Einstein's 1907 Jahrbuch Paper — First Step from SRT to GRT

0:00 The American scientific contact, this paper is indeed quite remarkable because we recall that when Einstein began to write it in September of 1907, there existed apparently unassailable empirical evidence against what everyone took to be a key prediction of his 1905 electrodynamics paper. first mass, and so too against the principle of relativity. Well, undeterred by this evidence, Einstein went on to enlarge his principle of relativity to include measurements made in accelerating reference of them. And his masterstroke in this whole business was to realize the equivalence between phenomena of gravitation and acceleration. What I want to do today is to discuss the problem I want to address today, is how this and how we first applied it in the 1970-album paper. I'm going to, I will approach this problem as follows. I'm going to seek connections between concepts that were important to Einstein's invention of the 1905 relative to the theory, of electric and magnetic fields, see connections between that and Einstein's efforts to generalize the mass energy equivalence to any sort of mass, and then look for connections between those two topics, and the 1970 Gedanken experiment that led to his discovery of the equivalence between the effect of a uniform gravitational field and an oppositely directed constant acceleration. and I will proceed as follows I will make this visible I will first review the status of Einstein's principle of relativity in 1907 then I will analyze an early in 1907 derivation by Einstein of E equals mc squared and then I will move on to the Arbrook paper itself, having set a stage for it, discuss how Einstein raised E equals mc squared to an axiom discuss the 1970 explore the roots of the coordinate and time transformations for accelerated reference systems that Einstein employed in the art book,

2:30 and then make some comments about predictions and results of generalizing special relativity in 1907. But a main point I want to make here is the continuity of Einstein's work between 1905 and 1907, how he used the same techniques that he used in 1905 again in 1907, and indeed these techniques have been used earlier by H.A. Lauer. So, there's one topic where you can begin at the beginning. In 1907, to review the status of Einstein's principle of relativity in 1907, in 1907, most physicists interpreted Einstein's principle of relativity, which one finds in his paper on the electrodynamics of moving bodies, to offer improvements and generalizations of H.A. Lorentz's theory of electrons, which in 1907 was not in agreement with empirical data. The so-called Lorenz-Einstein principle of relativity was taken to be the basis of a version of the sought-after electromagnetic world picture, or belt field, in which the laws of mechanics are reduced to those of Lorenz's electromagnetic theory. But when Einstein discussed a principle of relativity, it was of a quite different sort. Einstein's principle of relativity was axiomatic that is to say it's beyond experimental proof it covered electromagnetism and mechanics equally without trying to reduce one to the other and it included no assumptions on the constitution of electrons and when Einstein discussed his own view of the electrodynamics of moving bodies he used the term relativity theory or relative theory a term that had been coined in 1906 by Max Planck with the intent of separating off the Lorenz-Einstein theory of the electron from other theories of the electron. Sometime after having submitted the 1905 relativity paper to the Annalen der Physique, Einstein realized that the paper contained implicitly the mass-energy equivalents. It contained it implicitly in the expression for the kinetic energy of a point electron moving in an external electrostatic field along the direction of the electron's motion. The expression is well known, k is equal to m0 c squared gamma minus 1, where gamma is 1 over the square root of 1 minus v squared over c squared, and m0 is the electron's mass in its rest system.

5:00 suffice it to say that Einstein's derivations of E equals mc squared in 1905 of the fourth published paper in 1905 and in his two other derivations in 1906 were inconclusive for what he referred to in the title of the main 1907 paper as the consequences of the relativity principle for the inertia of energy he writes in his paper of the mass energy equivalent that an assumption of such unusual generality challenge for proving its necessity or correctness in the most general manner. Are there not special cases in which this assumption leads to incompatible consequences? And one special case that Einstein had in mind was what he called the dynamics of parallel translation of a rigid body, which he goes on in his paper to treat from the point of view of the relativites electrodynamics, the relativity electrodynamics, that is, he treats it with no assumptions on the constitution of the matter. And he treats it as follows. From the beginning of it, here it's a derivation of V equals MC squared, which is even true. He treats an arbitrarily shaped rigid body with a continuous volume charge distribution rho, and is the arbitrary body acted on by external electromagnetic forces. Although it's acted on by external electromagnetic forces, the body remains in equilibrium in its rest system, little k. Relative to capital K, the laboratory system, the external force increases the body's energy by an amount delta e, which is the integral of bt, rho, v dot e, dv, where all quantities are measured in the laboratory system, k. Simple Lorentz transformation into the body's rest system yields a delta E of gamma V integral V tau sum of K sub C, where gamma is before is 1 over the square root of 1 minus V squared over C squared. V is the relative velocity, relative velocity between root K and gamma K. Tau is an element of time, tau is time in the body's rough system, and sum of K sub C is the total effect of the external force over the surface of the charged body. Interesting results begin to appear, very simply, because although the, whereas the sum of a case of C vanishes in the body's rest system, it need not vanish in the laboratory system, because owing to the relativity of simultaneity, the integration limits on the time in the rest system depend on the coordinate in the rest system, C.

