he left Cornell in 1950 and went to Caltech where he has been ever since before I let him talk I want to tell you just a little bit more about him 3 or four years ago he started teaching a beginning Physics course at Caltech and the result has added a new dimension to his Fame his lectures are now published in two volumes and they represent a refreshing approach to the subject in the preface of the published lectures there's a picture of Fineman performing happily on the bongo drums my Cal Tech friends tell me that he
sometimes drops in on the Los Angeles night spots and takes over the work of the drummer but Professor Fineman tells me that that's not so another of his Specialties is safe [Music] cracking one Legend says that he once opened a lock safe in a secret establishment removed a secret document and left a note saying guess [Music] who I could tell you about the time that he learned Spanish before he went to give a series of lectures in Brazil but I won't this this gives me enough this gives you enough background I think so let me
let me say that I'm delighted to welcome Professor feineman back to Cornell his General topic is the nature of physical law and his topic for tonight is the law of gravitation an example of physical law professor fin [Applause] it's odd but in the infrequent occasions when I've been called upon in a formal place to play the bongo drums the introducer never seems to find it necessary to mention that I also do theoretical physics I believe that's probably uh that we respect the Arts more than the Sciences the artist of the Renaissance said that man's main
concern should be for man and yet uh there are some other things of interest in the world even the artists appreciate sunsets and the ocean waves and the march of the Stars across the heavens and there is some reason then to talk of other things sometimes as we look into these things we get an aesthetic pleasure pleasure from him directly on observation but there's also a rhythm and a pattern between the phenomena of nature which isn't apparent to the eye but only to the eye of uh analysis and it's these rhythms and patterns which we
call physical laws what I want to talk about in this series of lectures is the general characteristics of these physical laws that's even another level if you will of higher generality over the laws themselves and it's U really what I'm talking about is nature as seen as a result of detailed analysis but only the most overall General qualities of nature is what I mainly wish to speak about now such a topic has a tendency to become too philosophical because it becomes so General that a person talks in such generalities that everybody can understand him and
it's considered to be some deep philosophy if you however I would like to be very rather more special and I would like to be understood in an honest way rather than in a vague way to some extent and so if you don't mind I'm going to try to give instead of only the generalities in this first lecture an example of physical law so that you have at least one example of the things about which I'm speaking generally in this way uh I can use this example again and again to give an instance to make a
reality out of something which otherwise be too abstract now I've chosen for my special example of physical law to tell you about the theory of gravitation or the phenomena of gravity why I chose gravity I don't know I had whatever I chose you would have asked the same question actually it's uh was one of the first great laws to be discovered and it has an interesting history you might say yes but then it's old hat I would like to hear something about science more modern science more recent perhaps but not more modern modern science is
exactly in the same tradition as the discoveries of the law of gravitation it is only more recent discoveries that we would be talking about and so I have no I do not feel at all bad about telling you of the law of gravitation because I am in describing its history and the methods the character of its Discovery and its quality talking about modern science completely modern this law has been called the greatest generalization achieved by the human mind and you can get already from the my introduction I'm more interested not so much in the human
mind as in the Marvel of nature who can obey such an elegant and simple law as this law of gravitation so our main concentration will not be on how clever we are to have found it all out but on how clever she is to pay attention to it now uh what is this law of gravitation that we're going to talk about the law is that uh two bodies or bodies exert a force upon each other which is inversely as the square of the distance between them and varies directly as the product of their masses and
the mathemati mathematically we can write that great law down and the formula some kind of a constant times a product of the two masses divided by the square of the distance now if I add the remark that a body reacts to a force by accelerating or by changing its velocity every second to an extent inversely as its mass it it reacts uh changes velocity more if the mass is lower and so on inversely is the mass then I have said everything about the law of gravitation that needs to be said everything else is a consequence
a mathematical consequence of those two things that I said that's a remarkable enough phenomenon in itself that the next lecture will consider this in more detail now I know you're not all here I know some of you are but you're not all mathematicians and so you cannot all immediately see all of the consequences of these two remarks and so what I would like to do in this lecture is to briefly tell you the story of the discovery tell you what some of the consequences are what the effect of this discovery had on the history of
