Einstein's Work. • Developed the special and general theories of relativity. • Was instrumental to the development of early quantum theory but never agreed with. Free kindle book and epub digitized and proofread by Project Gutenberg. Project Gutenberg · 59, free ebooks · 6 by Albert Einstein. The Meaning of Relativity by Albert Einstein. No cover available. Download.
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Copyleft: Einstein Reference Archive (soundofheaven.info) , Permission is granted to The Structure of Space According to the General Theory of Relativity . ativity, Einstein wrote a paper attempting to modify Newton's theory of gravitation to fit special relativity. Was this modification necessary? Most emphatically yes!. In November Albert Einstein explained a radically new world view to the Prussian Academy of Sciences with the General Theory of Relativity. Accordingly, masses and rays of light do not merely move through space and time - space and time themselves merge into a structure that.
After all the trouble that the reader has been put to, to find out the issue, perhaps he is disappointed to learn how small is the difference between the predictions of Newton and Einstein. And, as we said in Chapter X. Philosophical Magazine, Vol. At this point Einstein took up the problem, and decided that a natural "conspiracy 11 must be a natural LAW operating. We notice at once the remarkable resemblance between 84 and And similarly for Jx 2 in 1 2.
But we doubt whether even the best of these can possibly give to a novice an adequate idea of what it is all about.
What is very clear when expressed in mathematical language sounds "mystical" in ordinary language. On the other hand, there are many discussions, including Einstein's own papers, which are accessible to the experts only.
This book is an attempt to satisfy the needs of this kind of reader. The Remedy 31 V. The Solution of the Difficulty 39 VI.
Introduction 95 XI. A Non-Euclidean World! What Is a Tensor? Mixed Tensors XX. Contraction and Differentiation 1 78 XXI. Deflection of a Ray of Light, cont.
In order to appreciate the fundamental importance of Relativity, it is necessary to know how it arose. Whenever a "revolution 11 takes place, in any domain, it is always preceded by some maladjustment producing a tension, which ultimately causes a break, followed by a greater stability at least for the time being.
What was the maladjustment in Physics in the latter part of the 19th century, which led to the creation of the "revolutionary 11 Relativity Theory?
Let us summarize it briefly: Now, if there is an ether, does it surround the earth and travel with it, or does it remain stationary while the earth travels through it? And so an experiment was performed by Michelson and Morley see p. This unexpected result was explained by a Dutch physicist, Lorentz, in 1 , in a way which will be described in Chapter II.
The search for the ether wind was then resumed by means of other kinds of experiments.! Eddington, in the Encyclopedia Britannica, 14th ed. At this point Einstein took up the problem, and decided that a natural "conspiracy 11 must be a natural LAW operating.
And to answer the question as to what is this law, he proposed his Theory of Relativity, published in two papers, one in and the other in So fruitful did his analysis prove to be that by means of it he succeeded in: The General Theory and which led to several important predictions which could be verified by experiment; and which have been so verified since then. No other physical theory has been so powerful though based on so FEW assumptions.
As we shall see. Let us now see what experiment they performed and what was the startling result. In order to get the idea of the experiment very clearly in mind, it will be helpful first to consider the following simple problem, which can be solved by any boy who has studied elementary algebra: Imagine a river in which there is a current flowing with velocity v, in the direction indicated by the arrow: Now let us see how long the round trip from A to C and back to A would take.
If he headed directly toward C , the current would carry him downstream, and he would land at some point to the left of C in the figure on p. Therefore, in order to arrive at C , 9 he should head for some point D just far enough upstream to counteract the effect of the current. Then we get: But what has all this to do with the Michelson-Morley experiment?
In that experiment, a ray of light was sent from A to B: Such was the plan of the experiment. Now what actually happened? The Dutch physicist, Lorentz, then suggested the following explanation of Michelson's strange result: In the first of these papers Lorentz mentions that the explanation proposed here occurred also to Fitzgerald.
One might ask how it is that Michelson did not observe the shrinkage? The obvious answer is that the measuring rod itself contracts when applied to AB, so that one is not aware of the shrinkage. To this explanation of the Michelson-Morley experiment the natural objection may be raised that an explanation which is invented for the express purpose 14 of smoothing out a certain difficulty, and assumes a correction of JUST the right amount, is too artificial to be satisfying.
