The Casting Of Einsteins Dice

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One sees in this paradox the germ of the special relativity theory is already contained. Einstein's recollections of his youthful musings are widely cited because of the hints they provide of his later great discovery. However, Norton has noted that Einstein's reminiscences were probably colored by a half-century of hindsight. Norton lists several problems with Einstein's recounting, both historical and scientific: Rather than the thought experiment being at all incompatible with aether theories which it is not , the youthful Einstein appears to have reacted to the scenario out of an intuitive sense of wrongness.

He felt that the laws of optics should obey the principle of relativity. As he grew older, his early thought experiment acquired deeper levels of significance: Einstein felt that Maxwell's equations should be the same for all observers in inertial motion. From Maxwell's equations, one can deduce a single speed of light, and there is nothing in this computation that depends on an observer's speed. Einstein sensed a conflict between Newtonian mechanics and the constant speed of light determined by Maxwell's equations.

Regardless of the historical and scientific issues described above, Einstein's early thought experiment was part of the repertoire of test cases that he used to check on the viability of physical theories. Norton suggests that the real importance of the thought experiment was that it provided a powerful objection to emission theories of light, which Einstein had worked on for several years prior to In the very first paragraph of Einstein's seminal work introducing special relativity, he writes:. It is well known that Maxwell's electrodynamics—as usually understood at present—when applied to moving bodies, leads to asymmetries that do not seem to attach to the phenomena.

Let us recall, for example, the electrodynamic interaction between a magnet and a conductor. The observable phenomenon depends here only on the relative motion of conductor and magnet, while according to the customary conception the two cases, in which, respectively, either the one or the other of the two bodies is the one in motion, are to be strictly differentiated from each other. For if the magnet is in motion and the conductor is at rest, there arises in the surroundings of the magnet an electric field endowed with a certain energy value that produces a current in the places where parts of the conductor are located.

But if the magnet is at rest and the conductor is in motion, no electric field arises in the surroundings of the magnet, while in the conductor an electromotive force will arise, to which in itself there does not correspond any energy, but which, provided that the relative motion in the two cases considered is the same, gives rise to electrical currents that have the same magnitude and the same course as those produced by the electric forces in the first-mentioned case.

This opening paragraph recounts well-known experimental results obtained by Michael Faraday in The experiments describe what appeared to be two different phenomena: In the latter half of Part II of that paper, Maxwell gave a separate physical explanation for each of the two phenomena. Although Einstein calls the asymmetry "well-known", there is no evidence that any of Einstein's contemporaries considered the distinction between motional EMF and transformer EMF to be in any way odd or pointing to a lack of understanding of the underlying physics. Maxwell, for instance, had repeatedly discussed Faraday's laws of induction, stressing that the magnitude and direction of the induced current was a function only of the relative motion of the magnet and the conductor, without being bothered by the clear distinction between conductor-in-motion and magnet-in-motion in the underlying theoretical treatment.

Yet Einstein's reflection on this experiment represented the decisive moment in his long and tortuous path to special relativity. Although the equations describing the two scenarios are entirely different, there is no measurement that can distinguish whether the magnet is moving, the conductor is moving, or both. In a review on the Fundamental Ideas and Methods of the Theory of Relativity unpublished , Einstein related how disturbing he found this asymmetry:.

The idea that these two cases should essentially be different was unbearable to me. Einstein needed to extend the relativity of motion that he perceived between magnet and conductor in the above thought experiment to a full theory. For years, however, he did not know how this might be done. The exact path that Einstein took to resolve this issue is unknown. We do know, however, that Einstein spent several years pursuing an emission theory of light, encountering difficulties that eventually led him to give up the attempt. Gradually I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts.

The longer and more desperately I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results. That decision ultimately led to his development of special relativity as a theory founded on two postulates of which he could be sure.

Einstein's wording of the second postulate was one with which nearly all theorists of his day could agree.

His wording is a far more intuitive form of the second postulate than the stronger version frequently encountered in popular writings and college textbooks. The topic of how Einstein arrived at special relativity has been a fascinating one to many scholars: A lowly, twenty-six year old patent officer third class , largely self-taught in physics and completely divorced from mainstream research, nevertheless in the year produced four extraordinary works Annus Mirabilis papers , only one of which his paper on Brownian motion appeared related to anything that he had ever published before.

Einstein's paper, On the Electrodynamics of Moving Bodies , is a polished work that bears few traces of its gestation. Documentary evidence concerning the development of the ideas that went into it consist of, quite literally, only two sentences in a handful of preserved early letters, and various later historical remarks by Einstein himself, some of them known only second-hand and at times contradictory.