science what kinds of mysteries such a law entails some something about the refinements made by Einstein and uh possibly the relation to other laws of physics the history of the thing briefly is this that the Ancients first observed the way the planets seemed to move about in the sky and concluded that they all went around along with the Earth went around the Sun this discovery was later made independently by cernus after they had forgotten that people have forgotten that it had already been made now the next thing question that came up in to study was
exactly how do they go around the Sun that is exactly what kind of motion do they go with the Sun at the center of a circle or do they go in some other kind of a curve how fast do they move and so on and this discovery took a longer to make the times after cernus were times in which there were great debates about whether the planets in fact went around the Sun along with the Earth or whether the Earth was at the center of the universe and so on and there were considerable arguments about
this when a man named Tao Bri got an idea of a a way of answering the question he thought that it might perhaps be a good idea to look very very carefully and to record where the planets actually appear in the sky and then the alternative theories might be distinguished from one another this is the key of modern science and is the beginning of the true understanding of nature this idea that to look at the thing to record the M the details and to hope that in the information thus obtained May lie a clue to
one or another of a possible theoretical interpretations so Tao who was a rich man and owned I believe an island near Copenhagen outfitted his island with great brass circles and special observing positions situation chairs that you could look through little HS and recorded night after night the position of the planets it's only through such hard work that we can find out anything when these all these data were collected they came into the hands of Kepler who then tried to analyze what kinds of motions the the planets made around the Sun and he did this by
a method of trial and error at one stage he thought he had it he ass he figured out that they went around the Sun in circles with the sun off center and noticed that one planet I think it was Mars but I don't know uh was 8 minutes of Ark off and he decided this was too big for Tao Brady to have made an error and that this was not the right answer so because of the Precision of experiments he was able to proceed and find that to go on to another trial and found in
fact ultimately this three things first that the planets went in ellipses around the sun with the sun of the focus an ellipse is a curv you all artists know about because it's a for shorten Circle or children know about because somebody told them that if you take a string and tie it to two tacks and put a pencil in there it'll make an ellips these two tacks are the fosi and if the Sun is here the shape of the orbit of a planet around the Sun is one of these curves the next question is and
going around the ellipse How does it go does it go faster when it's near the sun slower when it's further from the Sun and so on we take away the other Focus we have the sun then and the planet going around and Kepler found the answer to this too he found this that if you put the position of the planet down in two at two times separated by some definite time let's say uh 3 weeks and then at another place in the orbit put the positions of the planets again separated by 3 weeks and draw
lines from the sun to the planet technically called radius radius vectors anyway lines from the Sun to the planet then the area that's enclosed in the orbit of the planet and the two lines that are separated by the planet's position 3 weeks apart is the same no matter what part of the orbit the thing is on so that it has to go faster when it's closer in order to get the same area as it goes slower when it's further away and in this precise manner some several years later he found the third Rule and uh
that had not to do with the exactly motion of a single planet around the Sun but related the various planets to each other and it said that the times that took the planet to go all the way around was related to the size of the orbit and that the times went as the square root of the cube of the size of the orbit and for the size of the orbit is the diameter all the way across the biggest distance on the ellipse so uh he has these three laws which are summarized by saying it's an
ellipse and that equal areas are swept in equal times and that the time to go around varies as a three half power of the size the square root of the cube of the size so it's three LS of Kepler which is a very complete description of the motion of the planets around the Sun the next question was what makes him go around well how can we understand this in more detail or is there anything else to say in the meantime Galileo was investigating the laws of motion incidentally at the time of uh Kepler the problem
of what drove the planets around the Sun was answered in some some by some people by saying that there were Angels behind here beating their wings and pushing the planet along wrong around the orbit as we'll see that that answer is not very far from the truth the only difference is that the Angels sit in a different direction and the wings going but the point that the Angels sit in a different direction is the one that I must now come to Galileo in studying the laws of motion and doing a number of experiments to seeing
