I'm Brian Greene and today I have been challenged to explain a topic in five levels of difficulty we're going to be talking about the nature of time the most familiar and the most mysterious quality of the physical Universe there is nothing that we experience that does not take place in some duration of time so if you can understand time you're on your way to understanding reality [Music] hello hello what's your name Kayla how old are you Kayla I am nine years old so if you're nine years old what does that mean about the Earth how many times has it gone around the Sun nine times nine times so there's a relationship between motion through space the Earth is going through space and the passage of time they're kind of connected in some way but there are differences right if I asked you to move through space you could do it freely right can you get up and let's see how easy it is to move through space can you move over to that location and can you come back anything getting in your way easy to do yep if I were to ask you to sit perfectly still in space can you do that I mean hold perfectly still that's good but if I ask you to hold still in time to not go to the next second or the next second can you do that no so there's definitely this difference between space and time some fundamental quality that distinguishes how freely we can move through space versus how freely we can move through time have you heard of Albert Einstein yes what do you know about him yes please here and I think I may be heading in that direction actually he showed us an approach to travel to the Future you want me to tell you how you do it you build a spaceship you go out into space really quickly you turn around and you come back to planet Earth and he showed us that when you're on that ship your clock will tick off time more slowly you will age more slowly so that Journey may only take you say a year six months out and six months back but you know what when you step out of the ship it'll be a hundred years into the future or a thousand years a million years into the future would you do that if you could I would probably be dead by that no you'd be alive that's the amazing thing I'd be to everybody else would be dead who stayed on Earth but your body would only age one year and yet it would be a thousand years into the future the question though is could you get back and I don't know the answer to that nobody does we don't know if you can travel back but we certainly know that you can travel forward has anyone ever tried to go forward and back I don't think so that same guy with the crazy hair Albert Einstein showed that there's actually a limit to how fast things can go and you know what the limit is the limit is the speed light because light travels 671 million miles per hour that is fast enough to go around the entire Earth seven times in one second so if we could build a spaceship that would go as fast as light we'd be able to do what Einstein noted there's something else that's really curious about time things tend to go in One Direction and we call it the arrow of time it sort of points from the past into what we call the future if you'd ask me why is there an arrow to time ask me why is there an error at the time I'm not really sure I have some ideas but I'd say we've still not completely nailed it down Kayla what have you learned about time from talking about it here that you can't really travel back through time and can you travel to the Future in Prince maybe maybe that's absolutely right I think it's unlikely we'll learn how to travel to the past but it's not been ruled out that's kind of exciting that it's still at least an open possibility if I was to ask you what is time what would you say time is kind of strange because it's almost a man-made idea there is the tangible of you know how the Earth revolves around the Sun or how we orbit around ourselves it's almost in a way does it exist if the way that we measure it is man-made before there's any life on planet Earth I think we all agree the universe existed did things change before there was life on Earth yes and how would you talk about that change without invoking this concept of time it's difficult to talk about something without adding time into it even if it is a human-made concept that the Universe evolved developed changed Through Time ultimately giving rise to Galaxy stars planets and on this particular Planet life that conception of time gives it feel that it's like Universal that it's out there it's the same for everybody it's independent of our actions or activities do you know that Albert Einstein shattered that view of time he found that if you and I say have identical wrist watches I'm sitting still and I'm watching you move I will find that your clock is taking off time more slowly than my clock you know it's really remarkable you can figure out this quality of time if you know one fact that the speed of light is constant have you ever heard that phrase my freshman year physics class yeah if you're clever you can use that with high school algebra maybe even a little high school trigonometry to make it even easier to derive that clocks take off time at different rate do you want me to show you how that goes yes please right so to figure out the effect of motion on time I'm going to use a really simple clock it's called a light clock it's two mirrors that are facing each other and what we do is we have a little ball of light called a photon right that goes up hits the top mirror then comes back down and hits the bottom mirror and every time it does that you go Tick Tock that's one unit of time