Civilizations at the End of Time: The Big Rip
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- Current science and cosmology tell us the Universe will slowly die and ebb away countless trillions of trillions of years from now, but another model - the Big Rip - says that end may come far sooner, ripped apart by dark energy. Could civilizations survive the Universe itself being torn apart at the atomic scale?
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Credits:
Civilizations at the End of Time: The Big Rip
Science & Futurism with Isaac Arthur
Episode 326; January 20, 2022
Produced, Written, and Narrated by Isaac Arthur
Editors:
Darius Said
Yamagishi
Cover Art:
Jakub Grygier www.artstation...
Graphics:
Jeremy Jozwik www.artstation...
Ken York of YD Visual / ydvisual
Udo Schroeter
Music Courtesy of:
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AJ Prasad • Dark Future - Staring ...
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What's even stranger, is that even though an infinite three dimensional space is, intuitively, much larger than an infinite one dimensional line, Cantor showed that, nonetheless, they both have the same cardinality. In fact, an infinite three dimensional space even has the same cardinality as a finite line. To quote Robert Kaplan, "there are just as many points in the infinite universe as on the horizontal bar of this T."
Infinity is weird.
@Michael Bishop Power sets are not related to my point, but yes, 2^(aleph null) is a larger infinity than aleph null.
@Michael Bishop Yes it is. The notation is not related to exponents, but is used because the power set of X is bijective to the set of all functions from X to a given set of two elements. (A one-to-one correspondence.)
We can just call it the "set of all subsets" if you prefer. Or just P(X). Any notation is fine.
Yeah, like the infinite density of a black hole's singularity or the theoretical " Hilbert Hotel " with infinately many rooms, potentially infinite universes in the theoretical multiverse, etc.
I believe when Cantor discovered it he is suppose to have said "I see it, but I can't believe it."
@@justin_5631 You are correct. "Je le vois, mais je ne le crois pas." In a letter to Dedekind. I think I'm inclined to agree with him.
What a joy it is to return to this series. This was the series that got me hooked on your videos, and your signature style keeps me coming back for more. Stay awesome Isaac.
Same for me! Love these I think my first ever video of Isaac’s was Iron Stars a few years ago, now I listen all the time
same here, i'm following since black hole farming
that was such a lrvel up compared to the recycled documentaries about space i was listening to, to fall asleep back then
All universa and all dimensions will be absorbed into one Empire! All will be connected! All will be inside! No outside anymore! All will be unifyed and connected to the machine, mother machine! All over is centre! All are Chi-Borgs! Alpha Omega Minorah Karma.
I love how you spend the time to add captions. I use them a lot for making sure I catch everything or know how to spell certain words or names for me to look up later. It’s also great for times when the area around me is noisy, which is often. Thank you!
The funny thing is he puts in the closed captions because *he thinks* he has a really bad speech impediment and people have trouble understanding him. I thought it was just a local dialect. We have so many different regional dialects in the United States. Good to know somebody's benefiting from his self-consciousness.
@@freeamerican2708 exactly!! let me tell you english is not my first language and over the years i’ve had to stop watching lots of videos because i could not understand a single word. isaac arthur to me is perfectly comprehensible i don’t think i’ve ever been confused listening to him even without captions!! (except when he throws in super scientific terms that i didn’t even know existed)
@@doublethenun I definitely had a little bit of trouble understanding certain words when I first started watching him years ago. I'd have to pop the captions on, see what a word or two was, then turn them back off. But after probably like the 3rd or 4th video, I never needed them again.
@@davecarsley8773 Ditto! I binged the old Upward Bound series while working on a pool and had to rewind a few times to make sure I heard him right, but by the end of the playlist I really stopped noticing.
I use the captions because of my lackluster hearing. Whatever the reason, they are much appreciated Isaac!
Math Note/Correction: As of the moment I've got 4 different contradictory explanations of why some of my comments on adding infinity this or that way, or how many numbers are in between 1-2 compared to total integers, is wrong or badly phrased. Everyone seems content with the overall explanation where it's relevant to the video, thankfully - An infinite Universe can still expand and infinity isn't a number - but needless to say, take that infinity math with a grain of salt :)
For everyone offering corrections on it though, please try to keep the explanations where someone who isn't a mathematician might have a chance to understand them or otherwise link to some page where someone does give such an explanation. And while you are welcome to call me an idiot, please do not call other commenters on the thread idiots just for saying your answer didn't make sense to them.
Edit: Also, yes, I am kicking myself for not thinking to make a R.I.P. joke on the the Universe dying by the 'Big Rip' :) Can't think of every good pun.