how balls roll down inclined Plains and pendul swarms and so on discovered a idealization a great principle called a principle of inertia which is this that if a thing has nothing acting on if an object has nothing acting on and it's going along at a certain velocity in a straight line it will go at the same velocity at exactly the same straight line forever unbelievable though that may sound to anybody who has tried to make a ball roll forever the idealization did is correct and that that there were no influences acting such as a friction
on the FL and so on the thing would go at a uniform speed forever the next point was made by Newton who discussed the next question which is when it doesn't go in a straight line then what and they answered this way that a force is needed to change the Velocity in any manner first for instance if you're pushing it in a direction that it moves it will speed up if you find that it changes Direction then the force have must have been sideways and that the force can be measured by the product of two
effects first how much does the velocity change in the small interval of Time how fast is the velocity changing how much is it accelerating in this direction or how much is the velocity changing when it changes its Direction that's called the acceleration and when that's multiplied by a coefficient called the mass of an object or it's inertia coefficient then that together is a force one can measure the for instance if one has a stone on the end of a string and swings it in the circle over his head then one can measure one finds one
has to pull the reason is that the speed of this the velocity the speed is not changing as it goes around the circle but it's changing its direction so there must be perpetually an in pulling force and this uh is proportional to the mass so that if we were to take two different objects first swing one and then swing another one at the same speed around the head and measure the force in the second one that second one uh the the new force is bigger than the other force in the proportion that the masses are
different this is a way of measuring the masses by how much how hard it is to change the speed now then newon saw I from this that for instance to take a simple example if a planet is going in a circle around the sun no force is needed to make it go sideways tangentially if there were no Force at all on it it would have just keep coasting this way but actually the planet doesn't keep coasting this way but finds itself later not out here where it would go if there were no Force at all
but further down toward the the sun in other words its velocity its motion has been deflected toward the Sun so what the angels have to do is to beat their wings in toward the sun all the time that the motion to keep it going in straight line has no known reason the reason why things Coast forever has never been found out the law of inertia is no known origin so the Angels don't exist but the continuation of the motion does but in order to obtain the falling operation we do need a force so it would
became apparent that the origin of that the force was toward the Sun as a matter of fact Newton was a ble to demonstrate that the statement that equal areas are swept in equal times was a direct consequence of the simple idea that all of the changes in velocity are directed exactly to the sun even in the elliptical case and maybe I'll have time next time to show you how that works in detail so from this law he would confirm the idea that the force is toward the Sun and from knowing how the periods of the
different planets vary with the distance away from the sun it's possible to to determine how that Force must weaken at different distances and he was able to determine that the force must vary inversely as the square of the distance now so far he hasn't said anything yes because he only said two things which Kepler said in a different language one is exactly equivalent to the statement that the forces is toward the sun and the other is exactly equivalent to the statement that the law is inversely is a square of the distance but people seen in
telescopes the Jupiter's satellites going around Jupiter and it looked like a little solar system so the satellites were attracted to Jupiter and the Moon is attracted to the Earth and this goes around the earth is attracted the same way so it looks like everything's attracted to everything else and so the next statement was to generalize this and to say that every object attracts every other object if so the Earth must be pulling on the moon just as the sun pulls on the planet but it's in known that the Earth pulls on things because you're all
sitting tightly in your seats in spite of your desires to float out of the hall at this time the pull of for objects on the Earth was well known in the phenomenon of gravitation and it was Newton's idea then that maybe the gravitation which held the moon in the orbit also applied was the same gravitation that pulled the objects toward the earth now it is easy to figure out how far the Moon Falls in one second because if it went in a straight line you know the size of the orbit you know it takes a
month to go around and if you figure out how far it goes in 1 second you can figure out how far the circle of the moon's orbit has fallen below the straight line that it would have been in if it didn't go the way it does go and this distance is 12th of an inch now the Moon is 60 times as far away from the Earth's center than we are we're 4,000 mil away from the center in the moon is 240,000 MIL away from the center so if the law of inverse square is Right an