7:30 and Einstein finds very easily that relative to the laboratory system the body's energy is increased by an amount delta E where delta E is greater than zero because C and K sub C are oppositely directed and he assumes that the external force operates continuously and is constant or very slowly varying over the body so he can do this in the most simple way. This is an unexpected result, he notes. It's an unexpected result because in the body's rest system, no net force acts. One would expect that to be the case in the laboratory system too. But owing to the relativity of simultaneity, this is not the case. Rather, the body's energy is increased. In order to illustrate further this unexpected result, Einstein considers now a charged body that persists in inertial motion under the influence only of its self-electromagnetic force. If there's no more external force, one considers only the self-electromagnetic force. One expects that the total kinetic energy of the body is K0, which is just the kinetic energy of a point object, plus terms that contribute only to the fact that the body is extended, where EE, E superegion, is the self-electromagnetic energy and E0E is the rest or electrostatic energy. But it turns out, a very simple calculation, it turns out that the expression in equation A depends on the rigid body's orientation. It's not supposed to be the case with kinetic energy. And Einstein notes that what the error here is that one tries to assess the kinetic energy of a rigid body as if no force is acting on it. not the case. One has to take into account the self-electromagnetic forces that say add in the term delta E, which yields a total kinetic energy of M0 plus E0 E over C squared times gamma minus 1. This is an extension of the 1905 result in charged bodies with extension. And he makes an interesting observation here at this point

10:00 in this 1907 paper, namely that the electrostatically charged body possesses an inertial mass which exceeds that of the uncharged body by the electrostatic energy divided by the square of the velocity of light. And I know here inertial mass because he will, in the 1907 Yard book paper, which he completes at the end of this year, generalize this result to gravitational to all masses. What remains here is what is the nature of the term delta E, which I would warn you will soon disappear from this whole discussion, but he notes that the term delta E as Einstein realizes is a consequence of the relativity of simultaneity and so too of the principle of relativity he associates the term delta E with what he calls an unknown polytext, which velocity in bodies that are observed from another inertial reference system. A flow of this, the paraphrase is argument, a flow of this unknown polytet is required because according to the principle of relativity, if a body is in equilibrium in one inertial reference system, like the body that we just considered, then it must be in equilibrium in every inertial reference system. That is to say, equilibrium cannot be Lorentz-transformed away. but at present he knew not how to rectify this point. As he noted, he could not speculate any further on this unknown qualitet because, as he put it, we are far from having a dynamics of parallel translation of rigid bodies since we do not possess a world picture or belt field according to the principle of relativity. That is, at that time, one did not have the means to calculate effects caused by the Constitution of Matter, something which Einstein wanted to stay away from. This brings us now to the 1907 Yachtel paper. In September of 1907, beginning of September, Einstein received an invitation to write a review paper on the relativity theory from Johannes Stark, who had been the editor of the Yard book since 1904. Stark received the completed Yard book paper on 4 December 1907.

12:30 There are some letters between Stark and Einstein, which have been published by Arnold Hermann, and they are mostly of interest to see what literature Einstein claimed was available to him while he worked in the patent office. difference between Einstein's presentation of relativity theory in 1905 and 1907 is that in 1907 Einstein continuously emphasizes, repeatedly emphasizes, that the reference systems in which clocks are synchronized and the principle of relativity is valid are non-accelerated reference systems and clearly in this paper he, at the beginning at any rate, he's preparing the reader for what will happen at the end of the paper, namely in the last section he will the principle of relativity to include accelerating reference systems as well. New results, the review of special relativity, or the 1905 relativity theory, concludes with a critical discussion of Walter Kaufman's experiments on the characteristics of high-velocity electrons, which are invariant with the Lorentz-Einstein theory, and this whole episode is treated elsewhere, and if I concern us. New results for the relativity theory appear in this section entitled On the Dependence of Mass on Energy. And here Einstein improves on his earlier May 1907 calculation of E equals mc squared. He replaces the rigid electrified body, something which he was uncomfortable with, with a system of charges surrounded by a massless envelope that's impenetrable to radiation. The argument is that the center of mass is that the center of mass of this whole thing, this bag of charges, is at rest relative to little k. Again, the center of mass is at rest in the system little k, which means that no net external forces act at little k. This device enables Einstein to do a number of clever things. One of them is to relate his results to previously, to newly obtained results by Max Planck on the pressure, temperature, and entropy of moving systems, which undoubtedly gave Einstein some additional insight into his unknown qualitet. But at this point, Einstein had realized a way to avoid his unknown qualitet altogether, and yet get right to the heart of the mass-energy equivalent. Now, by Lorentz's transformation,

