Jump to content

User:Jdlrobson/T193926

From Wikipedia, the free encyclopedia

A hallmark of Einstein's career was his use of visualized thought experiments (Gedankenexperimente) as a fundamental tool for understanding physical issues and for elucidating his concepts to others. Einstein's thought experiments took diverse forms. For special relativity, he employed moving trains and flashes of lightning to explain his most penetrating insights. For general relativity, he considered a painter falling off a roof, accelerating elevators, blind beetles crawling on curved surfaces and the like. In his great Solvay Debates with Bohr on the nature of reality (1927 and 1930), he devised imaginary contraptions intended to show, at least in concept, how the Heisenberg uncertainty principle might be evaded. In a profound contribution to the literature on quantum mechanics, Einstein considered two particles briefly interacting and then flying apart so that their states are correlated, anticipating the phenomenon known as quantum entanglement.

Introduction

[edit]
See also: Thought experiment

[1]

[2]: 26–27, 122–127, 145–146, 345–349, 448–460 

Special relativity

[edit]

Riding a beam of light

[edit]
Einstein's thought experiment as a 16 year old student

Late in life, Einstein recalled

"...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained."[3]: 52–53 

Einstein's recollections of his youthful musings are widely cited because of the hints they provide of his later great discovery. However, John D. Norton, a well-known philosopher of science, 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:[4]

1. At 16 years old and a student at the Gymnasium in Aarau, Einstein would have had the thought experiment in late 1895 to early 1896. But various sources note that Einstein did not learn Maxwell's theory until 1898, in university.[4][5]
2. The second issue is that a 19th century aether theorist would have had no difficulties with the thought experiment. Einstein's statement, "...there seems to be no such thing...on the basis of experience" would not have counted as an objection, but would have represented a mere statement of fact, since no one had ever traveled at such speeds.
3. An aether theorist would have regarded the "...nor according to Maxwell's equations" part of Einstein's remarks as simply representing a misunderstanding on Einstein's part. Unfettered by any notion that the speed of light represents a cosmic limit, the aether theorist would simply have set velocity equal to c and noted that yes indeed, the light would appear to be frozen, and then thought no more of it.[4]

Rather than the thought experiment being at all incompatible with aether theories (which it is not), Einstein appears to have reacted to the scenario out of an intuitive sense of wrongness. Regardless of the 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 1905.[4][5][6]

Magnet and conductor

[edit]
See also: Moving magnet and conductor problem
Magnet and conductor thought experiment

In the very first paragraph of Einstein's seminal 1905 work introducing special relativity, he writes:

"It is well known that if we attempt to apply Maxwell's electrodynamics, as conceived at the present time, to moving bodies, we are led to asymmetry which does not agree with observed phenomena. Let us think of the mutual action between a magnet and a conductor. The observed phenomena in this case depend only on the relative motion of the conductor and the magnet, while according to the usual conception, a distinction must be made between the cases where the one or the other of the bodies is in motion. If, for example, the magnet moves and the conductor is at rest, then an electric field of certain energy-value is produced in the neighbourhood of the magnet, which excites a current in those parts of the field where a conductor exists. But if the magnet be at rest and the conductor be set in motion, no electric field is produced in the neighbourhood of the magnet, but an electromotive force which corresponds to no energy in itself is produced in the conductor; this causes an electric current of the same magnitude and the same career as the electric force, it being of course assumed that the relative motion in both of these cases is the same."[7]

This opening paragraph recounts well-known experimental results obtained by Michael Faraday in 1831. The experiments describe what appeared to be two different phenomena: the motional EMF generated when a wire moves through a magnetic field (see Lorentz force), and the transformer EMF generated by a changing magnetic field (due to the Maxwell–Faraday equation). James Clerk Maxwell himself drew attention to this fact in his 1861 paper On Physical Lines of Force. In the latter half of Part II of that paper, Maxwell gave a separate physical explanation for each of the two phenomena.[8]