object that the Earth's surface should fall in 1 second by/ 12th of an inch times 3600 being the square of 60 because the force has been weaken by 60 * 60 for the inverse Square LW in getting out there to the moon and if you multiply a 20th of an inch by 3600 you get about 16 ft and low it is known already from Galileo's measurements that fell in 1 second on the Earth's surface by 16 ft so this mean meant you see that he was on the right track there was no going back now
because a new fact that was completely independent previously which is the period of the moon's orbit and its distance from the Earth was connected to another fact which is how long it takes something to fall in one second so this was a grammatic test that everything's all right further he had a lot of other predictions he was able to calculate what the shape of the orbit should be if the LA with the inverse square and found indeed that it was an ellipse so he got three for two as it were in addition a number of
new phenomena had their obvious explanations one was the tides the tides were due to the pull of the moon on the earth this had sometimes been thought of before with the difficulty that if it's the pull of the moon on the earth the earth being here the waters being pulled up to the Moon then the would only be one tide a day where that bump of water is under the moon but actually you know there are tides every 12 hours roughly and that's two Tides a day but you must there was also another school of
thought that had a different conclusion their theory was that it was the earth that was pulled by the Moon away from the water so actually Newton was the first one to realize what actually was going on that the force of the moon on the earth and on the water is the same at the same distance and that the water here is closer to the moon and the water here is further from the Moon than the earth than the rigid Earth so that the water is pulled more toward the moon here and here is less toward
the moon than the earth so there's a combination of those two pictures that makes a double tide actually the Earth uh does the same trick as the Moon it goes around a circle really I mean the force of the moon on the earth is Balan but by what by the fact that just like the moon goes in a circle to balance the Earth's Force the Earth is also going in a circle actually the center of the circle is somewhere inside the earth it's also going in a circle uh to balance the moon so the two
of them go around a Common Center here and if you wish this water is thrown off by centrifugal force more than the earth is and this water is attracted more than this average of the Earth at any rate the tides were then explained and and the fact that they were two a day a lot of other things became quite clear why the Earth is round because everything gets pulled in and why it isn't round because it's spinning so that the outside gets thrown out a little bit in at balances and why the Sun and Moon
around and so on now as the science developed and measurements were made ever more accurately the tests of Newton's law became much more stringent and the first careful tests involved the moons of Jupiter by careful observations of the way they went around over a long period of time one could be very careful to check that everything was according to Newton and turned out not to be the case the moons of Jupiter appeared to be first to get sometimes to 8 minutes ahead of time and sometimes 8 minutes behind schedule where schedule is the calculated values
according to Newton's Laws it was noticed that they were ahead of schedule when they were close when Jupiter was close to the Earth and behind schedule when it was far away a rather odd circumstance and Mr Roma having confidence in the law of gravitation came to an interesting conclusion that it takes light some time to travel from the moons to the Earth and that what we're looking at when we see the moons and not how they are now but how they were the time ago that it took the light to get here now when Jupiter's
near us it takes less time for the light to come and when Jupiter's further it takes longer time so he had to correct the observations for the differences in time and by the fact that they were this much too early or that much too late was able to determine the velocity of light this was the first demonstration that light was not an instantaneously propagating material I bring this particular matter to your attention because it illustrates something that when a law is right it can be used to find another one that by having confidence in this
law if something is the matter it suggests perhaps some other phenomenon and if we had not known the law of gravitation we would have taken much longer to find the speed of light because we would not have known what to expect of Jupiter satellites this process has developed into an avalanche of discoveries each new discovery permits the tools for much more Discovery and this uh be this the beginning of that Avalanche which has gone on now for 400 years in a continuous process and we're still avalanching along at high speed at this time another problem
came up the planets shouldn't really go in ellipses because according to Newton's Laws they're not attracted only by the Sun but also they pull on each other a little bit only a little bit but a little bit is something and will alter the motion a little bit so Jupiter Saturn and Uranus were big planets that were known and the calculations were made as to how slightly different than the perfect ellipses of Kepler the planets ought to be going Jupiter Saturn and Uranus by the pull of one on each other and when they were finished the