15:00 Einstein relates the system's energy between little K and capital K as very simply dE equals gamma dE prime plus that delta E term from before, where prime quantities and quantities of three subscripts are evaluated in the resting system. What he assumes now is that the external forces are not continuously operating, and they also disappear at the temporal boundary. that delta E term disappears, no longer needs it. And he finds that dE is equal to gamma dE prime. Therefore, he makes the point that the energy of a uniformly moving system can be a function of only two variables, the relative velocity V, and the energy content E zero relative to the resting system. From the equation A, he obtains E equals M zero plus E zero C squared minus C squared gamma. and now he makes he is able to generalize begin to generalize this result which he had obtained previously in the earlier 1907 paper but with regard to electrical quantities which he's here avoided now this E0 is simply the internal energy of the system whatever it might be and he makes the point that therefore the system acts as if it were a material point of mass M0 plus E0 over C squared writes there are lots of adjectives in here in this paper this result is of extraordinary theoretical importance because the physical system's inertial mass once again he still uses the term inertial mass and energy content appear to behave like the same thing in other words mass is confined energy is the point he's getting to and this is a general a broad generalization of all of his previous derivations of the equals mc squared. There ensues an analysis of the feasibility of testing the mass-energy equivalents using radioactive substances, and Einstein comes to the conclusion that five-figure accuracy is necessary for atomic masses. This is now available in 1907, but it doesn't bother him. It's just a minor shortcoming, because he has other things in mind for this business in English. mass is measured, how mass variation is measured generally, even in principle. And here he expands to gravitational mass as well. Repeating the equation, he notes that in the preceding

17:30 we have assumed implicitly that such a measurement of mass variation can be carried out with a usually employed instrument, the scale. Therefore, the relation, equation A, holds also for the gravitational mass, or in other words, inertia and gravity be under all circumstances exactly proportional. The proportionality between inertial and gravitational masses is valid universally for all bodies with an accuracy as precisely as can currently be determined, so that unless proven otherwise, we must accept it as universally valid. A big jump here between these two sentences It's a rather dazzling display here of what's going on, because what he does is to raise a statement which is valid to inaccuracy as precisely as can currently be determined. He raises the statement to a principle beyond experimental proof, something which is universally valid. and he has done this previously in a 1905 relativity paper where he raised the conjecture that the order B over C there is absolute motion, neither in mechanics nor in electrodynamics, to a principle valid beyond empirical evidence, namely the principle of relativity. He continues in 1907, in this 1907 paper, he notes that we shall find in the final section of this communication argument supporting this assumption. How Einstein developed this new argument in this final section entitled Principle of Relativity and Gravitation requires discussion of a Gedanken experiment. Now, there is an effect which all of us have the capacity to experience in writing the review paper. The integrated material can take on the meaning that we can understand it better, perhaps even understand it at a deeper level. Previously parts become connected, possibly in ways that can lead to new results. And this is what happened to Einstein somewhere between September and December of 1907. Gedanken experiments occurred to the prepared mind, and a key realization of Einstein toward

20:00 the invention of special relativity was his realization of the relative nature of the electric and magnetic fields, a realization that he had come to through considerations that concern a very simple case of electromagnetic induction, with which he begins the 1905 relativity paper, namely, just a permanent conducting magnet and conducting movement in relative inertial motion. Einstein discusses this work in a 1919 manuscript that has been brought to life by Gerald Houlton. Let me just show you part of it. Einstein writes that the difference between observers on the magnet and on the conductor could not be a real difference, but rather, in my conviction, only a difference in the choice of the reference point. The existence of an electric field was therefore a relative one, depending upon the state of motion of the coordinate system being used. Now, in 1970, he had shown that electromagnetic energy has inertia, and in 1905, he had shown that they're relative. the coalescence of these two results led to what he referred to in his 1919 manuscript as the happiest thought of my life let me quote to you the happiest thought of his life at least until 1919 the gravitational field it's worthwhile saying this in society the gravitational field has only a relative existence in a way similar to the electric field generated by electromagnetic induction falling freely from the roof of the house. There exists, at least in his immediate surroundings, no gravitational field. Indeed, if the observer drops some bodies, then these remain relative to him in a state of rest or uniform motion, independent of their particular chemical or physical nature. The observer, therefore, has the right to interpret his state as at rest. Those are my emphasis. The experimentally known matter independence of the acceleration of fall is therefore a powerful argument for the fact that the relativity postulate has to be extended to coordinate systems which relative to each other are in uniform motion. So, like the observers who rode the magnet and conductor in 1905, this falling observer has the right to consider to interpret his state as at rest. Now, we can speculate on what the mathematical support that Einstein gave to this happiest thought of his life was,

