumed that the universe is cube shaped have I?
I just finished my first year in college physics and I found this fascinating
Jonah Mackey same here! just took my first astronomy class last semester and love this although this isn't my major
by yur good wishes i have understood the lecture , my thanks to you , and all those who helped in this communication !
Very impressive lecture sir ... now days you are the my favourite lecturer... love you sir .
Thanks for your videos! I enjoy watching them, you explain things pretty clearly and in an interesting way.
Thank you for the very interesting material, but I am wondering how f(t) = t^(2/3) has an asymptotic behavior f(t)-> const > 0 when t->infinity?
Thank you, teacher ! I've always wanted to study astronomy but i ended up being a computer engineer. Luckly, i could understand you well. Thanks to my Physics 101 and 102 classes :)
It's now 2022. I find the occasional errors in notation helpful - because they are apparent, before inevitable correction. It is just remarkable how all this is engraved in marks on paper, a step away from a stick in sand. Thanks..
Great video again, but one question, I one hour you brought up the "what if" w=-1, and then proceeded to assume it was true. Where did we derive that negative 1 value for W?
You are right. I didn't actually derive it. In keeping with my general principle of trying to keep things simple I simply asserted it and demonstrated the consequences of it.
concerning a radiation or matter dominated expansion, the functions t^2/3 or t^1/2 do not tend to any asymptotic value...
at min 39, you said the contrary. Had I miss something?
Awesome series that I just watched. And I will watch it again ;)
There is one thing I did not understand and that's the dimensionality of the t^2/3 and t^1/2 that you arrived at. I have the feeling my basic calculus from 25 years ago may have failed me. ^^
His videos are always slightly unsharp but still amazingly sharp in explanation haha
Space expansion does not expand everything. For example the ruler on your desk is not expanding as the universe expands because the molecular forces holding the ruler together are much greater than the impact of space expansion. So the rulers don't expand.
I can't believe I'm learning the basic math behind the amazing concepts I watch in documentaries! Your channel, Sir, is AMAZING!!! Here's a great topic to cover next: High energy physics and the big bang! I was wondering: How do scientists know that x happened at 10^-23 (or whatever) seconds after the big bang? It's not the"x" part that I find puzzling, which AFAIK, scientists cover doing HEP exp., but about the exact timing that correspond to a certain energy-density level or content of the U.
Dr.Physics, have you ever heard of a rotating wave (classical rotation or spin) and could it be a possible reason for the expansion of the universe (as we know it). The classical rotation which also inherently explains relativity and gravity, must some how be brought into rotation by a binding energy. That binding energy is given up when an incidental light wave passes by and bends. Could that binding energy thus explain what dark energy is? I suspect so, but there may be more. Wonderful lecture as always, Bill Christie
Great movie for jumping right in! Takes the fear away. Thanks Dr Physics.
Wonderful explanation!
Thank you very much, DrPhysicsA. I really like this. At 12:26 you wrote a wrong equation, but you changed to right one later.
I believe there were some differences bw this FRW equation and the one on google.But It was an absolutely marvellous lecture.Thank you Sir.
The graph at 1:04:45 shows the expansion rates for radiation dominated, matter dominated and dark energy dominated expansion.
Around 48:30, when you are finding the pressure a photon exerts on a wall while traveling one-dimensionally, i understand that Force is the time-derivative of monemtu, but while finding the time-derivative, why is the "dt" part equal to the time the photon travels the entire length of the track twice? Shouldn't the dt equal the time it takes to bounce off the wall?
Thanks!
A black hole typically arises when a massive star collapses at the end of its life. The nuclear fusion which up to that point has held of the gravitational force stops. For smaller stars the collapse is halted by Pauli's exclusion principle (either at the electron of nucleon level). But for massive stars the gravitational collapse is too powerful. There is then no known force to stop the collapse to a point of infinite density.
very interesting lecture ,requires concentration
As the universe expands its diameter increases. Since the total mass remains the same that must mean that it's density decreases over time.
Respect and lots of love for you sir. Greetings from INDIA
Space probably only expands on a intra galactic scale. Even space within galaxies probably doesn't expand because the forces which hold galaxies together overcome any space expansion factor. That's even more the case when you consider forces operating in atoms.
Inter galactic scale, but I get it.
Space itself is our point of reference for every position and distance. So, if space stretches, our coordinate system is stretching, which makes our units of measure stretch with it. Where can we find a coordinate system independent of space and time that we can use to measure space against, so that we can tell it's stretching? In your example with the rubber band, it's like having coordinates drawn (as you have them) in the rubber band, and two dots that measure distance X (in rubber band coordinate units); after you stretch the rubber band, the two dots will still measure distance X, even if that distance looks larger to us who live outside of (and are unaffected by) the rubber band coordinate system.
