General Relativity: Top 05 Mishaps [inc INTERSTELLAR]
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- čas přidán 24. 09. 2020
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This is the Maths Inspiration show I'm going with Eugénie on 24 November: www.mathsinspiration.com/event...
We have passes for schools as well as for people watching from home.
Huge thanks to Eugénie von Tunzelmann for being my coolest friend and for taking the time to chat with me for this video. Check out all the films she has worked on!
www.imdb.com/name/nm1590981/
Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar
arxiv.org/abs/1502.03808
Read the free book "Reflections on Relativity" by Kevin Brown
www.mathpages.com/rr/rrtoc.htm
This is an archive of their old post about the time dilatiopause. Complete with retro ASCII equations.
groups.google.com/forum/?hl=e...
Thanks to Cleon Teunissen for emailing in with a bunch of useful details. www.cleonis.nl/
And they recommend this book chapter for more on why the shape of the Earth is an isochrone: geosci.uchicago.edu/~kite/doc/...
Speed dilation equation:
hyperphysics.phy-astr.gsu.edu/...
Gravity dilation equation:
hyperphysics.phy-astr.gsu.edu/...
CORRECTIONS:
- Yes, the diagram of the photon clock on the train has a light path of over 45° from the vertical which means the train is going faster than the speed of light. Let’s just agree the train (and everything within it) is not to scale!
- Let me know if you spot any more mistakes!
Thanks to my Patreons who mean I can film hours of myself talking about relativity and then ask Alex to 'edit that into something which makes sense'. Here is a random subset of those fine Patreon People:
Markus Herrmann
Chris Connett
Elaine Hewitson
Neil McGovern
Paul LeVan
Claire Greenhalgh
Erin Eldridge
Loren Thomas
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Glenn Watson
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As always: thanks to Jane Street who support my channel. They're amazing.
www.janestreet.com/
Filming and editing by Alex Genn-Bash
Animations by William Marler
Music by Howard Carter
Design by Simon Wright and Adam Robinson
Clips from Interstellar (2014) are all copyright some combination of Paramount Pictures and Warner Bros. and I thought we could all agree my use here is pretty fair. But they have already put a copyright claim in on this video, so there's that.
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b... - Zábava
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"Everything I say is assumed to be in a vacuum"
Me: stops listening because the sound waves of Matt's speech don't have a medium with which to reach my ears
Dad?
Sure they do: space, itself! Gravity waves. That's what they are - for all intents and purposes - sound waves *of* space itself. You just need a way to convert to/from air-sound and space-sound.
@@RockBrentwood Nah, the only thing they have in common is that they are waves. It is like saying that sound and light are the samething because - for all intents and purpose - light is an sound waves of electromagnetic field itself. You just need a way to converto to/from air-sound and EMF-sound. Oh, wait, that is called radio.
By the way, sound is a horizontal wave, while gravity is a transversal wave, like light. That means that they are more alike. For example, gravitational waves can be polarized, unlike sound waves.
EDIT: as @alysdexia correctly pointed out, the correct term is longitudinal wave, not horizonal. But that is why I said they can't be polarized, because they are longitudinal.
"You are technically correct - the best kind of correct".
@@Alkis05 It is like saying that light waves are sound waves of the electromagnetic field, itself - as indeed they are, for all intents and purposes. You just need a way to convert to/from EM waves and air vibrations to hear them. Oh wait. That's called a radio. The "only thing they have in common" is *precisely* what they need to have in common! QED.
The irony of hearing that "different people can experience time passing at different rates" when I was watching this video at 1.75 speed.
Now try doing it while high.
So if my calculations are correct you are happily travelling at 0.82 times the speed of light ! Congrats.
interesting.. I did the same thing but at 2x speed, though I often change it a bit if I am having a hard time understanding
I'll try this
@@atticusdodd6814 I find it difficult to understand at norm speed. My brain totally adapted to 2x speed.
Why are we even talking about this, this is more of a psychological and biological rather than physics.
Matt: “Here are 5 mishaps of General Relativity”
Me: “Cool”
Matt: “Mishap Number 0!”
Me: :|
Well 0! is 1 so... Makes sense.
@@riturajphukan632 ÷LLP
Interesting way to make use of a zero. What's that called... Outside the box thinking in my book.
😂😂😂😁😁😁
Must be a programmer.
"Went away and had a think" might be the greatest understatement ever 😂
"What are you doing today?"
"Not much, just accelerating upward by 9.81m/s²"
"So just hanging?"
upwards? relative to what¿
@@DearHRS , check out this video, where this is explained perfectly and relatively simply czcams.com/video/XRr1kaXKBsU/video.html
@@tomkocian6710 woosh
@@DearHRS We would have to assume he meant in the direction of the surface normal to level ground of the point on earth to which he is standing. He definitely should have clarified.
If Matt were to design a programming language, the array index would be the sequence: 0, -0, 2, 3, ...
That is a hilarious and terrifying concept....i need to lye down now....
The Parker Array
@@swaree beat me to it
I'm surprised and disappointed that he 2 and 3 instead of i and -i.
0, -0, 0i, -0i, 0+0i,…
30:31. I made the calculations. If your satellite orbits at 0 meters from the surface of the Earth, you do not need any corrections.
Genius
(Not sure if this is a legitimate error or a joke, but in any case...) Actually this is not the case, because people standing on the surface of the earth are not in free fall - they are not "in orbit". If you actually orbit at 0 meters from the surface of the earth, you will have to be going quite fast, which results in some special relativistic slowdown relative to earth observers.
@@digama0 I meant that as a joke. And I do not follow your comment (perhaps because I am not trained in physics beyond high school). Thanks though.
We can correct this with a cheeky bit of linguistics and say instead that you “place” your satellite at 0 m.
@@digama0 you are in orbit around the earth, though, even when you're standing still. You're in an orbit with an apoapsis of 0m (your current altitude), and with a periapsis close to the center of the earth. It just so happens though that that orbit intersects with the Earth's crust, which gives us an upward thrust to maintain our apoapse at 0m.