calculations I mean and the observations it was noticed that Jupiter and Saturn went according to the calculation but that Uranus was doing something funny another opportunity for Newton's laws to be found wanting but courage two uh men both who made these calculations Adams and larier independently and almost exactly the same time proposed that the Motions of Uranus were due to an unseen as yet new planet and S they wrote letters to their respective observatories telling them to look turn your telescope and look there and you'll find a planet how absurd said one of the observatories
that some guy sitting with pieces of paper and pencils can tell us where we' look to find something new planet and the other Observatory was more uh well less uh well the administration was different and uh they found the Neptune more recently in the beginning of the 20th century it became apparent that the motion of the planet Mercury was not exactly right and this caused a lot of trouble and had no explanation until a modification of Newton's this did show ultimately that Newton's laws were slightly off and that they had to be modified I will
not discuss the modification in detail it was made by Einstein now the question is how far does this law extend does it extend outside the solar system and so I show on the first slide evidence that the law of gravitation is on a wider scale than just the solar system here is a series of three pictures of a so-called double star there's a third star fortunately in the picture so you can see that they're really turning around and that nobody just simply turned the frames of the pictures around which is easy to do on astronomical
pictures but the stars are actually going around and by watching these things and plotting the orbit you see the orbit that they make on the next slide it's it's evident that they're attracting each other and that they're going around in the lipse according to the way expected these are a succession of pictures uh going for all these different periods of time I think yes it goes around this way they didn't see it well when it was too close and here it is in 195 my slide is very old it's gone around maybe once more since
and you'll be happy except when you notice if you have noticed already that this Center is not an a focus of the ellipse but it's quite a bit off so something's a matter with the law no it God hasn't presented us with this orbit face on it's tilted at a funny angle and if you take an ellipse and Mark its focus and then hold the paper at an odd angle and look at it in projection the the focus doesn't have to be at the focus of the projected image so it's uh because it's orbit is
tilted in space that it looks that way it looks like it's not the right pattern but it's all right and you can figure everything out satisfactory for that how about a diff a bigger distance there's forces between the stars does it go any further than these distances which are not more than two or three times the Solar System's diameter here's something in the next slide that's 100,000 times as big as a solar system in diameter and this is a large number of stars tremendous number of stars this white spot is not a solid white spot
it's just because of the failure of our instruments to resolve it but are very very tiny dots just like the other stars well separated from one another not hitting each other each one falling through and back and forth through this great globular cluster it's one of the most beautiful things in the sky as good as sea waves and sunsets and the distribution of this material it's perfectly clear that the thing that holds this together is the gravitational attraction of the stars for each other and the distribution of the material in the sense of how the
Stars Peter out as you go out in distance permits one to find out roughly how what the law is of force between the stars and of course it comes out right that it is roughly the inverse Square the accuracy of these calculations and measurements is not anywhere near as careful as in the solar system onward does gravity extend still further this is a little pinpoint inside of a big Galaxy and the next slide shows a typical Galaxy and it's clear that this thing again is held together somehow and the only candidate that's reasonable is gravitation
but when we get to this this size we haven't any way any longer to check the inverse Square law but there seems to be no doubt that these great agglomerations of stars and so these galaxies which are 50 to 100,000 light years across the solar system is well from the Earth to the Sun is only eight light minutes this is 100,000 light years that the gravity is extending even over these distances and in the next slide is evidence that it extends even further here is what is called a cluster of galaxies there's a Galaxy here
and here and here there galaxies here they're all in one lump of galaxies analogous to the cluster of stars but this time what's clustered are those big babies that I showed you in this previous slide now we uh this is as far as uh it's about 1/10th or well 100th maybe of the size of the universe in as far as we have any direct evidence that gravitational forces extend so the Earth's gravitation if we take the view has no Edge as you may read in the newspapers when the planet gets outside the field of the
