Transcript Slide 1
In fond memory of Professor A.K. Raychaudhuri who passed away on June 18, 2005 Why Einstein? ( Had I been born in 1844 ! ) Naresh Dadhich, IUCAA [email protected] (Ref: physics/0505090) Universality UNIVERSAL means: Same for All, Shared by All Primary Universal Entities: SPACE and TIME Both must be on the same footing… Universality “The distance between two points is observer dependent.” … & So must be the Time interval between Events ! Can Two Universal Things be Independent of Each other The feature that would distinguish one from the other – Will Break/Violate UNIVERSALITY ! No two universal things can be independent of each other. There must exist UNIVERSAL RELATION between them. The Relation between Space and Time. This can only be a VELOCITY = SPACE/TIME A Universal Velocity is required to relate Space and Time and to bind them together There must exist a UNIVERSAL VELOCITY A Profound Conclusion, A Great Prediction FROM A SIMPLE ARGUMENT - a simple logic, no physics at all. Universal Velocity Some thing/particle should have a velocity which is the Same for All Observers/Frames irrespective of relative motion between Observers, i.e. Universal! Is it possible in the Newtonian Mechanics? NO. Because w = u + v No Velocity can be the same for All Frames. If our "Crazy" logic is true, We a need new mechanics! “c” Let ‘c’ denote the Universal Velocity, the same for ALL OBSERVERS / FRAMES It is the LIMITING VELOCITY for ALL OBSERVERS What will CHARACTERISE such a thing moving with c? It cannot be at rest relative to ANY OBSERVER as NO observer can travel with ‘c’ Since it CAN'T BE AT REST Hence it CAN'T HAVE REST MASS ! IT HAS ZERO MASS Force Free Homogeneity and Isotropy in space y Homogeneity in Time: free of t Motion free of coordinates x Why not x t? • Homogeneity of Space and Time demands: As x y so must x t Match Dimension : Universal constant velocity required: ‘c’ ct Existence of c in Nature! Then x • Prediction : Homogeneity of Space and Time demands : • Universal constant velocity: • Existence of m = 0 particle c MOTION IS OF TWO KINDS • (i) Particle can … have Non-Zero (rest) Mass be held at Rest be given Arbitrary Velocity • (ii) Wave can have No Mass Never be at Rest not have Arbitrary Velocity - Determined by the Medium A Wave's velocity can be changed only by Changing the medium Moving the medium Universal Medium: Present Everywhere Can't be changed/moved A WAVE PROPAGATING IN IT WILL HAVE CONSTANT VELOCITY FOR ALL → UNIVERSAL! Universal Velocity we are looking for can hence ONLY be provided by a Wave propagating in a Universal Medium → VACUUM. THERE MUST EXIST A WAVE PROPAGATING IN VACUUM WHICH WILL HAVE UNIVERSAL CONSTANT VELOCITY. This is a profound prediction… If Einstein were born in 1844 … • If I were born in 1844 and thinking like this, I should be making such a profound prediction based on simple common sense argument in around 1870… • Right here we should have asked for a New Mechanics which keeps a Velocity Constant That could have been Nothing but SPECIAL RELATIVITY • It could have preceded Maxwell Electrodynamics! Preceding Maxwell • In 1875 Maxwell (Synthesizing Coloumb / Ampere / Faraday / Displacement Current) gave the Electromagnetic Theory • which precisely PROVIDED what one should have PREDICTED 5 years before him • He would have simply JUSTIFIED/VERIFIED the Prediction and IDENTIFIED Electromagnetic Wave / Light propagating in Vacuum • This was later experimentally verified by Hertz, and Michelson and Morley • It would have been a great verification of a profound prediction following from very simple and straightforward arguments! New Mechanics The universalisation of mechanics valid for both massive and massless particles (eg: photons) that gave us new mechanics - Special Relativity which synthesised • Space and time into Space-Time • Mass - Energy - Momentum into a quadratic relation • Light cone defining causal connection between events Gravity • The next natural question is GRAVITY MUST AS WELL BE UNIVERSAL • Gravity must act on both massive as well as MASSLESS Problem: A Massless particle cannot change its velocity CONSTANT for ALL YET IT MUST FEEL GRAVITY! What is required is to make a massless particle feel Gravity without changing its velocity? Curving path of a Photon…! The only way it