"S" is for Special = Speed.
"G" is for General = Gravity.
Nice mnemonic! Thank you!!!
this actually helps a ton when i try to remember which one im talking about, thanks!
@Ulti Now tell me, from your mnemonic, where acceleration fits.
@@puppetsock why should it?
@@billysgeo Why should acceleration fit into physics? Well, Bill. Perhaps you'd like to be able to do something besides linear motion at a constant velocity. Also, it is a frequent error to claim it belongs only in GR because people associate gravity with acceleration. So you often get people claiming that SR cannot understand the twin paradox because it involves the travelling twin accelerating to come home.
That's why we need to place acceleration in this scheme.
"...what I am now calling the time-dilatopause..." -- how about chronosynchronous orbit?
awesome :)
nice
@Ron Maimon why do you say that?
@Ron Maimon I don't see what relevance the Virial Theorem has here at all? I mean, the Virial Theorem pertains to a stable, self-gravitating, spherical distribution of equal mass objects, which is not what we are talking about.
The virial theorem compares to an infinitely far reference point not to one on the surface so Matt is (most probably) correct
Matt Parker, grinning, doing a slight jog towards a camera then crouching - all while wearing a headlamp - is my sleep paralysis demon
"If I was coming towards you at, say, half the speed of light..."
I can’t believe I only just discovered your channel through a minecraft speedrun scandal. And I’m glad I did. I’m really enjoying these videos!
Welcome to the maths verse. May I recommend him calculating pi by hand?
Same! One of my new favourite channels now.
Hey, I discovered Daft Punk through a teacher showing me Daft Hands in middle school! However you end up on great content is always valid, no matter how silly it might be.
Might I recommend his books Things to make and do in the 4th dimension and Humble Pi.. if you enjoy the videos, you'll probably like them
Bruh
Physicist: It can't happen there is no way
Nolan: Don't care make it happen
Physicist: Okay here
Nolan: and in the end it was all thanks to the power of love
Physicist: :/
Love.. Is the constant of life
Underrated comment
Kip Thorne is a saint
@@anshik.k.t 13th
Yeah, as so many fantasy epics, it's all ruined in the final act. Tip to authors: don't write yourself into an unescapeable corner, that way you don't have to create a nonsense explanation how the heroes escaped.
Matt, regarding your talks on Interstellar. Kip Thorne wrote the book "The Science of Interstellar" where he broke down every section of the movie and explained it based on Truth, Educated Guess, and Speculation, according to our current understanding of science. It's a really great read if you love both basic science and extreme sciences of other dimensions.
More importantly, he goes into your exact question of 'Where do they draw the line between accurate physics and the needs of narrative, visual storytelling?" in Chapter 8. Basically, in terms of the imaging, they chose to display a more modest black hole spin of 60% of the maximum for visual reasons. They thought that the 'squishing' of one side of the visual event horizon and the extreme Doppler shift of the light from opposite sides of the black hole would over confuse audience members, so they went with the slower spinning hole for visuals.
I highly recommend you get the book and read it, it's an awesome read.
Seems like he did read the book, as the video deals with just what Thorne wrote about.
Sixty symbols
@UnderTheRain It will be if you doze off and not pay attention.
@dee dee "all people" is clearly an exaggeration. I bet it's not that confusing for the people involved in the making of the movie.
@@sebastianjost as someone trying to market a movie, though, would you really want to cater to that tiny proportion of humanity?
Cleon Teunissen here, I'm the guy who notified Matt about the cancelation of gravitational time dilation and velocity time dilation for all clocks on Earth that are on the same level.
I notice that in the comments several people are very curious *why* that is a consequence of the relativistic physics. Here is how I think you can get a fairly good sense of it.
The expectation of that cancelation is the logical consequence of an idea that Einstein started exploring around 1907. This was a precursor to the general theory that didn't yet feature spatial effects.
Imagine a very very large disk-shaped spacecraft, so large and rotating with such an angular velocity that at the perimeter the disk is pulling 1 G of acceleration.
If I move to a level closer to the center then a for a local clock more proper time will elapse; closer to the center the circumnavigating velocity is smaller.
In 1907 Einstein was using a precursor to the Principle of Equivalence. The idea was that all forms of pulling G's are fundamentally indistinguishable. So: on that rotating disk, when you go to another level, you should not be able to tell, *by way of making time measurements*, whether the G-load you are experiencing is due to acceleration of the floor of a rotating spacecraft, or due to standing on the surface of a gravitating body.
With that equivalence stipulation in place: the higher the G-load, the bigger the time dilation as a function of height. (If that disk would spin twice as fast two things change in lockstep: more velocity time dilation, and you're pulling more G's)
If follows logically that if the principle of equivalence holds good then a feature of a gravitational potential is that there is a corresponding gravitional time dilation.
In Geophysics there is the concept of *Geopotential height*. The shape of the Earth is regarded as an equilibrium shape. To very good approximation global sea level is an equipotential surface. (But yeah, if you measure sufficiently accurate you find local gravity anomalies)
For every value of geopotential there is a corresponding surface. Of course the most interesting geopotential is the actual sea level surface of the Earth. But sure: above the Earth surface the concept of geopotential is well defined too..
If a clock is on a *mountain* you do get a difference: a different amount of proper time elapses. You see: gravity falls off inversely proportional to distance, and the equilibrium shape corresponding to solid body rotation (of a fluid) is a case of Hooke's law.
The full theory has more than the graviational time dilation effect; there are *spatial effects* too. However, when the gravitational field is weak the spatial manifestation is far smaller than the time manifestation.
Summerizing:
If the principle of equivalence holds good then (to a very good approximation) for all clocks on sea level the same amount of proper time will elapse.
Cleon Teunissen
Very nice. You use GR on a daily basis?
Nice buddy 👍
Math QUESTION
Factor higher degree polynomial
czcams.com/video/D99PASilPrY/video.html
See it one time..