How difficult is it for everyone to be civil while explaining things they understand but others don't? Just imagine how hellish your life would've been if all of your teachers yelled at you or called you names all the time while teaching?
Didn't somebody famous once say "If you can't explain it to a child you don't understand it well enough." (paraphrasing) ;)
I can forgive you claiming that infinity+ number = infinity but, other infinity, while it is the same infinity (the same as when you will multiply it as well), which then would explain on it's own that you can expand or contract infinite things into still infinite things, BUT your discussion about energy conservation and problem with dark energy is worse.
Energy is just a number. It is conserved in closed systems (or through the Noether's theorem due to symmetry to be precise). The universe does not need to be closed system. And the symmetry needed for the energy being constant is not valid. So energy is not constant in the universe. Just like that. It is constant (conserved) on small scale, or as long as some issues (dark energy) do not arise.
Edit: After a moment it is getting better, as there is more info about energy from other places, so kind of open system approach. And this is only like 3rd of your episodes that I had issues with your explanation being false and unscientific. So just small percentage of quite specific field, while much, much more is just awesome!
@@sagarj5743 Apparently fairly hard for some folks :) though I should emphasize most folks were polite, there were just a couple bad ones thus far, one that needed deleted, and I figured I should slap the reminder on there as for many that's all it takes.
@@junorus I appreciate the forgiveness, but you seem to be saying I was claiming Energy is absolutely conserved when I flat out said that was probably not the case. I think you should re-watch that section, though here is the text of the transcript if you'd like to highlight what statement is false.
"One of our laws in physics is conservation of energy, that it can be neither created nor destroyed, merely changed in form. However, spacetime itself takes energy to exist, so when new bits of it get added, that takes energy, energy that doesn’t seem to come from anywhere, hence why we call it Dark Energy, dark in the context of being mysterious in function and origin. Amusingly while Conservation of Energy is often stated as ironclad law I doubt anyone is still living who actually learned that law while physicists believed it was without exception, as its been about a century since the Big Bang and Hubble Expansion hit the scene"
im never this early for an isaac arthur video and ive even already got a drink and a snack ready!
Gotta be a great feeling!
One thing other TH-cam celebs could learn from Isaac is that of engaging with their fans. I've left about a dozen comments on his Patreon forum and I am pretty sure he responded to all of them. Part of the reason I upped my support.
just when you thought you had enough existential crises to worry about
Isaac: "time might drain out of the hourglass and leave the Universe in a frozen instant"
nice
I started learning to fly last year, and would be thrilled to see some one else go through it. Too few people take advantage of the fact you can just go to an airport, and learn to fly. It changes your perspective on things in so many ways. You never see the world the same way again.
Very true the firsttime i took a small plane up into the air and saw my town from above . Mind blowing
I love these brain-stimulating videos, Isaac! Being buried in the world of meteorology, I sometimes forget to let some out-of-the-box thinking soak-in. Also, I once again must compliment you on the excellent lead-in your sponsor at the end. Perfectly executed! Thank you, as always.
For some reason, i love to watch these videos while working out. I dont know how many times I've heard you talk about space travel or speculative sociology while pushing my muscles to their limits. Thanks Isaac
4:40 - 6:40 This segments has a lot of errors in it.
It's true that there are different size infinities, but ∞+1 is still ∞. A good way to compare two sets by size is to try and match up their elements in pairs, you can match up ∞+1 and ∞ with (0,the additional element)(1,0)(2,1)(3,2)(4,3)... we say they're still the same size.
The set of real numbers is indeed bigger than the set of naturals, but with a Hilbert curve you can map all points of a plane on a single line, ergo they're the same size of infinity again. iirc Hilbert curve works for 3d space as well, so again it's the same size of infinity.
Most of this is just semantics, and not really relevant to the subject, so it doesn't invalidate the video or anything, but I don't want people to get the wrong idea.
Glad to see that this section hurt someone else's brain enough to force a long comment :-)
If you want to understand infinity, your best bet is to take a Discrete Mathematics course, wait until your head stops hurting, then take the course again. :)
I wanted to make that exact same comment, but luckily checked if somebody has made it already. Thanks.
For anyone interested, vsauce's "how to count past infinity" video is a much more accurate treatment of comparing different infinities.
I understand almost none of the science or logic and yet I love watching videos like this.
I love the graphics this is a great channel, thanks for closed captions my phone got wet and I can't afford to fix it for a while.
