DOCSLIB.ORG

Space and Time in Life and Science

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Space and Time in Life and Science GENERAL ARTICLE Space and Time in Life and Science Vasant Natarajan, V Balakrishnan and N Mukunda Space and tim e are conceptsthatseem to be em - bedded in our very consciousness. A s we grow up, our `intuitive understanding' of these con- cepts seem s to grow as well. A nd yet the fact is that our understanding of space-tim e in the deepest scienti¯c sense is far from com plete, al- though w e have covered a considerable distance along the route. There m ay stillbe m any sur- prises aw aiting us on the road ahead. 1.It Began w ith G eom etry A ll of us have som e intuitive ideas about the natures (left) Vasant Natarajan is at the Department of Physics, of space and tim e in which we are em bedded. Space IISc. His research interests appears to be the stage on which all events, experi- are in high-resolution laser ences and phenom ena take place, w hile tim e is like a spectroscopy, optical background against w hich this happens. A llobjects,in- frequency measurement, and cluding ourselves,exist in space and change w ith tim e. use of laser-cooled atoms to search for time-reversal In this article, w e shalldescribe in sim ple and qualita- violation in the laws of tive term show ourunderstanding ofspace and tim e has physics. developed over the centuries,and w hat we have learnt about their properties. W e w illsee that m any strands (right) V Balakrishnan is at com e togetherin thisstory { notonly from m athem atics the Department of Physics, IIT- Madras, Chennai. His and physics,but also,in som e im portant respects,from research interests are in b iology. dynamical systems, stochastics and statistical physics. In one ofhis essays,SchrÄodinger1 saysthisabouttheem - inent philosopher Im m anuel K ant (1724{1804): \K an t (centre) N Mukunda is at the ... term ed space and tim e,as he knew them ,the form s Centre for High Energy ofour m entalintuition { space being the form ofexter- Physics, IISc, Bangalore. His interests are classical and n al, tim e that of intern al, intuition ." W e begin with quantum mechanics, this quotation both because it is so profound and be- theoretical optics and cause som e of K ant's other ideas w illappear later on. mathematical physics. A llofus have at least a prelim inary or com m on-sense RESONANCE September 2008 843 GENERAL ARTICLE 1 The great physicist Erwin understanding ofthe nature ofspace through oursenses, Schrödinger(1887–1961; Nobel m ainly sightand touch.2 W e see objectsarranged in var- PrizeinPhysics, 1933),whodis- iousw aysrelative to one another;w e touch them ifthey covered wave mechanics and was oneofthefoundersofquan- are nearby;w e develop a feeling for shape,distance,per- tum mechanics,wasalsoawon- spective;and so on. T hus,through direct sensory expe- derfullylucidwriter on manypro- riences, space seem s to have a de¯nite character, even found subjects. His famous though the idea ofspace by itselfisquite abstract. T im e, books include Science and Hu- on the other hand,is m ore subtle. W e cannot reach it manism, Expanding Universes, Statistical Thermodynamics, through our senses directly;w e can experience it and be What is Life?, Mind and Matter, aw are of its passage only internally through the m ind My View of the World, Space- in a non-sensory way. Because we cannot see or touch Time Structure, and Nature and tim e, extension in space seem s a little easier to grasp the Greeks. than duration in tim e. T hus,space hasto be abstracted from externalexperience,tim e from internalexperience. 2 It is an interesting fact that about 80% of our sensory input O ver and above this subtlety, space and tim e are re- comes from oureyes, andabout ally not sim ple concepts at all. A n obvious fundam ental 40% of our brain capacity is de- di®erence between the two is that space appears to be voted to processing visual infor- `controllable'{ in the sense that w e can m ove from one mation – we are very ‘visual’ point to another,w ith seem ingly arbitrary freedom . O n creatures. the other hand,tim e seem s to be som ething over w hich we have no control{ it just m arches inexorably on. W e are caught up in this m arch with no apparent choice. The old adage { `tim e and tide waitforno m an'{ cap- turesthisnotion perfectly. T hisalso m eansthatw e have m em oriesofw hathashappened up tillnow ,butno idea ofw hat the future holds (contrary to w hat soothsayers and horoscope-w riters m ight tellyou!) Let us begin with space. The word geom etry, as you know ,m eans `m easuring the earth (or land)'. T he ori- gins ofgeom etry go back severalm illennia to the great E gyptian civilization (see also B ox 1). G eom etry arose in ancient Egypt from the repeated need to survey and re-establish boundaries ofland holdings after the annual °oodsofthe riverN ile. H ere isa passage from the G reek traveller and historian H erodotus (482?