SETI from Deep Space - Claudio Maccone (SETI Talks)

[00:00:10][Music] well thank you very much uh let me say that I'm really glad to have a chance to give a talk here at the city Institute where there are many many scientist and and people working in the city business that they really admire for what they do they have the vision of the future they do work that in the quotes uh established scientific Community sometimes is not yet full F understood but in my opinion is a profound research and step forward so let me come straight to the point um I am not a member of the city Institute but I have to say that I've been working in city for many years and I am a member of of the city permanent study group of the International Academy of astronautics now in this regard we came uh to consider many possibilities that is doing City not just in the ordinary ways that is using radio telescopes but possibly use uh spacecraft in order to do c from different new point of views so what I'm going to tell you about today is an idea that was actually put forward by Professor Frank Drake as far as I can remember as back in 1987 in a conference that was held in Hungary that was a called the bioastronomy the second bioastronomy conference and Frank Drake came along and he gave a wonderful talk about the possibilities of using the sun let me go back this is this is the title slide using the Sun as a gravitational lens now of course he was thinking about doing so for seti that is the gravitational lens of the Sun as I will explain more in detail so this is just a very preliminary in itive idea of the story the sun has the largest possible mass in the solar system we all know about that now since according to the general theory of relativity of Einstein space time around any mass is bent so it becomes curved the bottom line is that radio waves reaching the Sun from wherever in the universe more spe more specifically in the Galaxy are made to focus by the sun mass and so the key point point in the story that I'm going to present is to build a spacecraft and send a space mission out to the minimal focal distance where we can pick up these signals highly intensified by the gravitational lens of the Sun so this is what friend Drake presented in 18 1987 and I was just a new camera that you know just fascinated by set so I dare to talk with Professor Drake and they said uh you know I'm honored to meet you and I am a newcomer and they said you are a newcomer yes okay and then it spoke with me about this concept of the gravitational lens so in conclusion what I'm presenting today that is the book that you see here is the the result of 20 years of thoughts and calculations about this space mission that friend Drake put in my mind and is still there actually okay so I I I am sorry that the cost of the book is so high it's $340 in the US and and this is because Publishers of course um can decide about the cost of books this is a technical book unfortunately this is not a popular book I would have difficulties I have to admit to write a popular book because English is not my mother tongue so I don't know all the subtle ways to capture the attention of readers you know in a Charming way here we have set cha who does that much better than he can possibly imagine so someone else will have to write the popular version of what I'm talking about and this unfortunately is a mathematical treaties basically and or physical mathematical treat and this is why it cost so much let me please show you the book cover and let me tell you more about this because this is the picture down here is really showing the idea in a visual fashion but of course we would need artist to give us more artist concert about all this so this is just a preliminary vision of the story sorry okay let me go back so this is the the previous part in lasted and you see that this plane here represents so as to say the plane where the space mission is taking place now at Infinity that is at the Horizon we have this bright light meaning that over there at infinity or anyway at a very large distance from the Sun there is an intense source of radio waves now what could that possibly be it could be if you are a cosmologist an object at the edge of the universe like aaser that are well known to to throughout an awful lot of of radio but if you are not a cosmologist and you are rather a set scientist that could be an extraterrestrial civilization sending out signals why not from the physical point of view this is practically the same because both the quazer and the Extraterrestrial would send radi waves as indeed we do because the Earth is throwing out an awful lot of radio waves especially the military raders so we are already doing so right now inadvertently if you wish but this is what is going on so over there is the source of radio now the radioes travel and these are basically parallel lines until they reach the vicinity of the sun this is the Sun and you see that actually it was depicted in a lower little lower level with respect to the plane because this is to mean the gravitational well of the Sun so this is why the sun is is slightly lower than the plane right just to let you understand that gravity is around there and of course this gravitational well is is bending the TR cies of light rays and so this is why you can see these curves here and since the light rays are made to be then they must focus on the other side there is no way and this is where they focus so this F this point here where they focus can be correctly called the focus of the gravitational lens of the Sun so far so good I guess that everything is clear but then I have to tell you the big news which is also a big difficulty for a real space Bish well when you go over for all the calculation in general relativity then you find that the this focal dist this focal point is actually distant from the Sun 550 astronomical units now this is a big number for space missions just imagine that the orbit of Pluto from from the is about 40 astronomical units so you know it's it's far up far out but there is no way to to do the same Mission closer because it is easy to prove and in a moment I will prove it more serious way that if you just keep staying closer to the Sun you get nothing because you are in the shade of the body of the sun itself okay so this is the minimal minimal focal distance and it can be proven that all points along the straight line coming from the sores and passing through the center of the Sun and going Beyond this minim 550 Au distance all points along this sun this light and actually in this area here brighter area are focuses of the sun gravitational lens so here we find something quotes unexpected from the intuitive point of view because what we are used to consider In classical physics that is in classical Optics in this case is that classical Optics like the glasses that we use only have a very well defined focal distance and your eye must be exactly on that point to see well now this is not the case for the sun because it can be proven that any point from 550 onward theoretically up to Infinity is indeed focal point so this is not a focal point in the traditional sense it is actually a focal straight line starting for from 550 and going over to Infinity so here is the first novelty in the story but many more will come along okay now these things that you see down here is the spacecraft that I called focal spacecraft because the whole mission seems to me to be correctly called focal space mission now of course when spacecraft is going to be designed there are usually discussions among the the designers you know I as as it was said at my introduction I spent 20 years of my life at a space company in my town my town is Torino the with the shroud of jurin jini in English and I spent 20 years there at a space company called alenia spatio where I came to conceive this space mission and actually I have to say that by the year 2000 I submitted a formal official proposal to the European Space Agency ASA Esa in order to have this Mission considered for possible fundings now sorry to disappoint you they did not find my mission but nevertheless the file is there so I