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.[9]: 135–138 

Yet Einstein's reflection on this experiment represented the decisive moment in his long and tortuous path to special relativity.[10] 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 1920 article (unpublished), Einstein related how disturbing he found this asymmetry:

"The idea that these two cases should essentially be different was unbearable to me. According to my conviction, the difference between the two could only lie in the choice of the point of view, but not in a real difference <in the reality of nature>."[11]

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.[10]

"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."[3]: 49 

That decision ultimately led to his development of special relativity as a theory founded on two postulates of which he could be sure.[10] Expressed in contemporary physics vocabulary, his postulates were as follows:[note 1]

1. The laws of physics take the same form in all inertial frames.
2. In any given inertial frame, the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion. [Emphasis added by editor][12]: 140–141 

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.[13][note 2]

Trains, embankments, and lightning flashes

[edit]
See also: Relativity of simultaneity

General relativity

[edit]

Falling painters and accelerating elevators

[edit]
See also: Equivalence principle
A thought experiment used by Einstein to illustrate the equivalence principle

Curved spacetime

[edit]
See also: Spacetime § Introduction to curved spacetime
Einstein's argument suggesting gravitational redshift

Quantum mechanics

[edit]

Background: Einstein and the quantum

[edit]

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.[15]: 1–4  Concerning Einstein's estrangement from the general direction of physics research after 1925, his well-known scientific biographer, Abraham Pais, wrote:

Einstein is the only scientist to be justly held equal to Newton. That comparison is based exclusively on what he did before 1925. 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.[16]: 43 

In hindsight, we know that Pais was incorrect in his assessment.

Einstein was arguably the greatest single contributor to the "old" quantum theory.[15][note 3]

  • In his 1905 paper on light quanta,[17] Einstein created the quantum theory of light. His proposal that light exists as tiny packets (photons) was so revolutionary, that even such major pioneers of quantum theory as Planck and Bohr refused to believe that it could be true.[15]: 70–79, 282–284  [note 4] Bohr, in particular, was a passionate disbeliever in light quanta, and repeatedly argued against them until 1925, when he yielded in the face of overwhelming evidence for their existence.[19]
  • In his 1906 theory of specific heats, Einstein was the first to realize that quantized energy levels explained the specific heat of solids.[20] In this manner, he found a rational justification for the third law of thermodynamics (i.e. the entropy of any system approaches zero as the temperature approaches absolute zero[note 5]): at very cold temperatures, atoms in a solid don't have enough thermal energy to reach even the first excited quantum level, and so cannot vibrate.[15]: 141–148 
  • Einstein proposed the wave-particle duality of light. In 1909, using a rigorous fluctuation argument based on a thought experiment and drawing on his previous work on Brownian motion, he predicted the emergence of a "fusion theory" that would combine the two views.[15]: 136–140  [21] [22] Basically, he demonstrated that the Brownian motion experienced by a mirror in thermal equilibrium with black body radiation would be the sum of two terms, one due to the wave properties of radiation, the other due to its particulate properties.[1]
  • Although Planck is justly hailed as the father of quantum mechanics, his derivation of the law of black-body radiation rested on fragile ground, since it required ad hoc assumptions of an unreasonable character.[note 6] In his 1916 theory of radiation, Einstein was the first to create a completely general explanation.[23] This paper, well-known for broaching the possibility of stimulated emission (the basis of the laser), changed the nature of the evolving quantum theory by introducing the fundamental role of random chance.[15]: 181–192 
  • In 1924, Einstein received a short manuscript by an unknown Indian professor, Satyendra Nath Bose, outlining a new method of deriving the law of blackbody radiation.[note 7] Einstein was intrigued by Bose's peculiar method of counting the number of distinct ways of putting photons into the available states, a method of counting that Bose apparently did not realize was unusual. Einstein, however, understood that Bose's counting method implied that photons are, in a deep sense, indistinguishable. He translated the paper into German and had it published. Einstein then followed Bose's paper with an extension to Bose's work which predicted Bose-Einstein condensation, one of the fundamental research topics of condensed matter physics.[15]: 215–240 
  • While trying to develop a mathematical theory of light which would fully encompass its wavelike and particle-like aspects, Einstein developed the concept of "ghost fields". A guiding wave obeying Maxwell's classical laws would propagate following the normal laws of optics, but would not transmit any energy. This guiding wave, however, would govern the appearance of quanta of energy on a statistical basis, so that the appearance of these quanta would be proportional to the intensity of the interference radiation. These ideas became widely known in the physics community, and through Born's work in 1926, later became a key concept in the modern quantum theory of radiation and matter.[15]: 193–203  [note 8]