{434? B C ): Keywords Space, time, geometry, relativ- \T he K ing m oreover (so they said) divided the coun try ity. am ong allthe Egyptians by giving each an equalsquare 844 RESONANCE September 2008 GENERAL ARTICLE Box 1. The O riginsofG eom etry Ancient Babylon and Egypt are well known as the civilizations in which the subject of geometry originated. However, there were other nodal centres as well. You are undoubt- edly familiar with some ofthe great and unique achievements ofancient Indian mathemat- ics, such as the invention ofthe decimal place-value system ofnumbers, negative numbers, and zero. It is important to note that these remarkable mathematical advances (which took place from about 500 AD onwards) were preceded by equally signi¯cant achieve- ments in the Indian sub-continent in even earlier times. In recent years, much new light has been shed on the scope and advanced nature of truly ancient Indian mathematics. It is being gradually recognized that ancient India (especially the Indus Valley Civilization) was in many respects (including mathematics) fully the peer of the ancient Egyptian and Babylonian civilizations. The historians ofscience J J O'Connor and E F Robertson (see http://www-history.mcs.st-andrews.ac.uk/HistTopics/Indian mathematics.html) write, \... the study of mathematical astronomy in India goes back to at least the third mil- lennium BC and mathematics and geometry must have existed to support this study in ancient times." They go on to quote V G Childe in N ew Lighton the M ostAncientEast (Routledge and Kegan Paul Ltd., London, 1952): \India confronts Egypt and Babylonia by the 3rd millennium with a thoroughly individual and independent civilization of her own, technically the peer of the rest." What is clear is that astronomy was a prime mo- tivating factor behind the development of geometry, trigonometry and related topics in ancient India. parcelofland,and m ade this his source ofrevenue,ap- pointing the paym entofa yearly tax.And any m an who was robbed by the river ofa partofhis land would com e to Sesostris and declare what had befallen him ;then the K ing would send m en to look into it and m easure the space by which the land was dim inished, so that there- after he shou ld pay the appointed tax in proportion to the loss. F rom this, to m y thinking, the G reeks learn ed the art ofm easuring land." Geometry was the So geom etry was the product ofpracticalhum an needs product of practical to m easure space,m uch as trade and com m erce led to human needs to arithm etic. Sim ilarly,the practicalneed to m easure tim e measure space, (for exam ple,to keep track ofdaily sunrises or the an- nual°oods) gave rise to clocks and calendars. H um an much as trade and scienti¯c and technological progress has required ever- commerce led to m ore accurate clocks. A brief history of tim ekeeping arithmetic. over the centuries is presented in B ox 2. RESONANCE September 2008 845 GENERAL ARTICLE Box 2. A B riefH istory ofTim ekeeping Timekeeping on earth by nature is as old as the planet itself, since all it requires is a periodic process. The periodic rotation and revolution of the earth give rise to daily and yearly cycles, which have been used by nature as a clock much before human beings evolved. Many living organisms including humans show daily (or diurnal) rhythms reg- ulated by the sun, and seasonal patterns that repeat every year. It is therefore natural that the earliest man-made clocks also relied on the sun. One example was the sundial, which consisted of a pointer and a calibrated plate on which the pointer cast a moving shadow. Ofcourse this worked only when the sun was shining. The need to tell the time even when the sun was not out, such as on an overcast day or at night, made it necessary to invent other kinds of clocks. The earliest all-weather clocks were water clocks, which were stone vessels with sloping sides that allowed water to drip at a constant rate from a small hole near the bottom. Markings on the inside surface indicated the passage of time as the water level reached them. Other clocks were used for measuring small intervals of time.