In regards to the relativity of simultaneity , Einstein's paper develops the concept vividly by carefully considering the basics of how time may be disseminated through the exchange of signals between clocks. The Special and General Theory, Einstein translates the formal presentation of his paper into a thought experiment using a train, a railway embankment, and lightning flashes.

The essence of the thought experiment is as follows:. A routine supposition among historians of science is that, in accordance with the analysis given in his special relativity paper and in his popular writings, Einstein discovered the relativity of simultaneity by thinking about how clocks could be synchronized by light signals. The dissemination of precise time was an increasingly important topic during this period. Trains needed accurate time to schedule use of track, cartographers needed accurate time to determine longitude, while astronomers and surveyors dared to consider the worldwide dissemination of time to accuracies of thousandths of a second.

However, all of the above is supposition. In later recollections, when Einstein was asked about what inspired him to develop special relativity, he would mention his riding a light beam and his magnet and conductor thought experiments. He would also mention the importance of the Fizeau experiment and the observation of stellar aberration. The routine analyses of the Fizeau experiment and of stellar aberration, that treat light as Newtonian corpuscles, do not require relativity.

But problems arise if one considers light as waves traveling through an aether, which are resolved by applying the relativity of simultaneity. It is entirely possible, therefore, that Einstein arrived at special relativity through a different path than that commonly assumed, through Einstein's examination of Fizeau's experiment and stellar aberration.

We therefore do not know just how important clock synchronization and the train and embankment thought experiment were to Einstein's development of the concept of the relativity of simultaneity. We do know, however, that the train and embankment thought experiment was the preferred means whereby he chose to teach this concept to the general public. In his unpublished review, Einstein related the genesis of his thoughts on the equivalence principle:.

While attempts in this direction showed the practicability of this enterprise, they did not satisfy me because they would have had to be based upon unfounded physical hypotheses. At that moment I got the happiest thought of my life in the following form: In an example worth considering, the gravitational field has a relative existence only in a manner similar to the electric field generated by magneto-electric induction.

Because for an observer in free-fall from the roof of a house there is during the fall —at least in his immediate vicinity— no gravitational field. Namely, if the observer lets go of any bodies, they remain relative to him, in a state of rest or uniform motion, independent of their special chemical or physical nature. The observer, therefore, is justified in interpreting his state as being "at rest.

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The realization "startled" Einstein, and inspired him to begin an eight-year quest that led to what is considered to be his greatest work, the theory of general relativity. Over the years, the story of the falling man has become an iconic one, much embellished by other writers. In most retellings of Einstein's story, the falling man is identified as a painter. In some accounts, Einstein was inspired after he witnessed a painter falling from the roof of a building adjacent to the patent office where he worked.

This version of the story leaves unanswered the question of why Einstein might consider his observation of such an unfortunate accident to represent the happiest thought in his life. Einstein later refined his thought experiment to consider a man inside a large enclosed chest or elevator falling freely in space.

While in free fall, the man would consider himself weightless, and any loose objects that he emptied from his pockets would float alongside him. Then Einstein imagined a rope attached to the roof of the chamber. A powerful "being" of some sort begins pulling on the rope with constant force. The chamber begins to move "upwards" with a uniformly accelerated motion. Within the chamber, all of the man's perceptions are consistent with his being in a uniform gravitational field. Einstein asked, "Ought we to smile at the man and say that he errs in his conclusion?

Rather, the thought experiment provided "good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a generalised postulate of relativity. Through this thought experiment, Einstein addressed an issue that was so well known, scientists rarely worried about it or considered it puzzling: Objects have "gravitational mass," which determines the force with which they are attracted to other objects.

Objects also have "inertial mass," which determines the relationship between the force applied to an object and how much it accelerates. Newton had pointed out that, even though they are defined differently, gravitational mass and inertial mass always seem to be equal. But until Einstein, no one had conceived a good explanation as to why this should be so. From the correspondence revealed by his thought experiment, Einstein concluded that "it is impossible to discover by experiment whether a given system of coordinates is accelerated, or whether An extension to his accelerating observer thought experiment allowed Einstein to deduce that "rays of light are propagated curvilinearly in gravitational fields.

Many myths have grown up about Einstein's relationship with quantum mechanics. Freshman physics students are aware that Einstein explained the photoelectric effect and introduced the concept of the photon. But students who have grown up with the photon may not be aware of how revolutionary the concept was for his time. The best-known factoids about Einstein's relationship with quantum mechanics are his statement, "God does not play dice" and the indisputable fact that he just didn't like the theory in its final form.