Therefore, Einstein before 1925 originated most of the key concepts of quantum theory: light quanta, wave-particle duality, the fundamental randomness of physical processes, the concept of indistinguishabity, and the probability density interpretation of the wave equation. In addition, Einstein can arguably be considered the father of solid state physics and condensed matter physics.[25] He provided a correct derivation of the blackbody radiation law and sparked the notion of the laser.

What of after 1925? In 1935, working with two younger colleagues, Einstein issued a final challenge to quantum mechanics, attempting to show that it could not represent a final solution.[26] Despite the questions raised by this paper, it made little or no difference to how physicists employed quantum mechanics in their work. Of this paper, Pais was to write:

The only part of this article that will ultimately survive, I believe, is this last phrase [i.e. "No reasonable definition of reality could be expect to permit this" where "this" refers to the instantaneous transmission of information over a distance], which so poignantly summarizes Einstein's views on quantum mechanics in his later years....This conclusion has not affected subsequent developments in physics, and it is doubtful that it ever will.[12]: 454–457 

In contrast to Pais' negative assessment, this paper, outlining the EPR paradox, is currently among the top ten papers published in Physical Review, and is the centerpiece of the development of quantum information theory,[27] which has been termed the "third quantum revolution."[28] [note 9]


The Solvay debates on the nature of reality

[edit]
See also: Bohr–Einstein debates

EPR Paradox

[edit]
See also: EPR paradox and Quantum entanglement

Demonstration section to illustrate bug

[edit]

Notes

[edit]
  1. ^ Einstein's original expression of these postulates was as follows: (1) The laws according to which the nature of physical systems alter are independent of the manner in which these changes are referred to two co-ordinate systems which have a uniform translatory motion relative to each other. (2) Every ray of light moves in the "stationary co-ordinate system" with the same velocity c, the velocity being independent of the condition whether this ray of light is emitted by a body at rest or in motion.[7]
  2. ^ One popular textbook expresses the second postulate as, "The speed of light in free space has the same value c in all directions and in all inertial reference frames."[14]
  3. ^ The old quantum theory refers to a mixed collection of heuristic corrections to classical mechanics which predate modern quantum mechanics. The elements of the theory are now understood to be semi-classical approximations to modern quantum mechanical treatments.
  4. ^ The 1819 observation of the Arago spot (a bright point at the center of a circular object's shadow due to diffraction), Foucault's 1850 differential measurements of the speed of light in air versus water,[18] and above all, the success of Maxwell's equations in explaining virtually all known electromagnetic phenomena were considered to have proven the wave nature of light as opposed to a corpuscular theory. "Einstein, a virtual unknown [in 1905] who was contradicting the wave theory of light, had hardly more credibility than a crackpot..."[15]: 79 
  5. ^ This statement is only exactly true for perfect crystals. Imperfect crystals, amorphous bodies, etc. retain disorder which does not freeze out at absolute zero.
  6. ^ Planck's derivation required that hypothetical "resonators" in the walls of a cavity take on equally spaced states of definite energy, with intermediate energies being forbidden. Use of equally spaced energy levels allowed Planck to calculate the sum of an infinite series. In reality, atomic energy levels are not equally spaced, and Planck's derivation breaks down.
  7. ^ Bose claimed that both Planck's and Einstein's methods of deriving the law relied on a previously derived classical result, Wien's distribution law, for the factor which was "a most unsatisfactory point in all derivations." Einstein privately corrected Bose on this point, showing that he was wrong in believing that Wien's distribution law presupposed classical wave theory.
  8. ^ In his Nobel lecture, Born gave Einstein full credit for having been the source of his idea: "...we missed the correct approach. This was left to Schrödinger, and I immediately took up his method since it held promise of leading to an interpretation of the ψ-function. Again an idea of Einstein’s gave me the lead. He had tried to make the duality of particles - light quanta or photons - and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons. This concept could at once be carried over to the ψ-function: ψ2 ought to represent the probability density for electrons (or other particles)."[24]
  9. ^ Although Einstein's post-1925 scientific efforts were dominated by his abortive work on unified field theory, he still produced a number of major publications. In addition to the EPR paper, these include his introduction of the concept of wormholes,[29] his prediction of gravitational lensing,[30] and a paper that established that gravitational waves are possible (correcting an older publication that had reached the opposite conclusion).[31]