I wonder if civilizations could exist over such immense timescales. The longer they are around, the longer the opportunity for bad actors to arise bent on destruction. Or for the unintended consequences of a decision to result in annihilation. I don’t think you could ever be certain a civilization has escaped the Fermi bottleneck.
Thank you for confirming an idea I had in college was reasonable - namely that big rip + quark pairs would generate huge numbers of additional quarks. I brought it up to a professor of mine and he dismissed it saying that they would simply get redshifted into oblivion but that never really made sense to me. How could something get redshifted in its own reference frame?
You should do a video on if we encounter a civilization that is technologically behind us, i think it would be very interesting to see the script flipped
Primitive aliens, maybe?
@@isaacarthurSFIA YES! Perhaps we could uplift them Stellaris style.
I've thought the same thing b4...nice to read it from someone else
@@wofuljac uplift ? and then...umm...ill just say that mine and your Stellaris playthroughs are not the same. ;D
you mean like dolphins
One of the best channels around, I have always an extremely hard time listening to any science based channel because it's
A. Some talking in such simple terms that it feels like I am being talked down to by a "more enlightened individual."
Or
B. A PHD level course in video format with no explanation on anything not directly related to the topic no matter how important.
Your videos fit neither, they are articulate in simplification of what I can assume are highly complex and difficult topics in a way that anyone can understand. All the while making the simplification of said topic have no trace of that talked down to feeling.
that's what's called a teacher i think
I think it varies from your own understanding level a lot, putting aside the quality, as some people goes along with some kinds of language more than others.
I could recommend The Science Asylum or PBS Space Time as both are awesome channels about science to me, but someone else could easily put them in one of the 2 cited categories.
Anyway, I enjoy a lot how Isaac expands to the science-fiction universe with very regards with the science in it.
I love Thursdays !!! Thanks issac, grabbing my popcorn now
The discussion of infinite around 5:00 differs from current mathematics. We compare the size of infinites by proving whether there are or cannot be one-to-one functions between them. We've proven the countable infinites to be less than the uncountable ones (see Cantor's diagonalization), and certain categories are equal. In particular, the sum of irrationals between 0 and 1 is equal to the sum of irrationals between 1 and 2; even though one would seem to be twice the size, doubling an infinite does not change its cardinality.
23:00 that would be a crazy possibility, ducking into a black hole to escape the end of reality
Minor correction. The notion of different ordinalities (where infinity + 1 is not infinity) is not the same as the concept of cardinality (where infinity + 1 is infinity). These are very different properties of sets and they require different assumptions.
In standard definitions of the real numbers and the extended real numbers, there is no such concept that differentiates infinity + 1 from infinity in any way. To have a meaningful distinction between the two you either have to use a nonstandard definition like the surreal numbers or you need to restrict your discussion to natural numbers (nonnegative integers). In that circumstance, if you have a certain kind of ordering (definition of something being “greater than” another thing) then you might be able to make sense of the concept of infinity + 1 being distinct from infinity.
This usually done using what is called the successor function on numbers represented as sets. Usually the empty set (the set of nothing in it, or the set of even primes greater than 7, etc.) is defined to be 0 and we define the successor function to be the function that takes a set and adds the set itself as an element. We end up calling that output the next number. For example, 1 is defined to be the set that contains 0 as the successor function takes the contents of the empty set (all 0 of those elements) and adds the empty set itself as an element. This means that 0={} and 1={0}. Likewise, 2 is defined to be the set 1 along with the set 1 itself as an element. Meaning that 2={0,1} (the set of the first two natural numbers). These are called ordinal numbers, the finite ordinal numbers.
This process continues ad infinitum. However, we have a notion of greater than built into this definition. We can say that a number (a set) is greater than another if the latter is an lament of the former. 0
Super-excited to watch this, let's go!
When redshift was first discovered and explained, was there a discussion whether it's caused by time acceleration instead of the expansion of space?
Probably, but we are only now catching up to their questions...
Sorry, I'll show myself out.
Expansion of space, known as Hubble's Law (en.m.wikipedia.org/wiki/Hubble's_law)
You are in your element here, because you are especially good when working with huge scales, particularly scales of time. Iron Stars is my all time favorite episode, this was a delight too.
Also my all time favorite...must have watched it 9-10 times
Just bear in mind that if it takes ~10^1500 years for iron stars to form, there are usually on the order of 10^1400 years before each *single* fusion reaction happens between two or three nuclei. Even taking into account slowing down computing to speed up subjective time, that's taking it a ways too far. Something like 10^1300 black hole eras of time would go by between each of those fusion events. Way too slow for most concepts of supporting civilization.
