The Einstein Field Equations | Tensor Calc Finale
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- Опубликовано: 3 июл 2024
- Today we use all the tools we've got in our back pocket to "derive" the Einstein Field Equations of general relativity. It's more of a motivation than a derivation, I suppose.
This series is based off the book "Tensor Calculus for Physics" by Dwight Neuenschwander:
amzn.to/3rEema3
Video relating metric to gravitational potential:
• Relating Metric Tensor...
Video deriving contracted bianchi identity:
• The Bianchi Identities...
Deriving the Riemann Curvature Tensor:
• Tensor Calculus Ep. 15...
Uniqueness of Riemann Curvature Tensor:
vixra.org/pdf/1912.0357v1.pdf
or
physics.stackexchange.com/que...
0:00 Intro
1:40 Goal: Generalize Poissons Equation
4:40 Criteria for Field Equations
12:09 What Could They be in Terms of?
15:13 "Guessing" the Form of the EFE's
18:41 Finding the Coefficients
32:23 Writing Down Einsteins Equations
33:52 Important Interpretation
34:04 Conclusion
The saint like patience it takes to hold that yo mama joke in for 3 years...
Great Video Andrew! Love the new beard. ~ Love Mom 💕
Congrats! 3 years eh, what a tall task.
"grad school which is she[e/a]r stress" lmfao 😂
Nothing's going on, now get tf back into the basement!
Calm down papi
when's the next collab vid papa
That’s right pappa keep him on check.
Why does this feel right🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣bro somewhere meanwhile in iran.
Sorry Iranian physicists.....😬😶🌫️
I genuinely can’t wait for the time when I come back to these videos as a grad student. Very exciting stuff, and I’m sure these will help a lot. Thanks in advance!
Can't wait to watch this one. I know it's going to be a banger already 🔥🔥🔥
Hopefully u make more videos on Tensor Calc in the future. ABSOLUTELY LOVED THIS SERIES. Thank you so much Andrew.
Hoping that the tensor calc videos get compiled into a playlist.
Thanks for this!
I do have a playlist already made!
Had so much fun going through the entire lecture series. Thank you for creating such a well taught series on tensor calculus.
I loved this . Nicely done!!!!
Can’t wait to binge yours (EandFs, BPRPs etc etc)content after my exams!
Keep up the great work!
Hey Andrew! I commented something along the lines under a other Video of yours but i will do it again because it fits here: You are a huge roll model for me. Im a 14 year old boy from germany and my main goal in life is getting a Ph.D. in Physics. You give me the motivation to work for that goal because you tell me that I can reach it. The reason why im posting this under exactly this Video is because even though I live all of physics the einstein field equations are that one thing that I defenetly want to understand some time in the future. Maybe its because its the theory thats considerd "the hardes " of all theorys in physics by some people. Or because I just find GR genius. Anyways keep going with your Videos man!!!
Thank you!
Vid dropped right before my GR exam, thank you andrew!
This was my favorite series where I had no idea what was going on the whole time. Fr tho awesome work 👍🏻
Great conclusion! I really appricate the overview. Picked up a GR book for myself after this since I didn't get the chance in grad school.
Seriously, you've been an incredible help. I struggled for so long to understand tensors, but your series made all the difference. The way you explained and derived concepts was truly exceptional. I'm looking forward to use Tensors in about three years, once I've completed school. I know the videos are a bit old now, and you might not even come across this message, but I wanted to express my gratitude. I wish you nothing but the best for your future. :))
Thanks so much for the kind words, Im glad you found the series helpful!
"So what this says is if we put a massive object like your momma in space, then we can calculate directly how the curvature of space changes"
-Andrew Dotson
I finished this series in a matter of two weeks. I'm a middle-aged man that has always had an interest in Relativity, Quantum Mechanics, and the mathematics behind it. This series is phenomenal, and now I journey on to your friend, eigenchris, to get his take on things. Thank you!
Thanks for giving the series a chance, glad you got something out of it! Eigenchriss series will definitely take you farther.
33:50 is what everyone should be here for
You should teach at my college. I’d love to have you, you’re a great teacher!
Congrats on this man. Been a blast to see!
Can't believe only six thousand people saw this. This is gold! And that beard looks great😀
I found this series in the past and made through the starting video a few times. But recently high school ended. I took the break to build prereqs before the start, properly go through the series, take notes. And today I am done with it finally. This series was very nice to follow through. Thank you!
Thanks for checking it out! Glad you enjoyed it
Really cool, wish I knew anything about tensor calculus
Finally finished the whole series and I must say this shit bussin. Thank you Andrew.
Andrew ive been watching your vids for a while now i would so love to see you make a video on quantum gravity and the skills and requirements one needs to understand the math of it. I know youve said before you dont know that stuff like well enough but you seem like a smart guy and it would be cool to hear from you! Thank you! I love your vids that mention string theory. Hi and keep up the good videos, from a viewer in Montreal!
Congratulations. You did a great job with this series. Go Feynman method.