have to be frank one of the reasons why I am here in the United States is also to consider a possible resubmission of this proposal probably in a better form to NASA to have NASA consider the first quotes in Interstellar or precursor Interstellar mission that would be different from all space mission done so far because all space mission that so far were just at best for the exploration of the solar system but this goes far out much outer out of the solar system so this is the space as I could possibly imagine that and you see two big antennas tied to each other by this sort of string that in this space jargon is called the tether now the basic idea I'm sorry I'm using the gesture you know the Italians like to to use the hands all the time so please forgive me but the basic idea is that these two antennas would revolve in this way around the center so this is the real space it is very small but the two antennas revolve in the in the orthogonal plane to the direction of exit from the solar system and this is is done with a precise purpose that is in order to allow interferometry to be done which is one step ahead in order to get better angular resolution and better seeing so as to say of the whole lot on the other side okay so this is the intuitive description of the story and now let me please repeat very shortly the same story in a more scientific way so once again imagine please that on your left at Infinity is the radio Source whatever it is next civilization equation radio Galaxy bright star whatever so the waves are parallel but when they get close to the Sun they are bent by the mass of the Sun and the equation that is giving you the bending is this so if you call by Alpha of R the bending angle that is this angle over here the value of this angle is is not the same for all rays but it depends critically on the distance R from the center of the Sun and this is precisely why these two rays are you know have a steeper inclination with respect to the axis whereas this one has a smaller inclination sorry and if I keep going to Infinity so if I put my scer spacecraft up to Infinity of course in the end they would be parallel there would be no inclination at all so this is the critical point and you can now realize immediately why there is this minimal focal distance this is the 550 a you point and you cannot get anything at closer distances because the sun is blocking the propagation of waves so waves radio waves cannot go through the sun they are stopped by the sun incidentally here I'm just going to say very brief sentence for people versed in gen relativity you know phys if we are talking about gravitational waves that is the waves of gravity predicted by generativity the story is different because gravitational waves can cross through the Sun so the focus for gravitational waves is much closer than 550 Au and actually turns out to be in between the within the solar system and between the orbits of Uranus and and nepture but that's another story because you need a gravitational wave detector so I'm not going to to discuss this in this presentation okay next I told you about this deflection angle and let me tell you something from the history of the point uh sorry from the point of view of the history of science now this is a remarkable year 1907 when Einstein realized that his theory of gravity yielded a factor of four here in the deflection angle this is important because if you stick to the older theory of gravity Newtonian theory of gravity you get here only a two now what does that mean it means that the bending angle for Einstein is twice as much as the bending angle for Newton and so the distance that we have to reach for Einstein is half as much as the distance that we should reach according to Newton so we should really say thank you Professor Einstein because you have half the distance and you have made our mission possible certainly much better than what Newton would have said next this is just what I meant these are the masses of the of the sun Rus s schar shield look I know that in America some person pronounced SW child or something like that he was German and I am from Europe so if you don't mind car as they say in Germany anyway he found the first exact solution to the Einstein fi the creation and that's why radius is basically the radius of a black hole that is if you could put the whole mass of the sun inside thear radius which is only about 3 kilometers for for the Sun so you would have to compress things really a lot but then if you could do that that would be the the radius of the black hole having the same mass as the sun okay next oh here we go over to poetry if you let me use this this term now now this beautiful set of sentences that I'm not going to read was written by Professor Fran Drake and I'm sorry that he is not here I met him two days ago anyway this was written by professor fenre in the preface or forward I'm sorry forward that he wrote to my book years ago and basically he describes the novelty of the fact that every Star every Star is a gravitational lens of course because it bends SpaceTime around itself now Frank Drake is pointing out that each civilization and if there are civilization more advanced than us probably they realized that a long time ago already each civilization May and actually has to take advantage of this because it can be proven that if you use two stars as magnifying lenses for radio communications practically speaking you can communicate from one Stellar system to another one which with much lower powers in the game than if you just communicate by virtu of ordinary antennas that humans do but this is Trivial because there is no comparison between the size of the antennas that human have built so far and the size of the Sun so it's like using the Sun or any similar Star as a big antenna and this is precisely what is needed of across vast distances as we have in the galaxy and and outside so I'm not going to describe all this incidentally I leave the presentation and probably this will be put on the on the website of the set Institute so you can retrieve all this later so there is no no time anyway this is a beautiful description because Frank was the person who suggested to me all these sorry uh no sorry I'm going to no sorry just a moment Frank suggested to me all these and and uh oh gosh where am I going no that's too much so so yeah yeah yeah sorry about that no no but look can you take me the sorry about that okay so that was the poetic part of the story now let me give you more technical details and also start looking uh back please this is still back excellent perfect now these slides only points out what I said already that is there is an Infinity of focuses starting at 550u and going over to Infinity along this axis that is the source center of the sun position of the space period this is obvious but then we start facing many problems I just mentioned one well the fact that we don't have to stop the spacecraft at 550u is wonderful excellent it would have been extremely costly for us to stop a spacecraft just there this is not the case second the farther it goes beyond 550u the better it is because as you remember from the previous diagram the corresponding radio waves are passing at a higher distance from the center of the sound now in Practical terms this means that they are not being hit or less heit Anyway by the Flames that of course distort the the radio waves so here we are stumbling into a really big difficulty that is quotes in Easy term the theory of the Flames which in scientific terms is called the theory of the solar Corona now the sun is not a spherical ball without Flames there are Flames so we have to take this into account and so there is there are two chapters in my book that are actually considering the mathematical theory of the corona as it was done by JPL experts and I about 10 years ago and this is the best thing that we can have at the moment but I am sure that more models might better model might be found by some young bright person and we terribly need that okay next gain of every Star now here is the key Point let me explain this in Easy term and then I go over to the