You my friend need more subscribers. Your videos are a true work of art. You have taken my curiosity and answered the questions that come along with it. Keep it up man
I don't get why or how, but your videos just keep giving me story ideas - so many story ideas!
Isaac, THANK you!
Brian Egan's book "Diaspora" has a fun take on this idea.
Yet another informative video. Learned quite a bit for this topic is not something I looked at that much.
Great episode. Weird to think that a time machine that could travel forward just a few seconds could potentially be such a game changer.
Your videos are so good, the narration, music, visuals, scripts, and conceps all come together to make for a great time!
Isaac addresses all the questions I've ever had about the universe and has introduced me to so many more topics. Isaac conceptualizes the processes in which all of these fantastical ideas would theoretically function. I predict a lot more videos once JWST starts beaming back pure GOLD! Also, thanks for your service. 12B OIF/OEF
Isaac Arthur just explained how we can prestige existence into a new game plus. If we break singularity in our lives, perhaps we will all be infant gods in our own universes. If that doesnt send a shiver down your spine, I dont know what would.
Coincidentally, "Big Rip" is what I call my civilization-ending flatulence
Ahahaha! Didn't take long before someone made a fart joke.
I don't comment a lot but these long videos are awesome. Brilliant work as always.
I think the idea that energy cannot be created not destroyed is a large assumption considering how little we really know.
As a private pilot and fan of your stuff and a lot of TH-cam pilots I’m all for you making flight videos as long as you’re being safe about it, of course :)
Awesome! Thank you!
Love this channel. Just love it.
I'd be interested in hearing more about using dark energy for power production. In principle, could that work even at current dark energy levels? If conservation of energy isn't exactly true, maybe perpetual motion isn't exactly impossible.
Being the most advanced civilization in the universe's history, maybe they can just create the beginning of the universe, answering the question of where it is we came from.
I've been thinking lately what we know as black holes are more like boundaries of spacetime of differing densities. Our observable universe would be bound by the behaviors associated with black holes. For example, black holes have a formation period, followed by expansion and eventually slowly contracting. Hawking showed that black holes can absorb and emit radiation, which is how they grow and shrink. So if we live inside a spacetime bubble, a black hole, we could expect the universe to expand through hawking radiation. This radiation bleeds through the boundary and transforms into both space and time. A large black hole has a longer lifetime than a small black hole. A consuming black hole is increasing its lifetime, so it's possible we live inside a black hole that is consuming matter and expanding. The grand universe is comprised of cascading spacetime bubbles
I for one would love to see longer video's not short one's...love this topic Isaac
It must be a great feeling knowing you have a vast fan base, that your content is informative and well constructed and that you're providing free knowledge and story telling on a platform that people use for mostly mind numbing content.
Thank you kindly.
Great, another video I will watch literally hundreds of times while falling asleep. Cheers
"Infinity is not a number."
"Infinities can be vastly different in size."
"The universe at the Big Bang was already infinite in size, we're just expanding into a bigger infinity."
Isaac, I'm just an engineer; you're making my brain hurt! Can't we talk about tensile strength of nanotubes?😁
I see that others have already offered correction to the description of infinities, but I'll add my own explanation.
To start with infinity +1, this is equal to an infinity that is exactly the same size as the first infinity. To see this, think of all the natural numbers, from 0 to infinity, arranged in a line, like a number line. You can shift the number line 1 place to the right, adding 1 to each number on that line, and then reinsert 0 at the beginning. Doing this, you've added one element to the set, or one number to the line, but you have the same number line you started with.
You can also add infinity to infinity and still get the same size infinity. To do this, take your number line and add all the negative integers numbers from 0 to negative infinity to it. We now have a line that goes to infinity in two directions, so it isn't the same line. However, we can fold the line over so the infinities are in the same direction (i.e. multiply all the negative numbers by negative 1) and subtract 1/2 from each of the numbers from this half the line so they don't end up in the same place as our other points. This will give us a number line with a point every half a whole number, so the line has twice the density of points. To get our original line back we just need to multiply each point by two.
Because adding infinity to infinity in this way is equivalent to multiplying by 2, and any finite multiplication can be reduced to a series of addition and multiplication by 2, this means we can multiply infinity by any integer and get the same infinity back.