Congratulations Andrew! It's been a long time coming.I noticed that you wore the same shirt in your first and last video of the series! l
What a happy accident
Hey Andrew, I'm a 1st year doctoral student in nuclear astrophysics and I love your videos!
Finally I can start with my QFT series, thanks for the lecture series it helped out a lot ⭐
Also I will be waiting for your video on intuition of Ricci Tensor and Ricci Scalar.
You are so good❤️❤️❤️
I have commented a few times before, but under a different screen name because I was using my work account. Anyway, I have finished my second run-through of this series, retaking notes for better organization. It is spectacular! You have so many more videos that I want to watch, but I am now going to combine the notes I took from this series with the notes I took from Eigenchris. It's a necessity, I think, to get the maximum bang for my buck in learning tensor calculus. Thank you for this series, Andrew. It is quite incredible!
Thanks so much for checking out the series, I hope it was helpful! Eigenchriss videos are top tier for this stuff.
If you thought anything could be presented better, I’d love to know your feedback 🙌🏻 thanks again
@@AndrewDotsonvideos My only criticism is that you can sometimes get your whiteboard/chalkboard jumbled. Especially, when you're forced to move a line or two from one spot to another. Perhaps, it would be good to do your derivations once before filming so you can plan ahead and anticipate when you'll run out of space. Other than that, like I said, my second run-through of these videos has been incredibly enlightening!
I honestly wish I had these back when I was in grad school 😂Hopefully these videos will help out all the current grad and future grad students working with tensors.
Lol, I'm just a lost 17 year old kid who's probably stumbled onto one of the greatest GR resources of all time ^w^
Same here bro I'm 18 and i don't understand anything (for now) maybe will watch this video in the future when my mind is ready to handle it
A fantastic channel who does a decent recap is Dr physics A. I’ve followed him and Andrew for about a year and I’m only 18 and have got a much better understanding thanks to them both. They truly are god sends
@@samuelhawksworth1923 wait- are you doing A level physics too??
@@freniisammii if you do physics at uni you’ll have a book on GR and a whole unit on partial differential equations
@@bellumthirio139 what's the book called? I do believe I have some resources on PDEs as well actually but not much lol
Get this man a Netflix deal
It's the end of an era! Been a long time coming though and a wild ride :D
Outstanding video as always!
I'm looking forward to your video going over the different curvature tensors. Will you be including the Einstein and Weyl tensors? I know, they're built out of the other ones, but they're all built from Riemann in the first place.
Tensor calculus for physics majors: Season two when?
Though I am studying in High school 😸
but I really like u and ur videos and my favourite subject is Physics
❤️ to u from India.
Hoping a career like u .... being a theoretical physicist.
Thank you Thank you Thank you
After so many years
Taking my college’s undergrad GR course next semester, cant wait
Awesome
Dude thaaaannnk you byond measure apprecited!! The 3 year joke was halarious btw. I caught it right away!!! Lmfao🤙.
How *do* physicists introduce higher order terms? I'd really love a video on how "making science"/research in theoretical physics works
Can you please make a video explaining the Energy-Momentum Tensor in detail?
Andrew, thanks for this journey, it was beautiful and I genuinely understood everything u said, I've never felt so satisfied by learning something and not going over my notes even once. Also could you please make a video on Gauge invariance (or just explain it to me as a comment) because I'm having some trouble understanding what Gauge transformations are (and do), I'm following Leonard Susskinds lectures on special relativity, field theory and electrodynamics and in lecture 7 he goes over guage theory and he basically said that u can add terms to the Lagrangian (density) of the form 'dS/dx^{\mu}' and said S could be anything, but there must be some constraint as to what S can be, and I just can't figure it out (i need ur help pls).
Took me two months, but finally finished. Good series. 42 pages of notes....almost as long as some of my psets
2 months?
@@meowwwww6350 well…the series is a set length based on the length of each video and the total number of videos so I guess mostly everyone takes the same amount of time, technically. I just tend to get occupied with other things rather than binging all at once.
@@Drewbie_T oh yeah 👍 but i usually binge all of them at once so it doesn't take as long as your time frame.
Wow I’d love to get your thoughts on the different sections. Your feedback would be super valuable! Could you send me and email? Sorry I’m just seeing this comment now.
@@AndrewDotsonvideos I intend to start and finish this playlist over summer, so I would really love it if you can compile some of the feedback into a video and maybe provide some pointers as an introduction to this playlist. I think it would be worthwhile for future students :)
I....still don't know what a tensor is but I've been studying for my University Physics E&M final all morning and I wanted to take a break to watch ppl talk about stuff I dont understand
How would that change if you were near a trapezoidal shaped rotating charged black hole?
Could you do a video on classical mechanics in tensor notation ?
When are the videos on the interpretation of the riemann and ricci tensor and ricci scalar as well as the einstein hilbert action dropping?
I'm just curious, for your research, do you do tensor calculations by hand, or do you use things like Cadabra or xAct. People from the gravity side of things usually use xAct. How about those in particle physics?
what do you use to write on the computer ?