Load more

Recommended publications
  • Mathematical Languages Shape Our Understanding of Time in Physics Physics Is Formulated in Terms of Timeless, Axiomatic Mathematics
    comment Corrected: Publisher Correction Mathematical languages shape our understanding of time in physics Physics is formulated in terms of timeless, axiomatic mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would ofer a perspective that is closer to our experience of physical reality. Nicolas Gisin n 1922 Albert Einstein, the physicist, met in Paris Henri Bergson, the philosopher. IThe two giants debated publicly about time and Einstein concluded with his famous statement: “There is no such thing as the time of the philosopher”. Around the same time, and equally dramatically, mathematicians were debating how to describe the continuum (Fig. 1). The famous German mathematician David Hilbert was promoting formalized mathematics, in which every real number with its infinite series of digits is a completed individual object. On the other side the Dutch mathematician, Luitzen Egbertus Jan Brouwer, was defending the view that each point on the line should be represented as a never-ending process that develops in time, a view known as intuitionistic mathematics (Box 1). Although Brouwer was backed-up by a few well-known figures, like Hermann Weyl 1 and Kurt Gödel2, Hilbert and his supporters clearly won that second debate. Hence, time was expulsed from mathematics and mathematical objects Fig. 1 | Debating mathematicians. David Hilbert (left), supporter of axiomatic mathematics. L. E. J. came to be seen as existing in some Brouwer (right), proposer of intuitionist mathematics. Credit: Left: INTERFOTO / Alamy Stock Photo; idealized Platonistic world. right: reprinted with permission from ref. 18, Springer These two debates had a huge impact on physics.
    [Show full text]
  • HYPOTHESIS: How Defining Nature of Time Might Explain Some of Actual Physics Enigmas P Letizia
    HYPOTHESIS: How Defining Nature of Time Might Explain Some of Actual Physics Enigmas P Letizia To cite this version: P Letizia. HYPOTHESIS: How Defining Nature of Time Might Explain Some of Actual Physics Enigmas: A possible explanation of Dark Energy. 2017. hal-01424099 HAL Id: hal-01424099 https://hal.archives-ouvertes.fr/hal-01424099 Preprint submitted on 3 Jan 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike| 4.0 International License SUBMITTED FOR STUDY January 1st, 2017 HYPOTHESIS: How Defining Nature of Time Might Explain Some of Actual Physics Enigmas P. Letizia Abstract Nowadays it seems that understanding the Nature of Time is not more a priority. It seems commonly admitted that Time can not be clearly nor objectively defined. I do not agree with this vision. I am among those who think that Time has an objective reality in Physics. If it has a reality, then it must be understood. My first ambition with this paper was to submit for study a proposition concerning the Nature of Time. However, once defined I understood that this proposition embeds an underlying logic.