22:30 which I'll do in a moment, but no matter what path we speculate he took to provide mathematical support, what's astonishing is that even in its historical context, the physics of this 1970-Darkin experiment is so incredibly straightforward. Because it turns on assumption... It's in 1919. It turns on an assumption, the physics of the 1970 experiment turns on an assumption that all physicists make, particularly astronomers, namely the equality of inertial and gravitational mass. What Einstein did was to push this assumption, widen this assumption, to include acceleration and gravity too. might have done it. This argument is based on some points in some of Einstein's published papers, but you can figure out elsewhere. Once you make the assumption of the quality of gravitational and neural mass, the rest, in quotes, follow the figure Einstein. Here we have the observer who falls from the roof, carries with him reference system K' an observer standing on the ground has a reference system k, the y-axes of k and k' are aligned with one another, and the assumptions made here that all velocities are small enough so that Newton's laws can be used. That's all Einstein needs, nothing new. Relative to the observer standing on the ground, the equation of motion of the following observer is m sub i d second y d t squared equals minus m g plus m g g plus f, where m i and m g are the inertial and gravitational mass, f is any other force, contains all other forces that act on the body. You do is you do a transformation, that y prime equals y minus a t squared over 2, d prime is t, very simply you get m sub i, this might appear, m sub i d second y prime dp prime squared plus mia equals minus mgg plus f prime now as usual one sets the inertial and gravitational mass is equal to m and you come out with that but you're not finished yet there's something else that's needed if you want to widen the principle of relativity to include

25:00 accelerating reference systems one additional assumption must be made and for which in my opinion is essential theory-laden visual imagery of a freely falling observer in whose immediate surroundings there is no gravitational field and so he has the right to interpret his state as at rest. Mainly, to make these two terms vanish, you have to replace the acceleration with an oppositely directed gravitational field or replace a uniform gravitational field with an oppositely directed acceleration, no matter which way you want to put it. And you have, then, what emerges is Newton's laws again. So the point is Newton's law of motion. The point is that to the falling observer, who uses the coordinate y prime, and the observer standing on the ground who uses the coordinate y, both will interpret all motion according to Newton's laws of motion, even though the freely fully observed will experience no gravitational field. Could you lower that slide again? Sure. Oops. Not a little knot. Okay. Make it fall. Why did you put an arbitrary A in there in the first place? Why don't we get back to that? Let me continue on. I'm trying to understand your assumption. That you can replace a constant acceleration by an opposite directed gravitational field. Now, it has been pretty well established that Einstein, in 1907, did not know of Earthbrush's experiment. So, we can ask, we can inquire as to what clue he might have had with regard to explicit comments to the effect that one sets the inertial and gravitational mass is exactly equal to one Well, one clue could have come from a book that we know he read before 1905, namely Henri Poincaré's Science and Hypothesis. A theme in Poincaré's book is to ferret out tacit or implicit hypotheses in scientific research. And for example, Poincaré draws attention to the way that we measure the masses of planets that have satellites using Newton's gravitational law.

27:30 Poincare writes, what we measure in this manner is not the mass and the ratio of force to acceleration. It is the attracting mass. It is not the inertia of a body. It is the attracting power. Now, not going to spell out anything directly himself, implicit in Poincare's, in the statement of Poincare, is the following line of argument that we all use in physics classes, namely that the force f that a planet exerts on a satellite is the inertial mass of a satellite times the acceleration of a satellite where using Newton's gravitational law f equals g times the product of the mass of a planet the mass of a satellite those are the gravitational masses provided by r squared as usual you cancel out the mass of the satellite from both sides of the equation assuming the tacit assumption made by astronomers is that the inertial and gravitational masses are equal and needless to add that the inertial and gravitational masses of the planet too is equal and as i mentioned before what einstein did was to widen this to include acceleration and gravitation because after all these masses do multiply uh quantities inertial mass multiplies the acceleration, gravitational mass multiplies the acceleration under gravity. This being the case, then, just as in special relativity, there ought to be coordinate and time transformations from a moving reference system, that is to say an accelerating reference system, to one which is at rest. In this way, a dynamics problem is transformed into a statics problem, just like the procedure and electrodynamic since Maxwell. In fact, for this purpose, Lorenz, in his 1895 treatise on electrical and optical phenomena and moving bodies, which we know Einstein had read before 1905, used three different reference systems. Einstein learned well from Lorenz, because Einstein used three different reference systems in his 1905 relativity paper, and he did so again in 1907, as we will see in a moment. Now, straight away paper, we're finally in the part on gravitation, Einstein presented the problematic. Is it conceivable that the principle of relativity is valid also for systems that are

