Beyond Beyond AstronomyAstronomy

The Theory of RelativityThe Theory of Relativity

Albert Einstein surprised the world in 1905 when…Albert Einstein surprised the world in 1905 when… he theorized that time and distance can not be measured absolutelyhe theorized that time and distance can not be measured absolutely they only have meaning when they are measured relative to they only have meaning when they are measured relative to

somethingsomething

Einstein published his theory in two steps:Einstein published his theory in two steps: special theory of relativityspecial theory of relativity (1905)…how space & time are (1905)…how space & time are

interwoveninterwoven general theory of relativitygeneral theory of relativity (1915)…effects of gravity on space & (1915)…effects of gravity on space &

timetime

What is “relative” in relativity?What is “relative” in relativity? motion…all motion is relativemotion…all motion is relative measurements of motion (and space & time) make no sense unless measurements of motion (and space & time) make no sense unless

we are told what they are being measured relative towe are told what they are being measured relative to

What is absolute in relativity?What is absolute in relativity? the laws of nature are the same for everyonethe laws of nature are the same for everyone the speed of light (in a vacuum), the speed of light (in a vacuum), cc, is the same for everyone, is the same for everyone

What is Relative?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 Earth’s surface sees the plane fly westward on the Earth’s surface sees the plane fly westward overheadoverhead

at a far distance sees the plane stand still and the Earth at a far distance sees the plane stand still and the Earth rotate underneath itrotate underneath it

A Good ParadoxA Good Paradox

ParadoxParadox…is a situation that seems to violate …is a situation that seems to violate common sense or contradict itself.common sense or contradict itself. the paradox is resolved when the rules of nature the paradox is resolved when the rules of nature

are better understoodare better understood

Ideas & consequences of relativity are not Ideas & consequences of relativity are not evident in everyday life.evident in everyday life. we do not experience the we do not experience the extremeextreme speeds & speeds &

gravity required gravity required so we have no so we have no commoncommon sense about relativity sense about relativity

The “Up” ParadoxThe “Up” Paradox In childhood, we regard “up” as a single direction above our In childhood, we regard “up” as a single direction above our

head.head. When we realize that people in Australia do not stand upside-When we realize that people in Australia do not stand upside-

down…down… we revise our common sensewe revise our common sense ““up” is defined relative to the center of the Earthup” is defined relative to the center of the Earth

Reference FramesReference Frames Two or more objects which do not move relative to each other Two or more objects which do not move relative to each other

share the same reference frame.share the same reference frame.• they experience time and measure distance & mass in the same waythey experience time and measure distance & mass in the same way

Objects moving relative to the other are in different reference Objects moving relative to the other are in different reference frames.frames.

• like the plane and ground belowlike the plane and ground below• they experience time and measure distance & mass in different waysthey experience time and measure distance & mass in different ways

Since ground observers see light move at Since ground observers see light move at cc, the plane passenger is always slower., the plane passenger is always slower.

Time DilationTime Dilation To an observer outside the train, To an observer outside the train,

the ball appears to move faster.the ball appears to move faster.• makes makes common sensecommon sense

Now lets consider Jackie moving by Now lets consider Jackie moving by at close to the speed of light .at close to the speed of light .

• she bounces light instead of a ballshe bounces light instead of a ball

The outside observer can The outside observer can notnot see see the light moving faster than the light moving faster than cc..

• yet the light yet the light doesdoes travel a longer travel a longer distance as seen by the observerdistance as seen by the observer

• so time so time mustmust run more slowly for run more slowly for Jackie!Jackie!

Ticket to the StarsTicket to the StarsAlthough we can not travel faster than the speed of light…Although we can not travel faster than the speed of light…

• special relativity will make the journey seem shorter special relativity will make the journey seem shorter ifif we can travel we can travel close to the speed of lightclose to the speed of light

Time moves more Time moves more slowly for the space slowly for the space traveler.traveler.

The distance to be The distance to be covered is contracted.covered is contracted.

Space travelers can Space travelers can reach distant stars in reach distant stars in their lifetimes.their lifetimes.

Their friends and Their friends and family will not be there family will not be there to greet them when to greet them when they return home to they return home to Earth.Earth.