Andrew is something still left in tensors? ? 😮 if there is one please tell me them😀
I’m proud
Hi! I just had a quick question... what kind of tablet do you use for this? Thanks!
Damn Andrew, you eating enough? Seems like Papa Flamy not feeding you well.
well done
But varying the EH action is way cooler .
I think this is the only useful series for anyone on youtube about tensor calc .
also it would have been better for a finale , if you did it with you hbar=1 hat .
What device are you using to write your notes? I am just curious since I bought an iPad and that device has a much bigger screen.
FeelsStrongMan
Hey, I have a query. Can't we just add cosmological term while keeping it simple stupid because when taking divergence that will go to zero as divergence of metric will be zero and when talking about 00th term metric will just be 1 and then we can assume cosmological term to be 0 because of how small the value is and do our work and add it at last. Same can be done when taking about i j th component as metric will be -1. Is there any problem or mistake in this? If yes then please mention.
Do exterior calculus next please!!
The joke at the end X)))))
I too use Monster Energy™ to enhance my tensor calculus abilities.
already a dislike damn, Papaflamy is early
Xd
😂😂😂 that's nice one
Nice!
wow
Footnoted comment refreshed
If you define motion as the state of some space compared to it's adjacent space - it's improbable for a space's state to correspond with that of a marsian spaceship on Earth's surface, while relatively low space state probability implies a fast entity - , because there's no experiment for determining who's in motion and who's at rest, then the well orderable* - one is less than two for example - set of real numbers**, could provide a dimensional yardstick for modelling a sequence of states, resolving the omnipotent existential guarantee problem that is required for physical accounts of the world including a - Gregorian*** for instance - temporal dimension and which, from this, undermine causation****, so calculations for a solution to the time independent Shrodinger equation could qualify as science, in contrast to those for it's time dependent form.
"Matrix Mechanics... is the Heisenberg, Born and Jordan interpreti[on of] the physical properties of particles as matrices [- a mathematical generalization of the tensor in Einstein's physics - , which] evolve in time[, from this are subject to the criticisms discussed here and are] equivalent to the Schrödinger wave formulation of quantum mechanics (en.m.wikipedia.org/wiki/Matrix_mechanics#).
However, if time is the physical property of the universe required for the second law of thermodynamics : something physical is less organized with time, then time could be modelled by the set of real numbers without Gregorian connotation, which is fictional from this perspective, while either the world, or universe blowing up, would change the configuration of the universe, which is hedged against disappearing by the conservation of energy law***** : total energy in the universe is constant, implying that time dependent Schrodinger equation solution calculations, are just as scientific as those done for the time independent form of the equation, but even an idea is a physical property to a physicalist and consequently, there aren't any bona fide relational concepts as benchmarks for comparison, given this perspective (RUclips : Interview with Quine - Brian Magee (1978)).
You could also argue that time must be a scalar - an informationless quantitative entity, like either a real number in math, or mass and speed in physics - instead of a vector - like velocity, which is speed in a certain direction for instance - , for the consistency of Einsten's equation, E = mc2 = mcc = m x c x c, where x means multiplied by and c is the speed of light, equal to three hundred million metres per second, which defines energy as the product of mass and the square of the speed of light, because a non-general definition of time implies information, from this transforming time, the speed of light and therefore energy - the product of a scalar and a vector is a vector - , measured in joules, from a scalar into a vector, while a claim of godless spacetime as information, because spacetime is a singularity****** - which Dali characterized - , is easily undermined, by pointing out that without the law of non-contradiction, notspacetime with god, is just as imaginable and from competition, nothing is left.
A maybe inexaustive list of the ways of coming to know of something, is perception - the senses - , reason, emotion, intuition, faith and revelation, with a logical impossibility - a flying pig is logically, but not technically, possible, while a happy sun is logically impossible : there's a contradiction of the statements terms - constituting a non-sensical combination of some of these items, so with this in mind, even a combination of reason with faith say, makes sense, because defining a valid argument - the conclusion is entailed by the premises, where a premise is one or more propositions and a proposition is a sentence with a subject and predicate, which says something about the subject - from first principles is not required for linguistically deploying this compound idea - concept - , which from this, could be the foundation for a test of what qualifies as knowledge - justified true belief (RUclips : Richard Feynman. Why).
Newton : 'An apple dropped on my head when sitting under a tree and I had a revelation, that the gravitational attraction of bodies is proportional to the product of their masses and inversely proportional to the square of their distance from each other, but without a model of how y results from x, divine intervention is required for the argument's plausibility.'
Teleologician : 'Any body's purpose is to find it's natural resting place at the center of the Earth, which is corroberated by a suspended apple dropping onto the floor when released.'