gravitation it keeps on going ever weaker and weaker inversely as the square of the distance dividing by four each time you're twice as far away until it mingles with the strong fields and gets lost in the confusion of the strong fields of other stars but all together with the Stars in its neighborhood pulls the other stars to form the Galaxy and altogether they pull on other galaxies to make a pattern a cluster of galaxies so the Earth's gravitational field never ends but Peters out very slowly in a precise and careful law probably to the edges
of the universe the law of gravitation is different than many of the other well is is very important in the economy or in the Machinery of the universe there are many places where gravity has its practical applications as far as the universe is concerned but atypically among all the other laws of physics gravitation has relatively few practical applications I mean the new knowledge of the law it has a lot of application it keeps people in their seats and so but it has few the knowledge of the law has few practical applications relatively speaking compared to
the other laws this is one case in which I picked an atypical example it is impossible by the way by picking one example of anything to avoid picking one which is atypical in some sense that's the wonder of the world the only application I could think of were first in some geophysical prospecting in predicting the tides nowadays more modernly in working out the Motions of the satellites and uh and Planet probes and so on that we send up and also modernly to calculate the predictions of the planet's position which have great utility for astrologers to
public their predictions and horoscopes in the magazines that's the strange world we live in that all the advances and understanding are used only to continue the nonsense which has existed for 2,000 years now that that shows that gravitation extends to the great distances but Newton said that everything attracted everything else do I attract you excuse me I mean do I attract I was going to say excuse me do I attract you physically I didn't mean know what I mean is to is it really true that two things attract each other D can we make a
direct test and not just wait for the planets and look at the planets to see if they attract each other and this experiment the direct test was made by Cavendish on equipment which you'll see indicated on the next slide if I got my slides right well I made a mistake I was talking about um the the the importance of the gravitation and I was overwhelmed by my clever remark about astrologist and forgot to mention the important places where gravitation does have some real effect in the behavior of the universe and one of the interesting ones
is the formation of new stars in this picture which is a gaseous nebula in inside our own Galaxy and there not a lot of stars but it's gas there are places where the gas has been compressed or attracted to itself here uh it starts perhaps by some kind of shock waves to get collected but the remainder of the phenomenon is that gravitation pulls the cloud of gas closer and closer together so big mobs of gas and dust collect and form balls which as they fall still further the heat generated by the falling lights them up
and they become Stars and we have in the next slide some evidence of the creation of new stars it is unfortunately harder to see than I thought it was when I looked at it before but this is not exactly the same as this this bump here is further out than here and that this also has a new DOT here there are I have found better examples but we're unable to produce a slide there is one example of a star patch A Light That Grew GRE in a place in 200 within 200 days so that when
this it was in in the same kind of condition of a gas cloud when the gas collects too much together by gravitation Stars Are Born and this is the beginning of new stars so the Stars belch out dirt and gases when they explode sometimes and the dirt and gases then collect back again and make new stars sounds like perpetual motion I now uh turned to the subject I meant to introduce which was the experiments on the small scale to see whether things really attract each other and I hope now that the next slide does indicate
this is a second try yeah Cav Dish's experiment the idea was to hang by a very very fine quartz fiber a rod with two balls and then put two large lead balls in the positions indicated here next to it on the side then because of the attraction of the balls there would be a slight Twist of the fiber it had to be done so delicately because the gravitational force between ordinary things is very very tiny indeed and there it was and it was possible then to measure the force between these two balls Cavendish called his
experiment weighing the Earth We're pedantic and careful today we wouldn't let our students say that we would have to say they measuring the mass of the Earth you know but the reason he say that said that is the following by a direct experiment he was able to measure the force and the two masses and the distance and thus determine the gravitational constant you say yes but we have the same situation on the earth we know what the pull is and we know what the mass of the object pulled is and we know how far away
we are but we don't know the either the mass of the Earth or the constant but only the combination so by measuring the constant and knowing the facts about the pull of the Earth the mass of the Earth could be determined so indirectly this experiment was the first determination of how heavy or how massive is the ball on which we stand I it's a kind of an amazing achievement to find that out and I think that's why Cavendish named his experiment that way instead of determining the constant in the gravitational equation weighing the Earth he
