I'm a psychology professor with an interest in physics. I love these daily equations. Please keep on doing as many as you can. Thank you for your ability to promote and explain the beauty of physics!
Thanks Brian- I'm 73, never took physics or calculus, and I was able to follow- not saying I could do it but I got the principles and will now watch all of these. Hate being house-bound when you've ignited my inner Cliff Klaven.
Thanks for the explanation! The example, despite being a bit contrived illustrates nicely the need for an increased mass - to conserve momentum. A less contrived way to show that a mass increase is required is to use the impulse momentum theorem viewed from an objects instantaneous rest frame and comparing it with the equation that arrives from a static frame at rest.
Just happened on this series... A Daily Equation - what a great & practical format for many of us folks. Liked the jousting analogy & KE explanation in this one 👍. Many thanks for the videos Brian😊!
I think the biggest thing i like about these, are that, now that school is out for most children and young adults, no one is learning anything. And if worst case scenario the education system falls apart (probably not likely but hey) then we still need not just the information out there to go and find, but we need those individuals who would pull information they know and understand, and instead of just lazying about and being the keepers of that information, they share it like this, often times information most people wouldnt bother to try to understand. This way, the most mind blowing of information, isnt lost in the crisis (again, probably not gonna happen, but i hear a lot of people talk about how thankful they are the internet is still operating). I once heard, maybe NGT talk about it, but something was said along the lines of, "if everyone who was knowledgeable enough to make a cell phone from scratch, how long would it take for us to reinvent it, if all those people disappeared?" Of course we arent only talkin about people disappearing but the information they carry with them being lost in time. It seems many civilizations succumb to this tragedy. Im just saying, teachers and professors, those with knowledge who's profession is to teach others, i think they should all be doing stuff like this, sharing their knowledge freely and openly.
"Relativistic mass" is a broken concept, because it works only for the special relativistic (SR) formula for momentum, p[rel]. When learning relativity, it is a mental crutch that attempts to preserve the Newtonian form of momentum by making mass depend on velocity. In fact, it isn't that the mass is changing; it is that the functional dependence of momentum on velocity, differs from the Newtonian p = mv; namely, p[rel] = mv/√(1-[v/c]²) = m(γv). And it is this change in the formula for momentum that makes attaining v=c impossible for any body with non-zero mass. The culprit is still that factor, "γ," but it is properly attached to the "v," not to the "m." That this is so, can be seen by trying to plug this "relativistic mass" into the Newtonian formula for kinetic energy, KE = ½mv². It gives the wrong result. The actual formula is KE[rel] = (γ - 1)mc² = (1/√(1-[v/c]²) - 1)mc² ≠ ½γmv². (Dr. Greene's derivation of the Newtonian KE from E = mc² is exactly right, however.) "Mass of a body" is a property of the body itself, not of its state of motion - or, in fact, of the state of motion of some arbitrary observer! Because it is a central principle of SR that physics "looks" the same in any inertial frame of reference. Two observers in uniform relative motion to one another should assign the same value to the mass of a body. Fred PS. See the excellent, less technical explanation of this by Dr. Don Lincoln on the Fermilab channel.
Can't wait for this. Thx Brian for the stuff you have shared during the years. Amazing how many implications there are for all basic ingredients of physics when relativity is set in motion.. .time, space, and now mass.
This series is great! Something to look forward to every day in these stressful times. This made me realize I've never heard a relativistic reasoning of escape velocity. Probably because its simpler in Newtonian terms but this would be much more interesting. For instance: How does the increasing energy/mass of the rocket affect the curve as you accelerate to escape velocity? Would a substantially larger mass have a much higher escape velocity or is it negligible? I know I can look it up but I may try to work it out on paper first. Thanks for everything you and the folks at WSF do! EDIT: Apparently I incorrectly assumed the mass of the escaping object mattered... Not sure how it doesn't matter at thought-experiment level masses, though. Ignoring factors like solar system instability if you were hauling a cube that was equal to the mass of mars it would have to greatly increase escape velocity since the earth would be pulled towards the ship as you accelerated. May try to work this out, but a fun side note (if i'm correct) you weigh approximately 1.6x your weight at 11.186km/s relative to your weight on earth.
Hi Brian - great show. I would love you to show where in the Einstein equations can be found the singularities that led to the theoretical predictions of the existence of black holes.