@@mauijttewaal As to whether I actually use GR: Ah, no. In fact, while I have a physics background, my day job isn't in physics. The overall theme of my physics website (classical mechanics) is 'physics of rotation'. So I was primed towards being alert about the Earth's equatorial bulge. I don't remember where I learned about the concept ot the Geoid as an isochrone. Most likely Kevin Brown's website, but I have no recollection of that.
I am glad you talked about gravitational anomalies, because that was my first question when Matt said this.
Fun fact: Mathew McConaughey's biggest problem with the script for Interstellar was that in the sequences requiring him to wear a space suit he wouldn't be able to take his shirt off on camera.
Bahahahahahaha
.
Thats the problem with many idiots who think of themselves as bigger than all.
Are you serious?
@@WhiteChocolate74 Pretty much every comment that starts with "fun fact" is a joke or wrong.
@@timseguine2 you never know with these Hollywood types
All right, all right allll riiiiight!
Holy moses, the equal cancelling time dilation of the earth's surface is kind of mind boggling
Now the simple question: Why?
Was/Is this effect important for creating the shape of the earth?
@@patricktho6546 naive explanation (i didn't run the numbers) would be that the surface of the earth at a given height above sea level follows a well defined potential line (or rather surface) where the centrifugal forces and gravity cancel out, i.e. the forces due to velocity and gravity.
We can assume that their time dilation therefore also cancels out since they are inherently linked and at the same potential for force and thus also time dilation.
I hope you understand what I meant.
The interesting thing now would be to see if this is true for any given angular velocity which would also require to know how much the earth or any given body would deform with their spin.
Which is non-trivial, maybe I run the numbers at some point just for fun.
@@metalhat3534 naively this sounds good.
But that would say, that this is true for every "solid, jet deformable", rotating object in a complete Vakuum.
@@metalhat3534 this explanation is good enough for me. The only thing I could add is that the sea-level detail basically just implies that water is free to move to wherever that velocity-gravity equilibrium lies all over the earth, moon tides notwithstanding.
@@metalhat3534 The idea of looking at places where the forces cancel out probably does not work since the forces are only opposite to another on the equator (For example at the poles there is no centrifugal component at all to cancel the gravity and your surface would stretch to infinity there).
The argument has to rather come from the ides that all the particles on the surface have the same energy level.
This quote from Wikipedia might help:
"Gravitational time dilation in a gravitational well is equal to the velocity time dilation for a speed that is needed to escape that gravitational well [...] Applying this argument more generally one gets that (under the same assumptions on the metric) the relative gravitational time dilation between two points equals to the time dilation due to velocity needed to climb from the lower point to the higher."
Since all the points in the surface have the same energy level any velocity > 0 would allow you to move from one point to another and thus there can be no difference in time dilation.
I am not an expert on the matter though, so take this with a grain of salt.
Einstein: *makes a mistake*
Einstein: *spends 11 years coming up with a theory to explain it*
Matt: *makes a mistake*
Matt: *makes a video making fun of himself for making it*
I don't think einstein made a mistake there. It was just inference and observations
You missed the bit where Matt made that same mistake again during this very video
We don't know what Matt will come up with in another decade...
@@smeatar He also made the mistake of calculating at sea level. The last point assumes sea level is perfect and that again the earth doesn't bulge. What if you are a mile high as many cities are. need more maths
@Anessen Does calling someone an idiot make you feel a better person?
Nolan : We have to achieve 61,361 times Time Dilation
Kip : It's impossible
Nolan : No, it's necessary.
*No Time for Caution by Hans Zimmer sounds in the background* #epic
Damn, I wanted to write this comment
I can't figure out why Kip would say it's impossible. I've done the calculations myself and it works for a non-rotating black hole. But even if you think about it naively, it must be possible because the amount of time dilation approaches infinity as you near the event horizon. The only impossible thing is finding a perfectly stable orbit with that amount of dilation. But a moderately unstable orbit would do. The problem with the film is that the planet would have to be located within the Roche limit to have that dilation (spinning or no), and so it would be ripped apart immediately.
Dan Reynolds In other words, it’s impossible
@@danreyn SO ITS IMPOSSIBLE?
I like that Tom took the effort to explain how the time dilation was caused by spin, but didn't explain frame dragging.
Hollywood "we need to get the time dilation within the realm of physics" Also Hollywood "The guy can survive in a black hole"
Technically, known physics breaks down beyond the event horizon, so it's possible they discovered models that allow for some kind of existence within black holes.
@@cpasr8065 The journey there might be a bit rough though 😅
Stephen Hawking said an astronaut wouldn't notice passing through the event horizon.
@@neilgerace355 Hawking radiation tells us that there must be a "firewall" just beyond the event horizon that will burn you to a crisp before you were pulled apart ("spaghettification") by gravity.
Really, there's just a lot we don't know about black holes.
I'd love to see the Doppler shifted version of Gargantua
right?! tell me if you found it!
The bigger problem with interstellar was the energy delta required for all these maneuvers. Who cares if an hour on the surface is 7 years, when it takes months to get there with those puny rockets. And where did you get all the rocket fuel from?
it's on page 27 of the paper they wrote: arxiv.org/pdf/1502.03808.pdf
I'm kind of sad that they didn't write it into the script. Like, they get there, and everyone is assuming that they're going to go toward the bright blue place, and the pilot says that that's a common mistake and they have to go toward the dark red place. It's like being on the highway: you want to see dim red lights ahead of you; if you see bright blueish ones, that's oncoming traffic. It would be bad filmography if it was just a visual and you don't go to the attractive place, but good filmography if the attractive place is a trap for the unwary. (I have a vague memory that they had this idea, but it was too late to implement by the time they saw the rendering.)
Adele Lopez awesome! Thanks
35:46 It is little physical properties like these, where the shape of something and the symmetry make it possible to cancel out a lot of tough math, that really makes me love physics
Ah, General Relativity. The most honored wartime general.
