Relativity 110d: Cosmology - FLRW Geodesics, Cosmological Redshift, Horizons, Comoving Coordinates

[@yogitshankar6348]

what a series, you are in my eyes as high as 3b1b! thank you for this gem

[@NishaRani-nf9gr]

I am amazed to see how can someone explain Subjects like this with such a ease. Thanks a ton for providing us opportunity to learn these topic which I couldn't have understood otherwise.

[@paulbuchinger4585]

You are absolutely great! Einstein would be proud!

[@dimitrispapadimitriou5622]

Another great video from eigenchris . Some notes / additional information about the topics of this video: - Our universe's Hubble horizon will approach ( asymptotically) a deSitter horizon in the far future, due to the presence of a positive cosmological constant ( assuming, of course , that " Dark Energy is really a constant Λ ). So, our future horizon will approach a maximum and stay there forever after . - These cosmological horizons are " subjective": Every place in our universe is surrounded by its own horizon. - A Particle horizon is a " past" horizon, while the cosmic event horizon is a " future" horizon. - Most cosmologists do not take very seriously ( as it was stated in the video ) the " Big Rip" scenario and one of the main reasons for this is that models with w

[@jigold22571]

If I could go back in time.You would be the perfect instructor ❣️🙏

[@專門定的]

13:15 I think the correct formula is Δr*a(t) = L_0, but at 13:15, you display a different formula by L_0, 15L_0, 1000L_0 and correspond to a(t)=1,15,1000

[@LetsFindOut1]

Chris thanks so much for these videos. I'm doing a video on spacetime diagrams and cosmological horizons and would love to use some snippets of these co-moving coordinates and equations. Would you be ok with that if I properly credit your channel and/or donate? (sorry for the proposition here, i didn't know how else to reach you and really found this video helpful) thanks, Rich (Let's Find Out)

[@eigenchris]

Sure, you can use anything as long as you give me credit. Don't feel obligated to donate unless you want to. I'll just add that it's probably a good idea to fact-check anything I say in this video that you want to repeat, and check the sources in the description if needed. I do my best to get everything right, but I'm not perfect.

[@LetsFindOut1]

@@eigenchris I really appreciate that Chris. Thanks. I'll absolutely credit you. You're much more knowledgable about the maths than I am. I'm really just trying to give a more pop-sci account of GR and spacetime, so I never tell my viewers my view is any sort of authority as I've only taken a few calculus and intro physics university courses. Your images are just really useful to show both the general kinds of maths involved and the basic ideas behind coordinates. Thanks again for being so generous. -Rich

[@ShadowZZZ]

Nice job explaining the physical interpretations of mathematical results when working with FLRW metric in cosmology (This is generally one of the most infamous difficulties in physics). It would have been nice to see analytical solutions of the integrals you solved in the derivations for all light like geodeciscs, but it's fine. You did well explaining why we or atoms don't expand with the universe, because such a system doesn't meet the assumptions necessary for the theory of cosmological expansions, hence FLRW doesn't apply. For cosmological horisons it would have been nice if you had also shown the 3 types of horizons curves as a function of age of the universe, because then you can see how one horizon can be behind another one but at a later time past the other one. All in all neat summary, you only mentioned the most relevant bits.

[@deltalima6703]

Trivial results but rigorously obtained, and thus interesting. 👍

[@vinvic1578]

Hi eigenchris ! I absolutely love your videos. I was wondering, do you plan on covering QFT eventually on this channel ?

[@eigenchris]

I don't know QFT well enough to cover it. My next planned video will be on spinors, which will touch on some QFT stuff like the Dirac equation. But it won't be the main focus.

[@ShadowZZZ]

I recommend this lecture playlist if you want to learn QFT kzbin.info/aero/PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS

[@vinvic1578]

@@eigenchris Wow cool thanks a lot for the answer ! That makes sense :)

[@vinvic1578]

@@ShadowZZZ thanks I love it !

[@mastershooter64]

@@eigenchris Will you please consider making a series where you teach graduate QM and relativistic QM? like taking someone who has knowledge of undergrad QM and making them know enough physics to start studying QFT

[@CarlosRodriguez-mx2xy]

The Best!! As always. Thank you very much.

[@comoenclase]

very well explained

[@bassam999zz5]

You are the best from Algeria

[@franciscoarana7608]

Hi Eigen. Fantastic job. I have a question. In the approximation value of different horizons, minute 32.10, the particle horizon, with finite limits in the integral, is bigger than the event horizon, with infinite limits. 45 Gly, vs 16 Gly. I don’t understand why. Thanks so much

[@foxhound1008]

Really enjoy your channel. Was hoping to pose a question. In General relativity, gravity is not a force. However, even in General relativity, planets orbit their common center of mass….the moon and earth orbit their center of mass (barycenter). Th moon and earth are exchanging momentum as they orbit the COM. Usually, when objects exchange momentum, they do so thru a force. In GR momentum is still conserved. So, is momentum conservation upheld by the moon “freefalling” in the gravitational field of the earth? And equally, the earth is freefalling in the gravitational field of the moon.

[@eigenchris]

That's a great question, but it's unfortunately one I don't know the answer to right now. I think there are ways of attributing energy (or momentum) to spacetime itself. As an example, there are ways of attributing energy to a gravitational wave. But unfortunately that's outside my knowledge right now. This is a wikipedia article you can try using as a starting point to answer your question: en.wikipedia.org/wiki/Stress%E2%80%93energy%E2%80%93momentum_pseudotensor

[@MartinGonzalez-gf5ht]

Hi Chris, I really enjoy your videos. One covering inflation would be great!