That involves some very heavy mathematics! And the Einstein equations you refer to, are the Einstein field equations (EFE) of General Relativity. They are a unified system of partial differential equations, whose solutions are the possible structures of spacetime, given possible distributions of mass-energy. The singularity comes, not directly from the EFE's, but from the Schwarzschild solution to those equations. That solution is the one that governs the gravitational field outside any spherically symmetric mass, including mundane cases, like the Earth, the Sun, planets & their satellites, etc.; as well as extreme cases, like white dwarves, neutron stars, & black holes. In the Schwarzschild solution, which is itself an equation, there is a factor that contains "r" (distance from the center of the body) in the denominator, so that when r=0, that term in the equation "blows up." In every case the Schwarzschild solution applies to, that equation ceases to apply inside the body (just as the Newtonian 1/r² dependence, from Newton's Law of Gravity [NLG] does!), so that the singularity is avoided - except for the black hole solution, in which there is no "body" any more - it's simply a region of extremely curved spacetime with a singularity at the center, where spacetime curvature is infinite. [Incidentally, in both the rel. and non-rel. models, it isn't the EFE or NLG that no longer apply inside a mass - they do! Rather, the solutions of those laws that apply there, are different.] Fred
@@ffggddss thanks to your detailed explanation! but can I say it this way, singularity is more of a math object than a physics object because it's where all of our current theory fails.
@@dinghanxue704 When one occurs in a physical theory, that theory must either be re-cast so as to eliminate the infinities (as happened in particle physics with "renormalization"), or it must be altered or discarded. Fred
Read Gauss! Gauss to Bessel Goettingen 9 April 1830 … The ease with which you delved into my views on geometry gives me real joy, given that so few have an open mind for such. My innermost conviction is that the study of space is a priori completely different than the study of magnitudes; our knowledge of the former (space) is missing that complete conviction of necessity (thus of absolute truth) that is characteristic of the latter; we must in humility admit that if number is merely a product of our mind
Wow, really wish I had learned this in school like this, it makes so much more sense to see the series expansion and to realize all the types of energy that goes into your "total mass" great stuff I hope you do more of these!
Love your talks, truly awesome and thanks. This episode reminded me of a question I had ages ago on relativistic mass, which is: does it warp space and bend light with regards to an observer at “rest”? In other words if an object speed by fast enough would we see it shift the observed position of the stars behind it relative to us? Also, since the mass can get arbitrarily large based if velocity and the length is contracting could an object appear to be so massive and dense that it looked like a black hole to an outside observer? This certainly can’t be possible since if it was say a space ship they could slow down and then magically un-black hole themselves, I’m thinking there is something about relativistic mass I’m not getting, lol. Anyway, if you happen to read this any brief insight would be appreciated.
Disagree. This is what I read from Wikipedia: In Einstein's first 1905 paper on E = mc2, he treated m as what would now be called the rest mass, and it has been noted that in his later years he did not like the idea of "relativistic mass". I know Wikipedia may not be 100% accurate, but please correct me if the references are not correct.
1) Matter warps space. 2) Space warps at the speed of light ( meaning if the Earth moves from point A to B, the space warping around it at those points has the speed of light restriction in the change of warpage ) 3) Now accelerate an object close to the speed of light, and try to see the resistance to change of the space warpage with an object that is moving at almost the maximum limit. This resistance of the entire universe's gravity warping thru very fast moving matter is why mass seems to increase, and why you can't get to speed of light limit. 4) Only by warping space around an object could you move faster.
Thank You for the uploads. I know it doesn't get the funding, or relate to your stringy concepts. Is there anything you can share about loop quantum gravity. Lately it doesn't get the attention it deserves. Keep in mind, this comes from someone, who's strength doesn't lie in mathematics
Hi Dr. Brian Greene PhD! You forgot to mention that this relative mass, only applies to the observable physical universe. Examples where this relative mass wouldn't apply is inside black holes, at the edge of the universe where the expansion rate of space-time is unmeasurable, quantum vacuum energy state (quantum gravity), and inside the vortices on the surface of the Sun (Sun spots).
"Ah, it stopped ringing, thank god!" - me about my phone regardless of the situation lol In other news, might I suggest Planck's Law of Black Body Radiation?
Thanks for reaching out to your followers dr green, really cool. I hope you get to the q&a because it would be great to have a chance to get a question in. Wkr rob
I am a eleventh grade student and I have a keen interest in relativity and particle physics. I do apologize to you sir if I am wrong, if so I would be thankful if you correct me.... E=mc^2 means that E energy is liberated when mass of an object changes by m when it moves with the speed of light c. So when v approaches c , mass tends to infinity(by m=m0/sq root(1-v^2/c^2)). Thus change in mass tends to infinity. So energy liberated will also be infinite!! How is that possible..... Furthermore, in E=mc^2 mass interchanges to energy. So mass of the body must decrease. But when v approaches c, we see relativistic mass is increasing ( mass tends to infinity) by m=m0/sq root(1-v^2/c^2) ....... I am really fascinated by this series and I would like it to continue for eternity....!!! Thank you Prof. Brian Greene.
I have been watching your videos/talks since 2011. Your show on Spacetime, QM, Cosmology, String Theory are just awesome. Are you coming to University of Maryland at College park in future to give a lecture?
Since we are still wandering around the E=mc^2, could You please, drop in a word about the energy-momentum relation, and how Paul Dirac (this Guy deserves a separate episode on his own..) extended Einstein's approach to include the motion energy? Great series, Professor!