Order or Simultaneity of EventsOrder or Simultaneity of Events

The red & green flashes occur simultaneously for you.The red & green flashes occur simultaneously for you.• Jackie’s fast motion causes the green light to reach her firstJackie’s fast motion causes the green light to reach her first• you both agree on thatyou 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 she sees both lights travel the same distance at velocity cc• yet she sees the green light firstyet she sees the green light first• so the green flash occurs before the red flash in her reference so the green flash occurs before the red flash in her reference

frameframe

Length ContractionLength 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 shipshe tries to measure the diameter of your ship• but time moves more slowly for herbut 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 IncreaseMass Increase

As Jackie moves by at high speed, you give both her & her identical As Jackie moves by at high speed, you give both her & her identical sister a push.sister a push.

• time runs more slowly for Jackie, so she feels the push for a shorter timetime runs more slowly for Jackie, so she feels the push for a shorter time• Jackie accelerates less than her sister doesJackie accelerates less than her sister does• Newton’s 2Newton’s 2ndnd Law (F = ma) says if F is same, Jackie’s mass must be Law (F = ma) says if F is same, Jackie’s mass must be

greatergreater 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 GravityThe 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 with publication of his general theory of relativitygeneral theory of relativity• it is primarily a theory of it is primarily a theory of gravitygravity

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 he could explain its actions, but not how it was transmitted through

spacespace• Einstein theorized that the “force” of gravity arises from distortions Einstein theorized that the “force” of gravity arises from distortions

of space (or of space (or spacetimespacetime) itself!) itself! spacetimespacetime…the 4-dimensional combination of space & time …the 4-dimensional combination of space & time

that forms the very fabric of the Universethat forms the very fabric of the Universe matter shapes and distorts spacetimematter shapes and distorts spacetime

• space(time) itself can be curved space(time) itself can be curved • you may think you are traveling a straight lineyou may think you are traveling a straight line• but your motion is actually curvedbut your motion is actually curved

Matter Distorts SpacetimeMatter 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 MotionAccelerated 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 for objects moving at a constantconstant velocity with respect to each other velocity with respect to each other• everyone (every reference frame) can claim to be stationaryeveryone (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 your velocity increases 9.8 m/s every second…you are acceleratingaccelerating• you feel a force (1 you feel a force (1 gg) which pushes you to the “floor” of your ship) which pushes you to the “floor” of your ship

• Jackie sees you moving away Jackie sees you moving away from her stationary position.from her stationary position.

• you claim that Jackie is moving you claim that Jackie is moving awayaway

• but she sees you pinned to the but she sees you pinned to the floor while she is still floatingfloor while she is still floating

• this proves you must be this proves you must be acceleratingaccelerating

• you are feeling a force; she is notyou are feeling a force; she is not Apparently we can distinguish Apparently we can distinguish

between motion & non-motion.between motion & non-motion.

The Equivalence Principle The Equivalence Principle This scenario bothered Einstein.This scenario bothered Einstein.

• his intuition told him that his intuition told him that allall motion should be relative motion should be relative• until he had a revelation…the idea for the until he had a revelation…the idea for the equivalence equivalence

principleprinciple The effects of gravity are exactly equivalent to

the effects of acceleration.

• Suppose you were in a closed room.Suppose you were in a closed room.• whether on Earth or accelerating through space at 9.8 m/swhether on Earth or accelerating through space at 9.8 m/s22

• you would never know the differenceyou would never know the difference• your weight would be the sameyour weight would be the same

Accelerated Motion or Standing Accelerated Motion or Standing Still?Still?

• Now…back to Jackie!Now…back to Jackie!• because you are feeling a because you are feeling a

force, she claims that you are force, she claims that you are acceleratingaccelerating

• she is the stationary oneshe is the stationary one But the equivalence principle But the equivalence principle

of general relativity tells us of general relativity tells us that…that…

• you can legitimately consider you can legitimately consider this force to be the weight of this force to be the weight of gravitygravity

• you are firing your rockets in you are firing your rockets in order to remain stationary (to order to remain stationary (to hover)hover)

• the weightless Jackie is in free-the weightless Jackie is in free-fallfall

General relativity makes all General relativity makes all motion relative again!motion relative again!

