Limitations of Newtonian Physics 18 th and 19 th Centuries Newtonian Physics was accepted as an ultimate truth Science is never absolute Hundreds of experiments can t prove my theory right but only one experiment can prove it wrong. Einstein Last two decades of 19 th century Some experimental results appear those were impossible to reconcile with Newtonian Physics. In the beginning of 20 th century, three new theories were developed: Special theory of relativity General theory of relativity Quantum theory Newtonian Physics gives incorrect predictions in four types of situation When speeds are very high Special theory of relativity deals with this When gravitational forces are very strong When distances are extremely small Quantum theory deals with this When distances are very large At speed of 30, 000 km/s Roughly around the world in 1 second), 1 % off. At speed of 290, 000 km/s (very close to speed of light), 1500 % off General theory of relativity deals with this. Comparable to atomic size An object can not be both small and slow moving General theory of relativity deals with this. Newtonian physics is a good approximation to reality
Post Newtonian Physics Theory of Relativity and Quantum Theory Modern Physics Time, space and mass now become observer dependent Transformation from Newtonian to post Newtonian physics is less radical than that from Aristotle to Newtonian Physics Newtonian Physics rejected the Aristotle Physics Post Newtonian physics only limits the validity of Newtonian Physics Newtonian physics agrees with observation in NORMAL human situation Speeds are very slow compared to c Distances are larger as compared to molecules but smaller than galaxies Forces are not many times stronger than on the earth. Outside the NORMAL (or Newtonian range) Newtonian Physics is wrong Philosophically transition from Newtonian to post-newtonian physics is a revolution --- continues today
Einstein Theories of Relativity Special Theory of Relativity General Theory of Relativity Special Theory of Relativity Non-accelerating reference frames Principle 1 Every non-accelerating observer observes the same laws of nature In a sealed room moving at constant velocity, you can not tell whether you are moving or standing still Principle 2 The speed of light in empty space is the same for all nonaccelerating observers, regardless of the motion of the observer Principle of the constancy of light speed key idea If some one is moving with the speed of light along Standing still with it, the light beam will appears to him as According to Newtonian physics According to Einstein every observer must observe every light beam to move at speed c, regardless of the observer s motion
In 1964 experiment A subatomic particle moving nearly light speed emitted electromagnetic radiations in both forward and backward directions According to Newtonian physics Forward moving radiation should be faster than c, while the backward moving radiation should move much slower than c, with reference to laboratory They were found to be moving exactly at same speed Einstein s prediction Deviation from Newtonian world view
Energy Probably the most famous scientific equation of all time, first derived by Einstein is the relationship E = mc 2 This tells us the energy corresponding to a mass m at rest. When mass disappears (For example fission), this amount of energy must appear in some other form. Einstein also showed that the correct relativistic expression for the energy of a particle of mass m with momentum p is E 2 = m 2 c 4 + p 2 c 2 => E = γ Rest energy The energy E is the total energy of a freely moving particle. We can define it to be the rest energy plus kinetic energy (E = KE + mc 2 ) which then defines a relativistic form for kinetic energy. Just as the equation for momentum has to be altered, so does the low-speed equation for kinetic energy (KE = (1/2)mv 2 ). KE ~ cp
General Theory of Relativity Theory of gravitation Background of theories of gravitation Aristotle s notion of motion Force can only be applied by contact. Force at distance is impossible. A constant force is required to maintain a uniform motion of a body. Averroes (Ibn-Rushd): idea of Force and Inertia Contributions of several Arab Astronomers lead to Copernicus s model of Astronomy, Galileo law of Falling and Newton s laws Al-Khazini and al-biruni: 1 st to realized that gravity decreases with distance Copernicus view of solar system: allowed a sensible consideration of gravitation Kepler s laws of planetary motion. Galileo s understanding of motion and falling bodies. m1m2 Newton s Theory of gravity F = G 2 r Reworked by Lagrange, Hamilton and Jacobi => powerful and general Include potential related to force
Newton s theory was considered proved correct Laplace discussed the stability of the solar system in 1799. Poisson used the gravitational potential approach to give an equation which, unlike Newton s, could be solved under rather general conditions. There was little reason to question Newton s theory except for one weakness which was to explain how each of the two bodies knew the other was there. Remarks about gravitation were made by Maxwell in 1864 After tracing to the action of the surrounding medium both the magnetic and the electric attractions and repulsions, and finding them to depend on the inverse square of the distance, we are naturally led to inquire whether the attraction of gravitation, which follows the same law of the distance, is not also traceable to the action of a surrounding medium However Maxwell noted that there is a paradox caused by the attraction of like bodies. The energy of the medium must be decreased by the presence of the bodies and He said As I am unable to understand in what way a medium can possess such properties, I cannot go further in this direction in searching for the cause of gravitation.