Thanks for these videos, very well explained, could explain afterward to my daughter who is 9 and she did not get excited by but understood and accepted the consequemces of the relativistic effects and was able to explain it back afterward. Good enough for me.
Hi Brian! Since you introduced the Taylor expansion here for Gamma, could you please do one episode on how that conversion happens from Gamma to the Taylor series? I can do this for my son but he would prefer to hear it from you! Thanks a lot. And please do keep going - I saw you at Fermilab in the early 2000s after you wrote Elegant Universe, and excited to see you do these now at WSF!
Hi sir I have a doubt By this equation if we are travelling with velocity v our mass increases but car, bike travells everyday thay also have thier mass but how thier mass dosnt increase ?????
16:20 Since the Taylor expansion is used for low speeds, i.e., small values of v, the effects of the second, third, and so on terms is negligible. As Klaatu said to Dr. Barnhard in "The Day the Earth Stood Still." BARNHARDT: Yes -- that will reproduce the first- order terms. But what about the effect of the other terms? KLAATU: Almost negligible... With variation of parameters, this is the answer. BARNHARDT: How can you be so sure? Have you tested this theory? KLAATU: I find it works well enough to get me from one planet to another.
Where can I start learning a lot of math? And I’m not talking about only some beginner course. I’d like to start from the beginning but become really good at it in some years. Any advice would help! I have some mathematical knowledge from high school.
Per Einstein: “It is not good to introduce the concept of the mass M = m/(1 v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than the ‘rest mass’ m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion.
Do you think that we subconsciously take advantage of this time dilation and perform better by the slow input of events I perceive from a moving object?
Thanks for the daily equation series! I have a related comment regarding relativistic mass. When I read Susskind's book, Black Hole Wars, I started thinking that there might be a nonequivalence between gravitational mass and inertial mass when comparing massive objects such as stars. For example, if we take an eight solar mass star, it will evolve and eventually undergo a supernova explosion resulting in a neutron star I'm guessing. But if we take a one solar mass star and accelerate it to .9928 the speed of light (which increases its inertial mass to about eight times), it will continue to evolve normally and eventually becomes a white dwarf. Even though the two stars' masses are the 'same,' the outcomes and evolution of them are quite different. So it seems that the equivalence between inertial mass and gravitational mass are not quite the same. Is this correct or is something missing? Ciao
What 's wrong with this: E=gamma*m*c^2 With a bit of manipulation we can get E^2 -v^2*E^2 /c^2=m^2 c^4 When v increases, the left hand side term decreases, which means the right hand side (m^2c^4) is decreasing. Which simply means the rest mass decreases. Does it mean an increase in velocity implies a decrease in rest mass?
How would the equations shared towards the end of this video relate to E^2 = (mc^2)^2 + (pc)^2 ? I know very little about this equation (or any relativistic equations) and I'm wondering how it fits into the story.
Some questions for a Q&A: 1. Why is c 3x10^8 m/s and not some other value? Not as in a maths derivation, but physically why does it have that particular value? 2. Why are the laws of physics the way they are? Why, for example, does F=ma, or why must matter and energy be conserved? How did these happen? 3. What happens to matter when it falls into a black hole? Where does it go? I assume the black hole gets larger, but how does that physically happen? Thank you!
That is a very good question, and something that I also asked myself. I might be wrong, but the conclusion that I got was that the mass of an object doesn't depend on the gravitational field/potential energy. Therefore, your mass won't change even though you change your distance to the center of the earth (the PE changes). However, the mass of the gravitating system as a whole will change. This is the reason why for instance the mass of a hydrogen atom is slightly less (PE is negative) than the sum of the masses of the electron and the proton.
So, the long explanation is absolutely awesome, but a strictly mathematical explanation would be the if V=C, then 1-(V^2/C^2) would be 1-1 or 0. Since it's in the denominator, you can't divide by zero, so V cannot equal C (it can be smaller, or it can be larger????).
The concept of relativistic mass isn't a real phenomenon unlike time dilation and other consequences of relativity. It is a mathematical construct. As he said in the video, it's a concept that can help people get an intuitive understanding of why particles with mass can't reach the speed c. In Newtonian mechanics we write momentum as 'p=mv' but with relativistic corrections to the equation, we get the equation as 'p=mv/√(1-v²/c²)'. Now just to keep the Newtonian form of the equation intact (and also the reason mentioned above) we group the 'm/√(1-v²/c²)' together and call it 'relativistic mass M' so that we can now once again have the 'p=Mv' form of the equation. Many people argue against doing this because with its uses it also brings in a lot of confusion especially for people who are just starting to learn the concepts.
As for the electron (or more likely to be used proton) in a particle accelerator, the force required to get it to speeds closer to c does increase. The energies that the LHC is capable to produce now (about 6.5 TeV for each proton) can get them to a speed that is about 3m/s slower than c.
