what it would be like to travel at the speed of light. In particular, what would one see in a mirror that is also moving at the speed of light? Einstein’s Mirror
patent office at Bern when all of a sudden a thought occurred to me: If a person falls freely he will not feel his own weight... I was startled. This simple thought made a deep impression on me. It impelled me towards a theory of gravitation.” The “Happiest Thought” of Einstein’s Life (1907)
what it is, provided that nobody asks me; but if I am asked what it is and try to explain, I am baffled.” St. Augustine (5th Century A.D.) Easier question: How do we measure time?
and everyday experience might suggest It depends on the observer In other words, it is relative “When the Special Theory of Relativity began to germinate in me, I was visited by all sorts of nervous conflicts... I used to go away for weeks in a state of confusion.”
called luminiferous aether. Electric and magnetic fields are ‘distortions’ or ‘twists’ of the aether. Maxwell hypothesised that ... James Clerk Maxwell (1831-1879)
shadows cast on Jupiter by its moons Measurements were made at position A, and then at B six months later The time lapse recorded implies that light has a finite speed
Roemer Jupiter's satellites 214,000 1726 James Bradley Stellar aberration 301,000 1849 Armand Fizeau Toothed wheel 315,000 1862 Leon Foucault Rotating mirror 298,000 +-500 1879 Albert Michelson Rotating mirror 299,910 +-50 1907 Rosa, Dorsay Electromagnetic constants 299,788 +-30 1926 Albert Michelson Rotating mirror 299,796 +-4 1947 Essen, Gorden-Smith Cavity resonator 299,792 +-3 1958 K. D. Froome Radio interferometer 299,792.5 +-0.1 1973 Evanson et al Lasers 299,792.4574 +-0.001 1983 Adopted value 299,792.458 Measurements of the speed of light Today c is defined to be exactly 299,792,458 m/s, and this is used to define the meter
as luminiferous aether The speed of light is the same (constant) in any direction, which explains the null results of M&M Although we have come one big circle, this realization of Einstein paved the way for his theory of relativity …
train moving on a straight track at a constant speed If you closed the windows, you would not be able to tell whether the train is moving or at rest! In other words … The laws of physics are the same for all observers moving at steady speeds with respect to each other Galileo Galilei (1564-1642)
who is actually at rest According to the driver of red car, blue car is overtaking But according to the driver of blue car, red car is reversing backwards
or Postulates: The speed of light is constant regardless of the motion of the observer or of the sender Galileo’s relativity principle: The laws of physics are the same for all observers moving at steady speeds with respect to each other
the train, wants to measure the speed of light He sends a light pulse straight up and down, and measures the time taken by his clock Meanwhile, you are outside the train watching the same experiment being performed You also try to measure the speed of light, by your own clock
moving, you see the light pulse to travel a longer distance But by Einstein’s first postulate, both Luke and you would measure the same speed Since, speed equals distance/time, you would think that the time taken for the experiment to complete is longer
almost one. So the time dilation effect is very small When speed approaches that of light, γ becomes larger and larger. Time slows down more and more Graph of gamma
would not notice himself ‘slow down’ Instead, he would everything outside the train slow down in time Time dilation affects all types of time: physical, mechanical, psychological, biological …
one. So the length contraction effect is very small When speed approaches that of light, γ becomes larger and larger. Length becomes zero Length contraction graph
as his student, and once called him ‘a lazy dog’. In 1908, Minkowski realized that time can be unified with three-dimensional space to give a four-dimensional ‘space-time’ Consider a horse in motion:
their 21st birthday together, Luke flies off in his X- wing at 24/25 c to a distant star system He travels for 7 years, then turns round and returns home at the same speed What are the ages of the twins when Luke returns? The Twin Paradox
… … so he will be younger than Leia when he returns According to Luke, Leia (and the Earth) will be moving and so it is her clock that will slow down … … so she will be younger than Luke when he returns! The Twin Paradox (cont’d)
is wrong, because he will experience acceleration in his X- wing and so he knows he is the one actually moving Detailed calculations show that Luke will indeed be younger than Leia when he returns Who is the younger twin?
of Doppler effect An object moving sideways at high speeds can appear red-shifted because of time dilation Observed in the jets of SS433 Transverse Doppler Effect SS433 is a binary star system. A black hole or neutron star is blasting out two jets of gas in opposite directions, at 0.25c
energy - chemical, - electrical, - magnetic, - mechanical, - heat, etc., can be transformed into each other, but the total amount of energy always remains the same Julius Robert von Mayer (1814- 1878) was the first to realise a relation between mechanical work and heat energy
measures its resistance to motion But if the object is already moving, then its mass measures how difficult it is to stop In this case, the ‘stopping power’ required is better described by …
the mass of the object when it is at rest. m0 is known as the rest mass and m is the relativistic mass. m = γm0 Note: When an object approaches the speed of light, its mass becomes larger and larger.