equations in Easy term the idea is that we use the Sun as a radio antenna okay in other words it is as is it is as if we had an antenna as big as the sun and of course this is wonderfully helpful for the telecommunication now radio scientists and radio astronomers and of course C astronomers use the no of gain which is this capital G and this applies to any Star not just to the star basically the idea is the gain is the focusing capability of the antenna in other words if you just have no antenna and you emit the Wes propagate in all Direction this is the worst case because you're wasting an awful lot of energy in all Direction but if you want to have a beam then you have a sort of paraboloid or any other shape that is focusing the beam in a certain direction now how much focusing is achieved is actually expressed by this notion of gain so this is what I understand by again it's it's a geometric focusing concept now it can be proven but this is not an easy proof at all I have to confess that the gain the radio gain in some sense of any Star at a wavelength Lambda is given by sorry is given by this Factor 4 Pi Square Times RG that is the partial radius or gravitational radius of the star over Lambda okay this is the great result I repeat this is not an easy thing to prove you have to go through electromagnetic Theory merge this with general relativity and then you find the result even more now let me Express in in Easy terms how wide or how narrow the beam must be well the point is this one if you define a variable row which expresses the distance where you are where your point is with respect to the axis respect to the focal axis then you have the first part which is exactly the same as in the previous formula that is 4 Pi Square time the radius over Lambda but multiplied by this factor which physics is called the Bessel function of order zero and is typical of is a typical pattern of radio communication that is the the the antenna diagrams even in in ordinary antenna Grant Theory are expressed in terms of this this thing the bestel function so anyway this gives you how much uh the the intensity that is the gain decreases when you go off axis and here I have to give you a bad news that is the alignment in between the source the center of the sun and the spacecraft antenna must be extremely strict just to quantify something of the order of 100 Metter so this is terribly bad I know I know we we were debating this point of course at JPL when discussing the so-called NASA Interstellar probe and let me tell you what they asked me they said what are you asking to track the spacecraft with the Precision of 100 m at the distance of 550 Au and I said yes well that's impossible I would save you other words okay but this is is was basically the meaning and they are absolutely correct well I will tell you later how I could possibly answer this question but this is a certain a very high difficulty the alignment is very strict indeed final line the bottom line well if you have a system space system that is made by more than one antenna so far we have been speaking only by about the antenna of the Sun but not about other antenas but this is not the case because as you remember we need the spacecraft to pick up what is focused there so in the game we have two antennas playing the the Sun antenna but also the spacecraft antenna okay now it can be proven that the overall gain that is the gain of the full system is made up by the multiplication of the two gains so you multiply the gain of the star times the gain of the antenna and this is the same story I'm not going through there much more good so far about the space mission the electromagnetic aspect and so on but now let me please extend our scenario as we say it now there are a few scientists not not really many but a few that are considering future space missions and the dream of course is to get to the nearest star nobody knows how to get there at the moment because the propulsion system propulsion problem is terrible nobody knows how to face them incidentally may I suggest that you have a look on your website at the website called centor dreams is anyone familiar with this okay some are good thank you now if you please have a look at this website which is written by by journalist called Paul gilster he describes in a perfectly understandable way what the scientist would describe with with technical papers essentially the the point is this one we do not know how to get to the nearest STS and here is where my proposal comes out the problem of course is that even the nearest Stars Alpha centor which is a triple star system is so far away that we cannot get there we do not know how to get there but my proposal is not to get there first my proposal is that the sun Focus comes first and then the real Interstellar target comes second so my proposal is to send just emission to the sun gravity Focus which is of course much closer how much closer well roughly speaking to3 times for Alpha centor but of course it is much much closer for any other star system because the stars are far away so here is the real possibility for making this space Mission become reality in our days not in the far future it would be possible to set up a space mission like that it doesn't require anything special you just need a large antenna on board and of course you need a propulsion system capable of taking you to 550u but 550u is not as far away as Alpha centor not to mention any other star so this is what I think my proposal is is new with respect to other proposal you know now I hope you'll forgive me if I make a comment about the United States which is the country that is hosting me that I love but I love but but let me say it seems here that all the people are so much impressed with Star Trek that they all want to go faster than light you know go faster than but faster than light is not possible at the moment I'm not ruling out that in a 100 years or even less it will be possible for instance I'm thinking about quantum entanglement which is a very promising field but all this at the moment is still in the minds of top theoretical physicist not in the physical realities of space companies whereas this stuff is within the possibility of space companies so I'm not talking about too far future and talk about present good now just to mention another problem this is very complicated mathematical problem let me just mention to you what the spirit of the story is incidentally this would be an ex excellent theme for PhD students who have to write PhD thesis and you know they want to show up that they know mathematics better than the that the teachers which is hopefully the case but anyway so the the story is this way consider for instance that we want to go opposite to the alpha centor system okay in other words if we want to get radio images very largely magnified all of the alpha centor system then we have to send our focal space at exactly in the opposite direction with respect to the sun obviously now if you look at the declination that is the latitude of alpha centor this is minus 60° is Alpha centur is in the S hemisphere it is not visible from you and you have to go down with respect to the equator minus 60s now this means that our spacecraft has to go up 60° in the opposite direction agreed now this is bad news for the engineers designing the space mission because people in the space business know that any as they say inclination change that is changing the trajectory with respect to the E cliped by an angle of 60° is terribly demanding in terms of fuel so once again if I was going to ask the engineers to design a space mission getting out of the of the ecliptic plane by an angle 30 de they would say oh my you know this is too bad so once again we have a problem now let me tell you how this problem could possibly be faced well the solution is here the again the largest mass in the solar system is the sun if you imagine to approach the Sun from below at a suitable distance so you have to compute that the sun would let the spacecraft exit it along an hyperbolic orbit with the focus at the sun and the sun would give you for free any inclination change you may