30:00 accelerated relative to one another? And he begins to reply to this question with a version of the 1907 Gadotkin experiment, namely two reference systems, sigma 1 and sigma 2. Sigma a uniform rate of acceleration with respect to sigma 2. Sigma 2 is at rest, and in sigma 2, there acts a uniform gravitational field opposite in direction to the acceleration A of sigma 1. Assuming that the inertial and gravitational masses are equal, then Newton's laws predict the same motion in sigma 1 and sigma 2. And so Einstein notes that we have no cause from our experience to distinguish between sigma 1 what follows, we shall accept the full physical equivalence of the gravitational field and the corresponding acceleration of the coordinate system. In 1912, he was referred to this statement as the equivalence principle. So to summarize, his business would replace the acceleration with gravity and vice versa. Acceleration becomes a relative quantity, just like the electric field in electromagnetic induction, at least for constant accelerations at this point. He then goes on in the 1970-year-old book paper to use the special theory of relativity to search for a new definition of simultaneity in uniformly accelerated reference systems. And he proceeds as follows. Again, what I want to emphasize here is the continuity of this thought from 1905. Now, ever since Maxwell, Well, the procedure for doing electrodynamics of moving bodies was threefold. First, to write the equations of electromagnetism relative to an ether-fix reference system. Secondly, apply the Galilean transformations to move the problem situation into an inertial reference system. What happens is that effects appear that were not detected in ether-driven experiments. So, starting in 1892, Lorentz was the first one to search systematically for further transformations on the Galilean coordinates that could somehow also incorporate the various hypotheses for the causes of counter-effects that were supposed to explain the failure epigrifice experiments. counter-effects such as the contraction of moving bodies

32:30 and the appearance of proper charge distributions on the surface of conducting magnets and charged bodies at rest on the moving Earth as the Earth moves through the ether. For expediency in discussing these three different reference systems, I will discuss Yves Lorenz's 1904 paper as an example of what he has been doing. Lorentz used three different reference systems for this purpose an etherfix reference system S of X, Y, Z, T an inertial reference system S of R coordinates subscript into R of course, TOR equals T, that's the physical time no reason to believe that time depends on relative motion you don't observe it, you don't measure it, you don't feel it the inertial and etherfix coordinates are related by means of the usual layered transformation. The new thing is to use a non-physical reference system, S prime, in which the equations of electromagnetism assume the same form as they would take relative to the etherfix reference system. For this purpose, additional transformations on the electric and magnetic field quantities are necessary as well. Note that Lorentz relates the inertial reference system to this etherfix reference to the non-physical reference system, and TL is the local time, which was just considered to be a mathematical coordinate, that's all. Now Einstein in 1905 used three different reference systems, laboratory reference system and a reference system little k that could be taken as the body's, as a moving body's resting system, all coordinates and times are relativistic. and then a reference system S prime, where here S prime's axes are aligned with K's but X prime's spatial coordinates are Galilean but his time coordinate is relativistic. In 1970 he does the same thing, work once when I try it again at basic axioms line and now three different reference systems again, the reference system S which remains at rest and is an inertial reference system a reference system, sigma, that accelerates with a constant acceleration, A, relative to S, and then what became known as a local Lorentz frame, S prime, where S prime is now one rank higher,

