# 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.

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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 he theorized that time and distance can not be measured absolutely they only have meaning when they are measured relative to something 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 special theory of relativity (1905)…how space & time are interwoven general theory of relativity (1915)…effects of gravity on space & time general theory of relativity (1915)…effects of gravity on space & time What is relative in relativity? motion…all motion is relative 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 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 laws of nature are the same for everyone the speed of light (in a vacuum), c, is 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. A plane flies from Nairobi to Quito at 1,650 km/hr. The Earth rotates at the equator at 1,650 km/hr. The Earth rotates at the equator at 1,650 km/hr. An observer… An observer… on the Earths surface sees the plane fly westward overhead on the Earths surface sees the plane fly westward overhead at a far distance sees the plane stand still and the Earth rotate underneath it 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 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 we do not experience the extreme speeds & gravity required so we have no common sense about relativity 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. Two or more objects which do not move relative to each other share the same reference frame. they experience time and measure distance & mass in the same way they experience time and measure distance & mass in the same way Objects moving relative to the other are in different reference frames. Objects moving relative to the other are in different reference frames. like the plane and ground below like the plane and ground below they experience time and measure distance & mass in different ways 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. To an observer outside the train, the ball appears to move faster. makes common sense makes common sense Now lets consider Jackie moving by at close to the speed of light. Now lets consider Jackie moving by at close to the speed of light. she bounces light instead of a ball 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 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. The red & green flashes occur simultaneously for you. Jackies fast motion causes the green light to reach her first Jackies fast motion causes the green light to reach her first you both agree on that you both agree on that But Jackie considers herself stationary in her reference frame. But Jackie considers herself stationary in her reference frame. she sees both lights travel the same distance at velocity c she sees both lights travel the same distance at velocity c yet she sees the green light first yet she sees the green light first so the green flash occurs before the red flash in her reference frame so the green flash occurs before the red flash in her reference frame

Length Contraction As Jackie moves past you at high velocity… As Jackie moves past you at high velocity… she tries to measure the diameter of your ship she tries to measure the diameter of your ship but time moves more slowly for her but time moves more slowly for her so she measures a shorter length than you do (distance = velocity x time) 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. 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. 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 time runs more slowly for Jackie, so she feels the push for a shorter time Jackie accelerates less than her sister does Jackie accelerates less than her sister does Newtons 2 nd Law (F = ma) says if F is same, Jackies mass must be greater Newtons 2 nd Law (F = ma) says if F is same, Jackies mass must be greater Objects moving by you have a greater mass than when at rest. 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… Albert Einstein stunned the scientific world again in 1915… with publication of his general theory of relativity with publication of his general theory of relativity it is primarily a theory of gravity it is primarily a theory of gravity Isaac Newton saw gravity as a mysterious force. Isaac Newton saw gravity as a mysterious force. he could explain its actions, but not how it was transmitted through space 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! 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 spacetime…the 4-dimensional combination of space & time that forms the very fabric of the Universe matter shapes and distorts spacetime matter shapes and distorts spacetime space(time) itself can be curved space(time) itself can be curved you may think you are traveling a straight line you may think you are traveling a straight line but your motion is actually curved but your motion is actually curved

Matter Distorts Spacetime Matter distorts spacetime like weights on a taut rubber sheet. Matter distorts spacetime like weights on a taut rubber sheet. The greater the mass, the greater the distortion of spacetime. The greater the mass, the greater the distortion of spacetime.

Accelerated Motion The special theory of relativity states that all motion is relative… The special theory of relativity states that all motion is relative… for objects moving at a constant velocity with respect to each other for objects moving at a constant velocity with respect to each other everyone (every reference frame) can claim to be stationary everyone (every reference frame) can claim to be stationary What if you fire your rockets and move away from Jackie? What if you fire your rockets and move away from Jackie? your velocity increases 9.8 m/s every second…you are accelerating 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 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. This scenario bothered Einstein. his intuition told him that all motion should be relative his intuition told him that all motion should be relative until he had a revelation…the idea for the equivalence principle 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/s 2 you would never know the difference your weight would be the same

Accelerated Motion or Standing Still? Now…back to Jackie! Now…back to Jackie! because you are feeling a force, she claims that you are accelerating because you are feeling a force, she claims that you are accelerating she is the stationary one she is the stationary one But the equivalence principle of general relativity tells us that… But the equivalence principle of general relativity tells us that… you can legitimately consider this force to be the weight of gravity you can legitimately consider this force to be the weight of gravity you are firing your rockets in order to remain stationary (to hover) you are firing your rockets in order to remain stationary (to hover) the weightless Jackie is in free-fall the weightless Jackie is in free-fall General relativity makes all motion relative again! General relativity makes all motion relative again!