possibly need in other words you can design the trajectory but the last fly by of many as many as you is must be the sun fly by because this is the only fly by that gives you free inclination no fuel at all now this is very good but it has a an opposite side that is how close to the sun do you have to fly and if you fly Too Close you know it may be very hot over there so this is risky now we could change and rather than using the Sun for that we could use Jupiter which is the second largest mass in the sstem this was indeed used already in a space mission by the European Space Agency called ulis people familiar with that know that ulysis went out of the ecliptic plane after flly bying Jupiter so this was done already we could do it it's up to us to decide you know of course then there are the flight times involved so it's a very complicated mathematical problem that that you know I am too old to face okay this so the message is for the young guys then let me say something about the solar Corona now anybody interested can read this paper down here by John west of JPL published in arotica in 99 essentially in my book there are two chapters entally here is the book if anyone would like to have a look at the end of the talk here is the book so in my book there are two chapters devoted to this and essentially let me come straight to the point this is the key diagram in the full story of the solar Corona now let me tell you how to read this diagram please on the horizontal axis you have the distances from above the surface of the Sun in units of the sun radius so this this first one that you see here means one sunand radius which is the surface of the sunand okay and then you go over to 1.05 and so on up to 1.4 actually we could go over to two because the solar Corona that is the Flames extend roughly up to two Sun radi from the center now on the vertical axis here you have the real focal distances that the spacecraft has to reach in order to find the real Focus now you say but you said the real focus is 550 you well I'm sorry to disappoint you again this is true that that would be true if there were no electrons in the Solar Corona but actually in the lower stratification of the solar coron there are a number of free electrons and they are doing exactly the opposite of what we want that is if the gravity is focusing our radio waves the electrons are doing the other way thing that is they are defocusing they are they are diverging it's a Divergent lens the one created by the electrons in the corona not a convergent lens so in other words there is a fight in between the gravitation that wants to focus and the electrons in the corona then wants to have the Divergence so the conclusion is that it depends on the frequency that you are observing and the the real conclusion is that the real focus is pushed out from 550u to higher distances according to the frequency that you are observing okay so this is the bad effect of the corona but we cannot face do anything else then face it now on the vertical axis there is this real Focus you see that it starts at 550 Au in a u of course and it goes up to 1, 1100 they use now these curves here are the curves of the real focal distance according to different frequencies for instance the first this one is for a frequency of 59 GHz the second this one here from above is for a frequency of 122 GHz and here is the most important one the red one this one here the red curves goes the red one here goes on the frequency of the peak of the cosmic microwave background and this is precisely what I would suggest to observe in the first focal space mission so let me please open up a small parenthesis but I have to explain this now we all know that the universe is filled with this relic of the Big Bang called The Cosmic microwave background now the spectrum of this thing is a perfect plank curve that is the black body radiation curve for a temperature of 2.7 Kelvin de we all know about that Nobel laurates discovered that penan and Wilson in the 164 1964 and then many other space mission have been built to observe the inhomogeneities in the in the cosmic microw background I'm just thinking of Kobe um the American Mission Kobe and then the next mission W map and then the European Mission uh plank okay so they are all doing the same thing but the difference is that the angular resolution in observing the the CMB is improving in time now if you go over and compute the peak of the micro backround you find that this is about 360 GHz which corresponds to this curve in our diagram now please look at this point this point means that the real focus is above 750 Au and actually the computer gives me 763 Au so in other words still if we want to please the cosmologist and use use the focer space mission in order to look at the cosmic microwave background with an huge angular resolution much better than anything we can do humans because we are two small guys then we must reach 763 Au and not just 550 period is is that clear so honestly I would propose in any space mission to try to reach that distance it will be reached anyway it's just matter to wait 20 more years these are the the distance is in the game and there is nothing we can do about that so anyway I wanted to point this out and if you look at the distance from the center of the sun where these waves are passing you find 1.1 so they are above the sun surface but not too far so the effect of the of the corona is unfortunately remarkable what to do about that well here is one suggestion but of course there may be others suggesting my suggestion was to have a space that is actually doing interferometry I told you already about that so I suggested to use two antennas that revolve around the rear space which is this little thing in there and they are tied to each other by a tther and this this is precisely what you would see you see you have antenna number one here so it's it's a dish in my calculation this was a 12 meter dish but we can improve it I mean it's up to the engineers to to decide about that this would be the second antenna this is the focus spacecraft this is the teder on one side this is the T on the other side and of course you release slowly the tther and so they move not in a circle but in a spiral and this is called aredian spiral because apparently the first mathematician who found the equation of the Spiral was no less than Archimedes in Greek Roman times so these are two archimedian spiral and practically speaking what you get is that they move around in this way and they cover a much larger field of view than if you had only one antenna so this is very good news and this is precisely the technique that radio astronomers do every you know vbi and synthesis synthesis radiom so we all know about how to handle that the point is just to increase the the T length or decrease the L okay next now I would like to to suggest to you three different targets for this space mission one is the G galactic black hole one is the Triple Star Alpha centor and and the third target may be any extrasolar planet for instance I selected Glee 581 but it could be anyone let me go over to the details so you see how the spacecraft and and the full mission is different according to the Target you want to observe so let's start with the galactic black hole now the good news is that in recent years as you certainly know the last 15 years a lot of research has been done about the monster that is located at the center of the Galaxy why monster because this black hole appears to have a mass now they say 4 million times the mass of the Sun so it is a monster how can you possibly imagine such a massive object and yet our galaxy is a quiet one so there is much worse probably in another galaxy but that this is their job not not our job so anyway just imagine please this now here is the sun I use the old value of 32,00 light years because when I was a student they taught me that this was the right value in between the center of the Galaxy and and the sun now they said this is 25,000 sorry but but doesn't change too much the story anyway it does it does only change slightly the story now here you have this monster the galactic