@@ananyaraghuvanshi8699 As far as I know mc2 is the term that can be used for objects at rest(so not for light), and pc2 can be used for those in motion : for photons. Correct me if I'm wrong.
How does the uncertainty principle interact with the speed of light. Can you get going fast enough so you don't know if you are exceeding the speed of light?
If you notice, he keeps using the term heft when talking about mass. The one thing he did not make clear is that the amount of matter does not change, in other words, it does gain matter and thus increase its gravitational force. That is a point that confuses people because Physicists decided to use the word mass when they really meant inertia (or as he says, "heft").
Greetings Brian Greene. It has been more than a year i have been trying to get a grasp of the concept of the sum 1+2+3+...= -1/12. ( Ramanujan's Sum). Also i have heard that this series is a fundamental theorem in STRING THEORY ,so i feel its the best if i ask you ! I hope you answer me !
Man I ove that these shows are on at this time, thak you! I have a question, is there any link between e = mc squared and e = hn? does mass also equal frequency? This is probably a stupid question if there is such a thing, but hey,,, anyway thanks Brian!
You are looking at two equations that are over simplified. E is not just mc squared since that only applies to objects that are stationary and have mass. The full equation includes additional terms. Also E=mc^2 is the low-momentum approximation, the full equation is E^2 = m^2 c^4 + p^2 c^2 where p is the relativistic momentum. Using the full equation, you can then compare to hn.
So it's impossible to change speed of light, but what about mass, could we accelerate an object almost to a finite speed, than detach large chunk of it and give additional push to the rest of mass?
Einstein always talked about persepctive, would it not be that from the perspective of the viewer that mass approching the speed of light would appear to gain in mass, but from the subjects perspective there would be no change?
Einstein, or someone, figured out an example with two lightclocks with a lightbeam reflecting perpetually between mirrors at the tops and the bottoms of two individual boxes and one of them was moving and you are sitting on it. Albeit the box can only travel up to a certain speed still below lightspeed, thus light can always intercept the mirrors in the box from within at the speed of light but with redshifting. The maximum speed of an object is apparently approximately three quarters of the speed of light. The distance the light is perceived to travel may vary depending on the observers motion and viewpoint, but the speed of light is always a constant in vacuum as confirmed in numerous experiments. I contend that when light reflects off an object it gets redshifted, i.e. its energy level is fading for each reflection. It might thus be correct to imagine that in Einstein’s particular example a lightbeam inside the box gets redshifted and scattered bit by bit for each reflection. It might be that the box riding gentleman (you) doesn’t perceive the light beam as if it was slowing down inside the fast moving box. It might be that he is only experiencing an increasing redshift of the lightbeam, up to a certain point on his course when what’s left of the lightbeam dissolves. Sorry Einstein, but you have no experimental evidence to support your intriguing example. Time perception though is another matter altogether, just not for measuring the speed of light at any other speed than the speed of light.
Just one request keep this on!
I'm a psychology professor with an interest in physics. I love these daily equations. Please keep on doing as many as you can. Thank you for your ability to promote and explain the beauty of physics!
Well said
Thanks Brian- I'm 73, never took physics or calculus, and I was able to follow- not saying I could do it but I got the principles and will now watch all of these. Hate being house-bound when you've ignited my inner Cliff Klaven.
Could we please do the equation of the Wave function or the Harmonic oscillator
YES PLZ
Thanks for the explanation! The example, despite being a bit contrived illustrates nicely the need for an increased mass - to conserve momentum. A less contrived way to show that a mass increase is required is to use the impulse momentum theorem viewed from an objects instantaneous rest frame and comparing it with the equation that arrives from a static frame at rest.
Very nice example with the 2 riders. Never seen before.
Just happened on this series... A Daily Equation - what a great & practical format for many of us folks. Liked the jousting analogy & KE explanation in this one 👍. Many thanks for the videos Brian😊!
At 7:33.... why is the thrust speed is decreased by a factor of gamma?
Thank you very much from New York. Looking forward to new episode every day!
Thank you very much Professers Greene
Loving this, thanks Brian and WSF!
I think the biggest thing i like about these, are that, now that school is out for most children and young adults, no one is learning anything. And if worst case scenario the education system falls apart (probably not likely but hey) then we still need not just the information out there to go and find, but we need those individuals who would pull information they know and understand, and instead of just lazying about and being the keepers of that information, they share it like this, often times information most people wouldnt bother to try to understand. This way, the most mind blowing of information, isnt lost in the crisis (again, probably not gonna happen, but i hear a lot of people talk about how thankful they are the internet is still operating). I once heard, maybe NGT talk about it, but something was said along the lines of, "if everyone who was knowledgeable enough to make a cell phone from scratch, how long would it take for us to reinvent it, if all those people disappeared?" Of course we arent only talkin about people disappearing but the information they carry with them being lost in time. It seems many civilizations succumb to this tragedy. Im just saying, teachers and professors, those with knowledge who's profession is to teach others, i think they should all be doing stuff like this, sharing their knowledge freely and openly.