    [Show full text]
  • Terminology of Geological Time: Establishment of a Community Standard
    Terminology of geological time: Establishment of a community standard Marie-Pierre Aubry1, John A. Van Couvering2, Nicholas Christie-Blick3, Ed Landing4, Brian R. Pratt5, Donald E. Owen6 and Ismael Ferrusquía-Villafranca7 1Department of Earth and Planetary Sciences, Rutgers University, Piscataway NJ 08854, USA; email: [email protected] 2Micropaleontology Press, New York, NY 10001, USA email: [email protected] 3Department of Earth and Environmental Sciences and Lamont-Doherty Earth Observatory of Columbia University, Palisades NY 10964, USA email: [email protected] 4New York State Museum, Madison Avenue, Albany NY 12230, USA email: [email protected] 5Department of Geological Sciences, University of Saskatchewan, Saskatoon SK7N 5E2, Canada; email: [email protected] 6Department of Earth and Space Sciences, Lamar University, Beaumont TX 77710 USA email: [email protected] 7Universidad Nacional Autónomo de México, Instituto de Geologia, México DF email: [email protected] ABSTRACT: It has been recommended that geological time be described in a single set of terms and according to metric or SI (“Système International d’Unités”) standards, to ensure “worldwide unification of measurement”. While any effort to improve communication in sci- entific research and writing is to be encouraged, we are also concerned that fundamental differences between date and duration, in the way that our profession expresses geological time, would be lost in such an oversimplified terminology. In addition, no precise value for ‘year’ in the SI base unit of second has been accepted by the international bodies. Under any circumstances, however, it remains the fact that geologi- cal dates – as points in time – are not relevant to the SI.
    [Show full text]
  • A Measure of Change Brittany A
    University of South Carolina Scholar Commons Theses and Dissertations Spring 2019 Time: A Measure of Change Brittany A. Gentry Follow this and additional works at: https://scholarcommons.sc.edu/etd Part of the Philosophy Commons Recommended Citation Gentry, B. A.(2019). Time: A Measure of Change. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/5247 This Open Access Dissertation is brought to you by Scholar Commons. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Time: A Measure of Change By Brittany A. Gentry Bachelor of Arts Houghton College, 2009 ________________________________________________ Submitted in Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy in Philosophy College of Arts and Sciences University of South Carolina 2019 Accepted by Michael Dickson, Major Professor Leah McClimans, Committee Member Thomas Burke, Committee Member Alexander Pruss, Committee Member Cheryl L. Addy, Vice Provost and Dean of the Graduate School ©Copyright by Brittany A. Gentry, 2019 All Rights Reserved ii Acknowledgements I would like to thank Michael Dickson, my dissertation advisor, for extensive comments on numerous drafts over the last several years and for his patience and encouragement throughout this process. I would also like to thank my other committee members, Leah McClimans, Thomas Burke, and Alexander Pruss, for their comments and recommendations along the way. Finally, I am grateful to fellow students and professors at the University of South Carolina, the audience at the International Society for the Philosophy of Time conference at Wake Forest University, NC, and anonymous reviewers for helpful comments on various drafts of portions of this dissertation.
    [Show full text]
  • Time: a Constructal Viewpoint & Its Consequences
    www.nature.com/scientificreports OPEN Time: a Constructal viewpoint & its consequences Umberto Lucia & Giulia Grisolia In the environment, there exists a continuous interaction between electromagnetic radiation and Received: 11 April 2019 matter. So, atoms continuously interact with the photons of the environmental electromagnetic felds. Accepted: 8 July 2019 This electromagnetic interaction is the consequence of the continuous and universal thermal non- Published: xx xx xxxx equilibrium, that introduces an element of randomness to atomic and molecular motion. Consequently, a decreasing of path probability required for microscopic reversibility of evolution occurs. Recently, an energy footprint has been theoretically proven in the atomic electron-photon interaction, related to the well known spectroscopic phase shift efect, and the results on the irreversibility of the electromagnetic interaction with atoms and molecules, experimentally obtained in the late sixties. Here, we want to show how this quantum footprint is the “origin of time”. Last, the result obtained represents also a response to the question introduced by Einstein on the analysis of the interaction between radiation and molecules when thermal radiation is considered; he highlighted that in general one restricts oneself to a discussion of the energy exchange, without taking the momentum exchange into account. Our result has been obtained just introducing the momentum into the quantum analysis. In the last decades, Rovelli1–3 introduced new considerations on time in physical sciences. In his Philosophiae Naturalis Principia Mathematica4, Newton introduced two defnitions of time: • Time is the quantity one introduce when he needs to locate events; • Time is the quantity which fows uniformly even in absence of events, and it presents a proper topological structure, with a well defned metric.