Physically applying Minkowski spacetime transforms anywhere in the universe into an event, by describing such a place with three spatial and one temporal coordinate, generally written (x, y, z, t) for real numbers x, y, z and t, where a real number is an open set, which is any element of some set subset, x ∈ V ⊂ X, for ∈ meaning 'element of' and ⊂ meaning 'subset of', so defining space and time in a general sense and merely as - neither syntactically, nor semantically, equivalent - identifiers for open sets in this coordinate system - mathematicians specializing in physics include Hawking, who argues that at a sufficiently small scale immediately following the 'Big-Bang', a universal origin isn't meaningful and consequently, space and time are indistinguishable, then subsequently space could be uncountably infinite*******, with greatest lower bound, or 'infimum,' equal to negative infinity and 'least upper bound,' or supremum,' equal to positive infinity, in contrast to time with a greatest lower bound equal to zero, when modelled using the extended real numbers******** and Penrose - , simultaneously resolves the technical impossibility of causation from divinely specified time and physicalism's absence of relational conceptualization, which is the basis for relativity - whose field equations establish a foundation for Newton's law of gravitation - , by appealing to dualism.
* Zermelo proved that any set is well orderable if you assume the axiom of choice, but no formula can be defined for well ordering the set of real numbers in axiomatic, Zermelo-Freankel set theory including the axiom of choice, ZFC, which apparently resolves Russell's meta-mathematical set theory contradiction - the set of all sets that don't belong to themselves, is a set that doesn't belong to itself and is not a set that doesn't belong to itself - , while since ZFC is an axiomatic scheme from which the natural numbers, {1, 2, 3, ...}, can be enumerated, it is also subject to Godel's criticism that it must be incomplete - there are true statements about the natural numbers, that cannot be proven from ZFC - assuming it is consistent - no logical contradictions.
** The set of real numbers, ℝ, includes rational numbers that can be written in x/y form, where / means divided by and hence, includes any fraction in the unit interval, I = [0,1], of countably infinite rational-real numbers between zero and one inclusive, any integer x/1 = x ∈ ℕ = {...,-1,0,1,...} and therefore any natural number, x ∈ ℤ = {1, 2, 3,...}, as well as irrational approximations that can't be written as a ratio and who's decimal form includes an infinite non-repeating sequence of digits after the decimal point, for example Euler's number, e = 2.72, approximated to two decimal places, in contrast to rationals that either terminate, or repeat, for example, 1/2 = 0.5 and 1/3 = 0.33... = 0.3' where ' means repeating.
*** Pope Gregory XIII rewrote the calendar, synthesizing ecclesiatic and secular accounts of history and this may have been subsequently supported by Galileo, who defined speed as distance divided by time, then Kant - undecideable synthetic apriori proposition - and Einstein - relativity - , who developed technical apparatus in philosophy and science respectively, for the idea that at least our account of time, if not time itself, is partially subjective, although Russell raised an important objection to an wholistic ontological conception of god on the grounds that such an argument is a fallacy of composition (RUclips : Russell-Copleston debate on God (1948)).
**** x is a cause of y if y unequivocally physically follows x, implying that, assuming a - Gregorian for instance - temporal dimension, causation may not be feasible if it's technically possible for the world to blow up.
***** An object has potential energy equal to the product of mass, acceleration due to the Earth's gravitational field and height, Ep = m x g x h = mgh, where x is multiplied by, m is mass., g is 9.8 metres per second squared and h is height, implying the object has zero potential energy when h = 0, while the kinetic energy of the object is the product of half the mass and square of it's velocity - speed in a certain direction - , Ek = 0.5mv2 = 0.5mvv, where v is velocity, so a stationary object has zero kinetic energy and the Hamiltonian operator defines these quantities for elementary physical entities.
****** Singularity - if you trace spacetime back far enough tou get to (0, 0, 0, 0) - entities x and notx are not meaningful, when a singularity is something which is it's opposite, implying there is no law of non-contradiction : nothing is it's opposite.
******* Cantor's diagonal argument proves that there are countably infinite rational numbers, because for any rational number there is a corresponding natural number, which is not so for the uncountably infinite set of real numbers.
******** The extended real numbers is the real numbers including negative infinity and positive infinity, ℝ U {-∞, ∞}, where U means union.
We need String Theory,(please?)!!😎😷🐯
And I'm struggling to pass Calc 2
smart host sending support
"grad school which is sheer stress" 😂
Grad school is shear stress.
Refreshed : If you define motion as the state of some space compared to it's adjacent space - it's improbable for a space's state to correspond with that of a marsian spaceship on Earth's surface, while relatively low space state probability implies a fast entity - , because there's no experiment for determining who's in motion and who's at rest, then the well orderable - one is less than two for example - set of real numbers*, could provide a dimensional yardstick for modelling a sequence of states, resolving the omnipotent existential guarantee problem that is required for physical accounts of the world including a - Gregorian** for instance - temporal dimension and which, from this, undermine causation***, so calculations for a solution to the time independent Shrodinger equation could qualify as science, in contrast to those for it's time dependent form.
However, if time is the physical property of the universe required for the second law of thermodynamics : something physical is less organized with time, then time could be modelled by the set of real numbers without Gregorian connotation, which is fictional from this perspective, while either the world, or universe blowing up, would change the configuration of the universe, which is hedged against disappearing by the conservation of energy law**** : total energy in the universe is constant, implying that time dependent Schrodinger equation solution calculations, are just as scientific as those done for the time independent form of the equation, but even an idea is a physical property to a physicalist and consequently, there aren't any bona fide relational concepts as benchmarks for comparison, given this perspective (RUclips : Interview with Quine - Brian Magee (1978)).