"Relativistic mass" is a broken concept, because it works only for the special relativistic (SR) formula for momentum, p[rel]. When learning relativity, it is a mental crutch that attempts to preserve the Newtonian form of momentum by making mass depend on velocity. In fact, it isn't that the mass is changing; it is that the functional dependence of momentum on velocity, differs from the Newtonian p = mv; namely,
p[rel] = mv/√(1-[v/c]²) = m(γv).
And it is this change in the formula for momentum that makes attaining v=c impossible for any body with non-zero mass.
The culprit is still that factor, "γ," but it is properly attached to the "v," not to the "m."
That this is so, can be seen by trying to plug this "relativistic mass" into the Newtonian formula for kinetic energy, KE = ½mv². It gives the wrong result. The actual formula is
KE[rel] = (γ - 1)mc² = (1/√(1-[v/c]²) - 1)mc² ≠ ½γmv². (Dr. Greene's derivation of the Newtonian KE from E = mc² is exactly right, however.)
"Mass of a body" is a property of the body itself, not of its state of motion - or, in fact, of the state of motion of some arbitrary observer! Because it is a central principle of SR that physics "looks" the same in any inertial frame of reference. Two observers in uniform relative motion to one another should assign the same value to the mass of a body.
Fred
PS. See the excellent, less technical explanation of this by Dr. Don Lincoln on the Fermilab channel.
Can't wait for this. Thx Brian for the stuff you have shared during the years. Amazing how many implications there are for all basic ingredients of physics when relativity is set in motion.. .time, space, and now mass.
This series is great! Something to look forward to every day in these stressful times. This made me realize I've never heard a relativistic reasoning of escape velocity. Probably because its simpler in Newtonian terms but this would be much more interesting.
For instance: How does the increasing energy/mass of the rocket affect the curve as you accelerate to escape velocity? Would a substantially larger mass have a much higher escape velocity or is it negligible?
I know I can look it up but I may try to work it out on paper first.
Thanks for everything you and the folks at WSF do!
EDIT:
Apparently I incorrectly assumed the mass of the escaping object mattered... Not sure how it doesn't matter at thought-experiment level masses, though. Ignoring factors like solar system instability if you were hauling a cube that was equal to the mass of mars it would have to greatly increase escape velocity since the earth would be pulled towards the ship as you accelerated.
May try to work this out, but a fun side note (if i'm correct) you weigh approximately 1.6x your weight at 11.186km/s relative to your weight on earth.
Agreed
Hi Brian - great show.
I would love you to show where in the Einstein equations can be found the singularities that led to the theoretical predictions of the existence of black holes.
That involves some very heavy mathematics! And the Einstein equations you refer to, are the Einstein field equations (EFE) of General Relativity.
They are a unified system of partial differential equations, whose solutions are the possible structures of spacetime, given possible distributions of mass-energy.
The singularity comes, not directly from the EFE's, but from the Schwarzschild solution to those equations. That solution is the one that governs the gravitational field outside any spherically symmetric mass, including mundane cases, like the Earth, the Sun, planets & their satellites, etc.; as well as extreme cases, like white dwarves, neutron stars, & black holes.
In the Schwarzschild solution, which is itself an equation, there is a factor that contains "r" (distance from the center of the body) in the denominator, so that when r=0, that term in the equation "blows up." In every case the Schwarzschild solution applies to, that equation ceases to apply inside the body (just as the Newtonian 1/r² dependence, from Newton's Law of Gravity [NLG] does!), so that the singularity is avoided - except for the black hole solution, in which there is no "body" any more - it's simply a region of extremely curved spacetime with a singularity at the center, where spacetime curvature is infinite.
[Incidentally, in both the rel. and non-rel. models, it isn't the EFE or NLG that no longer apply inside a mass - they do! Rather, the solutions of those laws that apply there, are different.]
Fred
@@ffggddss thanks to your detailed explanation! but can I say it this way, singularity is more of a math object than a physics object because it's where all of our current theory fails.
@@dinghanxue704 When one occurs in a physical theory, that theory must either be re-cast so as to eliminate the infinities (as happened in particle physics with "renormalization"), or it must be altered or discarded.
Fred
Read Gauss!
Gauss to Bessel Goettingen 9 April 1830 …
The ease with which you delved into my views on geometry gives me real joy, given that so few have an open mind for such.
My innermost conviction is that the study of space is a priori completely different than the
study of magnitudes; our knowledge of the former
(space) is missing that complete conviction of necessity (thus of absolute truth)
that is characteristic of the latter;
we must in humility admit that if number is merely a product of our mind
Wow, really wish I had learned this in school like this, it makes so much more sense to see the series expansion and to realize all the types of energy that goes into your "total mass" great stuff I hope you do more of these!