    [Show full text]
  • Change Without Time Relationalism and Field Quantization
    Change Without Time Relationalism and Field Quantization Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften (Dr. rer. nat.) der naturwissenschaftlichen Fakult¨at II – Physik der Universit¨at Regensburg vorgelegt von Johannes Simon aus Schwandorf 2004 Promotionsgesuch eingereicht am: 19.04.2004 Die Arbeit wurde angeleitet von Prof. Dr. Gustav M. Obermair. Prufungsausschuss:¨ Vorsitzender Prof. Dr. W. Prettl 1. Gutachter Prof. Dr. G. M. Obermair 2. Gutachter Prof. Dr. E. Werner weiterer Prufer¨ Prof. Dr. A. Sch¨afer Tag der mundlichen¨ Prufung:¨ 23.07.2004 Tempus item per se non est [...] Titus Lucretius Carus [Car, 459 ff] Preface This thesis studies the foundations of time in physics. Its origin lies in the urge to understand the quantum measurement problem. While the emergence of classical- ity can be well described within algebraic quantum mechanics of infinite systems, this can be achieved only in infinite time. This led me to a study of quantum dy- namics of infinite systems, which turned out to be far less unique than in the case of finitely many degrees of freedom. In deciding on the correct time evolution the question appears how time – or rather duration – is being measured. Traditional quantum mechanics lacks a time observable, and for closed systems in an energy eigenstate duration is indeed meaningless. A similar phenomenon shows up in general relativity, where absolute duration (as well as spatial distance) becomes meaningless due to diffeomorphism invariance. However, by relating different parts of a closed system through simultaneity (in quantum mechanics as well as in general relativity), an internal notion of time becomes meaningful. This similarity between quantum mechanics and general relativity was recognized in the context of quantum gravity by Carlo Rovelli, who proposed a relational concept of quantum time in 1990.
    [Show full text]
  • A Critical Analysis of the Concept of Time in Physics
    A critical analysis of the concept of time in physics Claudio Borghi Liceo Scientifico Belfiore, via Tione 2, Mantova, Italy Abstract. This paper puts forward a broad critical analysis of the con- cept of physical time. Clock effect is conceived as a consequence of the variation of the gravitational or pseudo gravitational potential, and it is remarked that only some real clocks measure durations in agreement with the predictions of general relativity. A probable disagreement is ex- pected between radioactive and atomic clocks, in the light of Rovelli’s thermal time hypothesis. According to the recent contributions by Rugh and Zinkernagel, the relationship between time and clocks is investigated in order to found on a physical basis the concept of cosmic time. In the conclusive section is argued the impossibility of reducing thermal time to relativistic time. Key words: Time, Relativity, Thermodynamics, Cosmology 1 Introduction The following points resume the main concepts: 1) analysis of the operational definition of time in Newton and Einstein; 2) distinction between time dilation effect and clock effect in Einstein’s theory; 3) considerations about the nonequivalence between atomic clocks and radioac- tive clocks in the light of the clock hypothesis; 4) remarks about the existence, in nature, of thermal clocks that do not behave as relativistic clocks, and about the consequent nonequivalence between ther- mal and relativistic time, in the light of the thermal time hypothesis; 5) reflections about the operational definition of cosmic time in relation to the physical processes, then to the clocks that can be used for measuring it; arXiv:1808.09980v2 [physics.gen-ph] 2 Sep 2018 6) conclusive remarks about the need of a revision and a consequent refounda- tion of the concept of time in physics.