When I was an undergrad, I took a class titled "Spacetimes and black holes". It was an introductory course on general relativity, focusing on the implications of life in a curved spacetime. The interesting thing is that it covered in much greater detail stuff that more advanced classes on general relativity (like the proper "introduction to general relativity" I took in my masters) tend to skip over. In particular, they had us compute the GPS time dilation (and how neglecting to account for it would influence the triangulation accuracy) as a homework assignment. We also covered the bit about the no-time-dilation-at-see-level in class.
Actually, Nolan didn't bring on Kip Thorne, Thorne was one of the people with the original idea, which the Nolans turned into a script. Which explains why the plot is so physics-heavy :-)
Yes!
Kip Thorne and Jonathan Nolan wrote the original script together.
@@Hhhgdvbjkydxvdfgf Thorne came with the idea for a movie that deals General Relativity, Black Holes a Wormholes in the plot. Jonathan Nolan was assigned to write the script with the guidance of Kip Thorne with Steven Spielberg as the director. The project got cold and Jonathan Nolan just finished the first draft. Years later Jonathan Nolan offered Chris to be involved in the project. When Christopher Nolan received green light from the studios he rewrote the script and added and designed much of the concepts that deals with higher dimension objects (the tesseract), bootstrap paradoxes and I think the subplot that draws parallels with Heart of Darkness by Joseph Conrad.
@@foglias Yes C Nolan basically ruined the end of the film with that silly last act, which was the part he rewrote because J Nolan's end to the film was deemed to dark for Hollywood.
Raging S That's not at all how it happened. It's explained in the video. They left out some elements like the Doppler effect that would've messed things up visually, but largely the black hole looks how the equations said it should.
I'd add one talking about how people usually overlook the relativity part of relativity -- that both sides see the other as having the *exact same* time dilation/Lorentz contraction etc. And that everything still all works out without contradictions (as long as you're careful about the concept of simultaneity)! For me, that's the really amazing thing about relativity, and I wish it got more attention.
As a sub-mishap, the misunderstanding of the "twin paradox". The paradox isn't that the twins experience time differently -- that's certainly weird, but not paradoxical. The apparent paradox comes from asking how it can be that if both see the other as experiencing time slower, how can it be that one will actually be older when reunited at the end of the trip? Which leads into some interesting explorations of different inertial frames, but most presentations don't ever get that deep and it's a shame.
It's all down to the geodesics being the longest path, rather than the shortest path lines we are used to in Euclidean geometry.
Your exactly right that is where General Relativity gets it wrong, The GR mishap. That's what Einstien gets for forgetting Newtons' First Law.
Timothy Aaron Newton's First Law has nothing to do with this, and it is not contradicted by GR, but rather a consequence of GR.
Michael Dam Olsen Geodesics are the shortest path, not the longest.
@@angelmendez-rivera351 I'm sorry I meant Newton's 3rd law.
That lunatic grin of his while he does the demonstrations is just precious!
Yeah that was really well done. Like "This is is perfectly ordinary, people do it every day."
2:30 "everything i say is from here in is assumed to be in a vacuum. .. if i can throw a ball at 2 metres per second"
MIshap 6: basketball explodes because of vacuum
Not to be "that guy" but a standard basketball is already pumped up to almost twice atmospheric pressure, so all you'd have to do to deal with a vacuum would be to let some air out first.
Parker Relativity
Was looking for this comment, gg
Thanks for the likes :)
T-shirt with a Venn diagram - big circle general relativity and a small circle special relativity - I want one
"Spoiler alert: one of them is mine" -Matt Parker himself
Closely related to the Parker Square
Hopefully, this mnemonic will help with "mistake number 0":
General Relativity has a "G"; Special Relativity does NOT.
Here's a mnemonic that will help you remember the difference between mnemonic and pneumonic: mnemonic starts with an M (for "memorizing"), pneumonic does not.
(I mean this as a joke - I just had to use the opportunity)
EDIT: Before this comment was edited it said "pneumonic" instead of "mnemonic" - that's why I made this reply
When I was first learning it, my mnemonic was that (S)pecial deals with (S)peed, and (G)eneral deals with (G)ravity.
@@linearj2951 That's actually better!
Or the Parker mnemonic: Special Relativity is spelled with a V...
@@linearj2951 general, deals with acceleration.
So cool to see/hear a colleague VFX artist.
And yes the lens flare for example is so, important to sell the illusion That everything is shot by the same camera.
I worked on an indie film and I asked whether they’ve shot middle gray shots. And they were like: “what? Why?”. I said I need the noise pattern to overlay it on my set extensions.
The director was initially not really convinced that it would make a difference but since I’ve done several bigger productions he was like: “okay I’ll get it”. So I got some very shotty (poorly exposed) 50% grey shots cleaned them up and overlaid them on the shots and send them in for review.
The director was like: “wtf?!?? It suddenly doesn’t look like CG anymore! That’s just the noise pattern?”
Yup... CG is crystal clear and perfect, so I blur it based on reference frames to soften it but then it’s still static. Whilst everything is jittery on the screen because of the sensor noise or grain. You consciously don’t know why but you know it’s fake. And the reason is that lack of change in luminance because of the noise.
27:39 Oh BOY there's more? I forgot we were talking about relativity mishaps and I got completely lost in the world of spacebound IMAX and non-newtonian ray tracing... I was already expecting the outro and thinking about what to watch next, sad that the unbelievably cool Interstellar insight was over, when suddenly a wild Fact #3 appeared! Amazing video, keeping videos from being long and drawn out is a very valid concern, but when they're brimming with stuff like this one it's actually amazing to find a 40 minute video. A good example of each and every video being just like that is Summoning Salt, easily my favourite speedrunning youtuber (sorry everyone else who is still so cool), every episode feels like a full length documentary. And if I'm not wrong it's not a too far fetched association for this channel, in the Dream Stats video you casually drop that you sometimes watch speedruns, and I imagine many of your followers might be just as nerdish
Re: mishap -0: The insanely high orbital velocity is caused by frame dragging (the spinning black hole pulls the space around it as it spins), so it is general relativity that applies, as you can't do the frame dragging calculations from special relativity alone. So in referring to general rather than special relativity, the movie got it right.