black hole of course this is a sphere and please imagine that this thing this archimedian spiral are taking place in the perpendicular plane you know I couldn't draw it in a perpendicular way but you have to imagine that and you also have to imagine that all this thing is exactly the same but in the perpendicular plane okay so this is precisely the trick that I have suggesting we have the spacecraft our space going up to 550 U or more according to the frequency you want to observe and then you have these two t antennas that uh are tied to each other by a tet but but the Teter is deployed so that they move along Spirals and of course they cover a much larger field of view on the other side so the conclusion is that there is a trivial calculation that they now just just show you you you can write from the similarity of the two triangles this proportion minimal T lens is proportional to 550 U as Twice The Spar radius of the galactic black hole which is the diameter of the black hole is proportional to 32,000 lias or 25,000 whatever you want so so in this equation you only have one unknown which is the tether length all the rest is known so you solve for that and you find what the tether land is for a spacecraft going toward watch at the galactic center and the result is wonderful it's less than 2 kilometers now everybody in the space business know that this is absolutely feasible right now we already flew around the earth TS up to 18 km or even more so this is techn technologically within today's reach which is what I'm stressing because it makes the the space mission becoming real and not faster than light stuff okay so this is what I suggest for observing the galactic center now let's change the target let's go for Alpha centor system why Alpha centor well obviously because when the time will come when we really can fly to the nearest star if out of the question that Alpha sentor will be the first Target because it is the closest St and that's it so what can we do now well the first thing is that we should just fly in the opposite direction as I said reach the focus of the Sun and have a very highly detailed radio picture of whatever is in the radio Alpha centor system for instance today there is a strong research effort going on to find out whether in the alpha centor system there are or no no planets so far no planet has been discovered but who knows they could be there they could be small so we didn't see them so far okay so this is a big question mark now certainly by using this we would be able to find out whatever is in the system because we have such a magnification provided by the S now let me just tell you that if you try to apply the same trick of you know these two revolving antennas and the tther and so on for alas centor I'm sorry out of no way because the length of the tther would be 10 to the 6 kilomet so one 1 million kilom so so this is crazy we cannot have any T like that so this is to say that we cannot use that trick in order to watch at the alpha centor system obviously because the alpha centor is much closer than the center of the Galaxy this is what plays in the game so we must use something else now this is a picture of the gag Museum in New York but I tilted the picture in order to let you have an intuitive description of what a conical Helix is well a conical Helix as the name says is a helix that is it goes up like this with increasing radius but it is located on the surface of a cone okay so you start from one point which is the apex of the con and then you keep increasing that this is a conical now why do we have to think about a conical heasy no I'm sorry because this is the only way to have our spacecraft going around the focal axis between ourself and Alpha centor and get a larger field of view of the full system by changing the trajectory rather than by using the T trick okay now this is demanding because it's not an easy thing to have a space moving and along a conical Helix so people in the space business we have to think hard about how to get that into reality but honestly this is the only solution that they could possibly imagine because the field of view for Alpha Sor is so large that we cannot do it by other techniques final point just one extra Solar Planet for instance g whatever well here the story is another one extras solar planets are not as close to the Earth as alpas and Tor they are farther out but certainly not as far out as the center of the Galaxy so we have to devise techniques that somehow are halfway in between the the two ones that they described let me just give you one thing the my suggestion is to watch at these planets on high frequencies because as essentially that formula over there gives you the linear resolution provided by the sun gravitational lens and so if you want to see the details of these extra solar planets we should go for highest frequency as possible sorry that's all I can say I'm sure that much more could be possibly said but that's all I can say good now let me tell you about some real proposals starting with NASA now about 10 years ago a group was assembled at J JPL to study a mission called Thea ISP Interstellar probe and I was one of the persons in the team now here the story is completely different that is the Sun as we know is moving around the center of the Galaxy and it takes 200 million years to make a full turn but the sun emits its own wind which is actually a flux of proton called the solar wind so there is a region around the Sun in the shape let me say of a comet so it has a small nose here and an awfully long tail on the other side but there is a region in space around the Sun where the solar wind is predominant with respect to the interstellar wind which is the same story as the solar wind but coming from other stars okay and uh Frontier surface in between the solar wind dominated part and the interstellar wind dominated part is called the helops now the idea of the JPL people in designing this space mission is let's send the spacecraft in this direction so let's send the spacecraft into the direction of the nose of the inter of the ilost the nose is where the the the ilos is closer to the Sun okay so that we get there with the minimum amount of time obviously this is the key point now if you want to know the numbers roughly the theories predicts that the nose is about 141 Au so much closer than 550 which is why the JPL people consider the missions and they completely agree with them the only point that they suggested in in this study was that since the spacecraft is going on after 141 Au up to any distance so sooner or later it will also get to 550 then please be prepared and put aboard the spacer something that when the space get to the focus tells us that he has reached the focus so this could be a magnetometer could be a bolometer we we can discuss about that this is engineering stuff but the point I made during this study was that we should put something because this is not stopping at the heloa it's keeping going and sooner or later it will prove to us that this is the actual focal distance and not just what we computed so far we only could do Theory mathematics and not real stuff not actual experiments okay so this is the basic idea of the of the interstellar uh NASA Interstellar prob and I you know if if I will ever be allowed to submit a proposal to NASA or to any other space agency I would certainly suggest to continue the work there because much of the work is done already and then there is another advantage but let me also tell you for the moment that also the European space agency has done the same thing so this proposal by the German women schan grber associated with r mnat of of APL Applied Physics Lab at John Hopkins University is the same as the NASA proposal basically okay now here again is the same story so you have the solar system this is the orbit of Pluto and so on and so we get this way but now I wanted to point out the second Advantage apart from the uh what they said already and this is the second Advantage now these two plots show you all over the celestial sphere which is the direction of the incoming Interstellar wind in other words we are at the