imagine now we have another one of these light clocks but I'm going to have it in motion now what do you notice about that path it's much longer it's much longer right this one's going tick tock tick this is going to go tick tick tock in fact we can figure out the ratio let's consider time on the stationary clock compared to time on this moving clock well that ratio is going to be the ratio of the lengths then this would be given by D over L more time on the stationary because it's longer distance on the moving clock well this length over here that's the same as this L over here right so we want D over L now you may have recalled that in trigonometry there's a name for L over d sine of theta opposite is l hypotenuse is d right and so this ratio is just 1 over sine of theta so if we can figure out 1 over sine Theta we'll have our beautiful formula for the ratio of time on the stationary clock to time on the moving clock we just need one other fact the speed of light along this diagonal is equal to what we call C C equals speed of light but in order for this ball of light to hit that point on the mirror the component of the speed of light in the horizontal Direction better be keeping perfect Pace with the speed of the clock itself so let's assume that this clock is moving in this Direction with the speed equal to V so c times cosine Theta must be equal to the speed of the clock in motion and from this we learn that cosine Theta is equal to V over C there's another beautiful identity you may recall from your study of trigonometry that sine squared theta plus cosine squared theta is equal to one this is really just a Pythagorean theorem in Disguise and from that we can now solve for sine squared theta equals 1 minus V over c squared and if for sine Theta is the square root of this and now we're basically done because we already had over here that this ratio is 1 over sine Theta which now is 1 over square root of 1 minus V over C squared so you see as V gets very close to C this gets very close to one one minus something very close to one is very close to zero one over something close to zero is huge which means the ratio of time on the stationary to time the moving that can be a huge number as the speed of the moving clock approaches the speed of light now I did this for a light clock but it's true for any clock and this is what Einstein discovered in 1905 with his special theory of relativity do you think that in the near or foreseeable future of humans as we know ourselves now will there be a time where we are using these formulas and these Concepts in our daily lives as technology progresses the barrier between the limitations of experience and the truth of how the world behaves in extreme environments will be moved in the very same way that you know we can toss a pack of gum and we know where to put our other hand to catch it well we have that kind of intuition about these ideas I think it's quite possible what are you studying right now I'm doing physics and computer science so have you spent any time thinking about this weird quality of the laws of physics that there's no mathematical distinction in the laws between forward and time and backward in time is that something you're familiar with yeah and the one thing that really confuses me there I'm thinking about uh one of the most basic things we learn I guess from Interstellar is that the universe is expanding or space is expanding and so I'm thinking how does that square with gravity and electromagnetism which is like kind of predicated on the density of charges or masses the fact that space expands is perfectly compatible with our understanding of all the forces of nature because all of them continue to operate in a somewhat more subtle way but we have a beautiful prescription for taking any law that we understand in the simpler context a flat space time and juicing it up so that it works in a curved space-time the more philosophical question is in any of those formulations if you replace T by minus t and you do it properly in the equations the equations still work but if past and future are kind of treated on equal footing in the fundamental equations why are they so different from the perspective of experience when you're talking about the perspective experience could you is that just human subjective experience or actual observation for physics well certainly it starts with human subjective experience but then we are able to elevate it to a more objective description for instance when we introduce words like disorder and order an entropy in the second law of Thermodynamics and the equation usually the way we say it is s equals K log W entropy equals boltzmann constant times log of a particular quantity which is ultimately counting the number of distinct configurations that A system can be in what boltzmann and others showed is that entropy tends to increase toward the future but the key word there is tends to increase so this Arrow of time going from the past to the Future rests on a curious Foundation it's a statistical Foundation which says that it's more likely for eggs to Splatter than unsplatter it's more likely for glasses to smash than unsmash but not that it's impossible for those things to happen you just have to wait a really long time for there to be a reasonable chance of it ever taking place when you said that um you know it's more likely for an egg to smash or for glass to smash and that's probably because there's so many atoms so much stuff going on yes but I'm thinking if we zoom in on like a single thing I guess do we have variations that are extremely unintuitive because