He wants to go faster, so he adds more power to the engines of his X-wing … His speed will go up slightly, but his mass will go up drastically With more mass, more power is needed to increase his speed further, … and so on
speed of light? A photon has no rest mass: m0 = 0 Because it is impossible to find a photon ‘at rest’ So the above arguments are not valid: m = 0/0 = can be anything
motion has more mass than one at rest A hot gold sphere has more mass than a cold one So conservation is mass is not true, although this change of mass is very minute (since c is so large)
by burning 15 453 barrels of crude oil The total consumption of energy in Singapore in 1999! This shows that there is an enormous amount of energy locked inside matter
charged particles A heavy nucleus made up of protons and neutrons (which have roughly the same mass) Protons: +ve charged particles Neutrons: neutral particles
and B, with masses m and 2m, respectively The gravitational force on B is twice that on A But twice as much force is needed to get B moving the same rate as A So A and B fall at the same rate!
chair in the patent office at Bern when all of a sudden a thought occurred to me: If a person falls freely he will not feel his own weight... I was startled. This simple thought made a deep impression on me. It impelled me towards a theory of gravitation.” This means that gravity can be cancelled out by acceleration
is impossible to distinguish between the effects of accelerated motion and those of a gravitational field In short, gravity is equivalent to acceleration Explains Newton’s equivalence principle
created by acceleration If there were no windows in the elevator, Einstein would not be able to tell whether he is at rest on Earth or accelerating at a constant rate in space
experiments both show that light would be bent by gravity Predicted by Einstein in 1911 (and corrected in 1915) Experimentally verified during a solar eclipse in 1919 by Eddington
field This is related to the slowing down of time in a gravitational field … … since atoms vibrate slower and emit light with longer wavelength (smaller frequency)
small region on the surface of the Earth is almost flat A flat map is adequate to represent this region But a flat map cannot accurately represent the entire surface of the Earth. Distortions are inevitable, since the surface is actually curved.
off on a long space journey ... His spaceship accelerates at 1 g to the halfway point, and then decelerates at 1 g so that it comes to a rest at the destination How does Pooh’s time compare to Earth time?
current expansion rate (Hubble constant) back to the Big Bang 10 to 20 billion years old Look for the oldest stars (in globular clusters) 11 to 18 billion years old Best current estimate is 13.4 ± 1.6 billion years M10 Globular Cluster
galaxies on each other is slowing down the rate of expansion Required density for the universe to recollapse is 4.5 x 10-30 g/cm3 Observed density of luminous material (stars, galaxies) is about 3 x 10-31 g/cm3
space, and has discrete physical properties such as mass A wave is inherently spread out over many wave-lengths in space, and could have amplitudes in a continuous range Waves superpose and pass through each other, while particles collide and bounce off each other
totally absorbs all radiation that falls on it Any hot body (blackbodies included) radiates light over the whole spectrum of frequencies The spectrum depends on both frequency and temperature
in photographic darkrooms because it is not energetic enough to break the halogen-silver bond in black and white films Ultraviolet light causes sunburn but visible light does not because UV photons are more energetic Our eyes detect colour because photons of different energies trigger different chemical reactions in retina cells
speeds of all particles in the universe are measured to sufficient accuracy at a particular instant in time It is possible to predict the motions of every particle at any time in the future (or in the past for that matter) “An intelligent being knowing, at a given instant of time, all forces acting in nature, as well as the momentary positions of all things of which the universe consists, would be able to comprehend the motions of the largest bodies of the world and those of the smallest atoms in one single formula, provided it were sufficiently powerful to subject all the data to analysis; to it, nothing would be uncertain, both future and past would be present before its eyes.” Pierre Simon Laplace
of very small particles, one cannot measure any property of a particle without interacting with it in some way This introduces an unavoidable uncertainty into the result One can never measure all the properties exactly
Shine light on electron and detect reflected light using a microscope Minimum uncertainty in position is given by the wavelength of the light So to determine the position accurately, it is necessary to use light with a short wavelength
baseball at 40 m/s So momentum is 0.1 x 40 = 4 kg m/s Suppose the momentum is measured to an accuracy of 1 percent , i.e., ∆p = 0.01 p = 4 x 10-2 kg m/s
how ψ evolves or behaves in a given potential Analogue of Newton’s equation in classical mechanics Schrödinger’s Equation Erwin Schrödinger (1887-1961)
interference (double-slit experiment) Also possible with more massive particles, such as neutrons and α-particles Applications: Bragg scattering Electron microscopes Electron- and proton-beam lithography
negative energies Dirac identified them as ‘antiparticles’, with opposite charge to normal particles He (wrongly) identified the antiparticle of the electron with the proton
rays by Carl Anderson in 1932 Anderson saw a track in a cloud chamber left by “something positively charged, and with the same mass as an electron” Has the same mass as the electron but positive charge
can annihilate with its antiparticle to form gamma rays An example whereby matter is converted into pure energy by Einstein’s formula E = mc2 Conversely, a gamma ray with sufficiently high energy can turn into a particle – antiparticle pair Particle – antiparticle tracks in a bubble chamber
universe? A possible cloud of antimatter? A very small asymmetry between particles and antiparticles is predicted by the weak force During the big bang, for every billion antimatter particles produced, there were a billion and one matter particles This one matter particle out of a billion is all that is left today!
injected into the bloodstream It would decay by emitting a positron, which would annihilate with an electron in the blood to produce gamma rays How PET Works Gamma rays fly off in opposite directions into the detectors. This enables the location of the original electron to be pinpointed
the decay of the neutron: neutron → proton + electron + antineutrino Almost massless and interacts very weakly with other particles (via the weak force) Discovered only in 1956
George Zweig in 1961 Even more fundamental particles called quarks carrying charge 2/3 or -1/3 Mesons are composed of two quarks and baryons are composed of three quarks
(QED) describes electro-magnetism in terms of exchange of photons Weak force: W±, Z bosons Quantum chromodynamics (QCD) describes the strong force in terms of exchange of 8 gluons carrying ‘colour’ charge
superstring theory Assumes all fundamental particles are actually string-like objects rather than point-like objects Different particles correspond to different vibrational modes of the same string
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![Guest Instructor: H. Kemal İlter e-mail: [email protected] web site: www.baskent.edu.tr](https://files.speakerdeck.com/presentations/50541beb5281be000201679a/slide_0.jpg){kind=link}