center of the celestial sphere towards us because of the motion of the sun around the center of the Galaxy we have a flux of hydrogen helium oxygen and other things which roughly speaking all come from the nose of the heliosphere now here is an extremely lucky s circumstance meaning that we were just lucky and nothing else there is no relationship physically speaking with these these parameters that is this nose is really very close to the ecliptic plane this is just by chance because of course the ecliptic plane depends on how the Sun was born 4.5 billion years ago whereas whereas this stuff the inter Interstellar wind is is completely different story but we are lucky because the nose is actually just a few degrees away from the ecliptic and this saves us from changing the inclination of the spacecraft with a large angle which is exactly what propulsion engineers in space business want because then it would have been much demanding in terms of of fuel so here is one more reason to adopt this target for the mission to the gravitational lens of the sun because it is not so expensive in terms of fuel consumption ah but here is the final point in the story let me let me please tell you I told you already that the cosmic microwave background CMB is extremely important for cosmology because it's the remnant of the big bang and you you know we have spent already three space missions two Americans and one European to watch at the cosmic micro background with the highest possible resolution okay now in my book is written that if you use the Sun as a magnifying tool oh my then you get such a huge resolution that by far dwarves all the previous space missions because you have the sun in between so this gives you an enormously higher resolution roughly speaking I computed that the increase would be of the of the order of 1 billion times now this I am going to use as a lever the the archimedian lever to convince the cosmologists that this is serious stuff why the cosmologist well let me sorry let me speak in political terms because in the end science is all nice but in the end it comes to the politics now the community of cosmologist is extremely powerful in the astronomical world really they they're practically suggesting space mission like the ones I mentioned Kobe and W map and and plank in Europe that cost a lot of money and European and NASA agencies are putting money because the cosmologist as that to put so so if the cosmologist come to realize that using the Sun as a gravitational L would give them a billion times better angular resolution that all the previous space missions I guess that they would go for that and this would also help us poor City scientist who you know who have a hard life because many people don't reg city is a serious stuff and so on for so this is the political trick sorry to be tried in order to have the support of a larger Community than just the CTI side good so all this is described in in the book and what I'm talking about is the are the two final chapters of my book and the first part now let me come straight to the point the second half of the book is devoted to a completely different story it's not as nice physically speaking as the gravitational lens of the sun this is another story this is a mathematical description of an algorithm that would pick up very weak signals out of the background noise better than the forier transform fft that is the standard tool that the whole world uses including the C world now look I know that it's pretty late and I mean I'm I really used much of my time to describe the the sound gravitation L because this is so much more more romantic than than mathematics now here is the second part and I am sorry it is terribly mathematical if you give me 10 more minutes I would go so let's be Democratic would you mind if I speak for 10 more minutes about that just summarizing the story okay this is mathematical I say but but I'll try to to be clear now what is the KT first of all what what is the K and what is the L the K is the initial of a finish mathematician K karun and the L is the name of a French American mathematician Michelle Lev who came over here at Berkeley and I guess his wife is still his widow I'm sorry is still at Berkeley anyway there is a lower price at Berkeley for young people dealing to dealing with probability things so what is the KT the KT is named after these two gentlemen who discovered the full mathematical stuff in 1946 but let me explain things in a very easy fashion uh forget for a moment about all this mathematics and just consider an object for instance this book Newtonian physics so there is nothing easier than that and more intuitive than this book now this book has its own mass and in Newtonian physics I can use a system of fre axis X Y and Z to describe this book in terms of Newtonian Mass however because of the shape of the book which looks very much like a rectangle or something like that there are three directions S one two and three that are privileged with respect to any other direction agreed now this privilege direction are called by mathematician and scientists principal Axis or inera axis and so on and the basic idea is that if you change the reference frame so here you have your book and initially your reference frame was here but if you change it and you bring it exactly in the three privilege Direction your mathematical description is much simplified or in mathematical terms three time three Matrix becomes zero everywhere except for the three terms on the main diagonal that's all now this stuff was discovered in 1748 by Leonard Oiler the Swiss mathematician and this is precisely what happens now if you paid just a moment attention to this met this is the three three inertia Matrix that describes in Newtonian terms everything after the principal ax transformation you have all zeros except for the main diagonal so this is called the principal component analysis or principal axis transformation there are many names for that but this is the very simple idea now this axis are called igen vectors which is a name coming from the German ens mean proper essentially so you could call them prop proper vectors in other words each body each of us has his own igen vectors or her own igen vectors that is the vectors describing the masses of the body in the best position and they can be found mathematically you just need a good computer and something else now the idea of the klt is simply to pick up all that Knowledge from Newtonian stuff and to translate that into signal processing that is the theory of of getting a signal out of the background noise by assuming that you can expand this things here which is a random function of the time that is uh you have the time axis going that way and you have the y- axis going up and down in a random fashion that you cannot predict so it's not an analytical curve it's a random thing and in in the physical real world this means that you called by that thing capital x of T there is a name stochastic process but essentially in physics this means that this is whatever comes inside your antenna in other words you have a big radio telescope as here in the city business basically what comes inside your radi telescope is noise That Is Random fluctuation but there might be a signal buried in the noise much tiny much less intense than the noise so what you do is to pick up whatever comes inside I don't care what is there everything and I call this a stochastic process or random input but then or well random input over a finite time span so the the time range is from zero to capital T now incidentally this story of the final time span is important for mathematicians because in the Fier transform unfortunately you have to confine yourself to infinite time span or nearly so so this creates an extra number of mathematical complication this does not exist in the K from the very beginning anyway you pick up that and then you try to describe that as a sum an infinite sum you see this this sum ranges from one to Infinity of terms and each term is in loose terms statistically independent from the next neighbor it it's like a town everybody has his own apartment and