Gravity! This one’s sure to be a crowd-pleaser. We take advantage of some of our previous discussion of curvature and spacetime, but we also talk about Einstein’s physical motivations for inventing general relativity, and the origin of gravitational time dilation and the like.
The Biggest Ideas in the Universe | 16. Gravity
And here is the associated Q&A video. Distinguished mostly by a deeper dive into black holes, including the information-loss puzzle.
The Biggest Ideas in the Universe | Q&A 16 - Gravity
Hi doctor Sean! Thanks for the awesome videos! Please keep it up! =) I’m no longer being able to follow the math, but I still understand a little of the math here and there hehehehehe!
So, my questions:
1. I never understood why the graviton is needed, since it’s just the curvature of the spacetime that causes relativity… Can you please explain it?
2. I feel there’s a great insight awaiting for me in the vector transposing thing when we are talking about fields interacting… But I just couldn’t understand why should I bother to do the transpose, other than to see if the field has a curvature or not … It seems to me that the transpose of a vector gives rise to the force carrying particle fields… but… I cant understand why should I do the transposition in first place… I’m missing something…
3. I fell I have a good intuition about how the changes in velocity makes the time appear to go slower to someone observing it, and even length contraction I can understand… what I cant understand is the time being distorted to someone in a intense gravitational field.
That’s it! Thanks again!!!!
Is the expansion of space uniform? If so is our local group expanding? What about expansion even closer to home?
It was mentioned during the lecture that the r=2GM “singularity” is only due to a bad choice of coordinates, i.e. an “apparent” singularity. How can you exclude that also r=0 is also only “apparent”? I guess one shows that the curvature blows up as r\to 0.
I guess this could link well to the Hawking and/or Penrose singularity (or better, incompleteness) theorems, could you please discuss a bit of this in the Q&A?
Many thanks!
Really enjoyed but slightly envious that your treatment offered to those interested all the ideas that it took me giant efforts to vaguely understand when I was doing this stuff decades ago.
A couple of points for clarification: in the expanding universe metric you have a leading plus one on the diagonal where you normally use the convention of one plus and three negatives. (The other sign convention is one negative and three pluses but there’s usually
a change of sign needed somewhere. ) I’ve usually seen the cosmological constant included just by a coefficient applied to the metric tensor as an added left hand term. Are these approaches equivalent?
On the failure of the Ricci tensor alone to work as the left hand side of the field equations I seem to remember that the problem was the need to match the ‘zero divergence’ on the stress/energy right hand side ensuring energy conservation. Is that right? But as you noted in your CERN cosmology lectures energy conservation is surrendered anyway in cosmic acceleration. Of course Einstein had even less reason to allow for that than for cosmic expansion as astronomers have known about that acceleration for only twenty years. Maybe you’ll cover that stuff in this series if we’re lucky.
One other thing you said offhand that might have been a little confusing was that the full metric tensor had 128 terms related to 4 x 4 x 4 x 4. Of course that’s 256 but matrix symmetry disposes of about half the terms giving that 128, or really 136 I think, since it’s only the off-diagonal terms that match up.) Is that right?
Finally, the contraction process to boil down Riemann to Ricci tensors to Ricci scalar could maybe be explained a bit further since you already covered Einstein index summation and contraction is just like summing or integrating out terms. I know this video was very long but it was a treat and I think you left your audience asking for more.
I’m waiting for the Q&A with interest. I never thought this stuff could be explained so clearly
If Einstein’s equation says that Mass/Energy/Momentum in space is proportional to curvature, why when solving the equation to get the metric, do you basically set the stress tensor to 0. What is now the source of the curvature ?
In arriving at his metric Schwarzschild not only set the stress-energy density to zero (i.e. vaccum) he also assumed spherical symmetry. So that’s why the solution came out as it did, with curved spacetime. It implicitly assumed a spherically symmetric source and solved for the field outside of that source.
This has been an excellent series of videos that I have enjoyed watching although it will take some time to get my head around everything here including further research and additional research. There is so much more to learn and understand. I even have a physics degree although that was many years ago and I am now keen to relearn it and go further.
Many thanks.
32:10 Why is parallel transport of your own velocity equivalent to extremal distance?
(is the same as why extremal action is equivalent to equations of motion?)
51:05 How objects know when they are at fixed coordinates?
You were congratulating yourself on writing a GR text without mentioning Mach’s principle. I realize that in GR, Mach’s principle isn’t true. But there’s a lot of work by theoretical physicists trying to derive spacetime from entanglement of quantum fields. If they succeed, won’t that reinstate Mach’s principle. I don’t think there’s any experimental evidence it’s false in our universe…is there?
In the Q&A video of GRAVITY I especially enjoyed your short and clear presentation of the Maldacena and Susskind conjecture ER = EPR to solve the AMPS firewall paradox of black holes.
For those who may have missed this:
Black hole Firewalls – with Sean Carroll and Jennifer Ouellette (The Royal Institution 2014)
https://www.youtube.com/watch?v=_8bhtEgB8Mo
Regarding what you said at 1:43:00, that r = 0 is a moment in time and not a point in space because at r = Rs the observer’s t and r coordinates switch sign: I don’t quite understand why should we stick with Schwarzschild’s metric inside r = Rs since it causes t and r to flip signs for a distant observer, a person that is not moving into this region.
I’ve checked this metric (with hyperbolic sine) and it also solves Einstein’s equations, and in particular for r less than Rs, it has this form:
c²d𝜏² = -dS² = -[(Rs / r) -1)] . (c dt)² + [(Rs / r) -1)]⁻¹ . dr² + r². (dθ² + dϕ² . sinh²θ)
and it allows the outside observer to keep his original metric signature (-, +, +, +), thus no sign switching since he’s outside the horizon.
Instead it switches dS² into c²d𝜏² for the infalling person (which makes sense to me since this crazy person is going inside a black hole).
So my question is: has anyone tried this metric before? Is it in some fashion the same metric as that of Schwarzschild’s?
Thank you 🙂
I have always felt that the principle of equivalence is really just a good metaphor or analogy for gravity but has no real explanatory power. If you go all in and accept that the earth “really is” accelerating up towards the apple you can use Newton’s equation for gravitational acceleration at the surface of a sphere, a = GM/r^2, to reproduce the Hubble parameter ( approximately ) at the surface of a 1 Mpc sphere with a mass equal to the volume of the sphere times the average density of the universe. You calculate the gravitational “expansion” with Newton’s equation and then multiply by the age of the universe. It comes out to 37.21 km/s, which is a little off, but does produce results that are linear over distance and that accelerate over time. Interesting?