So what about multiplying infinity by infinity? Well we could attach a second number line at a right angle to the first to give us a plane, and consider all points with integer coordinates. We now have infinitely many points for each of the infinitely many points. What we can do is draw a line that goes through each of these infinitely many points. Any space filling curve (and a few other operations) can show this, but an easy one to describe is to start along the x axis, and at the first point where a diagonal back to the y axis will cross a point with integer coordinates, take that diagonal path. Then continue along the y axis until the first time a diagonal back to the x axis will cross a point with integer coordinates, and take the that diagonal path. Then repeat. The line you draw will be infinitely long, but will cross all points with integer coordinates. You can then straighten out that line, and put it next to the original number line. With a scaling operation, you can get this new line to be identical to the original number line. So squaring infinity will give you the same infinity back. Incredible.
Much the same as the multiplication case, any finite exponentiation can be reduced to a series of squaring and multiplication, so we can do all finite exponentiation too.
So what about all the numbers between the integers? For rational numbers, i.e. fractions, we can take every fraction, and make the numerator the x coordinate on our integer plane from the last case, and the denominator the y coordinate. We won't fill every point without putting some rational number on more than once, but that doesn't matter, because we can show that the rational numbers aren't a larger infinity than our natural numbers, and, since the natural numbers are a subset of the rational numbers (just a fraction with the denominator 1), it can't be a smaller infinity either. They must be the same size infinity.
It's beginning to look like all indignities are the same size. This isn't the case though.
Irrational numbers are where this stops. Any number that isn't a rational number has an infinite decimal expansion. You could write out infinitely many numbers with am infinite decimal expansion, one for each of our infinitely many natural numbers. If these sets are the same size, you should be able to write every single irrational number and give it a corresponding natural number. If we try this, we can go along afterwards and write a new number, where we look at the first decimal place of our first number, and write a different digit, then the second decimal place of the second number and write a different digit, and so on for all the irrational number we wrote down. This new irrational number has to be different from all of them by at least one digit, so we have more irrational number than natural numbers. We have a larger infinity. Indeed there are infinitely more real numbers between 0 and 1, than there are rational numbers.
So, there is a lot you can do to infinity without changing it's size, but you can still get different sized infinities. The inverse operations of the finite operations I discussed do also work, but infinity minus infinity and infinity divided by infinity are not well defined.
This blew my mind. Thx so much for the inspiring episode!
Thanks Mr. Arthur. This was your best in this series, in my humble opinion. Had not thought about the idea of massive energy generation & calculation to effectively slow subjective time to a standstill. Certainly an interesting thought exercise. I personally think we're going to hit a brick wall "digitizing" human consciousness and developing truly conscious AI for that matter, but I'm sure that's an extreme minority viewpoint in this crowd. Though it does annoy me that both concepts are somewhat treated as a fait accompli in futurist discussions.
Maybe I'm not remembering correctly but I thought physicists worked out math which shows the possibility that a universe that's spread out enough (post-big-rip) would be equivalent to a microscopic space "coming into existence". This would mean a cocoon to wait out the rip would be futile, from your perspective matter would never "come back"
That includes the most accessible explanation of Cantor's theorem I've heard in a while :D :D
The Omega in the Big Rip Time Estimate formula is a clever foreshadowing of the first mention of the Omega Point in this series
When dark energy pulls apart a quark and creates 2 quarks it might continue to pull on the new quarks and quickly create more quarks.
So, you might get a whole new universe being created from a single quark with dark energy turning energy into mass.
Now imagine that same reaction across the countless quarks in the universe.
Make sense. An infinite pull making infinite new particles. Thus a new universe.
I get why people get confused by how the universe can expand yet still be infinite in size. But I think it just a poor description that gets people confused. But in short of it. It is just that empty space between stuff is growing. Or is like all the stuff was shrinking while the empty space remains the same. It is an easy enough concept enough to understand. I actually do like the balloon dots on it analogy even if I know some scientist dislike it since it can give the idea that the balloon must expand it to something. Which maybe the universe is doing, but we do not know and should not assume so. But I think that even if they get this little misconception (which might not be a misconception at all, see previous sentence) it is better. Since the person now have a decently accurate picture of what is going on. All analogies will have limitations, or else they would not be analogies.
when I was 7 years old, the question of infinity hurt my brain. Now I am 50 and this video explained it all. Thank you, now thinking of infinity it don't hurt my brain any more.
I'm crazy about aviation and have a few favorite channels. e.g. Mentour Pilot and 74Gear. Both are made by professional pilots. The former is quite serious but full of great information and that latter, 74gear is hosted by a 747 pilot, who cracks me up laughing on a regular basis. So yeah, _Isaac Arthur_ I'd be super interested in your flying experiences. Thanks for a great episode.
