The Phantom Singularity | Space Time

The singularity, the point of infinite density at the core of a black hole but also so much more. In mathematics, singularities come in wild and wonderful varieties. The black hole itself contains more than one. *intro* Isaac Newton's universal law of gravitation was an incredible insight when he figured it out in the late sixteen hundreds. In fact, we still use it to fly spacecraft around the solar system today. However, it has its problems. Lets look at the math: Newton's equation gives you the gravitational force exerted between two masses. m1 and m2. They're the distance (R) apart. Straight forward enough, that R squared in the denominator, spells trouble. It means the force gets larger the closer the masses are to each other. That makes sense but what about when R when it gets really close to zero? Then the result of the equation; the force, becomes extremely large and is infinite when R becomes equal to zero. That doesn't really make a lot of sense; infinite force means infinite acceleration which means well, physics breaks. According to Newton's law, in order to fill that infinite gravitational acceleration you need to get zero distance from an object's centre of mass. That means all of that object's mass would need to be concentrated at that centre. A single point of zero size, which means infinite density and that of course would make it a black hole. We often use the word "singularity" to describe hypothetically infinitely dense core of a black hole. But in math, the meaning of this word is much more general. You know what? Instead of me trying to explain mathematical singularities, how about we get a real mathematician to do this properly? Guys, meet Kelsey Houston-Edwards of the new PBS show infinite series. Hey Kelsey Hey matt. Thanks for having me on! Kelsey, the math for black holes, goes to infinity for different properties and in different locations. What does this mathematical weirdness tell us? Well, mathematicians use the word Singularity pretty broadly It's really just any point that causes problems Commonly these problematic points are where quantities become bigger and bigger, approaching infinity, as they do near a black hole. Some singularities come about from your choice of reference frame or a coordinate system An example of a frame dependent singularity that might be familiar to SpaceTime viewers Is the event horizon of the black hole ask you to explain here on earth the north and south pole are examples of coordinate singularities it's possible to pass their time zones infinitely quickly but only because of your choice of spherical coordinates for the make sense but the gravitational singularity of the center of a black hole is a so-called real singularity right i mean curvature and the density are infinite from any friend preference right and there's no way to avoid a horrible crushing guests just by switching coordinate systems but the reality of the black hole singularity may give reason to doubt the theory that predict such a thing in fact it's happened many times before from models of the movement of water to human population growth mathematics predict physical singularity and we've been forced to reject the corresponding theory so you're saying Einstein is Rome less for me actually Einstein himself agreed on this point guide you should check out culture show infinite series where she goes into much more depth on the nature the singularities it's about show by the way so it's sometimes about real stuff mathematicians are lucky being limited by reality is so boring so does the fact that it includes a singularity mean there's something fundamentally wrong with Newton's law of gravitation well we already know the law isn't really so Universal when the gravitational field is too strong saying their star or a black hole news log gives the wrong answers and we need I'm Stein's general theory of relativity which is the far more complete theory of gravity so it is general relativity reserve news pesky singularity and no in fact it gives us even more singularities to understand this we need to look at something called the swath shield metric that's what you get when you solve the delightfully complicated Einstein field equations for the simple case of the spherically symmetric mass in an otherwise empty universe we going to simplify it to only allow movement directly towards or away from our massive object in that case it looks like this okay that sure is some ass hey this is space-time we can deal actually it's really easy to see the singularities in this equation but let me just walk you through what it tells us the swash altmetric allows us to compare two points or events in space-time around a mess of object from the perspective of different observers for example a short space time passed of some object so it's worldline might move an object a distance Delta R over short time step delta T that motion is towards or away from the massive object which is a distance R away that Delta is squared thing is the space-time interval and it's a strange and interesting quantity every inertial so I accelerating observer will agree on the same space-time interval for every pair of events and for every worldline we talk about this in a lot more details from our relatively playlist today we're going to keep it simple as long as our objects worldline doesn't require faster-than-light motion then the square root of the space-time interval is equal to the amount of time that the object itself feels over that interval we call that the objects proper time oh and our subscript s is a measure of the mass of the massive object in fact it's 2 times the gravitational constant times the mass there would have been some speed of light through the equation but we set them equal to 1 because we're that cool now the first thing to notice is that the singularity is still present in a swath shield metric are the distance to the center of mass remained in the denominator just as it was in use law when you use the trash or metric to calculate the curvature at r equals 0 that curvature is instant this gives us the same instant gravitational pool as Newtonian singularity and just as with the Newtonian case its gravitational singularity can only exist if infinite densities are possible but unlike Newton's law of gravity the swath shield metric actually tells us whether or not that infinite density is expected to see how we need to look at the second singularity in this equation a singularity that Newton's law does not contain see when distance to the center of mass is exactly equal to this RS theme then RS / r is equal to one at that point the entire equation starts behaving very badly it's as much a mathematical singularity as the one in the center of the black hole if you haven't guessed this bad behavior corresponds to the event horizon and rs is the SWAT shield radiance imagine an object sitting at the event horizon but not moving so Delta R would be 0 but this bracket is 0 also because 1-1 the entire space-time interval for a non-moving point at the event horizon is zero but remember to sublights being worldlines the space-time interval kills us the rate of slow of proper time so that mean time doesn't pass for an object hovering at the event horizon not quite time certainly doesn't pass at the event horizon no clock ticks can ever happen there but the prohibition against objects experiencing time at the event horizon is actually a prohibition against objects spending time at the event horizon no temporal theme nothing that normally experiences the passage of time can have a space-time interval of 0 at the event horizon the only way to get a nonzero space-time interval is to have a non zero Delta R an object at the event horizon has to change his distance from the black hole to