    [Show full text]
  • Multidimensional Time
    International Journal of Science and Research (IJSR) ISSN: 2319-7064 ResearchGate Impact Factor (2018): 0.28 | SJIF (2018): 7.426 Time: Multidimensional Time Ankit Thapliyal M.Sc. (Physics), HNBGU, Dehradun, Bhauwala, India (248007) Abstract: What is time? It’s a beautiful and mysterious question of all time in physics. Great scientist Newton told us that time is absolute and it’s uniformly ticking throughout whole universe. But Einstein did not agree with Newton at this point and gave us a revolutionary idea in physics, that was “time is relative”. He gave us famous theory of relativity which is the basis of modern physics. But there is some paradox which arose with this theory as a result of time dilation and one of them is twin paradox. However, we have many explanations about these paradoxes. But the question is how time appears faster or slower. Well the answer lies in the fact that universe have more than four dimensions and time which we assume to have single dimension is made up of more than two dimensions and that’s the true reason why we find sometimes it moves faster while sometimes it moves slower. Just as gravity goes through every possible dimension and appears weak in three or four dimensions and that’s exactly the case with time, we can relate its faster and slower speed at different places of universe with time’s multidimensional nature. Keywords: Time, Time dilation, Time multidimension 1. Introduction Now the question arises that, could this be the case with time? Till now we assume it as one dimensional but what if Time is considered as one of the mysterious things in physics time has more than one dimensions? all time.
    [Show full text]
  • Symmetries in Physics: Philosophical Reflections
    SYMMETRIES IN PHYSICS: PHILOSOPHICAL REFLECTIONS EDITED BY K. BRADING1 AND E. CASTELLANI2 CAMBRIDGE UNIVERSITY PRESS, 2003 CONTENTS 1. Introduction Section I: Continuous symmetries 2. Extracts from H. Weyl 3. Extracts from E. P. Wigner 4. Review paper: C. Martin, ‘On continuous symmetries and the foundations of modern physics’ 5. T. Ryckman, ‘The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism’ 6. K. A. Brading and H. R. Brown, ‘Symmetries and Noether’s theorems’ 7. J. Norton, ‘General covariance, gauge theories, and the Kretschmann objection’ 8. M. Redhead, ‘The interpretation of gauge symmetry’ 9. J. Earman, ‘Tracking down gauge: an ode to the constrained Hamiltonian formalism’ 10. D. Wallace, ‘Time-dependent symmetries: the link between gauge symmetries and indeterminism’ 11. A. Nounou, ‘A fourth way to the A-B effect’ Section II: Discrete symmetries 12. Extracts from the Leibniz-Clarke correspondence 13. Extracts from I. Kant 14..Extracts from M. Black 15. Review paper: S. French and D. Rickles, ‘Understanding permutation symmetry’ 16. N. Huggett, ‘Quarticles and the identity of indiscernibles’ 17. Review paper: O. Pooley, ‘Handedness, parity violation, and the reality of space’ 18. N. Huggett, ‘Mirror symmetry: what is it for a relational space to be orientable?’ 19. S. Saunders, ‘Physics and Leibniz’s principles’ 1 Wolfson College, Oxford. E-mail: [email protected] 2 University of Florence, Italy. E-mail: [email protected] Section III: Symmetry breaking 20. Extracts from H. Weyl 21. Extracts from P. Curie 22. Extracts from G. Jona-Lasinio 23. Review paper: E. Castellani, ‘On the meaning of symmetry breaking’ 24.