Brian, this classes are so amazing! Thank you very much!! Cheers from Buenos Aires!
Love your talks, truly awesome and thanks. This episode reminded me of a question I had ages ago on relativistic mass, which is: does it warp space and bend light with regards to an observer at “rest”? In other words if an object speed by fast enough would we see it shift the observed position of the stars behind it relative to us? Also, since the mass can get arbitrarily large based if velocity and the length is contracting could an object appear to be so massive and dense that it looked like a black hole to an outside observer? This certainly can’t be possible since if it was say a space ship they could slow down and then magically un-black hole themselves, I’m thinking there is something about relativistic mass I’m not getting, lol. Anyway, if you happen to read this any brief insight would be appreciated.
Thanks for this wonderful series. I am enjoying it so much.
Disagree. This is what I read from Wikipedia:
In Einstein's first 1905 paper on E = mc2, he treated m as what would now be called the rest mass, and it has been noted that in his later years he did not like the idea of "relativistic mass".
I know Wikipedia may not be 100% accurate, but please correct me if the references are not correct.
In my post above you will find the answer
After how many videos about mass, finally I understand it now Thank You!!!
Thank you for your time🙏Giant Scientist 👍👍
You are going great work during pandemic . Pro
"Alright, I'm going to have to answer this phone." I felt that. 😆
So deep explanation...❤️❤️❤️
Could you please do a video on the Heisenberg uncertainty principle?
Reminded me of my dad in this one! good vibes
1) Matter warps space. 2) Space warps at the speed of light ( meaning if the Earth moves from point A to B, the space warping around it at those points has the speed of light restriction in the change of warpage ) 3) Now accelerate an object close to the speed of light, and try to see the resistance to change of the space warpage with an object that is moving at almost the maximum limit. This resistance of the entire universe's gravity warping thru very fast moving matter is why mass seems to increase, and why you can't get to speed of light limit. 4) Only by warping space around an object could you move faster.
amazing brian thankyou
Thank You for the uploads. I know it doesn't get the funding, or relate to your stringy concepts. Is there anything you can share about loop quantum gravity. Lately it doesn't get the attention it deserves. Keep in mind, this comes from someone, who's strength doesn't lie in mathematics
Hi Dr. Brian Greene PhD! You forgot to mention that this relative mass, only applies to the observable physical universe. Examples where this relative mass wouldn't apply is inside black holes, at the edge of the universe where the expansion rate of space-time is unmeasurable, quantum vacuum energy state (quantum gravity), and inside the vortices on the surface of the Sun (Sun spots).
This was wonderful !! Thank you
"Ah, it stopped ringing, thank god!" - me about my phone regardless of the situation lol
In other news, might I suggest Planck's Law of Black Body Radiation?
Thanks for reaching out to your followers dr green, really cool. I hope you get to the q&a because it would be great to have a chance to get a question in. Wkr rob
Equation Request:
Hello Professor Greene,
I'd love to hear about the wave equation.
Thanks for this series!
Excellent! look forward for the next episodes... bravo
great format!
oh my goodness... wonderful... want... new focus ...to get it... thank you so much
Brian is love♥️😊
I am a eleventh grade student and I have a keen interest in relativity and particle physics. I do apologize to you sir if I am wrong, if so I would be thankful if you correct me.... E=mc^2 means that E energy is liberated when mass of an object changes by m when it moves with the speed of light c. So when v approaches c , mass tends to infinity(by m=m0/sq root(1-v^2/c^2)). Thus change in mass tends to infinity. So energy liberated will also be infinite!! How is that possible..... Furthermore, in E=mc^2 mass interchanges to energy. So mass of the body must decrease. But when v approaches c, we see relativistic mass is increasing ( mass tends to infinity) by m=m0/sq root(1-v^2/c^2) .......
I am really fascinated by this series and I would like it to continue for eternity....!!!
Thank you Prof. Brian Greene.
I have been watching your videos/talks since 2011. Your show on Spacetime, QM, Cosmology, String Theory are just awesome. Are you coming to University of Maryland at College park in future to give a lecture?
Since we are still wandering around the E=mc^2, could You please, drop in a word about the energy-momentum relation, and how Paul Dirac (this Guy deserves a separate episode on his own..) extended Einstein's approach to include the motion energy? Great series, Professor!
I love this!
Thanks for these videos, very well explained, could explain afterward to my daughter who is 9 and she did not get excited by but understood and accepted the consequemces of the relativistic effects and was able to explain it back afterward. Good enough for me.
Hi Brian! Since you introduced the Taylor expansion here for Gamma, could you please do one episode on how that conversion happens from Gamma to the Taylor series? I can do this for my son but he would prefer to hear it from you! Thanks a lot. And please do keep going - I saw you at Fermilab in the early 2000s after you wrote Elegant Universe, and excited to see you do these now at WSF!