[@eigenchris]

Thanks! Unfortunately I'm done with relativity for now and don't plan to upload new videos in the near future. I hope you can find material to help you learn it else where. I think inflation involves understanding de Sitter space, which I cover in the middle of "Relativity 110f", if that interests you.

[@alexpremium8614]

Thanks for helping me to sleep 😊

[@narfwhals7843]

Is there a way to distinguish the cosmological redshift from metric expansion from a "regular" redshift due to actual relative motion?

[@eigenchris]

My first thought is, you'd have to look at the redshift of many galaxies and average over all of them to determine the redshift due to cosmological expansion. Then you can subtract that from all galaxies and see if any redshift/blueshift remains. Light from the Andromeda galaxy is actually blueshifted (negative z-factor) because it's moving towards us. It's less than 1 MegaParsec away from us, so cosmological expansion has a pretty small effect on the distance between it and the milky way, and its kinematic speed is the main contribution to the frequency shift.

[@narfwhals7843]

@@eigenchris my question was more about how we can be confident that the expansion we observe at large scales is due to a metric expansion and the galaxies aren't actually just all "moving" away from us. As in, is the nature of the redshift evidence for GR or is it explained just as well by other means.

[@kikivoorburg]

@@narfwhals7843 Given we can observe galaxies "moving away from us" faster than c, that proves they're not actually moving away (since travelling faster than c through spacetime is not permitted) and instead it's spacetime that is contorting faster than c - which is precisely what cosmic expansion / redshift describes.

[@lowersaxon]

„Is only a mathematical model …“. Burrr, so I wont be torn apart!

[@gowrissshanker9109]

Hlo eigen, How come the position and momentum are independent variables in Hamiltonian mechanics? Consider SHM Hamiltonian when we change position , Momentum changes right? Both are related to each other right? Thank you

[@eigenchris]

If you take the x-y plane, and imagine a circular railroad track on it, the cars on that track would be forced to travel along at that circle. While you could view x and y as independent variables, for this problem, x and y are related by the circle equation: x^2 + y^2 = r^2. But you can still take partial derivatives with respect to x and y, treating them as independent. The circle equation does the job of forcing the correct relationship between x and y. It's the same in Hamiltonian mechanics. The x and p variables are related by Hamilton's Equations, but you can still treat x and p as independent and take partial derivatives with respect to x and p. Hamilton's Equations will do the job of forcing the correct relationship between x and p.

[@gowrissshanker9109]

@@eigenchris Thank you eigen🙂

[@lasa18]

Would you ever consider making a video not on standard cosmology, rather on VSL Cosmology?

[@eigenchris]

I probably won't. I've been doing relativity videos for 2.5 years. I'm a bit tired of it and I think I'm gonna stop here, take a break, and then move onto other topics.

[@zinken255]

What would happen if in reality a(t) was a(t,x,y,z)?

[@eigenchris]

If we assume the scale factor depends on space, the equations would likely be too difficult to reasonably solve. But we have no evidence to suggest the scale factor behaves this way.

[@asrafali8093]

Hi Chris, Chris, before making spinners series can you please make a video on killing vector in general relativity? I really want to know mathematically what it actually is.... Will you?

[@eigenchris]

I'm not sure if I will. I'll say "maybe". In the meantime you can check out Alex Fluornoy's video on the topic: kzbin.info/www/bejne/h6HJeatojriLaKM

[@AsrafAli-bq5ww]

Chris, why don't you make more videos?

[@eigenchris]

I took a break after my relativity series was done. I'm working on my next video series on spinors now.

[@TheErraticTheory]

Math is amazing because it can do anything. In video games you can even make pigs fly. BUT, that doesn’t mean it is reality. In point to fact this means we must rely upon observations and experiments to ensure that our math is actually representing reality accurately. Because it is easy to put math bandaids on problems to fill the gaps of our knowledge. However this is dangerously short sited. Predictions Experiments and Observations MUST take precedence.

[@kikivoorburg]

Congrats, you discovered the scientific method! I'm not sure why you decided to share this on this particular video, however, which describes a cosmological model built _specifically_ to explain the _very much real_ observations of redshift from galaxies outside our own. It sounds like you're attempting to imply the video "isn't covering the REAL data" to somehow undermine the model it's discussing. I hope that isn't the case! If it is, it would indicate you haven't researched the wealth of experimental data that backs up the Big Bang theory, accelerating expansion of the universe, and General Relativity as a whole. Nobody would even have thought of such intricate models if there wasn't _very good data_ to back it up (CMB, redshift measurements, gravitational lensing, etc.) P.s. "Mathematics can do anything" is only true if you take an extremely general definition of "mathematics": _following through the logical consequences of a given set of axioms._ Modern mathematics almost entirely functions via the axioms of ZFC set theory, which most certainly can't "do anything". In ZFC, 1+1=2 and you cannot force it to be something else. Of course, you may choose to redefine the _symbols_ "1", "+", "=", and/or "2" but symbols, like words, are arbitrary stand-ins for the actual concepts. In set theory notation we'd write "{{}} u { {{}} } = { {}, {{}} }", but the underlying idea is the same, and cannot be changed under ZFC. Mathematical models are powerful precisely _because they impose restrictions, not because they are free to "do anything"._

[@finalguardian0]

MY BROTHER WTF IS THIS

[@jctt96554]

😂😂😂

[@jctt96554]

I don't know too bro

[@원디러]

your voice is so monotone holy