+TheWak Music Thanks. Will do.
This video has been ridiculously helpful. Thank you sir!
What constitutes the walls of the box for the radiation to actually press against in the universe , and so cause pressure ?
Thank you very much for the great courses. But I would like to pose question: who was more wrong?
1. Columbus' sailors who thought the Earth was flat surface;
2. The autor of the video who says that the universe is a sphere.
20:15 Your left-hand side is basically the square of Hubble's constant, which will never be less than zero (the square of any number must be positive, unless we're talking imaginary numbers), so how can you make the argument that the "-k" term to the right of the potential energy part of the formula could ever get bigger than the potential energy term?
When the universe stretches and the energy of each photon is reduced, where does that "surplus" energy go? Thinking in terms of energy conservation? Ignoring photons hitting planets and such, most of the photons from the transition from opaque to transparent universe, should be intact and the same in number (at least not increasing), but each of them now has a lot lower energy than they once did - so where is the energy lost?
Its a rough and ready calculation and assumes that electrons combine with protons to form atoms at about 3000K. So time from Big Bang to time when Temp has fallen to about 3000K is about 300,000 years.
The binding energy of an electron to a proton (Hydrogen) is 13.6eV. This corresponds to a temperature of approximately 163,000K. However, the black-body radiation curve shows that you need to drop down to a temperature of approximately 3000K in order to not have enough high energy photons at that 13.6ev to ionize Hydrogen atoms. Hence, the Universe had to cool well below 163,000K in order to allow all the hydrogen to be stable.
i watch these videos for pure entertainment I have no idea what he's saying and I can't even begin to say I understand the origins of these ideas. I swear man I have no idea whats going on.
You will!
First step, Drop the Jesus. Necessary condition
Before I offend anyone I'm 1/2 joking
@@kzeich xDDD
Well energy density goes down but the volume increases so total energy remains the same.
plz Dr Physics !!! m very week in mathematics but i like Physics soo Much , i wanna study space-time as i want , like space curvature , vortex in spacetime caused by massive rotational objects like sprial Galaxy !! how to study that kind of Physics in Mathematics , which maths are needed for this ???? plz make video on it Thanks :)
I have no idea what is going on but I enjoyed 27 minutes of it anyway.
Exquisitely said.please can anybody tell me the professors name?thank you.
Bob Eagle CBE (Commander of the Order of the British Empire)
I am loving these clases.
You misunderstood me, I think. Here's what I don't get: How to set the time scale, when there's increasing uncertainty when we approach the big bang. Suppose we are pretty sure, from what we know from high energy physics, that x and y event happened more or less in this way and that there's has to be this interval between them (10^-10 seconds of separation). That I get, but how can we know the exact timing of the first event: if it was for instance 10^-14 or of 10^-6, etc. after the BB?
Ah I see what you mean. The examples I gave do assume that spacetime has 3 dimensions of space and 1 of time.
How can I contact you sir I have a question
Understand you could keep the "DE" term on the left-hand side of the Einstein field equations, and interpret the Cosmological constant term as an "intrinsic curvature" within the "fabric" of space-time, even in the absence of mass-energy, vaguely like the intrinsic curvature in a bow or a flatbed trailer, which "bow upwards" against applied loads -- does not have to be interpreted as an exotic energy field on the RHS of the eqtn
As I said at 18:30 it is by convention. Since k is a constant we can redefine it to be -k.
I totally agree whith you, rfoshaug (nice name). The stretching of the foton wavelenght is a real effect, independent of a reference frame that is standing stil relative to space. The cbr consists of fotons with a wavelenght in the radio region and is the same in every direction. If you traveling in a spaceship with great speed through space (change in reference frame) the fotons on the front of your spaceschip appear to have a smaller wavelenght, on the back smaller. A new kind of ether!
wow you just went through the entire Friedmann solution! excellent video!!
I was wondering the other day, if λ expands space, and exists within our universe then how it can remain a constant whilst space is altered? isn't that violating the laws of thermodynamics? is DE created from nothing? could it be a relationship between ρ and λ? what is your opinion on Roger Penrose alternative big-bang theory, he replaces inflation with black hole entropy expansion and replaces λ with leftover g radiation
And on related note, does this mean that by jumping up you travel slightly smaller distance than by going down and therefore the potential energy at your highest point is just slightly higher than the kinetic energy used to jump?
In the equation p^2/t^2 = 8πG/3c^3t^3p you concluded that p= 2/3 so that it would be dimensionally correct, but why didn't you consider the gravitational constant G, which has the units kg*m2*s-2 ? I got convinced in the end of the video when you got the same results by other methods, but this part especifically seemed strange.