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Beyond Astronomy The Theory of Relativity Albert Einstein surprised the world in 1905 when… he theorized that time and distance can not be measured absolutely they only have meaning when they are measured relative to something Einstein published his theory in two steps: special theory of relativity (1905)…how space & time are interwoven general theory of relativity (1915)…effects of gravity on space & time What is “relative” in relativity? motion…all motion is relative measurements of motion (and space & time) make no sense unless we are told what they are being measured relative to What is absolute in relativity? the laws of nature are the same for everyone the speed of light (in a vacuum), c, is the same for everyone What is Relative? A plane flies from Nairobi to Quito at 1,650 km/hr. The Earth rotates at the equator at 1,650 km/hr. An observer… on the Earth’s surface sees the plane fly westward overhead at a far distance sees the plane stand still and the Earth rotate underneath it A Good Paradox Paradox…is a situation that seems to violate common sense or contradict itself. the paradox is resolved when the rules of nature are better understood Ideas & consequences of relativity are not evident in everyday life. we do not experience the extreme speeds & gravity required so we have no common sense about relativity The “Up” Paradox In childhood, we regard “up” as a single direction above our head. When we realize that people in Australia do not stand upside-down… we revise our common sense “up” is defined relative to the center of the Earth Reference Frames Two or more objects which do not move relative to each other share the same reference frame. • Objects moving relative to the other are in different reference frames. • • they experience time and measure distance & mass in the same way like the plane and ground below they experience time and measure distance & mass in different ways Since ground observers see light move at c, the plane passenger is always slower. Time Dilation To an observer outside the train, the ball appears to move faster. • makes common sense Now lets consider Jackie moving by at close to the speed of light . • she bounces light instead of a ball The outside observer can not see the light moving faster than c. • • yet the light does travel a longer distance as seen by the observer so time must run more slowly for Jackie! Ticket to the Stars Although we can not travel faster than the speed of light… • special relativity will make the journey seem shorter if we can travel close to the speed of light Time moves more slowly for the space traveler. The distance to be covered is contracted. Space travelers can reach distant stars in their lifetimes. Their friends and family will not be there to greet them when they return home to Earth. Order or Simultaneity of Events The red & green flashes occur simultaneously for you. • • Jackie’s fast motion causes the green light to reach her first you both agree on that But Jackie considers herself stationary in her reference frame. • • • she sees both lights travel the same distance at velocity c yet she sees the green light first so the green flash occurs before the red flash in her reference frame Length Contraction As Jackie moves past you at high velocity… • • • she tries to measure the diameter of your ship but time moves more slowly for her so she measures a shorter length than you do (distance = velocity x time) Objects appear shorter to you in the direction which they are moving. Mass Increase As Jackie moves by at high speed, you give both her & her identical sister a push. • • • time runs more slowly for Jackie, so she feels the push for a shorter time Jackie accelerates less than her sister does Newton’s 2nd Law (F = ma) says if F is same, Jackie’s mass must be greater Objects moving by you have a greater mass than when at rest. The Topic is Gravity • Albert Einstein stunned the scientific world again in 1915… • • Isaac Newton saw gravity as a mysterious “force.” • • with publication of his general theory of relativity it is primarily a theory of gravity he could explain its actions, but not how it was transmitted through space Einstein theorized that the “force” of gravity arises from distortions of space (or spacetime) itself! spacetime…the 4-dimensional combination of space & time that forms the very fabric of the Universe matter shapes and distorts spacetime • • • space(time) itself can be curved you may think you are traveling a straight line but your motion is actually curved Matter Distorts Spacetime • • Matter distorts spacetime like weights on a taut rubber sheet. The greater the mass, the greater the distortion of spacetime. Accelerated Motion • The special theory of relativity states that all motion is relative… • • for objects moving at a constant velocity with respect to each other everyone (every reference frame) can claim to be stationary What if you fire your rockets and move away from Jackie? • • your velocity increases 9.8 m/s every second…you are accelerating you feel a force (1 g) which pushes you to the “floor” of your ship • Jackie sees you moving away from her stationary position. • • • • you claim that Jackie is moving away but she sees you pinned to the floor while she is still floating this proves you must be accelerating you are feeling a force; she is not Apparently we can distinguish between motion & non-motion. The Equivalence Principle This scenario bothered Einstein. • • his intuition told him that all motion should be relative until he had a revelation…the idea for the equivalence principle The effects of gravity are exactly equivalent to the effects of acceleration. • Suppose you were in a closed room. • • • whether on Earth or accelerating through space at 9.8 m/s2 you would never know the difference your weight would be the same Accelerated Motion or Standing Still? • Now…back to Jackie! • • But the equivalence principle of general relativity tells