you know things can happen in a way that isn't a statistical average if I take a film of that electron it's a little fanciful to describe it that language because you know about quantum mechanics and so forth but I take a film of a little particle moving around and I show you that film you'll be really hard-pressed to determine whether I've shown you the film running forward in time or whether I've shown you the film going in reverse time if I had two or three or four or a gazillion particles into the mix then it will be much easier for you to determine whether the film is going forward in time or backward in time but order and disorder don't have much meaning if there's only one particle and that's why the fundamental laws don't draw a distinction but the macroscopic experience does but it raises a key question where'd the order of the egg come from if everything goes toward disorder how do I get this orderly collection of atoms called an egg well you probably would say from a chicken but then I say to you where'd the chicken come from and you say from an egg but there's actually some real insight we can draw from this because if we keep going back with the chicken and egg story we'll go back through the evolutionary lineage of Life we'll go back to early moments of the sun and the Galaxy and ultimately the universe each step taking us to greater and greater order so we believe that the ultimate source of order is the Big Bang itself highly ordered beginning called the bank and we have been living through the degradation of that order ever since we still don't really have a solid explanation for why the Big Bang had to be or was high highly ordered at the moment it's really a deep assumption Einstein we wondered does time change with speed and that's another change with that before we didn't think possible but I guess we found out eventually some of the fanciful ideas I guess there's a tiny sliver of Hope yeah not only did we find that time changes with speed and special relativity but we also found that time changes with gravity Einstein showed that the rate at which a clock ticks slows down based upon the stronger gravitational field or gravitational potential actually that it is experiencing I think you mentioned Interstellar before do you remember the scene in interstellar they're going to a planet that's near a black hole they go down to the planet and they spend just a couple hours there but when they go back to the ship it's 23 years later on the ship because time is elapsing slowly near the strong gravitational field comparatively quickly far away and that's not science fiction that's actually how time behaves I've always heard people say oh general relativity you know it might not seem applicable but you know GPS due to satellites yeah we could synchronize those Clocks by accounting for relativity well but that's even a really really good point the GPS would become completely inaccurate in a very short period of time if the satellites weren't taking account of or the software wasn't taking account of the fact that time elapses differently for the clocks on the satellite compared to the clocks down here on Earth so we walk around with general relativity in our pockets even though most of us perhaps don't really know that have you started any projects yet or that's I'm just starting one right now I'm trying to figure out how stars in the galaxy are moving based on what they're made of which is interesting clearly time comes in to what you're doing to what extent do you have to Grapple with some of the subtle features yeah with my research in particular I really want to know what happened in the past and what happened in the future but you only get a single snapshot when you look up at the night sky right but if it's officially far back you're right and so we can learn a lot by looking at other galaxies and seeing what they were doing in in their present I suppose yeah just figuring out what's gonna happen next is is part of part of the issue yeah that's looking into the future I suppose and so have you taken general relativity are you taking that now or I took a course on general relativity yeah but you learned about black holes sure one of the weird things and wonderful things about wormholes is that they are tunnels if you will shortcuts from one point in space to another point in space but once you have a shortcut from here to there the beautiful thing is if you move the openings time will elapse differently at the different openings so there's a possibility of wormholes as time machines go One Direction you're going into the future go the other direction you'd be going into the past but that of course raises philosophical and logical Paradox paradoxism sort so what do you think what do you I throw it to you yeah I've heard a few different theories that people pause it maybe it is Back to the Future and you really change your own Universe I've also heard people say that you could have a multiple universes Spawn from this event or something yeah that's that's if you're going to be able to change the past that's the one that resonates most with me I think the same yeah so you go into the past and maybe you can prevent your parents from meeting but you're preventing them from meeting in a parallel reality which means that you will never be born in that reality but the origin of your birth is still completely understood it was in the universe from which you originated another one that's more subtle is the laws of physics May prevent you from interceding right and that raises uncomfortable issues for many people having to do with like free