MR. TOMPKINS IN WONDERLAND

[Music] [Music] [Applause] [Music] [Applause] [Music] this is the story of mr. CGH Tompkins whose initials stand for the fundamental constants of the universe the velocity of light the gravitational constant and the quantum constant unfortunately mr. Tompkins knowledge of mathematics is limited to the four operations of arithmetic of which he uses only two in his work at the bank [Music] ladies and gentlemen we are lucky enough to be living in an age when the physical laws of nature are still being discovered it is an age that will never come again tonight I would like to discuss several concepts developed in this century that have shaken the very foundations of the laws of physics as we thought we knew them from early childhood we go custom to the surrounding world through our five senses in this stage of mental development our fundamental notions of space and time and motion are formed our minds soon become so accustomed to these notions that later on we're inclined to believe it but any other concept of the outside world is an impossible one any idea of changing ours seems paradoxical to us three centuries ago the brilliant pioneering physicist Isaac Newton wrote these words absolute space in its own nature without regard to anything external remains always similar and immovable absolutes true and mathematical time of itself and from its own nature flows equally without relation to anything external however the very accurate measurements of which modern science is capable has shown that our classical intuitive ideas of the nature of space and time and motion and even of matter itself to a large extent are not really true the problem began to emerge as long ago as 1887 when Albert Michelson and Edward Morley decided to find out something about the relative velocity of the earth through the ether because 19th century physicists couldn't figure out what lights made waves in when light waves travel between the Sun and the earth they invented the ether this was a subtle kind of jelly invisible and without any mess but like any good jelly it could be made to quiver and where fall was easy to make waves in at least four electromagnetic waves like light waves heat waves and radio waves well Mickelson decided he could figure out how fast the ether wind blew past the earth if by using his interferometer he measured the velocity of light in two directions at right angles to each other and then computed the difference and figured out the resultant velocity of the ether with respect to the earth certainly it was reasonable to expect that the velocity of light in a direction along the Earth's orbit would be different from that at right angles well what Mickelson found out astounded everyone the velocity of light was exactly the same in all directions this meant that either the earth and the ether was stationary with respect to each other which seems practically impossible in view of the complex motion of the earth in the solar system and of the solar system in our galaxy or else there just was not any ether worse than that later experiments showed that the velocity of light in a vacuum always comes out exactly the same irrespective of the motion of the source from which it is emitted or of the device by which it is measured let's look at it this way if this signal lamp is putting out light rays with a velocity C and this train is moving with a velocity of 3/4 C and this is running along the tops of the boxcars with a velocity of 3/4 C we would say an Isaac Newton would say the velocity of this track with respect to the ground is one and a half times C and in those circumstances the light from the signal lamp would never reach the now certainly this would be the case if the signal lamp were throwing rocks instead of light rays because we could all be reasonably sure that the track was safe from being hit the fact is however but the light from the signal lamp would shine on the back of the and in fact if the trap took the time to measure while he's running the philosophy of are likely emitted by the signalman he would find that it is still C put it another way if an observer were to stand the head of the train off the tracks of course and to observe the velocity of the light emitted by the stick which is stationary by the mic put the lamp in the caboose which is traveling at a speed of 3/4 sleep and by the light from the flash lamp which the tempest holding as he runs along the top of the train that observer would find that all those velocities were the same C or 186 to 82 miles per second all of this bothered Albert Einstein when he was still a teenager in Germany in 1905 at the age of 26 having assimilated ideas from Lorentz Fitzgerald he published his now famous paper on relativity and by the way along with three other papers in the same year and established himself as one of the greatest physicists of all time Einstein had the courage to embrace the revolutionary idea that there were hardly any reasons except the tradition for considering that the classical notions of space and time were absolutely true one of the consequences of relativity is that the absolute speed limits in the universe turns out to be the velocity of light and consequently velocities like those of the on the moving train do not add linearly as lead and Isaac Newton have always assumed for the champ on the train the way they do it may be expressed in this way V equals V 1 plus V 2 divided by 1 plus V 1 times V 2 divided by C squared where V 1 and V 2 are the horses of the Train and of the with respect to the Train now if we substitute the actual velocities we obtain 3/4 C plus 3/4 C divided by 1 plus 3/4 C times 3/4 C divided by C square and this simplifies to yield twenty-four twenty-fifths of C a result still less than the velocity of light in fact this equation can never yield a value for the net velocity V of two moving citizens the value of the velocity of light it's rather a pity in a way that this concept has been called the theory of relativity because it's given rise to cliches about everything is relative in actual fact Einstein established a new principle of constancy the velocity of light is a constant a universal constant and his idea might be better called the theory of non relativity if we could find a world with the same physical laws as our own world but where the numerical value of the absolute speed limits the velocity of light were say 10 miles per hour all of the other relativistic effects that we find so difficult to grasp the contraction of an object in the direction of its motion the increase of mass with velocity