could be done is by bending space (spacetime) and letting particles (massive as well as massless) freely propagate in it On geodesics of curved space-time The solution … “Gravity can only be described by curvature of space-time” A New Theory of GRAVITATION ! GENERAL RELATIVITY The Greatest Feat of Human Thought! Universal Force dual No Force Universal Force Spacetime geometry Spacetime geometry Homogeneous Flat Inhomogeneous Curved Rabcd = 0 Rabcd 0 Gravity revisited… • Gravity is no more a force • It has been completely synthesized into the geometry of space-time • Law of gravity must follow from the curvature of space-time all by itself It is the properties of Riemann curvature that lead to EINSTEN'S LAW OF GRAVITATION which contains Newton's Law Curvature Of 4-Dimensional Space-time Manifold Riemann Curvature Tensor -► Rabcd • It satisfies Bianchi Differential Identities Rab(cd;e) = 0 Analogue of Curl Grad = Div Curl = 0, ; is a derivative relative to curved space-time • Its contraction yields Gab;b = 0 , Rab = Racbc, Gab = Rab - 1/2 R gab R = R aa The Einstein Equation of Gravitation Gab = κTab + Λgab , Tab;b = 0 b Ga is a second rank symmetric tensor with Vanishing Divergence A Second Order Differential Operator on the Metric Potential Λ gab is a new constant - to be determined by experiment / observation Higher Dimension • Einstein Equation Gab = kTab - Λ gab , D ≥ 2 • D = 2,3 not big enough for gravity dynamics • So we come to 4-D Is it big enough to accommodate gravity fully? How do we know it doesn't propagate in extra D? Gravity ≡ Curvature How do we keep curvature confined in 4-D ? • Does higher D get curved or Not ? • Higher D embedding 4-D is flat, Rabcd = 0 ? • For an arbitrary 4-D curved 10-D required • General 4-D Gravity can penetrate down to 10-D Extra dimension Required… Gravity is self-interactive • Self interaction means iterations, first, second, … 2 ≠ 0 = - ½ () 2 • Einstein equation contains first iteration (2, ( )2) gab = 0 Can’t stop at first… • Second iteration: Basic Field Entity : Rabcd R2abcd → also squares ( 2 )2 Self-interaction • Quasilinear Equation – Highest order of derivative, 2 to be linear • Gauss-Bonnet combination R2 – 4 Rab Rab + Rabcd Rabcd ensures quasi-linearity, ( 2 )2 cancel out Gauss-Bonnet is non-trivial in D 5 Thus we have to go to 5-D to physically realize second iteration of self-interaction Self-interaction D = 2 , 3: Not big enough for free Gravity D = 4: Not big enough for self-interaction If matter is confined to 3-space/brane, (this is for matter dynamics to decide) gravity does propagate in extra 5th D Gauss-Bonnet Gravity • In 5-D there is no Matter GAB = α HAB (R2) • Spacetime is homogeneous & isotropic • It should be Einstein space GAB gAB HAB Rabcd = κ (gac gbd – gad gbc) Constant curvature • Gravitational field – negative energy density • Hence 5-D Bulk is AdS Motivation for Brane-World Gravity Where does this iteration chain end? • If matter lives on 3-brane, it ends in 5-D AdS Bulk – AdS Bulk has Weyl = 0, No free gravity to go any further – It is embeddable in 6-D flat Spacetime • Iteration naturally stops at the second It is purely classical motivation for Brane-World like model. Seeing Beyond Einstein Other great theory - Quantum Mechanics At micro level - Matter consists of tiny pieces – quanta Energetically : Probe Object The Process of observation disturbs object 4 – momentum : pa 4 – wave vector : ka pa = hka Basic Quantum Relation In wave propagation uncertainty is inherent xp ħ Light wave propagates in vacuum Wave propagation requires oscillation of micro structure - quanta Vacuum must have micro structure It Can’t be INERT An ether ? What is established ? Vacuum Vacuum can’t provide a Reference Frame Because it is everywhere In the ocean also – No Reference unless there is a Flag Post So why can’t it have physical structure like an ocean ? Like Matter, Space also has Micro-Structure - discrete and quantum Deep down even space can’t retain • Its continuum nature • All tiny pieces / quanta So What are these pieces ? Basic Building Blocks of Space … ! We don’t know. Quantum Space-Time A New theory of Quantum Gravity ! Quantum Principle is universal Hence it Must be related to Space-Time Quantum Mechanics in Quantum Space – Time ! Unless that happens Quantum Theory is incomplete