Another consequence of frame dragging is that the orbit where time dilation cancels out relative to the surface of the earth is probably dependant on the orbital inclination, but since the kerr metric is a pain I don't know how big the impact is. (a back of the envelope calculation gives a factor of ~10^7 for the angular momentum correction relative to the orbital radius, so the difference should be around that order of magnitude at most, i.e. a few metres)
Interstellar did 2 papers about Black Holes. I think they knew, what they are foing :)
@@patricktho6546 foing, doing, fewing!
more pew, pew -- less foo, foo!
Math QUESTION
Factor higher degree polynomial
czcams.com/video/D99PASilPrY/video.html
See it one time..
Wouldn't frame dragging, i.e. staying put within a moving spacetime rather than moving through spacetime, exclude any relativistic effects? Like a warp drive? Or is that not how frame dragging does its stuff?
Woah, the fact that the dilations from differences in velocity and gravitational field perfectly cancel out... just mindblowing.
This seems like a pretty big coincidence. Is there some physics reason it has to be true?
Matt also specified that it applies at sea level, but presumably wouldn’t apply if the earth had slightly more or less water, or if the distribution was different such that it was the same quantity, but higher or lower.
I wonder how perfect is the perfect cancellation.
@@rbnhd Yes, it's not a coincidence. The 'surface' of the spinning Earth is defined as the surface where the centrifugal force + gravity is constant, which is called the geoid. This is the shape the Earth will naturally take, since it is really nothing but a rocky fluid that wants to reach hydrostatic equilibrium.
I find it hilarious that Interstellar hired an expert and the first thing the crew did was to demand something nearly impossible to be worked out for the sake of the film.
But they could claim that an expert approved.
that’s showbiz baby
"nearly impossible" is the key. That means that it is actually possible, however unlikely.
A thing I love about Raytracing, is that as is said it works in most cases by bouncing rays from the point of view outwards, which mimics early ideas on how our own eyes worked.
The thing I like about raytracing is that not only are you bouncing the rays from the point of view, but they have to also all end at the point of origin (the light source)
I'm too lazy to do it, but I hope someone does the math to figure out how much time dilation Matt's hands experience relative to his head in this video.
4.
@@honorarymancunian7433 So his hands were moving at sqrt(15)/4*c (0.96824% of the speed of light)!? I'm surprised he still has skin.
@@honorarymancunian7433 I highly doubt it
let's say his hands move at approximately 1m/s relative to his head, then the time dilation is sqrt(1-(1/299792458^2)) = 0.999999999999999994436. If he talked constantly from the Big Bang to now, he would be 13.8 billion years old and his hands would be 0.999999999999999994436 of 13.8 billion years old, so 2.42 seconds younger than him.
@@aman-qj5sx I find your lack of faith disturbing.
I really wished I had the chance to explore these topics in more detail back in Uni. Maths and Physics both were of interest, but I had to be silly and go off in the realm of music.
I'm super grateful of videos like these that help clarify basic misunderstandings of these topics (many that I probably have had in my half-hazard efforts of learning it afterwards!)
So you're into "string theory" 🎸
Isn't it haphazardly? Or can you say half-hazard too?
Hey, man. I got an EE degree, and I regret not minoring in music.
TBH even in physics you only get into General Relativity in graduate school, and even then only if it's relevant to your research. I'm getting my PhD in physics and I probably won't get to take a class on General Relativity (although you get lots of special relativity even in undergrad).
If you think about it, maths (eg the Bach family) & physics (obv for stringed instruments but for other instrument designs too) have a /lot/ of influence on music & instrument creators, even if they didn't realise it while working: don't put yourself down so much :)
Hearing you both dig deep into the physics of Interstellar and the compromises between the science and cinema was my favourite thing I've seen on CZcams in a long time! One of my favourite films and that's the kind of discussion I was hoping for on the special features but they went nowhere near as deep as you guys.
My man, you are a frighteningly charismatic educator and math/science communicator. Never stop creating content!
The great circle pun at 34:05 is so subtle and simple, yet so amazing...
Matt Parker, you absolute legend.
I learnt about the time dilation equations in year 10, and I'm only just now learning how they were formed... That light clock train example with pythag just made everything click so beautifully in my head and now I feel like when I look at that equation I actually understand why it is what it is instead of just having to memorise it. Thank you Matt, you are the teacher we deserve, and also the one we need 😁
The explanation about ray-tracing in reverse because you don't care about the light that doesn't hit the camera was badass and threw me into a crazy mindloop that I knew it was true and now I had to work backwards to think about how it makes sense when I'm playing a game or watching the movie. Awesome.
That's just how regular ray tracing is done, you project from the screen to the surfaces and calculate the reflections based on that (to some arbitrary limit of number of reflections) and how much each surface contributes to the pixel color. You don't start from the light sources because it would be very slow.
Also in the vein of confusing special and general relativity: People know that "quantum mechanics is incompatible with relativity and the solution to this will be the Theory of Everything", but it's actually general relativity only, not special, that has this problem. Quantum mechanics is usually expressed via the Schrodinger equation, which uses the Newtonian definition for momentum, but the Dirac equation covers the realm of quantum particles moving at relativistic speeds.
Because at high energies a one-particle theory doesn't make sense anymore...
Ha! Got you! The Earth isn't an oblate spheroid - it's a geoid. Literally meanining - "thingy that looks like The Earth".
"What shape is the earth?"
"Earth shaped"
@@seabassthegamer6644 And it's not shaped like the GPS reference geoid, that's a different geoid than the real geoid.