Consequently, Lorentz undertook to examine his contraction hypothesis in other connections, to see whether it is in harmony also with facts other than the Michelson-Morley experiment. He then published a second paper in , giving the result of this investigation. To present this result in a clear form let us first re-state the argument as follows: Now suppose an observer on the earth, say Michelson, is trying to measure the time it takes a ray of light to travel from A to B , both A and 8 being fixed points on the moving axis X r.
Surely the time measurements in the two systems are not different: In other words, as Lorentz saw it, t' was a sort of "artificial 11 time introduced only for mathematical reasons, because it helped to give results in harmony with the facts. As Jeans, the English physicist, puts it: Let us now see what Einstein did. As Einstein regarded the situation, the negative result of the Michelson-Morley experiment, as well as of other experiments which seemed to indicate a "conspiracy" on the part of nature against man's efforts to obtain knowledge of the physical world see p.
In other words, he felt that there was something fundamentally and radically wrong in physics, rather than a mere superficial difficulty. His exceedingly reasonable examination 20 is most illuminating, as we shall now see.
That is why 21 the system of units ordinarily used is called the "C. Let us now return to Einstein's re-examination of these fundamental units. Suppose that two observers wish to compare their measurements of time. Thus 5 will conclude, from this series of signals, that his watch and that of f are in perfect agreement. But let us now imagine that the entire solar system is moving through space, so that both the sun and the earth are moving in the direction shown in the figure: Now let the signals again be sent as before: S sends his message "1 2 o'clock," but sincejfjs moving awayjromjjta IRelatter wiffnot reaclTE in 8 minutes, but will take some longer time to overtake f , Say, 9 minutes.
Thus S receives Fs message at 1 2: Now if 5 and F are both UNAWARE of their motion and, indeed, we are undoubtedly moving in ways that we are entirely unaware of, so that this assumption is far from being an imaginary one. Of course, this is only an apparent error in Fs watch, because, as we know, it is really due to the motion, and not at all to any error in Fs watch. It must be noted, however, that this omniscient "we" who can see exactly what is "really" going on in the universe, does not exist, and that all human observers 24 are really in the situation in which 5 is, namely, that of not knowing about the motion in question, and therefore being OBLIGED to conclude that 's watch is wrong!
And therefore, 5 sends the message telling him that if sets his clock back one minute, then their clocks will agree.
In the same way, suppose that other observers, j4,B,C,ctc. They would all say then that all their clocks are in agreement. Whether this is absolutely true or not, they cannot tell see above , but that is the best they can do. Now let us see what will happen when these observers wish to measure the length of something. To measure the length of an object, you can place it, say, on a piece of paper, put a mark on the paper at one end of the object, and another mark at the other end, then, with a ruler, find out how many units of length there are 25 between the two marks.
This is quite simple provided that the object you are measuring and the paper are at rest relatively to you. But suppose the object is say, a fish swimming about in a tank? Now suppose that our observers, after their clocks are all in agreement see p. They send out orders that at 1 2 o'clock sharp, whichever observer happens to be at the place where the front end of the train, A' 9 arrives at that moment, to NOTE THE SPOT; and some other observer, who happens to be at the place where the rear end of the train, B , is at that same moment, to put a mark at THAT spot.
Let us now talk to the people on the train. And suppose that there are two clocks on the train, one at A', the other at B', and that these clocks have been set in agreement with each other by the method of signals described above. Obviously the observers A , B , C, etc. NOT admit that the clocks at A and B' 27 arc in agreement with each other, since they "know" that the train is in motion, and therefore the method of signals used on the moving train has led to an erroneous setting of the moving clocks see p.
Whereas the people on the train, since they "know" that A, B , C, etc. What is the result of this difference of opinion? Thus, when the people on the train make the marks simultaneously, as judged by their own clocks, the distance between the two marks 28 will NOT be the same as before.