Dimensions A point (0 D) moved in one direction creates a line (1 D). A point (0 D) moved in one direction creates a line (1 D). A line moved in a direction 90º to itself creates a plane (2 D). A line moved in a direction 90º to itself creates a plane (2 D). A plane moved in a direction 90º to itself creates a space (3 D). A plane moved in a direction 90º to itself creates a space (3 D). A space moved in a direction 90º to itself creates a 4 D space. A space moved in a direction 90º to itself creates a 4 D space. we can not perceive this hyperspace…any space > 3 D we can not perceive this hyperspace…any space > 3 D dimension … an independent direction of possible motion

Spacetime for All The reality of spacetime is the same in all reference frames. The reality of spacetime is the same in all reference frames. we can not visualize the 4 D spacetime since we cant see through time we can not visualize the 4 D spacetime since we cant see through time we perceive a 3 D projection (view) of spacetime we perceive a 3 D projection (view) of spacetime while spacetime is the same for all observers, their 3 D perceptions of it (e.g. space & time) can be very different while spacetime is the same for all observers, their 3 D 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 dimensionsBut… the following 2 D projections (views) of the same book all look very differentthe following 2 D 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 geometry you know is valid when drawn on a flat surface. The rules change if the surface is not flat. The rules change if the surface is not flat. flat (Euclidean) geometry spherical (curved-in) 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 even Newton had problems accepting this concept of action at a distance General relativity removes this concept. mass causes spacetime to curve mass causes spacetime to curve the greater the mass, the greater the distortion of spacetime the greater the mass, the greater the distortion of spacetime curvature of spacetime determines the paths of freely moving objects 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 increased mass results in greater curvature at distances away from it curvature is greater near the objects surface for denser objects curvature is greater near the objects surface for denser objects for objects of a given mass, this implies smaller 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 Suns 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 ship accelerates the watches flash 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 therefore, it will follow the straightest possible path through spacetime if spacetime is curved near a massive object, so will the trajectory of light 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 Einsteins 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. Einsteins Cross an Einstein ring galaxy directly behind a galaxy

Gravitational Redshift If time runs more slowly on the surface of stars than on Earth… If time runs more slowly on the surface of stars than on Earth… spectral lines emitted or absorbed on the surfaces of stars spectral lines emitted or absorbed on the surfaces of stars will appear at a lower frequency (cycles/s) than measured on Earth will appear at a lower frequency (cycles/s) than measured on Earth the length of 1 second is longer on the stars surface than on Earth the length of 1 second is longer on the stars surface than on Earth This gravitational redshift has been observed. This gravitational redshift has been observed.

Gravitational Waves General relativity also predicts that… General relativity also predicts that… rapidly accelerating masses should send ripples of curvature through spacetime rapidly accelerating masses should send ripples of curvature through spacetime Einstein called these ripples gravitational waves Einstein called these ripples gravitational waves similar to light waves, but far weaker similar to light waves, but far weaker they have no mass and travel at the speed of light they have no mass and travel at the speed of light They have not yet been directly observed. They have not yet been directly observed. but the loss of energy from binary neutron stars but the loss of energy from binary neutron stars the Hulse-Taylor binary the Hulse-Taylor binary is consistent with the energy being emitted is consistent with the energy being emitted as gravitational waves 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 we can not travel faster than the speed of light but what if we made the distance to our destination shorter? 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 1905: Einstein shows light can behave like a particle 1911: Rutherford discovers atoms consist mostly of empty space 1911: Rutherford discovers atoms consist mostly of empty space 1913: Bohr suggests that electrons in atoms have quantized energies 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 revolutionized our understanding of particles & forces it has made possible our modern electronic devices 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 Democritus of ancient Greece thought they were atoms physicists of the 1930s thought they were protons, neutrons, & electrons physicists of the 1930s thought they were protons, neutrons, & electrons the advent of particle accelerators has given us a zoo of new particles 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 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 mass charge charge spin angular momentum…or spin spin angular momentum…or spin All particles of the same type have the same spin. but they can have two possible orientations… up & down 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 are themselves made up of less massive particles we call these particles quarks we call these particles quarks quarks come in six flavors quarks come in six flavors protons & neutrons consist of different combinations of two of these 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 fundamental it is one of six particles called leptons it is one of six particles called leptons leptons do exist by themselves 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… when two identical particles of matter & antimatter meet… they annihilate each other into pure energy (E = mc 2 ) they annihilate each other into pure energy (E = mc 2 ) When conditions are right (like immediately after the Big Bang) collision of two photons can create a particle & its antiparticle collision of two photons can create a particle & its antiparticle we call this pair production 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 mass is always positive, allowing gravity to dominate on large scales each force is transmitted by exchange particles each force is transmitted by exchange particles exchange particles are all bosons exchange particles are all bosons the graviton has not yet been detected 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) 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 less we can know about its momentum The more we know about a particles momentum… the less we can know about its position 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. We can not know the precise value of an object's position & momentum (or energy & time at which it has that energy) simultaneously. 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 if we locate the precise position of an electron we have no idea of where it will go next we have no idea of where it will go next it appears in different locations over time, it is thus smeared out it appears in different locations over time, it is thus smeared out we can calculate the probabilities of where it could be located 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 but a wave has no single, precise location it is spread out over a volume, like an electron cloud it is spread out over a volume, like an electron cloud electrons bound in atoms can be described as standing waves 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 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 they can take on only particular values

Consequences of the Exclusion Principle In an atom… In an atom… electron in lowest energy level electron in lowest energy level has a certain orbital angular momentum has a certain orbital angular momentum a restricted range of locations a restricted range of locations quantum state is determined, except for spin quantum state is determined, except for spin two electrons can fit in this level two electrons can fit in this level a third must go to a higher 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 product of uncertainties in time & energy are constant the shorter the time, the greater the range of probable energies 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) 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 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 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 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 the other stays in existence it will eventually annihilate with another stranded particle it will eventually annihilate with another stranded particle we would observe Hawking radiation emitted just outside the event horizon 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. 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. 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. 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. 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. We will continue to learn more about the nature of the Universe as we continue to explore and probe its mysteries.

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