@@hammerth1421 Thanks for bringing that up. The geoids used in navigation (like the WGS-84 geoid) are very definitely different from the literal shape of the Earth. I believe the WGS-84 geoid is defined by gravity, not by the actual rocks and such directly. So, it is definitely Earth-like in shape, but intentionally different from the actual Earth shape in the details.
@@doctorbobstone don't forget that the "shape" of the gravitational geoid is not the same shape as the physical geoid due to density effects causing gravitational anomalies (the presence of which is used to help prospect for oil, etc.)
Chris Sloan What you are talking about is a non-topographic geoid, or smooth geoid. A smooth physical geoid is different from a smooth gravitational geoid, which is also different from the literal shape of the Earth, which includes its topography, and which is ot even really a shape, since it is constantly evolving chaotically.
Aww that's so awesome that you interviewed Eugenie in such detail! Usually, people don't really care about what goes into VFX...
It's interesting to see that many people did terrific calculations of what happens when a starship orbits a black hole, but no one seems to care about the strong tide effect that would instantly destroy anything close to it, including the ship and its passengers.
Yeah, the ship launches with a two-stage rocket and takes 6 months to reach the wormhole, but once it's through...
Suddenly it was Doctor-Who-style sci-fi, where the rules bend to what the drama wants.
@@NicD doctor who sci-fi is very fun and fantastical, and it goes more indepth in the expanded media as to how the mechanics of that universe function. and it is all completely rubbish scientifically, but fun nonetheless.
The tidal effects around a supermassive black hole are actually pretty small as being outside the event horizon puts you quite a distance from its center (no matter how close you get without falling in, you're still in pretty much a homogeneous gravitational field). It would be a problem around smaller black holes (on the order of 10s of solar masses), where you can get close enough so that the inverse square law makes a large difference over the distance of the ship/passengers' size
For anyone wondering, the reason why we don’t put satellites at the Time Dilatopause is that 3,000 km is in the heart of the inner Van Allen belt.
Thank you.
Van allen belt?
Also, you want the GPS satellites to be geostationary, which requires specific orbits.
@@xxFxDx GPS Satellites don't orbit at geostationary, though that isn't an unreasonable guess. They have semi-synchronous (12 hour) orbits and they're in 6 orbital planes of 55° inclination, with at least 4 satellites in each orbit. This makes sure that every place on earth can see 6 satellites at once for accurate location. There are currently 31 operational satellites with 7 more available to use as spares, which gives the current system extremely high accuracy (30 cm/1 ft resolution)
@@Wyvernnnn The Van Allen Belt is basically where the solar wind gets trapped by earth's magnetic field. Solar wind is a lot of charged particles and a radiation hazard. It's not a problem if you only briefly fly through it (Apollo astronauts, satellites going up to higher orbits, interplanetary probes, etc) but if you keep something in that orbit it's not gonna like it.
One mishap that this video actually fell for is that Matt claimed that once you transition from special relativity to general relativity, you begin to work with 4-dimensional spacetime. However, this is not correct. Special relativity already uses 4-dimensional spacetime. Specifically, it uses a Minkowski spacetime, which is a type of 4-dimensional vector-space which is hyperbolically flat, described by a pseudo-Riemannian manifold. The distinction between special relativity and general relativity is that special relativity assumes Minkowski spacetime, which is hyperbolically flat, while general relativity does not actually assume any particular spacetime.
Special relativity did not originally come with Minkowski spacetime, though; it was only subsequent papers that showed how they were connected. By contrast, you couldn't describe general relativity without (Riemannian) spacetime.
9:36 made me crack up. The editing and production of this channel is absolutely awesome, and hilarious
Fantastic! Thanx so much. I_ll use it in my course on SRT/GRT for the Physics-Teacher Study program. We're in lock down, so this kind of material is truly valuable these days …
Minute Physics has a fantastic series using a "time globe" that explains the time/space change and does it beautifully.
I was hoping for mishap number imaginary zero. Maybe another time.
Math QUESTION
Factor higher degree polynomial
czcams.com/video/D99PASilPrY/video.html
See it one time...
@@mr.knight8967 STOP SPAMMING
IMAGINARY ZERO IS ALSO REAL 0 I GUESS WE NEED CUBE RUTE OF ONE IN IMAGINARY PLANES
I've often wondered about the two different time dilations for satellites, and now I understand it much better. Thanks Matt!
There are lines on topographic maps called contour lines which connect points of equal elevation. The surface of the Earth is a "contour surface" connecting points of equal temporal dilation. This is the coolest thing I have ever learned. Thank you, Matt!
34:09 I've calculated the latitude of that guy near "let's say, the North Pole," based on his 1/4 speed compared to the equator guy, as ~75.5225° (assuming spherical Earth). I've looked around and there is Mount Parker in Nunavut, Canada (76.83506°N 93.75133°W) in the northern hemisphere, and also Parker Pass, Antarctica (75.88333°S 142.8333°W) in the south.
BTW: It seems to me that those speeds might not be correct. Looks like you have computed them from 40,075 km circumference and 24 hour (solar day) rotation period, which corresponds to roughly 361° rotation. I think you should have used sidereal day (23:56:04) instead, because that represents 360° rotation. Are those _relative Parker speeds?_
that's fab - well done Zheeraffa
Listening to minute 8:11
People in 1905: "Oh, Einstein is so powerful !"
Einstein in 1905: "Well, that's not even my 1%... I'll give you 11 years to prepare"
Almost 100 years later and the overwhelming majority of humanity still not ready.
Math QUESTION
Factor higher degree polynomial
czcams.com/video/D99PASilPrY/video.html
See it one time. .
Lets not go with the "ten percent of the brain myth" please, its nonsense.
en.wikipedia.org/wiki/Ten_percent_of_the_brain_myth
This is by far the best explanation of time dilation I've seen. Thanks so much!
That last bit about sea level and time dilation is just brilliant, thanks!!
Okay, so, if Kip Thorne says your equations are complex, you know you're in for a hell of a time.