will I'm immediately uncomfortable yeah so that one there's actually some people like Joe who did some wonderful studies of billiard ball tables where you imagine a billiard ball goes into a wormhole comes out and hits the very ball that was going into the hole and in that way if it could knock it of course we seem to be in some logical Paradox absolutely but the finding was the ball can come out and just sort of graze the other one but it can't affect it enough to prevent the sequence of events from happening and the way I like to think about it frankly is if there's one Universe not parallel universes like in the other solution moments in time just are they don't change the whole point of time is the variable along which change can happen so if you have the atoms of time the individual events there's no conception of them changing so whatever collection of influences were in play that allowed your parents to meet they will always be in play because you were always part of that moment do you think travel back to the past is impossible because of a deep physical like mathematical reasoning or just because of all of these problems that you've been talking about I suspect that when we fully understand the mathematics of the final physical laws if we ever come upon them I think there's going to be something built in okay that prevents this kind of free travel to the past but sometimes I I wonder if that's just coming from a more emotional place where I sort of want the world to be safe from this kind of paradoxes so what pretty clear based on any of the hypothetical proposals for traveling to the past that have come out of physics you can't travel to a moment in the past before the first time travel machine is built sure you know the twin paradox yeah sure where you know you fly off looks like you're moving fast but to you it looks like the other guy is moving fast so who actually ages more who ages less yeah a resolution I've heard is that because you have to be going away and then coming back you had to accelerate at some point and this breaks the the ambiguity yeah what if say the universe isn't flat what if the universe is curved and you go off in One Direction and then you come back in the same direction you pass by the Earth who's older then yeah do we have an answer yeah we do have an answer so the simplest version of that is imagine that the Universe has a shape of a donut imagine I'm on the circular part of this donut Universe all right and imagine I turn on two laser beams sending a beam of light going to my right and to my left and these beams will go around the entire entirety of space and will both come back and at some point they will hit me imagine they hit me at the same moment from my perspective now imagine someone's moving relative to my frame of reference say to my left they do the same experiment they fire the beam of light left and right notice that the beam that they fired to their left will have to travel farther to reach them because they're moving away from it whereas the beam that they fired to their right will not have to travel as far because in some sense they're moving toward it the two beams of light will not hit that moving Observer at the same moment to you or to them to them wow which means that there's a preferred frame of reference in this universe everybody is not on equal footing as they are when we teach to freshmen the special theory of relativity that's right exactly no everybody else is moving relative to me and it's real emotion so everybody else will be like the moving twin they will be younger and I will be older and when you think about past and future on a cosmological scale there was a long period when there were no human beings in the universe the fact of the matter is there will be these two long stretches with our presence being sort of a flicker in between to that thought inform anything about how you live in your brief flicker within that brief flicker I rage against thinking like that yeah I think that's the perfect way to put it yeah because it might be a brief flicker on a single moat of dust like floating in a cosmic eternity yeah but it's everything yeah there's nothing else that I'll ever experience and so in a way there's there's nothing else to me yeah there's an eternity but I'm never gonna see it I'm never gonna feel it it can be debilitating to imagine an eternal future of sort of nothing or none of what we do sort of persists on the other hand if you flip your perspective around and say how remarkable is it that we have this brief moment that allows us to think and feel and love and explore and illuminate wow how wonderful is that yeah so often when we try to give the basic idea of what time is I'm fond of saying look space is the language that allows us to say where events take place and time is the language that allows us to specify when they take place where would you jump off from there and trying to give a deeper understanding of the basics of time maybe part of the distinction in between time and space it's that you have a clear irreversible Evolution so how to explain what time is well it's a parameter that is measured by clocks I mean at the end this is what we know and allows us to talk about change and also that we know how to describe in terms of some set of equations which gives a clear sense of causality to note our recent paper where we were thinking about Einstein's ideas of special relativity but in a setting where the global shape of the space-time if you imagine there might be a curled up dimension of space a circular Dimension and thought about how special relativity