35:00 elevated one step higher from 1905, S prime carries space-time coordinates that are consistent with special relativity. And at a particular instant of time, S prime and sigma coincide. I'll just run quickly through Einstein's argument for setting up time in an accelerated reference system. How much time do I have? Oh, you keep going. Keep going, okay, I get it. Almost getting that accelerated. A time, t equals tau equals zero. Sigma and s coincide in our relative rest. Clocks and sigma are synchronized with clocks and s. called the time on the clocks and sigma the local time, just using Lorentz's expression again, little sigma. Capital sigma accelerates at a constant rate A relative to S at a fixed time T prime in S prime. S prime and sigma overlap, and clocks and sigma can be set with those in S prime, where B is AT, the same as the A from the fourth and the dominant experiment, the same arbitrary, in quotes, arbitrary acceleration. Einstein asked the question, can we say about the rate of clocks in the next time element, okay? At some time, T prime, sigma and S prime coincide. What happens in the next time element? Sigma moves on, and the time element power is assumed small enough so that one can still consider all rates of clocks and values you get from measuring rods has to be consistent with special relativity. Einstein assumes that this small time element tau the rates of clocks in sigma are unaffected by the acceleration and so the rates of clocks in s prime can be used to describe those in sigma according to special relativity if two spatially separated clocks in sigma that were originally in synchrony with two equally spatially separated clocks in s when s and sigma coincided with t equals t prime, t equals tau equals zero, these clocks continue to be in synchronic. But the price you pay for that is that as he pointed out in the original relativity paper, these clocks in sigma are no longer synchronous with each other. And therefore, neither

37:30 are they synchronous with the clocks in s prime. Therefore, sigma cannot be the time the physical time, in capital sigma because the clocks reading sigma are no longer synchronized with each other. So, instead, Einstein defines the time tau in sigma to be the totality of the readings on a single clock located at sigma's origin. Now, use S prime to define simultaneity in sigma. That is, two events are simultaneous in S prime, and so too in sigma when t1 prime equals t2 prime, therefore one finds that the relationship between a clock along sigma's axis off the origin with the clock at the origin, these two times are related by this expression, sigma degree tau, for again tau is the clock that registers is the time in sigma. Tau is the origin of sigma, and little sigma is the time on a clock, somewhere else off the origin along the x-axis, times 1 plus AC over C squared, where A is the constant acceleration, and C is the x-coordinate for the clock sigma. The equivalence between acceleration and gravitation fields, putting AC, called the phi, where phi is the gravitational potential at the point C in capital sigma. Well, immediately this predicts a gravitational redshift, Einstein notes it, although he doesn't use those words, and he assumes that the result holds also for a non-uniform gravitational field. another prediction follows in that Einstein attains covariance for the equations of electromagnetism provided that the velocity of light is replaced with this expression c times 1 plus ac over c squared which again sets equal a use of the equivalence principle to replace the acceleration with a gravitational potential leads to a second prediction the bending of light rays that are not propagated in the C direction. Einstein goes on to note that all these predictions that he's talking about are too small to be found, to be measured at that time. That is to say, any effects of the Earth's gravitational field

40:00 on electrical and optical phenomena are too small to be measured. He would say otherwise in 1911. the last point that he discusses in this paper he uses the standard method standard method to derive energy conservation or Poitain's theorem of electromagnetism he runs through the calculation and he provides the promised new argument supporting the extension of the mass energy equivalence to position, namely what he obtains is the usual stuff, after extending the integration surface out to infinity, he obtains the usual stuff, plus energy flows multiplied by phi over c squared, and again, using some more adjectives, this equation contains a very remarkable result, so every energy E belongs thus in the gravitational field, an energy of position, which is as large as the energy of position of a ponderable mass of magnitude E the C squared. The caveat is presented here, the warning is presented here, the caution that all of these results that he has been talking about, these predictions that he's been talking about, depend upon the validity of the assumption that one can replace a uniform gravitational field with an obviously directed constant acceleration. And that ends the 1907 paper. Now, although Einstein did not publish again on gravitation until 1911, we know he thought about it. It was of concern to him. For example, on 24th December 1907, 20 days after sending off the completed Yaw book paper to Scharck, Einstein writes to Konrad Habeck, at this time I am again busy with considerations on relativity theory in connection with the law of gravitation. I hope to clear up the so-called unexplained secular changes of the perihelion length of mercury, but so far, it does not seem to work, and it would not work until 1915. Now, to tie some loose ends together, what ever happened to Einstein's unknown qualitet? Well, this was explicated in 1911 by Max von Lao through a statement based on the axiomatic basis of Einstein's principle of relativity,