I love your accent around the E/O, L and R areas. I love your videos! This is my 2nd. *Subscribed.^_^*
If it does turn out that hiding inside the event horizon of a black hole allows one to avoid the Big Rip, then the first thing that comes to mind is something you mentioned in the Galactic Laboratory episode- the idea of sticking a bunch of neutron stars in a circle, to potentially create a sort of black hole with no singularity… it’s something an advanced civilization might attempt to create to hide in more safely than a normal black hole. No guarantee it would work, but they might feel it was worth a shot if death was guaranteed otherwise.
What if we think of time being the balloon?
The larger the balloon gets, the further the points from each other are, the slower time "processes".
Subjective time stays the same, but universal time (which would be required for this) would be affected and slowed... making the universes expansion seem to be increasing.
and gravity, the effect of mass, is the thing that's the "equalizer" for the expansion of time itself. A necessity to reduce the effects of time-expansion.
Like tiny holes on the balloon of time, the more mass, the deeper the hole.
So oddly. The survivable cyclical big rip makes me a heck of a lot happier to think about as a course for the cosmos than black hole computers & heat death. Just the forever young cosmos recreating itself like a Phoenix & civilization getting to live fast, struggle, improve, & experience a vibrant & active universe forever. And continuity only preserved by sentient beings that know how to survive the rip. Where it would otherwise be erased. Gives further inherent purpose to humanity if true.
You guys learning to fly would be awesome! That is a great goal for a couple, my wife and I did a helicopter discovery flight a few weeks ago and it was wonderful!
Isaac , Thankyou , Thankyou and Thankyou for explaining Infinity , I can now finally grasp the concept .
And just incase I forgot to mention it , I want to Thankyou.
Take Care . R .
Long term storage of knowledge and information is going to be very important. Taking measurements of the universe say today, and comparing those measurement to new measurements made every 100 years for the next million years or more. Of course, you can just say make a fresh copy of the previous measurements, but you might not for one reason of another.
But saying all that, only then could you start to really tell if model end times of the universe scenario would be the actual case.
This is so incredibly insightful
4:25 Honestly the idea of an infinite universe expanding doesn't confuse me much. What really blows my mind is that, assuming my physics knowledge is correct, and that at the very, very large scale one can approximate the universe as having some roughly constant, nonzero density:
The Schwarzchild radius grows linearly with mass, while the physical radius grows with the cube root, so beyond some certain size (and thus mass) of the universe, the Schwarzchild radius is larger than the physical radius, and it becomes apparent that the whole thing is one giant, not-fully-collapsed (there is not a singularity that contains all the mass) black hole.
As far as I can tell that would mean nothing for our apparent physics inside it, and it would mean nothing for "the outside" because presumably there would be nothing outside an infinite universe spanning black hole because it *is* the universe, but it's really, really weird to think about.
Reminds me of Douglas Adams' "Restaurant at the End of the Universe."
It's just so far out it's hard to speculate what happens in a quadrillion unfathomable years
There are some maths issues here:
1. If we're dealing with cardinal arithmetic, any infinity cardinal added to itself gives you the same thing. With ordinal arithmetic, what you say about this is correct.
2. There are more numbers between 1 and 2 than there are natural numbers.
4:04 Can the expansion expand faster than the Speed of Light or is that the limit and we can never see beyond that?
YEs, there's no problem with two galaxies moving apart at faster than light speed, it just means there's a ton of new space appearing between them, like two cities on a balloon planet that was expanding and them far enough apart people couldn't walk fast enough to walk between them.
10:00 Reality pixels, gonna remember that definition
“Infinity isn’t a number” - statements that keep me coming back!
Just yesterday I rewatched the Iron Stars video for fun, thinking if somehow even that could be continued. No coincidence, I'm sure?!
This is why I truly believe nothing is out there after we pass.
Given that the universe itself cannot survive, what logic would there be for something to exist after life.
amazing episode. thanks isaac
5:08 - 5:13 "Nonetheless, all the numbers between 1 and 2, if added up, are smaller than the sum of all integers."
This is incorrect. The integers form a countable set, while all the numbers between 1 and 2 form an uncountable set.
I can watch these back to back for hours but I fall asleep in uni lectures lol
The universe (spacetime) came into existence with a specific amplitude and, with each wavelength of spacetime it expands, that amplitude necessarily decreases, while the wavelength is unchanged because wavelengths don't change without interaction with another wave.