In 1900 Lorentz conjectured that gravitation could be attributed to actions which propagate with the velocity of light A paper published in July 1905 (submitted days before Einstein s special relativity paper), suggested that all forces should transform according the Lorentz transformations. In this case he notes that Newton's law of gravitation is not valid and proposed gravitational waves which propagated with the velocity of light. In 1907, two years after the special theory of relativity, Einstein was preparing a review of special relativity when he suddenly wondered how Newtonian gravitation would have to be modified to fit in with special relativity. At this point there occurred to Einstein, described by him as the happiest thought of my life. An observer who is falling from the roof of a house experiences no gravitational field He proposed the Equivalence Principle as a consequence... we shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame. After this Einstein did not publish anything on gravity until 1911.
Special theory of relativity begins with the idea that Laws of Physics are same for all unaccelerated observers What about accelerated observer? Imagine you are in an elevator accelerated upward. What do you feel? Starting point of general relativity Now if you are in the same elevator in outer space where there is no gravity and elevator is accelerated upward at 9.8 m/s 2. What would you feel? Same as you feel stationary on earth How can you tell if you are in an elevator in outer space being accelerated or stationary on earth? Heavy, as there were more gravitational pull than usual No way Every accelerated observer experience the same laws of nature No experiment performed inside a sealed room can tell whether you are accelerating in the absence of gravity or at rest in the presence of the gravity If you are accelerated through outer space and you turn on a flash light horizontally, what will happen to light beam? Go straight Bend downward Basic principle
Einstein s answer Bends downward Just like the horizontally thrown stone. Light beam curves far less b/c of its great speed. General theory of relativity requires that the experiment must come out the same way if performed in a stationary room in the presence of gravity. Gravity must bend the light 1 st observation was made in 1919 during sun eclipse Surprising prediction of special theory of relativity was Time is relative Surprising prediction of general theory of relativity Gravitational bending of light
Something bends? Concept of straightness Straightness? Defined with the path of light beam Then what do we mean by bending of light beam? Einstein had answer Space itself is bent by gravity Just like time is physical and is relative, space is physical too. Gravity effects both time and space Bending of space-time Space and time are intertwined Space has three dimensions Time is called fourth dimension No one (even Einstein) can visualize fourth dimension. Stephen Hawking: It is hard enough to visualize three-dimensional space, let alone fourth. Einstein s general theory of relativity mathematically describes this imagined four-dimensional Space-Time. What is space? An extended region that has no edges or boundaries
In 1972 experiment: A spacecraft orbiting Mars beamed back radar signal sent from earth. When line of sight from Earth to Mars passed near Sun, the radar beam travel time was measured. If it were a flat space and curved beam, the beam had to travel only 10 m more. Signal should have been delayed by about 30 billionths of a second (30 ns) According to Einstein s theory for curved space, the delay was predicted to be 200 millionth of a second (200, 000 ns). About 7000 times longer than predicted by flat space Experiment confirmed longer delay than predicted by flat space There are still doubts about General theory of relativity Because it is very difficult to find practical experiments that can test the theory Consensus is that space really is curved
The Concept is radically different from Newtonian physics In normal situations, it agrees to Newtonian physics, like fall of stone to earth or orbits of the planets According to this theory: Gravity bends space time Gravitational effects such as earth s motion around the sun is not caused by forces at all but are instead entirely due to the curvature of space time. It leads to the following picture of the universe: The universe began with single event some 12 billions years ago (Big Bang). The universe is expanding. There is no space outside the universe. There was no time before the big bang. Big bang created time and space
There are three possible shapes of the universe A closed Universe 3-D sphere with finite volume An open Universe Like a saddle-shaped surface Volume is infinite A Flat Universe No large scale curvature Angles of a triangle add up to more than 180 There will be smaller scale curvatures caused by stars Angles of a triangle add up to less than 180 Angles of a triangle add up to exactly 180
Two crucial factors determine the geometry Expansion rate Average mass density Slower expansion rate or larger mass density cause universe to bend on itself => closed universe faster expansion rate or smaller mass density cause universe to spread out => open universe Flat geometry needs fine adjustment of both What is the actual shape? To answer this we need above two factors Present expansion rate of the universe is known to only 20 % certainty 90 % of the matter in the universe is unknown. Recently there are some evidences that expansion rate of the universe is increasing.