Hi sir I have a doubt
By this equation if we are travelling with velocity v our mass increases but car, bike travells everyday thay also have thier mass but how thier mass dosnt increase ?????
BrIan Greene for President!
greetings from Italy, we love you!
Woohoo having fun!!! Boltzmann equation 🥳🥳
16:20 Since the Taylor expansion is used for low speeds, i.e., small values of v, the effects of the second, third, and so on terms is negligible. As Klaatu said to Dr. Barnhard in "The Day the Earth Stood Still."
BARNHARDT: Yes -- that will reproduce the first- order terms. But what about the effect of the other terms?
KLAATU: Almost negligible... With variation of parameters, this is the answer.
BARNHARDT: How can you be so sure? Have you tested this theory?
KLAATU: I find it works well enough to get me from one planet to another.
Hello Professor Greene
Love your series.
Could u do a series on the millennium problems??
Where can I start learning a lot of math? And I’m not talking about only some beginner course. I’d like to start from the beginning but become really good at it in some years. Any advice would help! I have some mathematical knowledge from high school.
@Brian Green Does rest mass change with temperatures???
Per Einstein:
“It is not good to introduce the concept of the mass M = m/(1 v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than the ‘rest mass’ m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion.
Do you think that we subconsciously take advantage of this time dilation and perform better by the slow input of events I perceive from a moving object?
Great teacher be continued please
I'm remembering this stuff from classes. Been awhile
Thanks for the daily equation series!
I have a related comment regarding relativistic mass. When I read Susskind's book, Black Hole Wars, I started thinking that there might be a nonequivalence between gravitational mass and inertial mass when comparing massive objects such as stars. For example, if we take an eight solar mass star, it will evolve and eventually undergo a supernova explosion resulting in a neutron star I'm guessing. But if we take a one solar mass star and accelerate it to .9928 the speed of light (which increases its inertial mass to about eight times), it will continue to evolve normally and eventually becomes a white dwarf. Even though the two stars' masses are the 'same,' the outcomes and evolution of them are quite different. So it seems that the equivalence between inertial mass and gravitational mass are not quite the same. Is this correct or is something missing? Ciao
Hehe love the home phone ringing. Think we all in quarantine can relate
I love it. Yaay yaay yaay.. review time!
What 's wrong with this: E=gamma*m*c^2
With a bit of manipulation we can get E^2 -v^2*E^2 /c^2=m^2 c^4
When v increases, the left hand side term decreases, which means the right hand side (m^2c^4) is decreasing. Which simply means the rest mass decreases. Does it mean an increase in velocity implies a decrease in rest mass?
Is there anyway you can elaborate more on the Higgs field decaying and quantum tunneling described in chapter 10 of “Until the end of time?”
How would the equations shared towards the end of this video relate to E^2 = (mc^2)^2 + (pc)^2 ? I know very little about this equation (or any relativistic equations) and I'm wondering how it fits into the story.
Some questions for a Q&A: 1. Why is c 3x10^8 m/s and not some other value? Not as in a maths derivation, but physically why does it have that particular value? 2. Why are the laws of physics the way they are? Why, for example, does F=ma, or why must matter and energy be conserved? How did these happen? 3. What happens to matter when it falls into a black hole? Where does it go? I assume the black hole gets larger, but how does that physically happen? Thank you!
Answer to part 1: The value of c depends on the units used, miles, kilometers , seconds.
which app are you using to draw on the iPad?
Make a video explaining fourier series.
Super video, thx again. Curious what tomorrow will bring.
Thanks, great episode! How does the potential energy appear in e=mc2? Does the relativistic mass depend on the gravitational field?
That is a very good question, and something that I also asked myself. I might be wrong, but the conclusion that I got was that the mass of an object doesn't depend on the gravitational field/potential energy. Therefore, your mass won't change even though you change your distance to the center of the earth (the PE changes). However, the mass of the gravitating system
as a whole will change. This is the reason why for instance the mass of a hydrogen atom is slightly less (PE is negative) than the sum of the masses of the electron and the proton.
So does the gravity force depend on mrel or m0?
@0:12: You forgot to cover why some people despise relative mass. Also, I wonder how the people that despise it handle your joust scenario.
So, the long explanation is absolutely awesome, but a strictly mathematical explanation would be the if V=C, then 1-(V^2/C^2) would be 1-1 or 0. Since it's in the denominator, you can't divide by zero, so V cannot equal C (it can be smaller, or it can be larger????).
Any updates on Q&A?
Sir always wondered why the mass of the electron don't get huge in the particle accelerator ?
And really appreciate you for giving your precious time.
The concept of relativistic mass isn't a real phenomenon unlike time dilation and other consequences of relativity. It is a mathematical construct. As he said in the video, it's a concept that can help people get an intuitive understanding of why particles with mass can't reach the speed c.