References

[edit]
  1. ^ a b Norton, John. "Thought Experiments in Einstein's Work". In Horowitz, Tamara; Massey, Gerald J. (eds.). Thought Experiments in Science and Philosophy (PDF). Rowman & Littlefield. pp. 129–148. ISBN 9780847677061. Archived from the original (PDF) on June 1, 2012.
  2. ^ Isaacson, Walter (2007). Einstein: His Life and Universe. Simon & Schuster. ISBN 978-0-7432-6473-0.
  3. ^ a b Einstein, Albert (1951). "Autobiographical Notes". In Schilpp, P. A. (ed.). Albert Einstein-Philosopher Scientist (2nd ed.). New York: Tudor Publishing. pp. 2–95.
  4. ^ a b c d Norton, John D. (2013). "Chasing the Light: Einsteinʼs Most Famous Thought Experiment". In Brown, James Robert; Frappier, Mélanie; Meynell, Letitia (eds.). Thought Experiments in Philosophy, Science and the Arts (PDF). Routledge. pp. 123–140. Archived from the original (PDF) on November 24, 2017.
  5. ^ a b Stachel, John. "How Did Einstein Discover Relativity". AIP Center for History of Physics. American Institute of Physics. Retrieved 15 April 2018. {{cite web}}: Check |archiveurl= value (help)
  6. ^ Norton, John D. "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905". PhilSci Archive. University of Pittsburgh. Archived from the original on July 10, 2017. Retrieved 15 April 2018.
  7. ^ a b Einstein, Albert (1905). "On the Electrodynamics of Moving Bodies ( Zur Elektrodynamik bewegter Körper)". Annalen der Physik. 322 (10): 891–921. Retrieved 7 April 2018.
  8. ^ Clerk Maxwell, James (1861). "On physical lines of force". Philosophical Magazine. 90. Taylor & Francis: 11–23. doi:10.1080/1478643100365918.
  9. ^ Miller, Arthur I. (1998). Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905–1911). New York: Springer-Verlag. ISBN 0-387-94870-8.
  10. ^ a b c Norton, John D. (2014). "Einstein's Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies that Led him to it". In Janssen, M.; Lehner, C. (eds.). Cambridge Companion to Einstein (PDF). pp. 72–102. ISBN 978-0521828345. Archived from the original (PDF) on Nov 24, 2017. Retrieved 15 April 2018.
  11. ^ Einstein, Albert (1920). "Document 31: Ideas and Methods. II. The Theory of General Relativity". In Janssen, Michel; Schulmann, Robert; Illy, József; Lehner, Christoph; Buchwald, Diana Kormos (eds.). The Collected Papers of Albert Einstein. Volume 7: The Berlin Years: Writings, 1918 – 1921 (English translation supplement) (Digital ed.). California Institute of Technology. p. 20. Retrieved 15 April 2018.
  12. ^ a b Pais, Abraham (2005). Subtle is the Lord: The Science and Life of Albert Einstein. New York: Oxford University Press. ISBN 978-0-19-280672-7.
  13. ^ Marquit, Miranda. "'Relativity' Speaking". PhysOrg.com. Retrieved 15 April 2018.
  14. ^ Halliday, David; Resnick, Robert (1988). Fundamentals of Physics (3rd ed.). New York: John Wiley & Sons. p. 954. ISBN 0-471-81995-6.