This has led to the general impression that, despite his initial contributions, Einstein was out of touch with quantum research and played at best a secondary role in its development. Einstein is the only scientist to be justly held equal to Newton. That comparison is based exclusively on what he did before In the remaining 30 years of his life he remained active in research but his fame would be undiminished, if not enhanced, had he gone fishing instead.

God’s Loaded Dice: Einstein and the Death of Classical Reality

Einstein was arguably the greatest single contributor to the "old" quantum theory. Therefore, Einstein before originated most of the key concepts of quantum theory: In addition, Einstein can arguably be considered the father of solid state physics and condensed matter physics. What of after ? In , working with two younger colleagues, Einstein issued a final challenge to quantum mechanics, attempting to show that it could not represent a final solution.

Of this paper, Pais was to write:. The only part of this article that will ultimately survive, I believe, is this last phrase [i.

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This conclusion has not affected subsequent developments in physics, and it is doubtful that it ever will. Can we see their radio waves doing that too? One of the other neat predictions is the perihelion shift in orbiting objects. Watching Mercury over the decades and centuries, human beings have made very, very precise measurements of its location. After Kepler came up with his great theories for planetary motion, Mercury only sort of kind of followed his rules.

When Newton came along, they still followed in the exact same, sort-of, kind-of way, that had mercury shifting a little bit every year. We can see those slight changes in about how far it appears from the Sun in the sky. The point at which it is furthest from the Sun appears to be rotating. You end up creating a spiral instead of a perfect ellipse. It was actually able to take into account where this shift came from. As I recall he came up with the theory, and then they were able to confirm that prediction right away. But with that, all of a sudden, a great mystery was completely solved.

We also have gravitational time delays. This actually means that time slows down the closer you get to the surface of a high-mass object. Here, the Earth actually counts.

Ep. 44: Einstein’s Theory of General Relativity

That is very cool. So, now we start getting into the ones that are harder to prove, or harder to understand. This was figured out by Irwin Shapiro, and is called the Shapiro effect. If you ping a radar signal from the surface of the Earth to Mars, and you measure the amount of time it takes for that radar signal to go from the Earth to Mars and back, you can actually get a time delay depending on how close that beam passes to the Sun.

To do this test, first Dr. Shapiro did calculations, then they went to Haystack Observatory in Massachusetts which is actually where I worked in high school and they shot radar signals to Mars when Mars was very close to the Sun on the sky. So the radar signal had to go just barely past the Sun, get to Mars and come back. This delay is caused by the light having to travel through the well of the Sun.

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Instead you have to drive into the valley and drive back out. Right, because with this experiment they were able to send the beam from the Earth to mars and then from mars, I guess it bounced back. One of the neat things in thinking about this is, light from an object is constantly getting held up in its path as it travels through these valleys that are invisible to the eye but real to an object travelling through gravitational space. So the light is constantly getting held up by this valley, and held up by that valley, where each valley is a divot in the space-time continuum created by a massive object.

A neat little way to visualise this that the folks behind the Einstein project at Stanford University came up with is imagine taking a paper plate and putting a super ball in the centre of it after piling honey into the plate. So you have a pile of honey, stick a super ball in it, put a couple of peppercorns in the honey.

The honey represents the gravitational field of the planet, your super ball represents the planet and the peppercorns are satellites. The ones that are slightly further away from the super ball are going to pretty much sit there, but maybe get carried along a little bit. As our planet rotates, we twist space-time around us the same way that super ball is twisting the honey around it. This is referred to as frame-dragging. It actually has the weird effect of a light beam travelling in the direction of rotation will be perceived to travel a little bit faster than a light beam travelling in the opposite direction of rotation.

Gravity Probe-B was this great satellite that had some of the most precisely built gyroscopes ever built by human beings. There were slightly different electromagnetic properties on the different parts of these ball bearings, and as they rotated they ended up creating electromagnetic fields that affected the final results. Luckily, they have the mathematical tools to correct for these inadvertent electromagnetic fields they ended up producing.

To understand quantum mechanics, one must be willing to concede that macro rationality simply does not apply at the level of infinitesimal physical reality. In the bizarre reality of the quantum , particles appear and disappear, transform as a result of observation, teleport, exhibit complementary qualities of wave-particle duality, etc. No matter how brainy, powerful, and celebrated he may have been, Einstein was not able to require persistently intransigent quantum phenomena to play by his rules.

Einstein was about the cheeky little subatomic particles that his colleagues simply refused to discipline properly. Einstein never stood a chance.

Einstein's thought experiments - Wikipedia

In the insubordinate realm of the quantum, the rowdy kids rule—and the truth lives and dies according to the heedless whims of unrepentant pranksters. In the quantum realm, if you want to play ball with the quarrelsome kids, then you have to play by their rules, which amount to nothing more than: All other bets are off.

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