As amplitude and wavelength approached a 1:1 correlation, the rate of time (for everything except the expansion) increased. When they became momentarily equal, this represented the maximum rate of time.
For example: The square root of 1 multiplied by 1 is 1 or 100%, whereas .5 x 1.5, or 1.5 x .5, (providing we adjust the 1 to 1 proportion at maximum so that both values together sum to 2), both result in a rate of time approximately .866% that of the maximum rate of time possible. Interestingly, one of these might be equated with the rate of time for an object at .5 the speed of light, per the Lorentz transformation, while the other could be equated with the rate of time deep inside a gravity well. Since these are proportions and can never be reduced to zero on either side, this also suggests that accelerating matter until it reaches a state of singularity is as unattainable as accelerating it to the speed of light.
For this reason, the early universe expanded hugely in what was a very short period of time, relative to any observer in that universe. Gradually, as each wavelength no longer had such a large impact on the size of the universe, and the rate of time continued to increase, the acceleration of the cosmic expansion seemed to slow, relative to everything else.
This had the seeming effect of halting the apparent acceleration (only the apparent acceleration) of the cosmic expansion, momentarily, after which it began to grow again as the amplitude continued to be reduced by cosmic expansion but was now smaller than the wavelength, yielding results of less than 100% for the rate of time.
As the reduction in amplitude relative to the wavelength (which also corresponds with energy available to do work, as well as entropy) continues to be reduced, the rate of time will continue to slow down. This creates what we, as observers, would perceive as the big rip due to the cosmic expansion accelerating faster and faster, when it is actually still expanding at the same rate but, as our rate of time becomes trillions of times slower than earlier, allows something akin to the heat death of the universe to take place while the stars are still forming, and living beings still exist.
Which brings us to the question of when. Some guestimates have been as little as 20 billion years. Unfortunately, the acceleration of the expansion of the universe probably ceased completely when the universe was 7.8 billion years old (subjectively) and then began accelerating. Given that the universe is 13.8 billion years old, one can subtract 7.8 billion years and get 6 billion years. This would seem to suggest that, if some sort of symmetry is applicable, then we may have as little as 1.8 billion years remaining, although symmetry may not be applicable.
This would certainly suggest an anthropic reason for why we have evolved so early in the life of the universe. So early, in fact, that we are faced with what we call The Fermi Paradox, where there appear to be very few, if any, other technologically capable civilizations out there. You show up early or you don't show up at all.
I'm not happy with it either but cheer up. My IQ isn't that much more than 150 and I've only spent several decades thinking about this, starting with teaching myself relativity and quantum physics (and my degrees are not in physics). It's just a hypothesis, not a theory. Yet.
Actually there is perfectly good math where infinity is a number. Also infinity + infinity is the same size infinity as whichever is larger. The integers are the same size as the even numbers. The rationals are the same size as the integers too. The reals are bigger than the integers though. Infinity really isa weird thing. You might be thinking of the density of numbers, but I won't comment on that as I didn't study much measure theory.
Sorry. Should have looked at earlier comments. I agree that these details on infinity shouldn't matter for the purposes of this video
Several years ago you talked about mega earths. Could you build an O'Neill cylinder with more surface area than a birch world, in terms of it being physically possible, not practical?
i dont think so.. it would collapse under gravity but thats just a guess
Issac Arthur: "...there's no continuity to a new big bang or recycling event..."
Galactus: "...ok am I a joke to you?!"
Imagine using the power of a super nova to boost an interstellar spaceship at tremendous speeds into deep space towards a distant galaxy.
There would be those that are so advanced that before they secomed would incorrectly be taken as gods. The survivors of such a calamity would either also incorrectly taken as gods because they survived and helped the new races or else they were Creators because they organized matter or created out of nothing (maybe one thing moving so fast that it has everything else in the form of energy?) and not just servived.
You should let Scott Manly build you a custom aircraft. His SSTOs are pretty awesome.
Issac the Subtitles at 9:34 don't match the audio, old script?
I wonder if controlling dark energy was possible could a super advanced civilization use it to split quarks and create an unlimited supply of mass and energy.
you just need fusion for the energy part .. why would you need unlimited mass tho?
@@raidermaxx2324 Get enough of it you got a star. Free fusion and heat.
Or get the matter and use it for fusion.
would love to see the pilot videos, that's awesome
I'm waiting for your video on The Big Crunch now...
It would be interesting to see a Civilization out there attempting to plug all the White Holes in the universe because they linked them to Dark Energy and wanted to prevent the Big Rip.
It just made me think of an episode of DS9 where some mad geniuses visiting the station are in a panic to fix the heat death of the Universe.