A maybe inexaustive list of the ways of coming to know of something, is perception - the senses - , reason, emotion, intuition, faith and revelation, with a logical impossibility - a flying pig is logically, but not technically, possible, while a happy sun is logically impossible : there's a contradiction of the statements terms - constituting a non-sensical combination of some of these items, so with this in mind, even a combination of reason with faith say, makes sense, because defining a valid argument - the conclusion is entailed by the premises, where a premise is one or more propositions and a proposition is a sentence with a subject and predicate, which says something about the subject - from first principles is not required for linguistically deploying this compound idea - concept - , which from this, could be the foundation for a test of what qualifies as knowledge - justified true belief (RUclips : Richard Feynman. Why).
Newton : 'An apple dropped on my head when sitting under a tree and I had a revelation, that the gravitational attraction of bodies is proportional to the product of their masses and inversely proportional to the square of their distance from each other, but without a model of how y results from x, divine intervention is required for the argument's plausibility..'
Teleologician : 'Any body's purpose is to find it's natural resting place at the center of the Earth, which is corroberated by a suspended apple dropping onto the floor when released.'
* Zermelo proved that any set is well orderable if you assume the axiom of choice, but no formula can be defined for well ordering the set of real numbers in axiomatic, Zermelo-Freankel set theory including the axiom of choice, ZFC, which apparently resolves Russell's meta-mathematical set theory contradiction - the set of all sets that don't belong to themselves, is a set that doesn't belong to itself and is not a set that doesn't belong to itself - , while since ZFC is an axiomatic scheme from which the natural numbers, {1, 2, 3, ...}, can be enumerated, it is also subject to Godel's criticism that it must be incomplete - there are true statements about the natural numbers, that cannot be proven from ZFC - assuming it is consistent - no logical contradictions.
** Pope Gregory XIII rewrote the calendar, synthesizing ecclesiatic and secular accounts of history and this was subsequently supported by Galileo, who defined speed as distance divided by time, then Kant - undecideable synthetic apriori proposition - and Einstein - relativity - , who developed technical apparatus in philosophy and science respectively, for the idea that at least our account of time, if not time itself, is partially subjective, although Russell raised an important objection to an wholistic ontological conception of god on the grounds that such an argument is a fallacy of composition (RUclips : Russell-Copleston debate on God (1948)).
*** x is a cause of y if y unequivocally physically follows x, implying that, assuming a - Gregorian for instance - temporal dimension, causation may not be feasible if it's technically possible for the world to blow up.
**** An object has potential energy equal to the product of mass, acceleration due to the Earth's gravitational field and height, Ep = m x g x h = mgh, where x is multiplied by, m is mass, g is 9.8 metres per second squared and h is height, implying the object has zero potential energy when h = 0, while the kinetic energy of the object is the product of half the mass and square of it's velocity - speed in a certain direction - , Ek = 0.5mv2 = 0.5mvv, where v is velocity, so a stationary object has zero kinetic energy and the Hamiltonian operator defines these quantities for elementary physical entities.
"Matrix Mechanics... is the Heisenberg, Born and Jordan interpreti[on of] the physical properties of particles as matrices [- a mathematical generalization of the tensor in Einstein's physics - , which] evolve in time[, from this are subject to the criticisms discussed here and are] equivalent to the Schrödinger wave formulation of quantum mechanics" (en.m.wikipedia.org/wiki/Matrix_mechanics#).
Physically applying Minkowski spacetime transforms anywhere in the universe into an event, by describing such a place with three spatial and one temporal coordinate, generally written (x, y, z, t) for real numbers x, y, z and t, where a real number is an open set, which is any element of some set subset, x ∈ V ⊂ X, for ∈ meaning 'element of' and ⊂ meaning 'subset of', so defining space and time merely as identifiers for open sets in this coordinate system, simultaneously resolves the technical impossibility of causation from divinely specified time and physicalism's absence of relational conceptualization, which is the basis for relativity - whose field equations establish a foundation for Newton's law of gravitation - , by appealing to dualism.
Yea Einstein Field Equations are cool but is the earth flat?
No its a dounut of corse
@@erikawimmer7908 Cmon, its a coffee mug.
If not a coffee mug, then a tetrahedron of course.
@@rikthecuber noooo dont tell Papa flamy. Hes scared of tori and i wnt him to be scared.
@@erikawimmer7908 I did not expect a reply from a 7 month old comment.
I read you other comment. I am also trying to learn from Andrew's tensor series to reach here. DrPhysicsA brought me here. But I realised I would need vector calc so I did that a bit.
And I did not understand what you meant by "tori". Did you mean tetrahedron?
@@rikthecuber No not tetahedron. tori is the plural of torus ( its latin ).
Einstein Field equations?