does what he or she pleases okay I am statistically independent from anyone else in theory but this is the case so each term is statistical Independence not just that each term is actually achieving a decomposition that is this capital Z represents the random variables that is a probability distribution that is fixed in time whereas the function of t f of T is a pure time function which is not related to probability so in other words this is a subtle ways to say that I have decomposed my random function in the statistical part and in the time behavior from the very beginning again this is a new thing with respect to for it's completely different now I don't want to arrest you too much but essentially in forier you have these conditions which means that the functions on which you expand your signal that are signs and cosines in for are orthogonal to each other orthogonal in the mathematical sense that is that the integral of the product of two equals zero or one if for the same variable this is the key point in the story and it was discovered by again the Swiss guy Leonard hoer around 1748 and it was after this discovery that Fier realized forier was a french guy live later 50 years later he realized that he could use the oiler formula which is just this but for S and cosine in order to reconstruct the coefficient in the series by performing the so-called inversion so historically speaking this was an important step ahead now let me just come straight to the point the same story applies to the klt and there it is but with one more complication that is in the KT I use a second orthogonality that is not just one as in forier Oiler and so on but the second one that applies to the random variable here in the sense of probability and this means that the autocorrelation this is what it is the mean value of the product is zero for different random variable but it cannot be zero for the same random variable otherwise that random variable would be zero so this Lambda here which is called the nigen value in the language of physicist is actually the variance of the of the R so let me put that in a easy way the easy is this things that the K is much more profound mathematic first of all because it uses two orthogonalities not one but then there is one more point that I have to stress the good old for staff relies on the idea that the only basis function that is the only set of axis on which I perform my expansions are signs and cosiness period here we do not make any assumptions on that from the very beginning we don't know what is the set of basis function but we discovered that along the solution of the problem because it can be proven and this is the next slide that the basis functions that is the Egan functions are the the solution of this thing which is an integral equation where the autocorrelation is the known part and the functions and the EG values are the unknown part so here is the most profound aspect of the story because you are not tying yourself to a specific set of functions on which you you you you expand you discover which one is the best set according to the different problem you Sol so this this means that the transform is really adaptable to different problems completely different problem so after the discovery of all this stuff there were cases where mathematician and physicist and engineer and could solve the integral equation let me please tell you that when I was a PhD student in mathematics I got my PhD because I was able to solve the integral equation for a special class of functions which are So-Cal White Noise integrals or timary scale gaussian processes I know this is technical but anyway the conclusion is that for that particular class the igen functions are Basel functions of the first kind and they are not SS and cosines they're different different animals okay and the igen values the Lambda n for that case are the zeros of that is the point where the function is zero of Center linear combination of the Bessel function and and um their first derivatives so anyway in conclusion the klt adapts itself to the problem that you are considering and in this sense it is capable of recovering out of the background noise a signal that comes inside your radio telescope with a much lower signal to noise rure than forier and this is precisely why the C Institute people and especially J T and friend and I'm grateful to them because they realize this this is not an easy thing to realize in the beginning for people trained with classical stuff you know but when you realize the much more wide vision that this can give you then you are ready to pay for the extra computational burden that your computer has to face in order to find out the egg and vectors and the vectors values and vors so the conclusion is that there is a group of people here at the city Institute let by Jil tartter and fr Dr and so that would like to put this algorithm on the Allen telescope array because we do not know what the hell of the signal the Extraterrestrial might send us now this is an important point because in other applications all this the K can be easily bypassed by the so-called match filter now the match filter is essentially something that gives you the best filter to filter out anything if if you know what the shape of the incoming signal is and this is of course the case in all engineering application on Earth because we know you know if there is an ESC going WR or whatever we know that but in the case of sa we are just facing the The Peculiar case the black sheep because we do not know what the hell is coming inside so rather than just ruling out all this because it is computationally demanding uh the suggestion is don't rule out anything and keep it and we'll see what comes out out of that so I don't want to insist more there would be more but if you if you really want to know more about that you read my book and there is all the the calculation that I have found in 20 years of time so conclusion of the story this book is to phase first phase space mission to 550u that was conceived by FR Drake for the good of sa but actually is now proving itself much more useful outside safety for instance cosmology as I said in the microw background and also other things you know alpas and Tor the black hole at the galactic center many other and the second part of the book on the contrary is devoted to this algorithm which is again was born out of set needs but if you think carefully of course it applies to everything because mathematics applies to everything thank you very much [Applause] this fantastic thanks Claudia um if I may ask the first question in your uh CMB uh Mission um what sort of angular resolution would you get um for looking at the CMB how much of the CMB Could you actually you get 10 Theus 8 AR second I show you that so I'm I'm going back okay here here it is so it's about a billion times better than the angular resolution of kobby w map and pl so how much of the I'm thinking of how much use would that be if you resolving the CNB um of adjust what's behind the sun are you actually going to see enough to make it useful for the cosmologists well the point is that we would be able to see the star formation for instance in much neater detail than we know about but that also applies to cosmological objects so for instance there has long been debates about what quers really are are they well they are prototype galaxies but okay but then the Stars might be there and so on and so forth my impression is that with such a huge Improvement in the angular solution we would be able to find out whether there are stars within quers or not do you have any other questions uh yes as the focus extends to Infinity right um or we at the focus of alpha Century or maybe at the focus of some galactic black hole already and just sitting where we are could observe the cosmic uh uh microwave background that way yes the the answer is yes and I thank you about that this is a question that I you know was asked to me many times the answer is yes but unfortunately there there is one drawback just consider the nearest case that is Alpha centor then you have to take into account the attenuation of the signal