DimensionsDimensions

• A point (0A point (0D) moved in one direction creates a line (1D) moved in one direction creates a line (1D).D).• A line moved in a direction 90º to itself creates a plane (2A line moved in a direction 90º to itself creates a plane (2D).D). A plane moved in a direction 90º to itself creates a space (3A plane moved in a direction 90º to itself creates a space (3D).D). A space moved in a direction 90º to itself creates a 4A space moved in a direction 90º to itself creates a 4D space.D space.

• we can not perceive this we can not perceive this hyperspacehyperspace…any space > 3…any space > 3DD

dimension… an independent direction of possible motion

Spacetime for AllSpacetime 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 4we can not visualize the 4D spacetime since we can’t see D spacetime since we can’t see through timethrough time

• we perceive a 3we perceive a 3D projection (view) of spacetimeD projection (view) of spacetime• while spacetime is the same for all observers, their 3while spacetime is the same for all observers, their 3D D

perceptions of it (e.g. space & time) can be very differentperceptions of it (e.g. space & time) can be very different

By analogy…By analogy…• we can all agree on the shape we can all agree on the shape

& size of this book in 3 & size of this book in 3 dimensionsdimensions

But…But…• the following 2the following 2D projections D projections

(views) of the same book all (views) of the same book all look very differentlook very different

The Rules of GeometryThe 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 SpacetimeMass and SpacetimeAccording to Newton, all bodies with mass exert a gravitational According to Newton, all bodies with mass exert a gravitational

force on each other.force on each other.• even Newton had problems accepting this concept of “action at a even Newton had problems accepting this concept of “action at a

distance”distance”

General relativity removes this concept.General relativity removes this concept.• mass causes spacetime to curvemass causes spacetime to curve• the greater the mass, the greater the distortion of spacetimethe greater the mass, the greater the distortion of spacetime• curvature of spacetime determines the paths of freely moving curvature of spacetime determines the paths of freely moving

objectsobjects

Orbits can now be Orbits can now be explained in a new explained in a new way.way.

• an object will travel an object will travel on as straight a path on as straight a path as possible through as possible through spacetimespacetime

The Strength of GravityThe Strength of GravityThe more that spacetime curves, the stronger gravity becomes.The more that spacetime curves, the stronger gravity becomes.

Two basic ways to increase gravity/curvature of spacetime:Two basic ways to increase gravity/curvature of spacetime:• increased mass results in greater curvature at distances away from itincreased mass results in greater curvature at distances away from it• curvature is greater near the object’s surface for denser objectscurvature is greater near the object’s surface for denser objects

for objects of a given mass, this implies smaller objectsfor objects of a given mass, this implies smaller objects

• All three objects All three objects impose the same impose the same curvature at a distance.curvature at a distance.

• White dwarf imposes White dwarf imposes steeper curvature at steeper curvature at Sun’s former position.Sun’s former position.

• Black hole punches a Black hole punches a hole in the fabric of hole in the fabric of spacetime.spacetime.

• Nothing can escape Nothing can escape from within the event from within the event horizon.horizon.

Gravitational Time DilationGravitational Time DilationWe use the equivalence We use the equivalence

principle to study the principle to study the effect of gravity on time.effect of gravity on time.

You & Jackie in the ship You & Jackie in the ship have synchronized have synchronized watcheswatches

• the ship acceleratesthe ship accelerates• the watches flashthe 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 LensingGravitational LensingLight will always travel at a constant velocity.Light will always travel at a constant velocity.

• therefore, it will follow the straightest possible path through spacetimetherefore, it will follow the straightest possible path through spacetime• if spacetime is curved near a massive object, so will the trajectory of lightif spacetime is curved near a massive object, so will the trajectory of light

During a Solar eclipse in 1919, two stars near the Sun…During a Solar eclipse in 1919, two stars near the Sun…• were observed to have a smaller angular separation than…were observed to have a smaller angular separation than…• is usually measured for them at night at other times of the yearis usually measured for them at night at other times of the year

This observation verified Einstein’s theory…This observation verified Einstein’s theory…• making him a celebritymaking him a celebrity

Gravitational LensingGravitational Lensing

Since that time, more examples of Since that time, more examples of gravitational lensinggravitational lensing have been have been seen.seen.