Just don't let him go home until he spits out all the equations.
Good thing we now have algebra softwares, they help a lot for making complex derivations without mistakes in a short time. Of course you still have to know what you're doing and understand the results.
The first few minutes was the first explanation I have ever seen in my life that made me actually understand time dilation.
Loved the interview with Tunzelmann !
amazing video as usual matt! i get so much inspiration from your content to make my own videos, thank you :)
Fun fact about General Relativity. Within it are what are called the Einstein field equations. Einstein himself could not solve them exactly; he had to approximate. He said that it may take years, even decades for someone to solve them without approximating.
Then Schwarzchild did it the next year for non-rotating uncharged bodies.
Math QUESTION
Factor higher degree polynomial
czcams.com/video/D99PASilPrY/video.html
See it one time...
Fun fact: the appolo guidance computer actually had -0 programmed in! Keeping the instruction codes symmetric.
Wait... You mean like if we would plot the integer number line on that computer it would be ...-2,-1,-0,0,1,2...?
If you want a binary representation of integers, there are two ways, one's complement and two's complement. One's complement has the interesting property that it allows for zero with the sign bit set, thus negative zero is a valid number (it is actually represented by all 1s). Two's complement doesn't have any similar option. It just ends up with one more negative number than positive. Almost all machines use 2's complement now. It need not be so, and in the early days of computing wasn't.
@@Morrvard No.
@@francisvaughan7460, And 9's complement is the decimal equivalent used in old calculators en.wikipedia.org/wiki/Pascal%27s_calculator#9's_complement
Modern computers also have -0 as a "real number" (actually, floating point number)
This videos keep getting better and better ☺️!
Dude, your so awesome! I accidentally bumped into this video and it's the first CZcams subscription ever for me.
Lots of Christopher Nolan movies play with time.
Memento? Christoper Nolan movie about someone who cannot form short term memories so is told backwards.
Interstellar? Covered in this video.
Dunkirk? 3 intersecting stories about the evacuation of Dunkirk. A week long, a day long, an hour long. All culminating in the finale of the movie.
Inception? Pushing into deeper layers of a person's subconscious, each of which has time running slower than the layer above it.
And if you think it ends there, his older brother, Jonathan Nolan, yeah, he's Westworld.
You want movies with time shenanigans, look for Nolan, press play, enjoy.
As a physicist and a movie nerd, Nolan is the best, my favourite director of all time
Where's TeneT?
"... It is a mess." - such an understatement. Took a undergrad GR class once and entire class was suffering just to derive the damn equation, while the professor giving signs of disappointment. Hahaha
This is so relatable it's not even funny.
Just because a scientific theory or set of ideas requires hard work on the part of the student does not mean the theory is a mess. Some GR courses spend the whole semester proving one equation, namely the Gravitation Field Equation and those students who fail to see the journey and only consider the destination have missed the point of the course.
@@stevehodson2613 I think you misunderstood me. By mess, I mean hard, not that it doesn't make sense. Apologies for the wording. But yeah, GR is something that is really hard and deriving it such that you can have an intuition on "what is actually happening" is even harder, which I call a mess. It all makes sense mathematically, but just as QM or QED, sometimes it's just mathematically perfect but a mess intuitively.
Again apologies for the wording.
Thanks!
@@mgmanzanillo thanks for clarifying but I have to disagree. My issue here is on a channel about educating the public in science to call a theory a mess is not only not accurate but pedagogically false. You and others may feel that the concepts of GR are weird, would you say that these concepts are messy? I wouldn't. In fact I would say that I need a more open mind to accept notions of the natural world that do not fit my immediate experience. Based on my subjective experience of GR would it be legitimate of me to conclude that GR is a mess based on my inability to have that open mind? I don't think it would be a rational response to seeing or experiencing something new for the first time to describe it as messy. Describing GR as messy does not say anything about GR itself but, and this is my criticism when it is used in the video, it does no justice to the theory and cements its reputation as being impenetrable.
@@stevehodson2613 Three points.
1. I did not say weird, I said it is hard to get an accurate intuition of how it really works. Those are very different, weird is something that does not make sense, and 'hard to have an accurate intuition' means it's hard to have an intuition (I can't simplify if further lol). Speaking of intuition, going on...
2. It's not really about having an open mind. Having an open mind helps but at the end of the day, it's skill that carries you forward. Your skill to understand equations allows you to have a more accurate understanding of what is happening because you can put a ball on a cloth all you want and say 'the cloth is like spacetime...' does not make you understand really what's going on.
3. Yes, you are allowed to call something messy based on your opinion. Of course that only goes a far as your opinion matters. As for me, it is messy, it is difficult (and I took a semester of classes for it) . And for the vast majority people, it is difficult and messy. Like even the people my fellow students who did not take that class, if I were to show them the derivations, they would say it is messy and difficult. Of course, if you did a PhD on the subject, the basic derivations you are doing at class will be child's play, but at the advanced GR problems they are tackling, I bet they would still consider it difficult. And that's why I don't consider Matt saying that "it's a mess" means that GR is impenetrable. It just means it's really difficult. Furthermore, for people me, it is just challenge waiting to be accepted. People who would not care, would not care, but people who do, would just think it funny because it is a challenge, a challenge to understand it. Unfortunately, even after taking a semester on it, I did not have the skill to have a intuition for it, I got the math/s right, but not how it really works. And that's fine...
Pardon for rambling.
Thanks!
So happy to hear about the liberty taken in that part of Interstellar. It always bothered me that the time dilation could be that huge, without them being swallowed by the black hole. A friend insisted that it was correct as Kip Thorne had worked on it. I guess this means that we were both right in a sense.
Absolutely fascinating. Thanks for making this video.
9:43
14:58 Proceeds to make the exact error he just told us about.
If General covers Special, then the film made now error by saying it's due to General Relativity.
He does specify gravitational general relativity
I thought that also!
Context
MP is speaking in a vacuum, so this must have been dubbed.