us that… • • • because you are feeling a force, she claims that you are accelerating she is the stationary one you can legitimately consider this force to be the weight of gravity you are firing your rockets in order to remain stationary (to hover) the weightless Jackie is in free-fall General relativity makes all motion relative again! Dimensions dimension… an independent direction of possible motion • • A point (0D) moved in one direction creates a line (1D). A line moved in a direction 90º to itself creates a plane (2D). A plane moved in a direction 90º to itself creates a space (3D). A space moved in a direction 90º to itself creates a 4D space. • we can not perceive this hyperspace…any space > 3D Spacetime for All • The reality of spacetime is the same in all reference frames. • • • we can not visualize the 4D spacetime since we can’t see through time we perceive a 3D projection (view) of spacetime while spacetime is the same for all observers, their 3D perceptions of it (e.g. space & time) can be very different By analogy… • we can all agree on the shape & size of this book in 3 dimensions But… • the following 2D projections (views) of the same book all look very different The Rules of Geometry • • The geometry you know is valid when drawn on a flat surface. The rules change if the surface is not flat. spherical (curved-in) geometry flat (Euclidean) geometry saddle-shaped (curved-out) geometry Mass and Spacetime According to Newton, all bodies with mass exert a gravitational force on each other. • even Newton had problems accepting this concept of “action at a distance” General relativity removes this concept. • • • mass causes spacetime to curve the greater the mass, the greater the distortion of spacetime curvature of spacetime determines the paths of freely moving objects Orbits can now be explained in a new way. • an object will travel on as straight a path as possible through spacetime The Strength of Gravity The more that spacetime curves, the stronger gravity becomes. Two basic ways to increase gravity/curvature of spacetime: • • increased mass results in greater curvature at distances away from it curvature is greater near the object’s surface for denser objects for objects of a given mass, this implies smaller objects • • • • All three objects impose the same curvature at a distance. White dwarf imposes steeper curvature at Sun’s former position. Black hole punches a hole in the fabric of spacetime. Nothing can escape from within the event horizon. Gravitational Time Dilation We use the equivalence principle to study the effect of gravity on time. You & Jackie in the ship have synchronized watches • • the ship accelerates the watches flash Moving away from Jackie, you see larger time intervals between her flashes. • time appears to be moving slower for her Moving towards you, Jackie sees shorter time intervals between your flashes. • time appears to be moving faster for you • you both agree So, in the equivalent gravitational field… • time moves more slowly where the gravity is stronger Gravitational Lensing Light will always travel at a constant velocity. therefore, it will follow the straightest possible path through spacetime if spacetime is curved near a massive object, so will the trajectory of light • • During a Solar eclipse in 1919, two stars near the Sun… • • were observed to have a smaller angular separation than… is usually measured for them at night at other times of the year This observation verified Einstein’s theory… • making him a celebrity Gravitational Lensing Since that time, more examples of gravitational lensing have been seen. They usually involve light paths from quasars & galaxies being bent by intervening galaxies & clusters. Einstein’s Cross an Einstein ring galaxy directly behind a galaxy Gravitational Redshift • If time runs more slowly on the surface of stars than on Earth… • • • spectral lines emitted or absorbed on the surfaces of stars will appear at a lower frequency (cycles/s) than measured on Earth the length of 1 second is longer on the star’s surface than on Earth This gravitational redshift has been observed. Gravitational Waves • General relativity also predicts that… • • • • rapidly accelerating masses should send ripples of curvature through spacetime Einstein called these ripples gravitational waves similar to light waves, but far weaker they have no mass and travel at the speed of light They have not yet been directly observed. • • • but the loss of energy from binary neutron stars the “Hulse-Taylor” binary is consistent with the energy being emitted as gravitational waves Science Fact or Fiction? Do the theories of relativity prohibit interstellar travel? • • we can not travel faster than the speed of light but what if we made the distance to our destination shorter? We might tunnel through hyperspace in a wormhole. A wormhole connects two distant points in the Universe. Or perhaps we could warp spacetime so that two locations of our choosing could touch momentarily. None of these ideas is prohibited by our current understanding of physics. Most scientists are pessimistic about the possibilities. • wormholes would also make time travel possible, with its severe paradoxes For the moment, the Universe is safe for science fiction writers! Quantum Mechanics At the same time Einstein was developing the principles of relativity, our theory of the very large… Physicists were developing new theories of the very small. 