They usually involve light paths from They usually involve light paths from quasars & galaxies being bent by quasars & galaxies being bent by intervening galaxies & clusters.intervening galaxies & clusters.

Einstein’s Cross an Einstein ringgalaxy directly behind a galaxy

Gravitational RedshiftGravitational Redshift

• If time runs more slowly on the surface of stars If time runs more slowly on the surface of stars than on Earth…than on Earth…• spectral lines emitted or absorbed on the surfaces of spectral lines emitted or absorbed on the surfaces of

starsstars• will appear at a lower frequency (cycles/s) than will appear at a lower frequency (cycles/s) than

measured on Earthmeasured on Earth• the length of 1 second is longer on the star’s surface the length of 1 second is longer on the star’s surface

than on Earththan on Earth This This gravitational redshiftgravitational redshift has been observed. has been observed.

Gravitational WavesGravitational Waves

• General relativity also predicts that…General relativity also predicts that…• rapidly accelerating masses should send rapidly accelerating masses should send

ripples of curvature through spacetimeripples of curvature through spacetime• Einstein called these ripples Einstein called these ripples

gravitational wavesgravitational waves• similar to light waves, but far weakersimilar to light waves, but far weaker• they have no mass and travel at the they have no mass and travel at the

speed of lightspeed of light They have not yet been directly They have not yet been directly

observed.observed.• but the loss of energy from binary but the loss of energy from binary

neutron starsneutron stars• the “Hulse-Taylor” binarythe “Hulse-Taylor” binary• is consistent with the energy being is consistent with the energy being

emittedemitted as gravitational wavesas gravitational waves

Science Fact or Fiction?Science Fact or Fiction?Do the theories of relativity prohibit interstellar travel?Do the theories of relativity prohibit interstellar travel?

• we can not travel faster than the speed of lightwe 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 We might tunnel through hyperspace in a hyperspace in a wormholewormhole..

A wormhole connects two A wormhole connects two distant points in the distant points in the Universe.Universe.

Or perhaps we could warp Or perhaps we could warp spacetime so that two spacetime so that two locations of our choosing locations of our choosing could touch momentarily.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 MechanicsQuantum Mechanics

At the same time Einstein was developing the At the same time Einstein was developing the principles of relativity, our theory of the very principles of relativity, our theory of the very largelarge……

Physicists were developing new theories of the very Physicists were developing new theories of the very smallsmall.. 1905: Einstein shows light can behave like a particle1905: Einstein shows light can behave like a particle 1911: Rutherford discovers atoms consist mostly of empty 1911: Rutherford discovers atoms consist mostly of empty

spacespace 1913: Bohr suggests that electrons in atoms have 1913: Bohr suggests that electrons in atoms have quantizedquantized

energies energies

They called this new discipline They called this new discipline quantum mechanicsquantum mechanics.. it has revolutionized our understanding of particles & forcesit has revolutionized our understanding of particles & forces it has made possible our modern electronic devicesit has made possible our modern electronic devices

Fundamental ParticlesFundamental ParticlesThe most basic units of matter, impossible to divide, are called The most basic units of matter, impossible to divide, are called

fundamental particlesfundamental particles.. Democritus of ancient Greece thought they were atomsDemocritus of ancient Greece thought they were atoms physicists of the 1930s thought they were protons, neutrons, & physicists of the 1930s thought they were protons, neutrons, &

electronselectrons the advent of particle accelerators has given us a zoo of new particlesthe advent of particle accelerators has given us a zoo of new particles Murray Gell-Mann in the 1960s proposed a Murray Gell-Mann in the 1960s proposed a standard modelstandard model where all where all

these particles could be built from a few fundamental componentsthese particles could be built from a few fundamental components

Fermilab particle accelerator in Illinois

Basic Properties of ParticlesBasic Properties of ParticlesImportant basic properties of a subatomic particle:Important basic properties of a subatomic particle:

massmass chargecharge spin angular momentum…or spin angular momentum…or spinspin

All particles of the same type have the same spin.All particles of the same type have the same spin. but they can have two possible orientations… but they can have two possible orientations… upup & & downdown