@@isaacarthurSFIA haha I remember that episode. I also remember they wanted to use a rediculous number of a specific device to prevent the end. Even Trek can be "Just use enough brute force to solve the problem."
@@rvaughan74 As Q once said, "Just change the gravitational constant of the Universe" when he was briefly made mortal in TNG.
@@isaacarthurSFIA I remembered that exact same episode while watching your video :D
Even trying to remember what exactly they wanted to do...will have to look up the episode. I think they wanted to stabilise subspace or something like that, in reality if there is such a thing as subspace that would probably be the place from which dark energy comes from so it makes sense.
Basically "2012" but in an universal scale.
The Big Rip: followed soon after by the Big Chucking in the Wastepaper Basket, the Big Sigh, and the Big Grabbing Another Sheet.
"Let's see if we can't get the math to work out this time."
“…even inside you and I.”
Beans must be powerful Planck attractors!
Where’s my nobel?
Fascinating episode. I love the notion of the INSIDE of a supermassive black hole being the last refuge thru the big rip and a liferaft into a remade universe. But Isaac, I do believe you are wrong about infinity. The set of all integers is not "bigger" than the set of all even numbers, as you were saying. Intuitively it seems twice as large, but logically it isn't. It doesn't really mean anything to say it's twice as large. Cantor demonstrated that each even number can be matched up with an integer. All sets that can be so ordered in one-to-one correspondence with integers are said to be DENUMERABLE, and this the class of infinity Cantor named Aleph Null. All your examples of infinity are this type, and they ARE functionally equivalent. There really is no greater-than sign to put between them. It's the magic of infinity... as a mathematical concept.
Now there is an inifinity that you could describe as "bigger" than your run of the mill denumerable sets, and that's the set of all real numbers. I won't go into the proof (search Cantor and mathematics of infinity), but the point is that the totality is indenumerable. That's because there isn't an algorithm that can generate them all. It's impossible to say "how many" there are, so they can't be "numbered." Cantor named them an Aleph One set to distinguish them from denumerable infinities. That does make them seem "bigger", but even in this case it might be a misleading way to describe their relationship. It might be better to think of them as how the irrational numbers compare to rational numbers. It's more about their logical structure than the "quantity" they contain.
Disclaimer: I am not a mathematician. I am just someone who was so entranced by infinity as an adolescent that I read a lot about it. If are reading and know it better, please correct me.
P.S. Many logicians and philosophers doubted that physical infinities exist. It seems to me like something that could ever be known (living as we are within Godel's incompleteness theorem) and that all science would fall within the finite.
so you arent a mathematician? ill just forget about everything you just said then
so Isaac finally decided to tear apart the civilizations he build in "Black hole civilizations" and "Iron stars"
There could be some continuity of the universe if you can predict how quarks would be ripped apart then set it up in a specific way.
Extremely hard, but I think that’s technically a possibility.
If the expansion of the universe is accelerating, and if the "budding" theory for the Big Bang is correct, that other parts of the Universe (that we can never see) budded off at different points, then could that accelerating expansion be due to increased gravitational attraction from those other parts of the Universe?
Michael morcock wrote a good book about this called dancers at the end of time. It's a good fiction and highly recommended it.
Wow super early. I loved the vidy about iron stars, hoping this will deliver the same punch. Deep time is mind melting
How could you be one of the 1st 1,000 of a new Arthur release? That would be a skill to share.
1:13 / 38:08
1:13 / 38:08
I will simply channel all of humanity's love and hug the universe back together
I'd love to see you fly, I'm a big aviation fan.
Thanks Isaac. 1 question could the big rip cause a new big bang. If the splitting of quark pairs produces new quark pairs could it produce enough material to start again, at a much larger scale 🤔. I asked this on the civilisations at the end of time. So glad it was kinda answered.
Thank you for the upload! Imagine a scenario where the galaxy is teeming with life and EVERYONE is trying to secure their spot under the central galactic black hole's event horizon. That's going to be a hot mess! Perhaps it could be a reason to keep your galaxy sterilized and your colonies small, nearby and under control. And your population limited. Another candidate for a Fermi paradox solution...
I imagine tons of white dwarfs and other assorted waste materials would also get dumped into that hole to make it even larger, especially to run heat engines off the fact that supermassive black holes have temperatures on the order of 1/10^14 K.
My brain hurts. Thanks for that! It’s good to experience.
Yes , Real life flight sim! try to include some of the guide notes so that we can know something about what your flying over please.