42:30 And to completely close a system, the closure of a system, one must take the derivative of a sum of stress-energy tenses, which contain as many energy momentum flows as you need to close your system. What about the problem of rigid bodies? Well, we learned from John Stachel's paper, Einstein's rotating this, based on correspondence Einstein archives that, indeed, beginning in 1908, Einstein had been concerned with the problems and paradoxes of rotating rigid bodies, and his consideration to this problem led him quite quickly to realize that Euclidean geometry was not useful, perhaps not even applicable, to rotating reference systems, surely a key result, a key point on its path to generalized relativity. Let me conclude now by saying that how the path to the completed theory of relativity led Einstein away from the path that he had taken in 1907 is beyond the scope of my lecture. What I wanted to do today is to explore how Einstein obtained key insights that coalesced in the 1907 Togonkin experiment. Perhaps it's useful here to paraphrase, or to paraphrase Einstein's recollection the 1895 Gedanken experiment, which led to, which was instrumental in his inventing special relativity theory, the Gedanken experiment of 1907 contained the germ of the general theory of relativity, namely the principle of equivalence. Despite preoccupation with problems concerning the light quantum during 1908 and 1911, and setbacks and blind alleys in Einstein's subsequent research during 1911 and 1915 toward the general theory of relativity, his tenacity and persistence, surely hallmarks of creative thinking, tempted moving toward the theory's final achievement. As Einstein wrote to Arnold Sommerfeld on 29 October 1912, compared to this problem, as said, general relativity, the original relativity is Charles' play. Well, thank you for that, to make a clear account.

45:00 Absolute time is not to be kept by that clock up there. In fact, I make it about three minutes fast at the moment, so let's have a few thoughts. I'd like to ask, to what extent, is there any evidence that Einstein read Newton's Principia? I think corollary sticks with the laws of motion and the discussion of the equipment I have no idea about this question. I don't know. In other words, he directly read the book, but he did read a book about Newton's theory. It's our book, I don't know what it means. Rosenberg, yeah. He's talking a lot about Newton's theory. He's read Mark also, of course. What's maybe even more pertinent is the fact that Newton has verified the equivalences of the three decimal places. I think what some of my studies turned to mind would have been a foul trick of nature to have it called the three decimal places. But also corollary 6 is very suggestive. Yes, well, as we said, he's certainly, at least in Red Mox. Any more questions? Just one small point, though. Why did you say that I thought the equivalent of gravitation on inertial mass was something put beyond experimental proof when the very quote you showed said, he said, when in the very quote you showed, he says, unless proven otherwise. Yeah, well, unless proven otherwise, he would accept it as universally valid. Well, true to be sure, possibly, but I think when he says something like that, he does accept it as universally valid. Unless proven otherwise. Yeah, I mean, he goes, well... That was the first half of the sentence. ...sport coming on it. Similarly, he did the same thing with the principle in 1905, where he raises the principle of relativity to an axio. It's true. In 1905, you could say the same thing about 1905. I wouldn't. I wouldn't. I wasn't mentioning you were saying that about the 1905, too. No, I wouldn't. I certainly wouldn't question it in 1905. Possibly it opened the question in 1907, but I don't think so, either.

47:30 I don't think he did either, but if somebody had come along with the experiment, if the average experiment would carry out to 12 dozen places had failed, I think he wouldn't have tried to fit the shoe someplace else, that's what you do imply, how we would have accepted that. And certainly, if someone had detected motion, would you expect anything, he would? No, no, that's, no, in that case, I think you're wrong, because if somebody detects motion that seems to imply absoluteness or whatever, then you can just say that it's a measure your inertial system. You can play the following game. You can say that that's data that tells you how much your inertial system, how much your reference system is non-inertial. You could, but there's no proof that Einstein would have played. Well, I mean, there aren't inertial systems, eh? Well, there's no proof that Einstein would have, I mean, you're just assuming that Einstein would have. When you elevate something to a possible, that means you place it behind the experimental test. I don't see why that follows. When you postulate something, it doesn't mean you place it on a experimental test. It means for the moment you accept it as a particle for your reason. Yeah, well, I mean, why, turning the argument around, what would you say about 1905, about the principle of relativity there? I mean, in that case, it would be a pretty peculiar principle. Well, Einstein says all evidence for the moment. I mean, the principle for the moment has failed to detect it. Well, he says you raise this conjecture to the principle. And if the concept of evidence turns up, money will then lower it again. Oh, well, of course, I mean, one does, but one basis, one's, one basis, one's theorizing on something that one takes. The point is, in 1905, there were principles of relativity, which were empirically based, so to speak. They were always open to experimental tests, and hence dealing with them theoretically was dubious, and there were false thoughts, etc. What I find is, take it as an axiom to see what consequences follow. And here, too, he takes the equivalence of mass, of gravitation on virtual mass, as a principle to see what consequences follow from it. Surely, if something, if some terrible experimental evidence shows up, then, of course, one reduces it, but it's a matter of what one believes. Well, then, we agree that it's not the only experiment. What? Then we agree that even the accident will not be under the experimental test. In science? In science.

