Albert Einstein's \'On the Electrodynamics of Moving Bodies,\' published in 1905, is a revolutionary scientific paper that introduced the world to the theory of special relativity. This theory fundamentally changed how we understand time and space, two of the most fundamental concepts in physics.Before Einstein, the prevailing view (based on Newtonian mechanics) was that time and space were absolute and unchanging. Einstein, however, proposed that time and space are not fixed. Instead, they are relative and can vary depending on the speed at which an object is moving. One of the most famous outcomes of this theory is the idea that as an object approaches the speed of light, time for that object slows down compared to an observer who is not moving at the same speed.The theory also led to the famous equation E=mc², which shows the relationship between energy (E), mass (m), and the speed of light (c). This equation suggests that mass and energy are interchangeable, a concept that has had enormous implications in physics.Einstein's paper on special relativity has had a profound impact on the scientific community. It has influenced almost every aspect of modern physics, changing our understanding of the universe. His ideas paved the way for numerous scientific advancements and have been crucial in the development of technologies such as GPS systems, which rely on the principles of relativity for accuracy.In summary, \'On the Electrodynamics of Moving Bodies\' is not just a milestone in the history of physics; it's a work that has reshaped our understanding of the very fabric of reality, challenging and expanding our knowledge of the universe we live in.
\plain (cid:12)gures". I have used the correct \plane (cid:12)gures" in this edition. 10 clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be 1 2 tv2=c2 second slow. Thence we conclude that a balance-clock7 at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions. x 5. The Composition of Velocities In the system k moving along the axis of X of the system K with velocity v, let a point move in accordance with the equations (cid:24) = w(cid:24)(cid:28); (cid:17) = w(cid:17)(cid:28); (cid:16) = 0;
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Required: the motion of the point relatively to the system K. If with the help of the equations of transformation developed in x 3 we introduce the quantities x, y, z, t into the equations of motion of the point, we obtain x = y = w(cid:24) + v 1 + vw(cid:24)=c2 p 1 v2=c2 1 + vw(cid:24)=c2 t; w(cid:17)t; z = 0: Thus the law of the parallelogram of velocities is valid according to our theory only to a (cid:12)rst approximation. We set (cid:18) V 2 = w2 = w2 (cid:19)2 dx dt (cid:24) + w2 (cid:17); + (cid:18) dy dt (cid:19)2 ; a = tan1 wy=wx; a is then to be looked upon as the angle between the velocities v and w. After a simple calculation we obtain V =
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This case had to be excluded. 11 It is worthy of remark that v and w enter into the expression for the resultant velocity in a symmetrical manner. If w also has the direction of the axis of X, we get V = v + w 1 + vw=c2 : It follows from this equation that from a composition of two velocities which are less than c, there always results a velocity less than c. For if we set v = c (cid:20); w = c (cid:21), (cid:20) and (cid:21) being positive and less than c, then 2c (cid:20) (cid:21) 2c (cid:20) (cid:21) + (cid:20)(cid:21)=c It follows, further, that the velocity of light c cannot be altered by compo-
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V = c < c: sition with a velocity less than that of light. For this case we obtain V = c + w 1 + w=c = c: We might also have obtained the formula for V, for the case when v and w have the same direction, by compounding two transformations in accordance with x 3. If in addition to the systems K and k (cid:12)guring in x 3 we introduce still another system of co-ordinates k0 moving parallel to k, its initial point moving on the axis of X with the velocity w, we obtain equations between the quantities x, y, z, t and the corresponding quantities of k0, which di(cid:11)er from the equations found in x 3 only in that the place of \v" is taken by the quantity v + w 1 + vw=c2 ; from which we see that such parallel transformations|necessarily|form a group. We have now deduced the requisite laws of the theory of kinematics corresponding to our two principles, and we proceed to show their application to electrodynamics.
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