incidentally was weighing the Sun and everything else at the same time because the pull of the sun is known in the same manner now one one other test of the law of gravitation is very interesting and that is the question as to whether the uh the pull is exactly proportional to the mass if the pull is exactly proportional to the mass and the reaction to forces the Motions induced by forces the changes in velocity are inversely proportional to the mass that means that two objects of different mass will change their velocity in the same manner
in a gravitational field or two different things no matter what their mass in a vacuum will fall the same way toward the Earth and that's Galileo's old experiment from the Leaning Tower I took my young son of two and a half to the Leaning Tower of Pisa and now he every time a guest comes he says Leaning Tower so anyhow it means for example that in a satellite uh I mean a a man-made satellite an object inside will go around the Earth in the same kind of an orbit as a satellite on the outside and
thus float in the middle apparently so that this fact that the force is exactly proportional to the mass and that the reactions are inversely proportional Mass has this very interesting Consequence the question is how accurate is it and it has been measured by an experiment by a man named OS in 199 and very much more recently and more accurately by Dicky and it is known to one part in 10,000 million the mass is exactly proportional I mean the forces are exactly proportional to the mass how it's possible to measure with that accuracy I wish I
had the time to explain but I'm afraid I I cannot it's a remarkably clever I'll give a hint how I give one hint there it suppose that you wanted to measure whether it's true for the pull of the sun you know the sun is pulling us all it pulls the Earth too but suppose you wanted to know whether you had a piece of lead here and the piece of of copper here or polyethylene and Lead it was first done with sandal wood now it's done with polyethylene whether the pull is exactly proportional to the to
the inertia the Earth is going around the Sun so these things are thrown out by inertia and they're thrown out to the extent that these two objects have inertia but they're attracted to the Sun to the extent that they have mass in the attraction law so if they're attracted to the sun in a different prop and they're thrown out by inertia one will be pulled toward the sun and the other away and so hanging on another one of those Cavendish quartz fibers the thing will twist toward the sun it doesn't twist to this accuracy so
we know that the sun's attraction for these two objects is exactly proportional to the centrifical effect which is inertia so the force of attraction on an object is exactly proportional to its coefficient of inertia in other words its mass I should say something about the relation of gravitation to other forces to other parts of nature other phenomena in nature and I'll have more to say of a general quality later but there is one thing that's particularly interesting and that is that the inverse Square law appears again it appears in the electrical laws for instance that
electricity also exerts forces inversely as a square of the distance this time between charges and one thinks perhaps inverse square of the distance has some deep significance maybe gravity and electricity are different aspects of the same thing no one has ever succeeded in making gravity and electricity different aspects of the same thing today our theories of physics the laws of physics are a multitude of different parts and pieces that don't fit together very well we don't understand the one exactly in terms of the other we don't have one structure from which all is deduced we
have several pieces that don't quite fit exactly yet and that's the reason why in these lectures instead of having the ability to tell you what the law of physics is I asked talk about the things that are common to the various laws because we don't know we don't understand uh the connection between them but what's very strange is that there are certain things that are the same in both but now let's look again at the law of electricity the law goes inversely as the square of the distance but the thing that is remarkable is the
tremendous difference in the strength of the electrical and gravitational laws people who want to make electricity and gravitation out of the same thing will find that electricity is so much more powerful than gravity that it's hard to believe they could both have the same origin now how can I say one thing is more powerful than another it depends upon how much charge you have and how much mass you have I'm certainly uh well the you can't talk about how strong gravity is by saying I take a lump of such and such a size because you
chose the size if we try to get something that nature produces her own pure number that has nothing to do with inches or years or anything to do with our own Dimensions we can do it this way if we take the fundamental particles such as which is an electron any different ones will give different numbers but to get an idea of a number take electrons two electrons a fundamental particle that's an object it's not something I can't I don't have to tell you what units I measure in it's two particles the fundamental particles and they