*eats popcorn*
You look young with the hat
I know that this video will attract mostly grads and all so I am going to shamelessly ask to please suggest me one nice book for waves and oscillations. I want Introductory level book but sufficient for undergrad. Thanks.
Waves and oscillations will be covered in any good book on classical mechanics, typically when dealing with harmonic motion and an intro to continuum mechanics. A good intro book on these subjects is Classical Mechanics by John Taylor, which is geared towards mid level undergrads.
@@JacobGaiter is David Morin's chapter 4 on oscillations good?
@@anmolmehrotra923 I am unfamiliar with this work so I cannot comment
@@JacobGaiter oh sure. Thanks for help
Comment refreshed again
If you define motion as the state of some space compared to it's adjacent space - it's improbable for a space's state to correspond with that of a marsian spaceship on Earth's surface, while relatively low space state probability implies a fast entity - , because there's no experiment for determining who's in motion and who's at rest, then the well orderable* - one is less than two for example - set of real numbers**, could provide a dimensional yardstick for modelling a sequence of states, resolving the omnipotent existential guarantee problem that is required for physical accounts of the world including a - Gregorian*** for instance - temporal dimension and which, from this, undermine causation****, so calculations for a solution to the time independent Shrodinger equation could qualify as science, in contrast to those for it's time dependent form.
"Matrix Mechanics... is the Heisenberg, Born and Jordan interpreti[on of] the physical properties of particles as matrices [- a mathematical generalization of the tensor in Einstein's physics - , which] evolve in time[, from this are subject to the criticisms discussed here and are] equivalent to the Schrödinger wave formulation of quantum mechanics (en.m.wikipedia.org/wiki/Matrix_mechanics#).
However, if time is the physical property of the universe required for the second law of thermodynamics : something physical is less organized with time, then time could be modelled by the set of real numbers without Gregorian connotation, which is fictional from this perspective, while either the world, or universe blowing up, would change the configuration of the universe, which is hedged against disappearing by the conservation of energy law***** : total energy in the universe is constant, implying that time dependent Schrodinger equation solution calculations, are just as scientific as those done for the time independent form of the equation, but even an idea is a physical property to a physicalist and consequently, there aren't any bona fide relational concepts as benchmarks for comparison, given this perspective (RUclips : Interview with Quine - Brian Magee (1978)).
You could also argue that time must be a scalar - an informationless quantitative entity, like either a real number in math, or mass and speed in physics - instead of a vector - like velocity, which is speed in a certain direction for instance - , for the consistency of Einsten's equation, E = mc2 = mcc = m x c x c, where x means multiplied by and c is the speed of light, equal to three hundred million metres per second, which defines energy as the product of mass and the square of the speed of light, because a non-general definition of time implies information, from this transforming time, the speed of light and therefore energy - the product of a scalar and a vector is a vector - , measured in joules, from a scalar into a vector, while a claim of godless spacetime as information, because spacetime is a singularity****** - which Dali characterized - , is easily undermined, by pointing out that without the law of non-contradiction, notspacetime with god, is just as imaginable and from competition, nothing is left.
A maybe inexaustive list of the ways of coming to know of something, is perception - the senses - , reason, emotion, intuition, faith and revelation, with a logical impossibility - a flying pig is logically, but not technically, possible, while a happy sun is logically impossible : there's a contradiction of the statements terms - constituting a non-sensical combination of some of these items, so with this in mind, even a combination of reason with faith say, makes sense, because defining a valid argument - the conclusion is entailed by the premises, where a premise is one or more propositions and a proposition is a sentence with a subject and predicate, which says something about the subject - from first principles is not required for linguistically deploying this compound idea - concept - , which from this, could be the foundation for a test of what qualifies as knowledge - justified true belief (RUclips : Richard Feynman. Why).
Newton : 'An apple dropped on my head when sitting under a tree and I had a revelation, that the gravitational attraction of bodies is proportional to the product of their masses and inversely proportional to the square of their distance from each other, but without a model of how y results from x, divine intervention is required for the argument's plausibility.'
Teleologician : 'Any body's purpose is to find it's natural resting place at the center of the Earth, which is corroberated by a suspended apple dropping onto the floor when released.'
Physically applying Minkowski spacetime transforms anywhere in the universe into an event, by describing such a place with three spatial and one temporal coordinate, generally written (x, y, z, t) for real numbers x, y, z and t, where a real number is an open set, which is any element of some set subset, x ∈ V ⊂ X, for ∈ meaning 'element of' and ⊂ meaning 'subset of', so defining space and time in a general sense and merely as - neither syntactically, nor semantically, equivalent - identifiers for open sets in this coordinate system - mathematicians specializing in physics include Hawking, who argues that at a sufficiently small scale immediately following the 'Big-Bang', a universal origin isn't meaningful and consequently, space and time are indistinguishable, then subsequently space could be uncountably infinite*******, with greatest lower bound, or 'infimum,' equal to negative infinity and 'least upper bound,' or supremum,' equal to positive infinity, in contrast to time with a greatest lower bound equal to zero, when modelled using the extended real numbers******* and Penrose - , simultaneously resolves the technical impossibility of causation from divinely specified time and physicalism's absence of relational conceptualization, which is the basis for relativity - whose field equations establish a foundation for Newton's law of gravitation - , by appealing to dualism.