In Newtonian mechanics we write momentum as 'p=mv' but with relativistic corrections to the equation, we get the equation as 'p=mv/√(1-v²/c²)'. Now just to keep the Newtonian form of the equation intact (and also the reason mentioned above) we group the 'm/√(1-v²/c²)' together and call it 'relativistic mass M' so that we can now once again have the 'p=Mv' form of the equation.
Many people argue against doing this because with its uses it also brings in a lot of confusion especially for people who are just starting to learn the concepts.
As for the electron (or more likely to be used proton) in a particle accelerator, the force required to get it to speeds closer to c does increase. The energies that the LHC is capable to produce now (about 6.5 TeV for each proton) can get them to a speed that is about 3m/s slower than c.
E2=(mc2)2+(pc)2.
What does this equation mean? Please make a video on it.
@@ananyaraghuvanshi8699 As far as I know mc2 is the term that can be used for objects at rest(so not for light), and pc2 can be used for those in motion : for photons. Correct me if I'm wrong.
@@ananyaraghuvanshi8699 I am not talking about cases, but as a whole, what does the equation E2=(mc2)2+(pc)2 mean?
How does the uncertainty principle interact with the speed of light. Can you get going fast enough so you don't know if you are exceeding the speed of light?
Very nice explanation professor. Can you explain how the concept of blackholes came into Einstein's mind?
Is the energy through acceleration being pumped into the system and converted into mass through e=mc^2?
I was also thinking the same ans came here to ask same.
thank you for uploading this valuable lecture in this hard situation~ everybody Cheer up~
How do you create those animation?
Sir I would like to have your views about the heisenburg uncertainty principle
I request World Science festival to upload it soon.......
What happens if the object/particule in question has no mass? A foton, for example.
If you notice, he keeps using the term heft when talking about mass. The one thing he did not make clear is that the amount of matter does not change, in other words, it does gain matter and thus increase its gravitational force. That is a point that confuses people because Physicists decided to use the word mass when they really meant inertia (or as he says, "heft").
Greetings Brian Greene. It has been more than a year i have been trying to get a grasp of the concept of the sum 1+2+3+...= -1/12.
( Ramanujan's Sum).
Also i have heard that this series is a fundamental theorem in STRING THEORY ,so i feel its the best if i ask you !
I hope you answer me !
respected sir, please make an episode on bells enequilty.
regarding EPR paradox.
thank you.
Please do some complex equations as well...
Thankyou very much , Pakistan
Dr. Greene do you think the universe is voxelated at Plank length?
Man I ove that these shows are on at this time, thak you! I have a question, is there any link between e = mc squared and e = hn? does mass also equal frequency? This is probably a stupid question if there is such a thing, but hey,,, anyway thanks Brian!
You are looking at two equations that are over simplified. E is not just mc squared since that only applies to objects that are stationary and have mass. The full equation includes additional terms. Also E=mc^2 is the low-momentum approximation, the full equation is E^2 = m^2 c^4 + p^2 c^2 where p is the relativistic momentum. Using the full equation, you can then compare to hn.
So it's impossible to change speed of light, but what about mass, could we accelerate an object almost to a finite speed, than detach large chunk of it and give additional push to the rest of mass?
What if I push an electron to the speed of light? (So light itself) does its mass increase??
The speed of light is a constant in our spacetime gravity well.
thank you 🍏
Einstein always talked about persepctive, would it not be that from the perspective of the viewer that mass approching the speed of light would appear to gain in mass, but from the subjects perspective there would be no change?
I loved binomial expansion
explain a general supersymmetric action please
Einstein, or someone, figured out an example with two lightclocks with a lightbeam reflecting perpetually between mirrors at the tops and the bottoms of two individual boxes and one of them was moving and you are sitting on it.
Albeit the box can only travel up to a certain speed still below lightspeed, thus light can always intercept the mirrors in the box from within at the speed of light but with redshifting. The maximum speed of an object is apparently approximately three quarters of the speed of light.
The distance the light is perceived to travel may vary depending on the observers motion and viewpoint, but the speed of light is always a constant in vacuum as confirmed in numerous experiments. I contend that when light reflects off an object it gets redshifted, i.e. its energy level is fading for each reflection. It might thus be correct to imagine that in Einstein’s particular example a lightbeam inside the box gets redshifted and scattered bit by bit for each reflection.
It might be that the box riding gentleman (you) doesn’t perceive the light beam as if it was slowing down inside the fast moving box. It might be that he is only experiencing an increasing redshift of the lightbeam, up to a certain point on his course when what’s left of the lightbeam dissolves.
Sorry Einstein, but you have no experimental evidence to support your intriguing example. Time perception though is another matter altogether, just not for measuring the speed of light at any other speed than the speed of light.
Can u explain the equation of UNIFIED THEORY we have so far (correct me if I am wrong) ??????
wouldn't you get a different result if you used the kinetic energy instead of momentum because the speed would have been squared?