repel each other inversely as a square of the distance due to electricity and they attract each other inversely as a square of the distance due to gravitation question what is the ratio of the gravitational force to the electrical force and that is Illustrated on the next slide the ratio of the gravitational attraction to the electrical repulsion is given by a number with 42 digits and goes off here it's all this is written very carefully out so has 42 digits now there in lies a very deep mystery where could such a tremendous number come from that
means if you ever had a theory from which both of these things are to come how could they come in such disproportion from one equation has a solution which has for one two kinds of an attraction and a repulsion with that fantastic ratio people have looked for such a large ratio in other places they're looking for a large number they hope for example that there's another large number and if you want a large number why not take the diameter of the universe to the diameter of a proton amazingly enough it also is a number with
42 digits and so an interesting proposal is made that this ratio depends is the same is a ratio of the size of the universe to the diameter of a proton but the universe is expanding with time and that would mean the gravitational constant is changing with time and although that's a possibility there's no evidence to indicate that it's in fact true and there are several difficulties where I mean partial indications that it doesn't that the gravitational constant has not changed in that way so this tremendous number remains a mystery I must say to finish about
the theory of gravitation two more things one is that Einstein had to modify the laws of gravitation in accordance to his princip with his principles of Relativity the first was one of the principles was that effect effects cannot occur instantaneously while Newton's Theory said that the force was instantaneous he has to modify Newton's Laws they have very small effects these modifications one of them is all masses fall light has energy and energy is equivalent to mass so light should fall and it should mean that light going near the sun is deflected it is and also
the force of gravitation is slightly modified in his theory so that the laws slightly changed very very slightly and it is just the right amount to account for the slight discrepancy that was found in the movement of mercury finally with Rec connection to the laws of physics on a small scale we have found that the behavior of matter on a small scale obeys laws so different very different than things on a large scale and so the question is well does gravity how does gravity look on a small scale what is what is called the quantum
theory of gravity there is no quantum theory of gravity today people have not succeeded completely in making a theory which is consistent with the uncertainty principles and the quantum mechanical principles I'll discuss these principles in another lecture now finally you will say to me yes you told us what happens but what is this gravity where does it come from and what is it do you mean to tell me that the planet uh looks at the Sun or sees how far it is takes the inverse of the square of the distance and then decides to move
in accordance with that law and move in other words although I've stated the ma mathematical law I hav't given you no clue as to the mechanism I will discuss the possibility of doing this in the next lecture which is the relation of mathematics to physics but finally in this lecture I would like to disc to remind just at the end here to uh emphasize some characteristics that the gravity has in common with the other laws that we have mentioned as we passed along the first is that it's mathematical and its expression the others are that
way too we'll discuss that next time second it's not exact Einstein had to modify it we know it isn't quite right yet because they have to put the quantum theory in that's the same with all our other laws they're not exact there's always an edge of mystery there's always a place that we have some fiddling around to do yet that of course is not a property probably not a property may or may not be a property of nature but it certainly is common with all the laws as we know him today it may be only
a lack of knowledge but the most impressive fact is that gravity is simple it is simple to State the principle completely and have no left have not left any vagueness for anybody to change the ideas about it's simple and therefore it's beautiful it's simple in its pattern I don't mean it's simple in its actions the Motions of the various planets and the perturbations of one on another can be quite complicated to work out what the follow how all those stars in the globular cluster move is quite beyond our ability it's complicated in its actions but
not in the basic pattern or the the the system underneath the whole thing is that's a simple thing that's common in all our laws they all turn out to be simple things although complex in their actual actions finally comes the universality of the gravitational law the fact that it extends over such enormous distances that Newton in his mind worrying about the solar system was able to predict what would happen in an experiment of Cavendish where cavendish's little model of the solar system the two balls attracting has to be expanded 10 million million times to become
the solar system and then 10 million million times expanded once again and we find the galaxies attracting each other by exactly the same law nature uses only the longest threads to Weaver patterns so that each small piece of her F of her fabric reveals the organization of the entire tapestry thank you [Music]