that takes place in between Alpha sentor and where we are and unfortunately the attenuation which goes with the one over the distance squared is is so large that we cannot use the alpha centor lens as you would be suggesting or any other lens even further out as an improvement to what we can do here okay so the answer is in principle you are absolutely correct but when you go down to the calculation you find that the attenuation already for asor and even worse for the nearby stars or or whatever is too big and we cannot get it and anyway this is this is treated in my book claudo that actually um may have answered my question but I was wondering how sure we can be of the fluctuations in the microwave background because they're you know they're supposed to be indicative of quantum fluctuations uh then via inflation causing you know variations in the microwave background but how sure are we that they are not a series of distributed gravitational lenses where the sources are too far away from us to directly detect optically or by radio but the fluctuations they're producing those fluctuations look I I I don't know about that this let me tell you this would require a study of the focal space mission just for cosmology alone so no City no anything else but just for cosmology we should do that but you see the difficulty for me is to convince the scientific community that focal is the first thing that we have to try because it it offers so much magnifications so if I could answer very honestly to your question my next step would be to go to Paul Davis who appreciates all these and say look you are a cosmologist now would you please assemble a team of cosmologist we would explain to them the focus bace mission that they certainly don't even know about because you know the there are so many different topics of interest and then we would go over to your question at the moment I have no answer for the question so thank you for such an interesting talk um and as far as I can tell you were just considering radio waves and microwaves uh could this be done in shorter waves Optical yes it can and actually well it can if we can overcome the corona problems C can you just block it with an Ault yes this can also be done correct yes uh look this was actually the first thought ever about all this coming from FR Drake so when FR Drake made the first presentation ever of the Sun as a gravitational lens in Hungary in ' 87 which stunned me so much he was just talking about that I remember a sentence of his he said you know by virtue of this trick we could see you could see the people walking in the streets on some nearby planet now this is easily said and difficultly computed so I don't know the detail about that okay my honest opinion is that we would need to to do one more study as the one for cosmology that I just mentioned for this aspect that is Us in the s for optical okay and also following question if you think about this in terms of uh you know telescope Optics effectively you have a very chromatic lens with a very large Central obstruction uh have you considered uh you know how that affects the bandwidth in which you can image and and also the yeah I know the size of the point spread function how that affects that okay thank you wow sorry to disappoint you in my book this is not considered but I know that there were people possibly uh Jeff Landis at Nasa you know NASA Glenn who once mentioned to me the point spread function of the S gravity lens so you won't find this in my book but if you talk to him he may be able to say more all right thank you in Practical terms terms oh sorry sorry uh in U practical terms it seems to me that um that getting cosmologists on board to support the focal mission is is difficult given that um you're talking generations to get out to 763 Au aren't you yes yes you're right this unfortunately is one of the drawback of the mission that is to get to 753 auu takes 50 years it depends on the propul system so the difficulty in not so much in proposing but in making this Mission become a reality is at least twofold first you need a strong scientific Community Support in the IDE and this is why I thought of the cosmologist because in my opinion they are the strongest group ever in the astronomical Community but apart from that there is another awful issues which is the propulsion system you know there are different ways of conceiving propulsion for deep space mission like this one I just mentioned one the nuclear electric what is this in plain terms it means that you're using electric propulsion but the energy comes from a nuclear reactor now this brings more problems first of all electric propulsion works for people who are not acquainted essentially you have a gason usually which is ionized and then there is a electrod set of electrod that push that out and they pick up the electrons when they get out but they get out of the space with such a momentum that this pushes the spec it's not so much High the momentum but it is continuous so it has been proven out of the question that within the solar system this is excellent for Planetary Exploration okay there are many missions both American and European that have been using that already period the question is are we going to use nuclear energy to feed that oh my this is another problem because the ecologists of course we say no no no no no if an an accident happens during the launch phase you are responsible if it's true but when you consider distances of that order there is no other way because there is no sun over there no light you you realize the point even the voyagers would have been dead long ago if they hadn't had a a thermal generator please correct me if I'm wrong exactly so here again is another problem you know we have to be careful because if by any means the newspapers publish oh this guy wants to use nuclear elect propulsion to go to the sun focus with by we are everybody is against for emotional reasons so the answer to your question is the times are huge but it all depends on the propulsion system now let me just give you one more answer recently was talking with people in the not in the FTL business but in other business called called vasir and very Advanced propulsion system now they would love to try that because so far all that has been on paper incidentally the Russian the Soviets whatever you have to call them already considered um nuclear propulsion for their own mission then the Cold War ended and the Russian handed over the the things to the Western but the West didn't notice or didn't notice appropriately so recently there was a top Russian official saying look we have the nuclear proportion we want to use it now if that will ever happen I would respectfully ask ask the American Community to do exactly the same as the Russians did because they did the right thing in order to reach high distances there is no way to escape the distance is what it is period I don't know if I disappoint you to is that the truth okay of course well people in the space business may may have better answer than I can not today okay good okay okay okay there's no further questions Claudio well we've got a small oh we've got one quick one reactor or a nuclear uh Radioactive powered battery you're talking about I would choose the second option but you see the the full matter is completely uh in the set of question marks let me tell you more in detail there was a set of conferences that you probably are acquainted with the so called stay sty bed technology and application conferences that were held in the late '90s early 2000s at albukerk New Mexico just by chance not too far from Los Alam okay by just by chance now there it is where we debated all these matters so there are people who are definitely favorable to nuclear stuff and who knows perhaps the military are very favorable to nuclear stuff but this is not known to scientists like like myself and so the the matter is still undecided okay we have to decide what to do period claudo as a a small token of our appreciation we have a little uh wow pin for you thank you so much join me in thanking clao for he's very fascinating thank you thank you very [Music]