Similarly, as we shall see on p. And since, as we mentioned on p. Now, of course, observers on the earth partake of the various motions to which the earth is subject the earth turns on its axis, it goes around the sun, and perhaps has other motions as wefl.
Hence it would seem that observations made by people on the earth 29 cannot agree with those taken from some other location in the universe, and are therefore not really correct and consequently worthless!
Thus Einstein's careful and reasonable examination led to the realization that Physics was suffering from no mere single ailment, as evidenced by the Michelson-Morley experiment alone, but was sick from head to foot!
Did he find a remedy? HE DID! Nor is it correct to assume that again as Michelson did for two different observers, which would imply that both observers agree in their time measurements.
Now what experimental data must we take into account here? They are: FACT 1: It is impossible to measure the "ether wind," or, in other words, it is impossible to detect our motion relative to the ether. This was clearly shown by the 33 Michelson-Morley experiment, as well as by all other experiments devised to measure this motion see p.
FACT 2: The velocity of light is the same no matter whether the source of light is moving or stationary.
Let us examine this statement more fully, to see exactly what it means. To do this, it is necessary to remind the reader of a few well-known facts: Imagine that we have two trains, one with a gun on the front end, the other with a source of sound on the front end, say, a whistle.
Suppose that the velocity, u , of a bullet shot from the gun, happens to be the same as the velocity of the sound. Now suppose that both trains are moving with the same velocity, v , in the same direction. The question is: Are they the same? But in the case of the sound wave which is a series of pulsations, alternate condensations and rarefactions of the air in rapid succession , the first condensation formed in the neighborhood of the whistle, travels out with the velocity u relatively to the medium, regardless as to whether the train is moving or not.
So that this condensation has only its own velocity and does NOT have the inertia! CASE I. Both trains at rest. Tram u jt. Both trains moving with velocity v. Thus we see that the velocity of sound is u feet per second relatively to the starting point, whether the source remains stationary as in Case I. Now, as a result of this, it appears, by referring again to the diagram on p. Thus we should be able to determine v. Or, stating it another way: Let us therefore see how, in the light of the discussion in Ch.
Let us express these acts algebraically, for two observers, K and K f , who are moving with uniform velocity relatively to each other, thus: It is assumed that at the instant when the rays of light start on their path, K and K' are at the SAME place, and the rays of light radiate out from that place in all directions.
How can they both be right? But what about the circles? They cannot possibly have both K and K as their centers! Now, at last, we are ready for the explanation. Although K claims that at the instant when the light has reached the point C p. Hence we see that they are not really contradicting each other, but ihat they are merely using two different systems of clocks, such that the clocks in each system agree with each other alright, but the clocks in the one system have NOT been set in agreement with the clocks in the other system see p.
That is, If we take into account the inevitable necessity of using signals in order to set clocks which are 43 at a distance from each other, and that the arrivals of the signals at their destinations are influenced by our state of motion, of which we are not aware p. We now see in a general qualitative way, that the situation is not at all mysterious or unreasonable, as it seemed to be at first. And now a pleasant surprise awaits us. We shall derive, now, from 6 and 7 , relationships between the measurements of the two observers, K and K f.
And all the mathematics we need for this is a little simple algebra, such as any high school boy knows.. Therefore x' - ct' - X x - ct 8 where X is a constant. By adding and subtracting 8 and 9 we get: Let us now consider the situation from the points of view of K and K'. Take K first: Thus 47 each observer considers that his own measurements are the "true" ones, and advises the other fellow to make a "correction.
Thus in 14 K says: We thus see that the Lorentz transformation was derived by Einstein quite independently of Lorentz , NOT as a set of empirical equations 49 devoid of physical meaning, but, on the contrary, as a result of a most rational change in our ideas regarding the measurement of the fundamental quantities length and time.
Thus, we can now appreciate Einstein's Principle of Relativity: Thus a person in a train moving into a station with uniform velocity looks at another train which is at rest, and imagines that the other train is moving whereas his own is at rest. And he cannot find out his mistake by making observations within his train since everything there is just the same as it would be if his train were really at rest.