    [Show full text]
  • Arxiv:2006.10084V3 [Quant-Ph] 7 Mar 2021
    Quantum time dilation in atomic spectra Piotr T. Grochowski ,1, ∗ Alexander R. H. Smith ,2, 3, y Andrzej Dragan ,4, 5, z and Kacper Dębski 4, x 1Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland 2Department of Physics, Saint Anselm College, Manchester, New Hampshire 03102, USA 3Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA 4Institute of Theoretical Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland 5Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore (Dated: March 9, 2021) Quantum time dilation occurs when a clock moves in a superposition of relativistic momentum wave packets. The lifetime of an excited hydrogen-like atom can be used as a clock, which we use to demonstrate how quantum time dilation manifests in a spontaneous emission process. The resulting emission rate differs when compared to the emission rate of an atom prepared in a mixture of momentum wave packets at order v2=c2. This effect is accompanied by a quantum correction to the Doppler shift due to the coherence between momentum wave packets. This quantum Doppler shift affects the spectral line shape at order v=c. However, its effect on the decay rate is suppressed when compared to the effect of quantum time dilation. We argue that spectroscopic experiments offer a technologically feasible platform to explore the effects of quantum time dilation. I. INTRODUCTION The purpose of the present work is to provide evi- dence in support of the conjecture that quantum time The quintessential feature of quantum mechanics is dilation is universal.
    [Show full text]
  • Space, Time and Relativity
    GENERAL I ARTICLE Space, Time and Relativity S Chaturvedi, R Simon and N Mukunda 1. Introduction Special Relativity is now a hundred years old, and Gen­ eral Relativity is just ten years younger. Even the gen­ eral literate public probably knows that these two the­ ories of physics - STR and GTR - profoundly altered previous conceptions and understanding of space and time in physics. We will try to describe these changes ~ginning with earlier ideas which had served physics fer almost 300 years, and seeing how they had to be (left) S Chaturvedi is Professor at the School of modified in the light of accumulating experience. Physics, University of 2. Newtonian Space and Time, Inertial Frames Hyderabad since 1993. His current research interests In his great work titled the 'Principia' published in 1685, are mathematical physics, geometric phases, Newton began by expressing in clear terms the natures coherent states, Wigner of space and time as he understood them. The impor­ distribution, and quantum tance of his enunciation of their properties cannot be entanglement. overestimated, because they provided something tangi­ (right) R Simon is with ble which could be used as a basis for further work, and the Institute of Math­ equally importantly which could be examined and crit­ ematical Sciences, icised in a fruitful manner. Quoting from Einstein: Chennai. His research interests are in quantum "... what we have gained up till now would have been information science and impossible without Newton's clear system" quantum optics. Newton was carrying forward what Galileo had begun. (center) N Mukunda is at the Centre for High Let us start by reminding you of the implicit and explicit Energy Physics, liSe, assumptions underlying Galilean- Newtonian physics, al­ Bangalore.
    [Show full text]
  • 200422 Finalarxivversion.Pdf
    Classical and Nonclassical Time Dilation for Quantum Clocks A. J. Paige,1, ∗ A. D. K. Plato,1 and M. S. Kim1 1QOLS, Blackett Laboratory, Imperial College London, South Kensington, London, SW7 2AZ, UK. Proper time, ideal clocks, and boosts are well understood classically, but subtleties arise in quan- tum physics. We show that quantum clocks set in motion via momentum boosts do not witness classical time dilation. However, using velocity boosts we find the ideal behaviour in both cases where the quantum clock and classical observer are set in motion. Without internal state depen- dent forces additional effects arise. As such, we derive observed frequency shifts in ion trap atomic clocks, indicating a small additional shift, and also show the emergence of non-ideal behaviour in a theoretical clock model. Ideal clocks and proper time are key concepts in special observer and quantum clock being set in motion is cap- and general relativity [1]. Full understanding of the union tured by translation operators, and that it is the trans- between relativity and quantum mechanics, must include formation under translation operators that enables the how these ideas extend to the quantum realm. Recent velocity boost to describe both situations. We demon- work in this area can broadly be divided by whether the strate how these translation operators can be understood quantum clocks follow classical or quantum trajectories. via considering the placement of the origin for the re- Adopting the former approach [2{5] enables the utiliza- quired potentials. In addition, we show that considering tion of techniques from quantum field theory in curved the velocity kick as the classical observer changing frames spacetime.
    [Show full text]