1905: Einstein shows light can behave like a particle 1911: Rutherford discovers atoms consist mostly of empty space 1913: Bohr suggests that electrons in atoms have quantized energies They called this new discipline quantum mechanics. it has revolutionized our understanding of particles & forces it has made possible our modern electronic devices Fundamental Particles The most basic units of matter, impossible to divide, are called fundamental particles. Democritus of ancient Greece thought they were atoms physicists of the 1930s thought they were protons, neutrons, & electrons the advent of particle accelerators has given us a zoo of new particles Murray Gell-Mann in the 1960s proposed a standard model where all these particles could be built from a few fundamental components Fermilab particle accelerator in Illinois Basic Properties of Particles Important basic properties of a subatomic particle: mass charge spin angular momentum…or spin All particles of the same type have the same spin. but they can have two possible orientations… up & down Particles do not really spin like a top. the term describes angular momentum which is measured in units of ħ Particles having half integer spin are called fermions. particles of which matter is composed Particles having integer spin are called bosons. such photons, gluons, & other exchange particles The Building Blocks of Matter Protons & neutrons, which are more massive than electrons… are themselves made up of less massive particles we call these particles quarks quarks come in six flavors protons & neutrons consist of different combinations of two of these flavors the up quark (+2/3) the down quark (1/3) Particles made from quarks (hadrons)… can contain 2 or 3 quarks a quark never exists alone The Building Blocks of Matter The electron is not made up of lighter particles. it is fundamental it is one of six particles called leptons leptons do exist by themselves Here are the six flavors of quarks & six leptons: Quarks & leptons are the fundamental particles of which all matter is made. Quarks & leptons are all fermions. All of these particles have been experimentally verified. Antimatter Every quark & lepton has its own antiparticle. when two identical particles of matter & antimatter meet… they annihilate each other into pure energy (E = mc2) When conditions are right (like immediately after the Big Bang) collision of two photons can create a particle & its antiparticle we call this pair production Forces of Nature Natural forces allow particles to interact and exchange momentum. mass is always positive, allowing gravity to dominate on large scales each force is transmitted by exchange particles exchange particles are all bosons the graviton has not yet been detected The EM & Strong forces are aspects of the same electroweak force. physicists are trying to unify all of the natural forces (GUT) Heisenberg Uncertainty Principle The more we know about where a particle is located… the less we can know about its momentum The more we know about a particle’s momentum… the less we can know about its position We can not know the precise value of an object's position & momentum (or energy & time at which it has that energy) simultaneously. x p h x = location; p = momentum; h = 6.626 x 10 –34 joule x sec Electron Clouds As a consequence of the uncertainty principle… if we locate the precise position of an electron we have no idea of where it will go next it appears in different locations over time, it is thus “smeared out” we can calculate the probabilities of where it could be located electron probability patterns for several energy levels of Hydrogen Wave-Particle Duality of Matter If we think of the electron as a wave, it has a well-defined momentum. but a wave has no single, precise location it is spread out over a volume, like an electron cloud electrons bound in atoms can be described as standing waves Just like light, all matter has a wave-particle duality. in different situations, it is more convenient to describe it as one or the other Pauli Exclusion Principle Two fermions of the same type cannot occupy the same quantum state at the same time. Quantum state… specifies the location, momentum, orbital angular momentum, & spin of a subatomic particle …to the extent allowed by the uncertainty principle Each of these properties is quantized. they can take on only particular values Consequences of the Exclusion Principle In an atom… electron in lowest energy level has a certain orbital angular momentum a restricted range of locations quantum state is determined, except for spin two electrons can fit in this level a third must go to a higher level This creation of higher energy levels makes chemistry possible. Although atoms are mostly empty space, the solidity of matter is explained. uncertainty principle ensures electrons are not packed into very tiny spaces exclusion principle ensures that each electron gets to have its own “space” These principles govern the sizes of nuclei. Quantum Tunneling Uncertainty principle also states product of uncertainties in time & energy are constant the shorter the time, the greater the range of probable energies a particle could briefly have enough energy to overcome a barrier (like escaping from a cell) this will not violate conservation of energy if stolen energy is returned before it is noticed Quantum tunneling can explain how two protons can fuse. protons can instantly overcome EM repulsion Virtual Particles Matter-antimatter pairs of particle can pop into existence. if they annihilate before the uncertainty time, they go unnoticed If one particle is lost to the event horizon of a black hole… the other stays in existence it will eventually annihilate with another “stranded” particle we would observe Hawking radiation emitted just outside the event horizon Ultimate source of this radiation is the gravitational potential energy of back hole The black hold would eventually evaporate. This effect has not yet been observed. Summary The view we have of the Universe is very limited. It skews our perspective and common sense. When dealing with objects that are very small, very fast or very massive – the results are non-intuitive. In order to understand the extremes in space and time, astronomers turn to advanced physics, chemistry and mathematics. Our advanced theories explain the Universe we observe, but interpreting the results can often border on philosophy. We will continue to learn more about the nature of the Universe as we continue to explore and probe its’ mysteries.