and the stretching of time would be a part of the experience of every primitive Savage look at that bicycle of course he's approaching the absolute speed limit here this makes moving objects look for shortened in the direction of their motion let me show you what I mean do you mind taking a ride with me frankly [Music] [Music] just drive around the square please driver I thought we'd get squeezed up to when we started you look as bad as ever no do I to people at the curb where foreshortened in the direction of our motion but not to each other because we're in the same frame of reference however if you look out of the window you will see how we look to the people who are not moving as we are you mean that one we are moving and they aren't we look squeezed up to those people and they look squeezed up to us precisely oh dear that young man should be more careful stop driver [Music] if that young man lives here they want to know that his inertia and for all practical purposes his mass increases enormous ly as he approaches the speed limits he certainly made a shambles with that bicycle insurance premiums must be very high here indeed they are driver take us back to where we started from I want to see what time it is it's 25 minutes to 2:00 I'm sorry I need to know what time it is in the town here is where we started from driver a town clock is on your side what does it read sorry my watch must be slow I can't understand it doesn't see many winding did it will get egg-shaped while we were moving no that isn't the explanation driver take us to the railroad station please it's time to meet my grandfather's train you see because we were moving near the absolute speed limits time was expanded or stretched for us our watches in fact all our bodily processes we're going slow relative to those of the townspeople but that would mean that the people in town are all now 15 minutes older than we are precisely you accountants are smarter than I ever gave you credit for actually this is a demonstration of the twin paradox it'd be difficult for people to keep appointments in this place I don't see how the trains run on schedule well it's difficult as in our own world owner the effect here is much more pronounced simultaneity of events really doesn't have any meaning [Music] [Applause] [Music] I wonder why they use purple headlights on the trains here they don't that's a regular white headlights it's the opposite of a redshift because the trains approaching us red chip excuse me it's a sort of Doppler effect surely you must have noticed how a train whistle increases in frequency or pitch when the trains approaching and decreases as the Train is going away well listen there's a high-speed train coming on the other track but it won't stop here can fathers train this obviously slowing down now you see as the train approaches it crowds the sound waves and the light waves together and as it goes away it stretches them out as a result to a stationary observer like you and I the frequency goes up or down depending on whether the train is coming toward him or going away from him good seeing you again Jelena I would like to have you meet my friend mr. Tonkin nice meeting you young man any friend of my grandson is a friend of mine how do you do professor is your grandson oh yeah I guess I look a lot younger since I shaved my beard off the company's pretty fussy about beards now that Benjamin Harrison lost to Grover Cleveland you remember we were talking about time dilation earlier you see grandfather travels a great deal for his company and as a result to us he seems to age much more slowly than we do provided he returns to the same point of course you remember how it was with the time on the town clock compared to our watches when we were travelling around the square now boys we have just about enough time to get dinner before I have to catch my train back to the coast certainly is good seeing my young grandson again young man you're gonna look just like your father when you grow older yes well I think the restaurants on the Town Square still open let's take a taxi [Applause] a town looks like a regular Christmas tree at night only when we're moving with respect to the lights the headlights on the cars are approaching us more rapidly than the streetlights so their spectrum shifts further into the violet look out of the back window and you'll see the opposite effect well the headlights aren't colored because they are moving at about the same speed as we are but we are moving away from the streetlights you're learning actually traffic policeman here can tell how fast drivers are going by the color of their headlights taillights present a problem however because they tend to disappear as they received their red light ships into the infrared I suppose you know that back home in our own world astronomers can calculate how fast galaxies are receding from us by how far into the red the spectral lines of familiar elements is shifted that's what is meant by the redshift ah here we are driver nestled in many aspects of relativity these effects depend partly on how the observer looks at them if he makes his observations with a flash camera for example he will get around a different kind of picture this ambiguity is true for time as well as space let me show you Einstein's own example of the relativity of time this fellow sitting next to a railroad trek halfway between two trees as a pair of mirrors arranged in a V so that he can watch lightning strike both of these trees at the same time in this way he can verify that the equidistant lightning flashes are simultaneous but his friend on a moving train with the same apparatus gets a different picture even though the lightning strikes when the two men are directly opposite each other since the passenger is travelling toward one flesh and away from the other he was saying that the right hand flesh occurred first now since we're sitting in the same frame of reference as the man on the ground it is easy for us to see that the passengers wrong but if we take away the frame of the world who is to say now which objects are moving and which are stationary and when the lightning strikes now who can say whether our men is right all the men on the train this is what is meant by the principle that simultaneity of events really only has meaning with respect to a particular reference system now this business of time slowing down the travelers is a source of a great deal of confusion among people trying to understand relativity after all if we can't really tell who is moving when objects pass each other in space as we've just seen and