  15. ^ a b c d e f g h i Stone, A.Douglas (2013). Einstein and the Quantum: The Quest of the Valiant Swabian. Princeton: Princeton University Press. ISBN 978-0-691-13968-5.
  16. ^ Pais, Abraham (1994). Einstein Lived Here. New York: Oxford University Press. ISBN 978-0-198-53994-0.
  17. ^ Einstein, Albert (1905). "On a Heuristic Point of View Concerning the Production and Transformation of Light". Annalen der Physik. 17: 132–148. Retrieved 22 April 2018.
  18. ^ Hughes, Stefan (2013). Catchers of the Light: Catching Space: Origins, Lunar, Solar, Solar System and Deep Space. Paphos, Cyprus: ArtDeCiel Publishing. pp. 202–233. ISBN 9781467579926. Retrieved 7 April 2017.
  19. ^ Murdoch, Dugald (1987). Niels Bohr's Philosophy of Physics. New York: Press Syndicate of the University of Cambridge. pp. 16–33. ISBN 978-0-521-37927-4.
  20. ^ Einstein, Albert (1906). "Planck's theory of radiation and the theory of specific heat". Annalen der Physik. 4. 22: 180–190, 800. Bibcode:1906AnP...327..180E. doi:10.1002/andp.19063270110. Retrieved 21 April 2018.
  21. ^ Einstein, Albert (1909a). "On the present status of the radiation problem". Physikalische Zeitschrift. 10: 185–193.
  22. ^ Einstein, Albert (1909b). "On the development of our views concerning the nature and constitution of radiation". Physikalische Zeitschrift. 10: 817–826. Retrieved 21 April 2018.
  23. ^ Einstein, Albert (1916). "Emission and Absorption of Radiation in Quantum Theory". Deutsche Physikalische Gesellschaft. 18: 318–323.
  24. ^ Born, Max (11 December 1954). "The statistical interpretation of quantum mechanics" (PDF). www.nobelprize.org. nobelprize.org. Retrieved 30 December 2016.
  25. ^ Cardona, Manuel. "Albert Einstein as the father of solid state physics". arXiv.org. Cornell University Library. Retrieved 23 April 2018.
  26. ^ Einstein, A; B Podolsky; N Rosen (1935). "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?". Physical Review. 47 (10): 777–780. Bibcode:1935PhRv...47..777E. doi:10.1103/PhysRev.47.777. Archived from the original on 25 Mar 2018.
  27. ^ Fine, Arthur. "The Einstein-Podolsky-Rosen Argument in Quantum Theory". Stanford Encyclopedia of Philosophy. Stanford University. {{cite web}}: Check |archiveurl= value (help)
  28. ^ "Quantum Information Theory". Centre for Quantum Computation & Communication Technology. Archived from the original on 23 Sep 2017. Retrieved 22 April 2018.
  29. ^ Einstein, A.; Rosen, N. (1935). "The Particle Problem in the General Theory of Relativity". Phys. Rev. 48: 73. Archived from the original on 11 Jul 2017. Retrieved 26 April 2018.
  30. ^ Einstein, Albert (1936). "Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field". Science. 84 (2188): 506–507. Archived from the original (PDF) on 26 Apr 2018.
  31. ^ Einstein, A.; Rosen, N. (1937). "On gravitational waves" (PDF). Journal of the Franklin Institute. 223: 43–54. Archived from the original (PDF) on 25 Apr 2018.
Retrieved from "https://en.wikipedia.org/w/index.php?title=User:Jdlrobson/T193926&oldid=1239425596"