keep its clock ticking that means falling below the event horizon and what's inside in with special movement continues to be the only way to fuel the ticking of an object proper time clock and come back to get bit of or some witness in a future episode there is one thing that can have the space-time interval 0 light actually anything capable of traveling at light speeds can only have a space-time interval 0 from its perspective a search on exist in a single instant and so it can hang out at the event horizon which also only exists that one instantly stretched out instant reactive crossing the event horizon is where the singularity really start to behave badly at the moment of crossing the denominator here in this workshop metric is 0 and the whole equation close up to infinity but what is actually insert here is nothing physical it's the fact that even and outgoing light ray takes infinite time to move any distance so using boring old time and distance delta T and daughter are doesn't let us trace the worldline smoothly across the event horizon that horizon is a coordinate singularity just like guilty talked about what that means we can fix it there are ways to construct a US based on taxes so this singularity just evaporates for example Eddington single Stein tortoise coordinates to compactified I with the stretching of space time to cancel out the infinities that's a bit much for right now but google away my friends anyway the upshot is that it's really a breeze to drop through the event horizon physically and mathematically of course once inside the event horizon we still have that central singularity to deal with unfortunately that one can't be done away with by simple change in coordinates that point of infinite density really exist actually Einstein's theory and the squash or solution that is derived from it suggests it must exist the apparent inevitability of this singularity may be evidence that general relativity is incomplete but you better understand why the central infinity is unavoidable in Einstein's theory we have to go back to that coordinate shift at the event horizon there's the causal roles of space and time switch places and the central singularity becomes not so much a location in space but an inevitable future actually to really get this we're going to need another entire episode standby to explore what happens when you switch the causal roles of time vs. space to space time cheers to kill Houston edwards for helping us understand mathematical singularities be sure to check out the PBS infinite series episode dealing with earthly singularities right here and as always we take you to our patreon supporters to really make the space-time a lot easier to do today a special shout-out to Henry's and students who is supporting us at the Big Bang level Henry join us for our patreon google hangout where he pretty much obliterated the entire Whitehall hypothesis by correctly pointing out that if they existed many great numbers we would see them thanks Henry for dropping the knowledge and the dollars it's a huge help last week we inaugurated the space-time journal club by looking at held why tells paper on an apparently positive vacuum test of the e/m drives the discussion continued with extreme enthusiasm in the comments so we'll definitely be doing more journal club episodes so now let's see what you have to say Joshua Hillary asks why the am dr hasn't been tested more given it isn't such a complicated experiment well that may be true but it's still an issue of resources it costs a lot to do proper careful experimental research of any type a scientist who decided to look into this is to devote grant money lads days personnel and most critically a lot of their own time and energy all of these us gas in the world of research to warn doing this sort of effort a given project has to be promising the a.m drive is not promising you shouldn't mistake media and Internet height for actual potential most physicists just aren't excited about this because a it shouldn't work and be there's no convincing evidence that it really does work there is the best defense of hints or come back to that in a moment but the amount of work being done on it currently is equal to or greater than what is warranted by its promise meanwhile there are many extremely promising new technologies to work on including propulsion tech and we don't even have the resources to give these they're doing attention terence console point out that even if the m dr produces only a tiny thrusts it's still interesting and i totally agree if it really does produce propellants trust then it's enormously exciting that would be true even if it's not ultimately useful for spaceflight which I'm not saying it wouldn't be but these sorts of huh that's odd moment are exactly what first opened new fields of study however it's important to remember that 999 out of a thousand heart that's odd moments and due to some unaccounted factor that is totally within our current understanding of nature we investigate anyway because we don't want to miss that one in a thousand but we don't pee our pants every time now the average person doesn't seem most of the weird unexplainable results that ultimately proved to be nothing interesting scientists do and so if they aren't getting super excited about the e/m drive it's not because they're closed minded it's because they know it for what it probably is perhaps it's worth someone somewhere investigating but it's not worth wet trousers a few people suggested that the e/m drive has been shown to work again and again that's just not the case some tests to find a trust or the amount of trust isn't consistent between testers some tests find a thrust in the wrong direction or no trust at all a vacuum test out of tu dresden in Germany observed trust that found the trust was the same even if they stood the am dr vertically a chinese paper from 2010 that claimed a positive test was retracted because the authors found that the thrust vanished when the power system is placed inside the e/m drive cavity this suggested the positive result could have been due to noise due to the unshielded power system frankly all this is about what i'd expect when you generate temperature differentials and large magnetic fields around a very sensitive position measuring device things are going to move around Stephen Department asks what I just put one of these devices in space to see if it works well see my previous comment about devoting resources but actually we may have done this or at least China may be doing it the state-owned china academy of space technology announced in december that it's testing the device in orbit they also announced positive ground tests following the retraction of that 2010 paper but nothing new has been published as of the making of this video until then there's no way to assist this but honestly orbital test don't eliminate most of the issues of vacuum chamber ground tips unless i am dr actually manages to push a satellite around that would be convincing a few scattered he reminds us the first rule of space-time journal club is we talk over our thoughts and remain open to all possible ideas and contributions from others before forming any solid conclusions well said Matthew and remember you are not your job you're not how much money you have in the bank. You're not the car you drive, you are not the content of your wallet you are not your car keys... you are star stuff

Channel: PBS Space Time

Views: 2,463,369

Keywords: singularity, black holes, black hole, space, time, spacetime, general relativity, relativity, gravity, math, physics, astrophysics, education, science, mathematics, event horizon, astronomy, supermassive, milky way, massive

Id: -q7EvLhOK08

Length: 18min 4sec (1084 seconds)

Published: Thu Jan 19 2017