Particles do not really spin like a top.Particles do not really spin like a top. the term describes angular momentumthe term describes angular momentum which is measured in units of which is measured in units of ħħ

Particles having half integer spin are called Particles having half integer spin are called fermionsfermions..

particles of which matter is composedparticles of which matter is composed

Particles having integer spin are called Particles having integer spin are called bosonsbosons..

such photons, gluons, & other exchange such photons, gluons, & other exchange particlesparticles

The Building Blocks of MatterThe Building Blocks of MatterProtons & neutrons, which are more massive than electrons…Protons & neutrons, which are more massive than electrons…

are themselves made up of less massive particlesare themselves made up of less massive particles we call these particles we call these particles quarksquarks quarks come in six flavorsquarks come in six flavors protons & neutrons consist of different combinations of two of protons & neutrons consist of different combinations of two of

these flavorsthese flavors

the up quark (+2/3)the up quark (+2/3) the down quark the down quark

((1/3)1/3)

Particles made from Particles made from quarks (quarks (hadronshadrons)…)… can contain 2 or 3 can contain 2 or 3

quarksquarks a quark never exists a quark never exists

alonealone

The Building Blocks of MatterThe Building Blocks of MatterThe electron is not made up of lighter particles.The electron is not made up of lighter particles.

it is fundamentalit is fundamental it is one of six particles called it is one of six particles called leptonsleptons leptons do exist by themselvesleptons do exist by themselves

Here are the six flavors of quarks & six leptons:Here are the six flavors of quarks & six leptons:

Quarks & leptons are Quarks & leptons are the fundamental the fundamental particles of which all particles of which all matter is made.matter is made.

Quarks & leptons are Quarks & leptons are all fermions.all fermions.

All of these particles All of these particles have been have been experimentally verified.experimentally verified.

AntimatterAntimatterEvery quark & lepton has its own antiparticle.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 = mcthey annihilate each other into pure energy (E = mc22))

When conditions are right (like immediately after the Big Bang)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 we call this pair productionpair production

Forces of NatureForces of Nature

Natural forces allow particles to interact and exchange momentum.Natural forces allow particles to interact and exchange momentum. mass is always positive, allowing gravity to dominate on large scalesmass is always positive, allowing gravity to dominate on large scales each force is transmitted by each force is transmitted by exchange particlesexchange particles exchange particles are all bosonsexchange particles are all bosons the graviton has not yet been detectedthe graviton has not yet been detected

The EM & Strong forces are aspects of the same The EM & Strong forces are aspects of the same electroweakelectroweak force. 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 PrincipleHeisenberg Uncertainty Principle

The more we know about where a particle is located…The more we know about where a particle is located… the less we can know about its momentumthe less we can know about its momentum

The more we know about a particle’s momentum…The more we know about a particle’s momentum… the less we can know about its positionthe less we can know about its position

We can not know the precise value of an object's position We can not know the precise value of an object's position & momentum (or energy & time at which it has that & momentum (or energy & time at which it has that energy) simultaneously.energy) simultaneously.

x = location; p = momentum; h = 6.626 x 10–34 joule x sec

hpx

Electron CloudsElectron CloudsAs a consequence of the uncertainty principle…As a consequence of the uncertainty principle…

if we locate the precise position of an electronif we locate the precise position of an electron we have no idea of where it will go nextwe have no idea of where it will go next it appears in different locations over time, it is thus “smeared it appears in different locations over time, it is thus “smeared

out”out” we can calculate the probabilities of where it could be locatedwe can calculate the probabilities of where it could be located

electron probability patterns for several energy levels of Hydrogen

Wave-Particle Duality of MatterWave-Particle Duality of Matter

If we think of the electron as a wave, it has a well-defined If we think of the electron as a wave, it has a well-defined momentum.momentum. but a wave has no single, precise locationbut a wave has no single, precise location it is spread out over a volume, like an electron cloudit is spread out over a volume, like an electron cloud electrons bound in atoms can be described as standing waveselectrons bound in atoms can be described as standing waves

Just like light, all matter has a wave-particle duality.Just like light, all matter has a wave-particle duality. in different situations, it is more convenient to describe it as one or in different situations, it is more convenient to describe it as one or

the otherthe other

Pauli Exclusion PrinciplePauli Exclusion Principle

Two fermions of the same type cannot occupy the same Two fermions of the same type cannot occupy the same quantum state at the same time.quantum state at the same time.