* Zermelo proved that any set is well orderable if you assume the axiom of choice, but no formula can be defined for well ordering the set of real numbers in axiomatic, Zermelo-Freankel set theory including the axiom of choice, ZFC, which apparently resolves Russell's meta-mathematical set theory contradiction - the set of all sets that don't belong to themselves, is a set that doesn't belong to itself and is not a set that doesn't belong to itself - , while since ZFC is an axiomatic scheme from which the natural numbers, {1, 2, 3, ...}, can be enumerated, it is also subject to Godel's criticism that it must be incomplete - there are true statements about the natural numbers, that cannot be proven from ZFC - assuming it is consistent - no logical contradictions.
** The set of real numbers, ℝ, includes rational numbers that can be written in x/y form, where / means divided by and hence, includes any fraction in the unit interval, I = [0,1], of countably infinite rational-real numbers between zero and one inclusive, any integer x/1 = x ∈ ℕ = {...,-1,0,1,...} and therefore any natural number, x ∈ ℤ = {1, 2, 3,...}, as well as irrational approximations that can't be written as a ratio and who's decimal form includes an infinite non-repeating sequence of digits after the decimal point, for example Euler's number, e = 2.72, approximated to two decimal places, in contrast to rationals that either terminate, or repeat, for example, 1/2 = 0.5 and 1/3 = 0.33... = 0.3' where ' means repeating.
*** Pope Gregory XIII rewrote the calendar, synthesizing ecclesiatic and secular accounts of history and this may have been subsequently supported by Galileo, who defined speed as distance divided by time, then Kant - undecideable synthetic apriori proposition - and Einstein - relativity - , who developed technical apparatus in philosophy and science respectively, for the idea that at least our account of time, if not time itself, is partially subjective, although Russell raised an important objection to an wholistic ontological conception of god on the grounds that such an argument is a fallacy of composition (RUclips : Russell-Copleston debate on God (1948)).
**** x is a cause of y if y unequivocally physically follows x, implying that, assuming a - Gregorian for instance - temporal dimension, causation may not be feasible if it's technically possible for the world to blow up.
***** An object has potential energy equal to the product of mass, acceleration due to the Earth's gravitational field and height, Ep = m x g x h = mgh, where x is multiplied by, m is mass, g is 9.8 metres per second squared and h is height, implying the object has zero potential energy when h = 0, while the kinetic energy of the object is the product of half the mass and square of it's velocity - speed in a certain direction - , Ek = 0.5mv2 = 0.5mvv, where v is velocity, so a stationary object has zero kinetic energy and the Hamiltonian operator defines these quantities for elementary physical entities.
****** Singularity - if you trace spacetime back far enough tou get to (0, 0, 0, 0) - entities x and notx are not meaningful, when a singularity is something which is it's opposite, implying there is no law of non-contradiction : nothing is it's opposite.
******* Cantor's diagonal argument proves that there are countably infinite rational numbers, because for any rational number there is a corresponding natural number, which is not so for the uncountably infinite set of real numbers.
******** The extended real numbers is the real numbers including negative infinity and positive infinity, ℝ U {-∞, ∞}, where U means union.
Me, a second semester watching this: Wtf are those letters.
When your a sophomore learning about quadratics and go hm interesting lets see if I can do that.
15 views, 15 likes and 2 dislikes? Huh?
(2 minutes after release)
people dislikes because they hate not because they didn't like the video :) such kids 🤦♂️
Proof that time is not absolute
Watching this after ive done my General relativity exam. I hate tensors and the notation
18:41 Completely Unnecessary! You could've just used the differential Bianchi identity (which you basically derived last video): en.wikipedia.org/wiki/Proofs_involving_covariant_derivatives
However , I appreciate how you went over an alternative method. Anyways, this was still an amazing video as always!
l santalo would b proud
"..which contains information about energy, momentum, pressure, GRAD SCHOOL WHICH IS SHEER(SHEAR) STRESS"
Spouting facts!🤣
What am I doing here? I'm in PreCalulus haha
"Tensor Calculus"? More like differential geometry for engineers amirite?
look how hot this smart man is SHEESH
If you define motion as the state of some space compared to it's adjacent space - it's improbable for a space's state to correspond with that of a marsian spaceship on Earth's surface, while relatively low space state probability implies a fast entity - , because there's no experiment for determining who's in motion and who's at rest, then the well orderable - one is less than two for example - set of real numbers*, could provide a dimensional yardstick for modelling a sequence of states, resolving the omnipotent existential guarantee problem that is required for physical accounts of the world including a - Gregorian** for instance - temporal dimension and which, from this, undermine causation***, so calculations for a solution to the time independent Shrodinger equation could qualify as science, in contrast to those for it's time dependent form.