Nope, he uses pulp sci-fi cameras and microphones. You know, the ones that can hear lasers?
@@MonkeyJedi99 Which means he has enough air in his lungs to say everything in the video _and_ is doing all this quickly enough to not explode while the camera's still running. *Hmmm...* 🕵️♂️
Math QUESTION
Factor higher degree polynomial
czcams.com/video/D99PASilPrY/video.html
See it one time..
I like how this vid is not even about explaining relativity but it explains it better than any video I've ever watched!
Okay so this video was the best explanation of relativity theory by far I've come across! good job matt
Was expecting a Eugene guy with a bald head in his later years. Got a Eugenie with a stunning beauty and interesting anecdotes.
Was definitely not disappointed 😃
Same here ^^
Hahaha me too. An older guy with a beard :))
In Russia name Eugene is unisex.
14:59 I'd say quite a lot of frame dragging is involved there, so General Relativity works fine in that context
I had read before that the time dilatopause occurred miraculously at sea level awhile and was typing a comment about that until you had mentioned the finalest point about how that sort of idea is specifically about the gravitational "isosurface" matches sea level instead.
got an even better clarification than i bargained for
I love that this works, and the maths checks out and the experiments check out, giving us a universal constant to build our understanding of everything else.
Also, i think thia would mean that even if we could travel as fast as light, the closer you get to it, the longer it would take to seemingly get there and suddenly, yum, blackholes and revelations.
I'm not smart enough for this to be anything other than ASMR when I'm trying to sleep
I love Matt because if you follow him you get unnecessary details as much as you like.
Ain't no such thing as unnecessary details. Ask Bletchley Park or Apple.😉
@@Biosynchro oh there is. But all of them are necessary :)
I laugh when I see Matt Parker’s face. I don’t know why! He’s got a hilarious mannerism. 😂😂😂 really enjoyable content.
I LOL'd when you said "So... we're neck and neck." Loved the video, and that is the best explanation of Sp vs Gen relativity I've heard. Thank you!!
i never understood why time dilation is a thing until seeing your animation, now it makes complete sense. it's still weird, but makes sense. also this is a comment of unnecessary nit-picking but i'm not convinced referring to Einstein as 'they' is necessary
Yeah his use of the singular they in almost every situation throws me off sometimes
@@Eidolon2003 it's almost certainly deliberate, and thinking about it I'm struggling to think of a reason not to do it, so long as you do so consistently you avoid a bunch of problems (some bigger than others)
@@SimonBuchanNz I don't have a problem with some people wanting to be called they, but getting rid of the singular pronouns entirely makes the language more ambiguous.
'They' is not necessary at all, and is in fact annoying. Einstein was a man, we should refer to him as such.
The animation also helped me understand it better!
Bring out your spherical cows! We're doing examples!
Thank you! This is exactly the explanation about time dilation in speed vs. gravity-well I didn't understand.
watch some roger penrose, never ceases to amaze. a photon can travel from the time of it's "birth" to the "end of time" and it takes no time at all. stuff moving at the speed of light experince zero time passing.
8:40 i got here from a veratasium video explaining (!) that gravity doesn't exist, it'll be a few minutes before i get that notion working in my head.
17:00 double negative is one of the few visual effects houses i haven't worked for, although i do know people there. :)
36:00 i caught out de grasse tyson saying that if you shrunk earth down to the size of a baseball it would be perfectly smooth, if you can see shadows then at any size it will not be smooth. but the fun fact is that not only is earth oblate, but slightly pear shaped too. although i've only seen that one video as source.
Interstellar is still absolutely legendary. But hey, even though unlikely that the black hole could spin that much, with nearly infinite opportunity, never say never. ¯\_(ツ)_/¯ 🤣
This is a great video Matt!
The supermassive black hole at the centre of NGC 1365 is reportedly spinning at least 85% of the speed of light. So yeh.
"The black hole had unhelpful cinematography." 😂
I remember figuring out the orbit radius of the "dilatopause" as Matt calls it awhile back. I don't recall exactly how I did it but I'm pretty sure I just tried to see where the equations for the Lorentz factor (subbing in the formula for circular orbital velocity for a given orbit radius) and the equation for gravitational time dilation matched up. Glad to know I came up with the right answer (1.5x the radius of the body).
This was one of the coolest videos I've seen in a long time
"easy and difficult are themselves very relative" I saw that coming from quite far away, but it didn't soften the impact.
Please keep punning.
I just want to take some time to appreciate the phrase, "The Dingy Side Of The Black Hole."
Beautiful.
It's what Pink Floyd's next album is going to be named
Okay the oblate spheroid/time dilation thing blew my mind. I did not know that. Great video!
Either read or watch Kip Thorne's presentation on "The Science of Interstellar" to hear straight from him what assumptions were made, how he did the calculations, etc, it's good to hear straight from the relativity expert himself!
Comparing himself to Einstein based on the mistakes he made is a classic Parker Peer Relationship.
Yea, Matt Einstein, we are looking forward to the great theory YOU will present in ten years ;-)
They're a regular Parker Einstein.
34:06 "some would say a GREAT circle" hehe, geographical nerd joke. Also, at 29:47, some nice logo's you've got there
That's first a geometrical nerd joke, and only second a geographical nerd joke.
Great circles are the generalization of the line in noneuclidian geometry, the use of the term in geography comes from the fact the geography deals with spherical geometry.
I thought I was the only one who noticed the logos...
recently I watched a video about how the effect of gravity is observed due a gravitational gradient tilting the 4-velocity vector of an object in that gradient away from the increasing-time-axis.
from that information it immediately follows that surfaces of equal gravitational potential such as sea-level exactly cancel out the effects of special relativity and gravity since it doesn't matter which source caused the gradient of time dilation. Thank you for pointing this out since this example helped me understand this interaction. mind = blown.
What a terrific episode! Thank you.
Strike that. A SUPER episode. Subscribed!!!