if this question really has no meaning who is to say which frame of reference is slowed down the answer lies in the difference between Einstein's special theory of relativity and his much later general theory of relativity it's all a matter of who accelerated and then slowed down at the journey while velocity is relative acceleration is absolute you can feel acceleration forces and know that this is true in the final analysis it is acceleration that causes the expansion or dilation of time where relativity comes in is that as with velocity in space there is no way to distinguish between acceleration forces and gravitational forces they are identical when an elevator going down suddenly stops you get heavy the forces due to acceleration and to gravity act together in the natural way if a rocket ship floating in space were to switch on its engines and accelerate upwards it's intuitively obvious that an astronaut experimenter could drop an apple and watch it accelerate toward the floor because the floor accelerates to own it similarly he could hang a picture on the nail feel his own weight here is a pendulum clock and if he has sufficiently refined measuring equipments he could detect the droop in the light beam from his projector on its way to the screen an outside observer might interpret this as due to the overlapping of a uniform rectilinear motion of the light beam and an accelerated motion of the cabin but does the same effect exist in a gravitational field Einstein showed that it did before astronomers set off for Africa to observe a total eclipse of the Sun he suggested that they measure the apparent angle between two stars one on each side of the darkened disk of the Sun and compare that measurement with the measurement of the angle at another season of the year when the Sun was not in the way they found this when the light rays close to the Sun the subtended angle between the two stars was increased by precisely the amount that Einstein had predicted due to local curvature of space in the presence of the gravitational field of the Sun thus bending the light along with the space and making it appear that this star was out here since any gravitational field is equivalent to some force producing acceleration of the frame of reference this also means that any space in which a gravitational field is present is also a curved space and conversely a gravitational field is just a physical manifestation of the curvature of space now the radii of space curvature are related to the distribution of masses by this particularly compact equation at Einsteins if we consider our space more or less uniformly filled with masses as our own is filled with stars and stellar clusters galaxies we should come to the conclusion that apart from occasionally large curvatures near masses like our Sun or other stars all of the space of the universe should possess a regular tendency to curve uniformly on very large radio mathematically there are several different solutions some of them implying that space curves outward infinitely like a sample surface others suggest that space finally closes upon itself to envelop the finite volume so that a light ray beamed out into space in one direction might eventually be expected to return from the opposite direction the second important consequence of this equation is that such curved surfaces should be in a steady state of expansion or contraction or perhaps with a contract periodically following an expansion at the moment our universe seems to be expanding good morning there are no mornings here where on earth are we surely you know better than that we're in a miniature universe one quintillion of the size of arrow certainly is dusty here its interstellar dust it has a density of only a couple of pounds per cubic mile of this stage of expansion but some of the pieces are pretty big oh I do believe you've lost it no it should travel around the curved space of this universe and we're back here at its speed Oh in about half an hour well how can that be well it's simply because due to the presence of matter within it this space is warped in a fourth dimensional way anything closes a finite volume look if I shine a light ray out in this direction we shall see it shining back at us like a star from over there in about 20 minutes in fact the most distant galaxies we can see in that direction are probably merely the back science of some of those that look much closer to us over there Oh I must have dropped off nearly as dusty as it was can you still see my notebook out there with the use yeah just barely it looks pink well now look behind you there are not as many of those heavenly bodies in the skies there were why are they all so pink those are galaxies star clusters they're all receding from us because justice without universe back home this one is still expanding it won't start collapsing again for another oh six or seven minutes collapsing no need to get upset about it it's just the same as with our own universe only in this one the pulsation cycle is so much faster because it's so small we've got over an hour before the next primordial explosion you will notice that the more distant galaxies are redder this is because the further away a galaxy is the faster it seems to recede and yet we're no more in the center of this universe than we are in our own at home this is a puzzle that's difficult to understand I don't suppose you understand it do you I thought not well I generally use one of these balloons with dots on it to demonstrate an analogy of the principle in my lectures the dots represent galaxies as the universe expands the galaxies move away from each other and no matter which galaxy you are in all the other galaxies move away from it and the further away they are the faster they seem to recede now as with many analogies there are a couple of things wrong with this one the dots shouldn't get any bigger because the internal gravity of real galaxies prevents them from expanding you may have noticed we still have the same local stars around us now as we did before also this is a two dimensional surface curved in a third dimensional way whereas ours is a three dimensional space and it's curved in a fourth dimensional way but the point is we believe that space itself is expanding the third dimension the radius of the balloon represents time and the passage of time increases the radius and expands the universe what what if somebody lets the air out of our balloon you mean can time flow backwards from what we're used to or it's a different rate a very interesting thought why not [Music] [Music] [Applause] [Music]