Works in that setting we came to result in this very basic setting you can send signals into the past not in a way that will violate causality did that surprise you that by going from the usual topology that doesn't have a closed part of space but making that one change you could have this radical impact I found quite surprising that you could have this exotic behavior of a signal propagation in a system that was extremely simple totally classical there was nothing weird except one dimension that was compactified was identified on a circle actually even the standard vanilla causal structure of special relativity may give some very unexpected behaviors when you combine it with other simple modifications of just the flat space time and the beauty of it is it's not like there is some high-powered mathematical methodology straightforward algebra that a high school kid would know is all that you need to extract these unusual results and they were unusual because even if you do not violate causality we discovered that a fast moving Observer that could be us on a rock it could send signals verifier and then back in a very small time so the old idea that of course we always hear about that if we ever make contact with extraterrestrial life they're far away we can't really have a conversation because we'll say hello and then like 10 000 years or a hundred thousand years later they'll answer us because it'll take that long for the signals but at least in this setup which we don't know is true of our universe but if it were then you could have a real time Conversation Over arbitrarily large distances yes which is that was unexpected yeah and so that shows how even ideas that seem to be well settled and well understood have surprises like why didn't Einstein realize this yes yeah maybe the idea of living on a Subspace or being confined in this extra dimension on a Surface may have been looked exotic but definitely did not look exotic after the 1990s many people have begun thinking about the possibility that space and time may be so-called emergent quantities that they're not as fundamental as perhaps Newton or Einstein would have thought where do you stand on that idea it seems not Unthinkable saying that something is emergent will make full sense only when we have some concrete model in which space and time emerging in which we make sense of this non-space non-time description of a theory I don't know if we are still at this stage in which I would say we begin to understand this scenario because often I tell my students the greatest scientific revolution has been not in the 20th century it has not been quantum mechanics nor general relativity no special relativity it has been the passage from the qualitative description of nature to quantitative one when you pass from asking how to how much right then you understand something and who do you credit with as that Newton do you go a little bit below I would say Galileo Newton of course the the completion of this idea is Newton one of the things that relativity also sheds a light on is what exists that if someone's moving relative to me what they consider now might be in my past what they consider now might be in my future which would suggest that all of time exists much says we're willing to accept that all of space exists does that hold water actually it resonates with me for various reasons one is that professionally we use space-time diagrams Penrose diagrams a lot of diagrams where space and times are just two axis on a board and when we describe a particle we have a line that goes up in time by the way this image also is the last image improves the last page there is this beautiful sentence which is also true saying that if he has the time he would like to describe people as being monstrous beings that extend in time much longer than in space if it's equal to one that's very true so this idea that you have a Continuum and the time should not be made to disappear as soon as it's gone it's very practical it's also what is behind the idea of histories in quantum mechanics when in the approach of various people including heart or collaborated a lot with Hawking there is this idea that what you describe is a history it's not a particular moment in time but it's an evolution this history treats space and time on a more equal basis but would you say there's more to it than the technical more to it than the diagrams more to it than sort of an interpretation of the mathematical equations when you go so far as the text solace in the fact that that in a sense that you will always exist because you will always be at the moments of space and time that you have occupied throughout your life well actually that's probably the only way in which you can take solace because all the rest right it's almost children's stories yeah I mean of course it's something that you come by yourself you arrive at this conclusion which is totally not objective and is part of your personal history by yourself but it was interesting to see that for instance Kurt Vonnegut had exactly the same thing I said no I mean the only thing that really makes you not fear what will happen or your own is that every instant is eternal instances exactly as each point in space it's not the space disappears it will always be there yeah the idea that something is irretrievable maybe it's an accident and we go back again to order the initial conditions in which we started absolutely foreign of time I hope that you have appreciated the subtlety and the richness of this quality of the world that we experience all the time thanks so much for watching [Music]