Surely this fact, and other similar ones, must have been observed long before Einstein? Yes, this certainly was known long before Einstein. Let us see what connection it has with the principle of relativity as stated by him: Referring to the diagram on p. This kind of relativity principle is the one involved in the question on page 53, and WAS known long before Einstein. But why should this extension be such a great achievement why had it not been suggested before?
In other words, the extension of the principle of relativity to electromagnetic phenomena seems to contradict fact 2 and therefore could not have been made before it was shown that fundamental measurements are merely "local" and hence the contradiction was only apparent, as explained on p.
But before we can discuss this in detail we must first see how the ideas which we have already presented were put into a remarkable mathematical form by a mathematician named Minkowski. It is now clear from the Lorentz transformation D. Thus we may say that we live in a four-dimensional world. Now if an event is designated by the four numbers x, y, z, f , in a given coordinate system, the Lorentz transformation p.
In studying "graphs 11 every high school freshman learns how to represent a point by two coordinates, x and y, using the Cartesian system of coordinates, that is, two straight lines perpendicular to each other.
Now, we may also use another pair of perpendicular axes, X' and Y' in the figure on the next page , having the same origin, , as before, and designate the same point by x and y' in this new coordinate system.
The equations 20 remind one somewhat of the Lorentz transformation p. Let us examine the similarity between 20 and the Lorentz transformation a little more closely, selecting from the Lorentz transformation only those equations involving x and t , and disregarding those containing y and z, since the latter remain unchanged in going from one coordinate system to the other.
Thus we wish to compare 20 with: Indeed, this is quite in accord with the discussion in Chapter VI. Otherwise, their claims are precisely identical; and this is exactly what equations 21 and 22 show so clearly.
Let us now return to the comparison of 22 and In other words, ff K observes a certain event and finds that the four numbers necessary to characterize it see p.
See p. And since we took p. That is, the magnitude of the angle depends upon v , the relative velocity of K and K f. And, just as in plane geometry the distance between two points remains the same whether we use the primed or the unprimed coordinate systems see p.
In this chapter we shall discuss mass measurements, as well as other measurements which depend upon these fundamental ones. We already know that if an object moves in a direction parallel to the relative motion of K and K , then the Lorentz transformation gives the relationship between the length and time measurements of K and K'.
Einstein found that the best approach to this difficult problem was via the Conservation Laws of Classical Physics. Then, just as the old concept of the distance between two points three-dimensional was "stepped up" to the new one of the interval between two events four-dimensional , see p.
And, when this is done an amazing vista will come into view! We express this mathematically thus: Thus, in a motor, electrical energy is converted to mechanical energy, whereas in a dynamo the reverse change takes place. Are you wondering what is the use of all this? You will see that they will lead to: Hence mass CAN be destroyed as such and actually converted into energy!
Some readers may be able to understand the following "stepping up" process now, others may prefer to come back to it after reading Part II of this book: The components of the velocity vector in Classical Physics, are: And, if we replace x, y, z by xi, X2, xs, these become, in modern compact notation: JxjJt ,2,3.
Similarly, the momentum components are: Thus, in going from 3-dimensional space and 1 -dimensional absolute time i. Consider first only the first 3 components of Thus, from this NEW viewpoint we realize that even in Classical Physics the Mass of a body is NOT a constant but varies with changes in its energy the amount of change in mass being too small to be directly observed!
Thus even an atom is equivalent to a tremendous amount of energy. Indeed, when a method was found see p. Travel near the speed of light, explore the twin paradox, black holes, the big bang, the history of the universe, curved space, gravitational waves, the jets of the Milky Way and many other captivating topics!
Free download of volume II: Enjoy the embedded colour films - even one of a moving light pulse! Have fun with many captivating riddles and curiosities. Be fascinated by special relativity, general relativity, Albert Einstein and cosmology. Mathematics is reduced to the bare minimum. First, the book introduces special relativity in a simple way. Read more. Special Theory of Relativity.
The theory of relativity. Mathematical Theory of Relativity.
Theory of relativity. Einstein's Theory of Relativity.
A Theory of Relativity. Theory of Relativity. General Theory of Relativity. Einsteins Recent Theory of Gravitation and Electricity. Theory of relativity of motion.