* Zermelo proved that any set is well orderable if you assume the axiom of choice, but no formula can be defined for well ordering the set of real numbers in axiomatic, Zermelo-Freankel set theory including the axiom of choice, ZFC, which apparently resolves Russell's meta-mathematical set theory contradiction - the set of all sets that don't belong to themselves, is a set that doesn't belong to itself and is not a set that doesn't belong to itself - , while since ZFC is an axiomatic scheme from which the natural numbers, {1, 2, 3, ...}, can be enumerated, it is also subject to Godel's criticism that it must be incomplete - there are true statements about the natural numbers, that cannot be proven from ZFC - assuming it is consistent - no logical contradictions.
** Pope Gregory XIII rewrote the calendar, synthesizing ecclesiatic and secular accounts of history and this was subsequently supported by Galileo, who defined speed as distance divided by time, then Kant - undecideable synthetic apriori proposition - and Einstein - relativity - , who developed technical apparatus in philosophy and science respectively, for the idea that at least our account of time, if not time itself, is partially subjective, although Russell raised an important objection to an wholistic ontological conception of god on the grounds that such an argument is a fallacy of composition (RUclips : Russell-Copleston debate on God (1948)).
*** x is a cause of y if y unequivocally physically follows x, implying that, assuming a temporal dimension, causation may not be feasible if it's technically possible for the world to blow up.
If time is the physical property of the universe required for the second law of thermodynamics : something physical is less organized with time, then time could be modelled by the set of real numbers without Gregorian connotation, which is fictional from this perspective, while either the world, or universe blowing up, would change the configuration of the universe, which is hedged against disappearing by the conservation of energy law : total energy in the universe is constant, implying that time dependent Schrodinger equation solution calculations, are just as scientific as those done for the time independent form of the equation, but even an idea is a physical property to a physicalist (RUclips : Interview with Quine - Brian Magee (1978)).
A maybe inexaustive list of the ways of coming to know of something, is perception - the senses - , reason, emotion, intuition, faith and revelation, with a logical impossibility - a flying pig is logically, but not technically, possible, while a happy sun is logically impossible : there's a contradiction of the statements terms - constituting a non-sensical combination of some of these itemz, so with this in mind, even a combination of reason with faith say, makes sense, because defining a valid argument - the conclusion is entailed by the premises, where a premise is one or more propositions - from first principles is not required for linguistically deploying this compound idea - concept - , which from this, could be the foundation for a test of what qualifies as knowledge.
However, if time is the physical property of the universe required for the second law of thermodynamics : something physical is less organized with time, then time could be modelled by the set of real numbers without Gregorian connotation, which is fictional from this perspective, while either the world, or universe blowing up, would change the configuration of the universe, which is hedged against disappearing by the conservation of energy law**** : total energy in the universe is constant, implying that time dependent Schrodinger equation solution calculations, are just as scientific as those done for the time independent form of the equation, but even an idea is a physical property to a physicalist and consequently, there aren't any bona fide relational concepts as benchmarks for comparison, given this perspective (RUclips : Interview with Quine - Brian Magee (1978)).
However, if time is the physical property of the universe required for the second law of thermodynamics : something physical is less organized with time, then time could be modelled by the set of real numbers without Gregorian connotation, which is fictional from this perspective, while either the world, or universe blowing up, would change the configuration of the universe, which is hedged against disappearing by the conservation of energy law**** : total energy in the universe is constant, implying that time dependent Schrodinger equation solution calculations, are just as scientific as those done for the time independent form of the equation, but even an idea is a physical property to a physicalist and consequently, there aren't any bona fide relational concepts as benchmarks for comparison, given this perspective (RUclips : Interview with Quine - Brian Magee (1978)).
A maybe inexaustive list of the ways of coming to know of something, is perception - the senses - , reason, emotion, intuition, faith and revelation, with a logical impossibility - a flying pig is logically, but not technically, possible, while a happy sun is logically impossible : there's a contradiction of the statements terms - constituting a non-sensical combination of some of these items, so with this in mind, even a combination of reason with faith say, makes sense, because defining a valid argument - the conclusion is entailed by the premises, where a premise is one or more propositions and a proposition is a sentence with a subject and predicate, which says something about the subject - from first principles is not required for linguistically deploying this compound idea - concept - , which from this, could be the foundation for a test of what qualifies as knowledge - justified true belief (RUclips : Richard Feynman. Why).
Newton : 'An apple dropped on my head when sitting under a tree and I had a revelation, that the gravitational attraction of bodies is proportional to the product of their masses and inversely proportional to the square of their distance from each other, but without a model of how y results from x, divine intervention is required for the argument's plausibility..'
Teleologician : 'Any body's purpose is to find it's natural resting place at the center of the Earth, which is corroberated by a suspended apple dropping onto the floor when released.'
Can daddy D react to Michael Reeves videos? I'll send money if you're worried about monetization. I just need to know that Andrew has, in fact, watched that glorious channel at least once.
3 years is worth it for the joke at 33:53
Where's the Dotson's Lost Lecture