50:00 Well, again, it's a matter of belief. How are you going to do this? Well, Poitier might have believed they really were. He might have believed there were some axioms with his logical definitions, and I'll really be honest about it. I don't think Einstein was a bad answer. Well, I think he believed that the physical conservation of energy would be on the spiral. No, because he tried for a while. It's the same thing as... He tried for a while to absorb his ways and explain the problem, and it failed. That's why he gave up the chemical modification of the physical conservation of energy, not because he had some... Well, I mean, he may also have been on the impression that if experimental tests are done, which reveal somehow or another that inertial and gravitational masses are not equal to one another, then there may be some way of getting around that and dealing with it anyway. Similarly, if you do an experiment on a physical system and conservation of energy seems not to hold, you just invent a new form of energy. I guess it's a very potentially infinite discussion. Yes, I think our time is rather short. I have two, three questions starting here. Let me draw the audience's attention to the fact that these morning speakers' historical accounts seem to be guided by very strong epithological convictions, which both these morning speakers tend to hide in some places of the lectures. Let me remind you again of one of the key words, which was reinforcement. in just at the very end, and Arda's keyword was hidden in one of his slides, and let me just remind you of this one, it's theory-loading visual imagery, and so I would like to, this was an observation, now comes my question, my question is you used a less terminological or characterization of Einstein's ongoing research from the special to the general relativity, and you used the word continuity. So my question would be, which are the methodological or epistemological terms for which you would characterize this sort of continuity? Well, continuity of mathematical techniques, first of all, which was commonly used, as I put it, as I noted, in the letter that I was before,

52:30 and continuity, I mean, similar to what the point that John brought up, continuity of the belief that one can raise certain statements to an axiomatic status. And Einstein was a master of building theories and principles of theory, statements which are overarching statements accepted as true, as above empirical truth, and to see what consequences follow from it, which he did done in 1905, which he did again, and we started to do again in 1970. by fear-related visual imagery, I meant using a term from cognitive science that, I mean, many people have seen things fall, you know, people jump out windows, et cetera, but to see it in the context of, to see the, of course, deep structure of it in the context of gravitational and inertial masses, and noting, as maybe Einstein did, in the, using the mathematical, using that mathematical argument that one finds in many physics textbooks too, but the line I've always found missing in physics textbooks is that line, you don't skip the step where you put in the gravitational, you put the gravitational inertial mass equal to one another, and you have one multiplying G, the other one multiplying minus A, and in order to get rid of those terms, you have to set G equal to minus A. a step that I believe, again, I've seen the deep structure and things falling freely, to note that the inertial mass multiplies A, gravitational mass multiplies G, one has to if the inertial and gravitational mass are equal to one another, then so must there be a relationship between acceleration and gravity too. Can we just two more questions, we have four more minutes, shall we say, and starting with actually no, I wasn't And there's a lot of things I'd like to discuss, but not into the question there. There's two other people. This is only a comment. It's a rather happy circumstance that, at that time, non-alerturistic quantum mechanics was not yet discovered, because in the Schrodinger equation

55:00 even assuming they would not stop up the formulation of the equivalence there is much more difficult I would try to calculate and also find these insurances thank you and the last one I would like to know the first Gedanken experiment you talked about the very first time that gravitation enters into a public Well, I guess so. I don't know if one can really say the first time, it's a bad thing to say, but he recollected the Sudanese from 1990, from 1907, so it may well have occurred to him. And at the time of writing the Yalbuk paper, as I said, in trying to tie things together, others had been working on gravitational theories at that time. For example, Pointer A, in a set of papers that wrote in 1905 and 1906, on the dynamics of the electron, wrote down a Lorentz-Covarian theory of gravity, however, based on the so-called electromagnetic world picture. And it was a vector theory of gravity, so it couldn't possibly succeed. but by means of various plane-round parameters, he did get the advance of the very land Mercury in the right direction. But there was nothing in it concerning inertial and gravitational, the quality of inertial and gravitational mass, but certainly not the equivalent principle. What he was doing was, and what everyone else was doing, was playing around with equations of electromagnetism, and not with Newton's mechanics. One very last. There is a later reminiscence by Einstein, which he's trying to recollect the development of the General Theodosian, in which he makes it much more detail about his attempt to set up a special observatory theory of gravitation. Which is on the Theodosian? No, the 35. And he says there that, it struck him immediately when he thought of doing this, that he would not have the following of gravitation on the original mass, and that's why he abandoned that attempt immediately. We did determine, we tried to do a special office to detail that, but it's well worth reading that very prior to that. Thank you. We have exactly 15 minutes of coffee, and may I remind you that we have a problem with buses at 2 o'clock, so we must try to keep it at the timetable.

57:30 Thank you.