Quantum state… specifies the location, momentum, Quantum state… specifies the location, momentum, orbital angular momentum, & spin of a subatomic orbital angular momentum, & spin of a subatomic particleparticle

……to the extent allowed by the uncertainty principleto the extent allowed by the uncertainty principle

Each of these properties is quantized.Each of these properties is quantized. they can take on only particular valuesthey can take on only particular values

Consequences of the Exclusion Consequences of the Exclusion PrinciplePrinciple

In an atom…In an atom… electron in lowest energy electron in lowest energy

levellevel has a certain orbital angular has a certain orbital angular

momentummomentum a restricted range of locationsa restricted range of locations

quantum state is determined, quantum state is determined, except for spinexcept for spin

two electrons can fit in this two electrons can fit in this levellevel

a third a third mustmust go to a higher go to a higher levellevel

This creation of higher energy levels makes chemistry possible.This creation of higher energy levels makes chemistry possible. Although atoms are mostly empty space, the solidity of matter is explained.Although atoms are mostly empty space, the solidity of matter is explained.

uncertainty principle ensures electrons are not packed into very tiny spacesuncertainty principle ensures electrons are not packed into very tiny spaces exclusion principle ensures that each electron gets to have its own “space”exclusion principle ensures that each electron gets to have its own “space”

These principles govern the sizes of nuclei.These principles govern the sizes of nuclei.

Quantum TunnelingQuantum TunnelingUncertainty principle also states Uncertainty principle also states

product of uncertainties in time & product of uncertainties in time & energy are constantenergy are constant

the shorter the time, the greater the shorter the time, the greater the range of probable energiesthe range of probable energies

a particle could briefly have a particle could briefly have enough energy to overcome a enough energy to overcome a barrier (like escaping from a cell)barrier (like escaping from a cell)

this will not violate conservation this will not violate conservation of energy if stolen energy is of energy if stolen energy is returned before it is noticedreturned before it is noticed

Quantum tunneling can explain how Quantum tunneling can explain how two protons can fuse.two protons can fuse. protons can instantly overcome protons can instantly overcome

EM repulsion EM repulsion

Virtual ParticlesVirtual ParticlesMatter-antimatter pairs of particle can pop into existence.Matter-antimatter pairs of particle can pop into existence.

if they annihilate before the uncertainty time, they go unnoticedif they annihilate before the uncertainty time, they go unnoticed

If one particle is lost to the event horizon of a black hole…If one particle is lost to the event horizon of a black hole… the other stays in existencethe other stays in existence it will eventually annihilate with another “stranded” particleit will eventually annihilate with another “stranded” particle we would observe we would observe Hawking radiationHawking radiation emitted just outside the emitted just outside the

event horizonevent horizon

Ultimate source of this Ultimate source of this radiation is the radiation is the gravitational potential gravitational potential energy of back holeenergy of back hole

The black hold would The black hold would eventually evaporate.eventually evaporate.

This effect has not yet This effect has not yet been observed. been observed.

SummarySummary The view we have of the Universe is very The view we have of the Universe is very

limited. It skews our perspective and limited. It skews our perspective and common sense.common sense.

When dealing with objects that are very When dealing with objects that are very small, very fast or very massive – the results small, very fast or very massive – the results are non-intuitive.are non-intuitive.

In order to understand the extremes in space In order to understand the extremes in space and time, astronomers turn to advanced and time, astronomers turn to advanced physics, chemistry and mathematics. physics, chemistry and mathematics.

Our advanced theories explain the Universe Our advanced theories explain the Universe we observe, but interpreting the results can we observe, but interpreting the results can often border on philosophy. often border on philosophy.

We will continue to learn more about the We will continue to learn more about the nature of the Universe as we continue to nature of the Universe as we continue to explore and probe its’ mysteries.explore and probe its’ mysteries.