Relativity
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description
Relativity. Of light and time…. Light takes a certain amount of time to travel from an object/ event to us…. The further away something is, the greater that amount of time is Sooo … We look at stars…. We see the past. Light year ( ly ) - distance that light travels in a year - PowerPoint PPT Presentation
Transcript of Relativity
Of light and time… Light takes a certain amount of time to travel from an object/ event to us…. The further away something is, the greater that amount of time is
Sooo… We look at stars…. We see the past
Light year (ly) - distance that light travels in a year
If a star is 1000 ly away, what we are seeing the star do actually happened a 1000 years ago
Light from the sun takes 8 minutes to reach us. Sun could explode
right now, and we would have no idea for 8 minutes
Speed of light (c) - 3.0 x 108 m/sOr about 180,000 miles/sec
But what if we could travel on a beam of light….. ???
Einstein in 1905– 26 years old Came up with this notion when pondering
what it would be like to travel on a beam of light
Describes the motion of particles moving at close to the speed of light.
Gives the correct laws of motion for any particle
In moving through space we also change our rate of moving through time
Newton’s Laws good approximation…..
Einstein’s Laws Always right
Theory of Special Relativity
Einstein states that space & time are inter-related and form what’s called space-time
Space-time exists in the universe, not the other way around There would be no time if no universe So the universe, and what you are doing in the universe affects
your time Time and Space are two parts of one whole known as “Space-time
Space- Time
Special Relativity
1st Postulate. The laws of physics are the same in any inertial (non-accelerated) frame of reference. This means that there is no experiment that can tell you if you are moving or not…. As long as you are not accelerating
2nd Postulate. The speed of light is the same for all observers, no matter what their relative speeds.
Car example
Effects include Time Dilation and Length Contraction
Why does speed of light have to be constant?
Why does the speed of light have to be constant?
Time Dilation
When traveling at speeds very close to the speed of light Fast clocks move slow The faster your moving the
slower time is going by for you relative to a stationary observer
Twin Paradox One twin stay on Earth, other
goes on trip at a speed close to the speed of light…. Twin comes back and twin on Earth is now much older than him
Travelling twin is effectively travelling forward through time
Note- The travelling twin thinks his time is
running normally… does not feel like his
clock is “slow”
Planet of the Apes
http://www.youtube.com/watch?v=JdG5t7p8ji8
Why does time dilation happen?
The speed of light is a constancy of nature, it is not only a finite speed, light waves play a special role in connecting space and time in ‘spacetime’ As well as connecting mass and energy in the equation E=mc2
Light clock example If speed of light constant for all observers and different observers see a beam of light take 2 different
paths (one longer than the other) then the speed can’t be different to account for the greater distance so the time must account for this.
Or imagine flying away from a clock at a super high speed. Each tick from that clock takes longer to get to you. In other words longer amount of time goes by for you between ticks than does a stationary person.
Video Travelling near the speed of light alters (stretches out) the spacetime around the object
Only noticeable at high speeds….
• http://www.etsu.edu/physics/plntrm/relat/special.htm – A smarter powerpoint
• equation describes time dilation
Δt - dilated time interval (Earth’s clock) Δt’ - proper time interval (Spaceship’s clock)*Notice that if v is close to c then Δt is large*If v is small compared to c then Δt’ is approximately equal to Δt
Time dilation is not noticeable at all until we get to very high speeds…
• http://www.shellac.org/slu/slutime.html– Relativity calculator
X –axis -- Fraction of speed of light traveller is moving at
Y axis – number of seconds past for stationary observer for every 1 second past for moving observer
Graph shows that time dilation is only significant at very high speeds… speeds approaching the speed of light!
• Special relativity video• http://www.youtube.com/watch?v=V7vpw4A
H8QQ
• http://www.youtube.com/watch?v=02tchltLm3c&feature=related
• http://www.youtube.com/watch?v=YzMrNFd4oOk&safe=active
Proof of time dilation
• Experiments with atomic clocks and jet plane– In 1972. Very accurate clocks flown around world
on commercial flights– Very small Time Dilation Noticeable on clocks– Amount of Dilation nearly exactly what was
predicted by Einstein’s Equations– Video clip
http://www.relativitycalculator.com/stationary_moving_clocks.shtml
A closer look at airplanes experiment…
More complicated than it soundsOne flew East…. And LOST TIME…. Another flew west and
GAINED timeSee data here…
http://hyperphysics.phy-astr.gsu.edu/HBASE/Relativ/airtim.html
Many things to consider Gravitational time dilation Kinematic time dilation Neither perspective is an “inertial reference frame” Spin of the Earth
More proof• Particle Accelerator is used to accelerate small particles called
‘Muons’ at rest compared to decay of Muons moving at .995c.
• Muons decay slower at relativistic speeds – meaning time slows down for them
Decay of muons moving at a speed of 0.995c with respect to the observer
More Proof… Lifespan of supernovae
• Supernovae seem to have longer “lives” when moving away from us at relativistic speeds.
Other things….• Sergei Avdeyev spent 747 days in space traveling around 17,000 mph relative to
people on earth allowing him to time travel 1/50th of a second into the future. (Guiness World Book of Records 2006, pg 109)
• Light does not experience time….. It travels through space w/out travelling through time
– Light takes 1000 years (from our perspective) to travel to something 1000 light years away, but from its perspective it makes that same trip instantaneously.
• Can we make a trip to a star 1000 light years away in less than 1000 years?
– From our (the traveller’s) perspective, YES. From the Earth’s perspective, NO.
• GPS Satellites & receivers have to take into account relativistic effects when calculating position, otherwise they would be extremely inaccurate
Length Contraction
When travelling at speed close to the speed of light… An object will shrink in length, according to a stationary observer If a meterstick is travelling at .87 c, then it would appear to be only 50
cm in length. If a meterstick is travelling at .995 c, then it would appear to be only 10
cm in length What one observer see as time dilation, another sees as length
contraction http://cse.ssl.berkeley.edu/bmendez/ay10/2002/notes/lec11.html
Illustration of length contraction• Figure n shows an artist’s rendering of the length contraction for the
collision of two gold nuclei at relativistic speeds in the RHIC accelerator in Long Island, New York, which went on line in 2000. The gold nuclei would appear nearly spherical (or just slightly lengthened like an American football) in frames moving along with them, but in the laboratory’s frame, they both appear drastically foreshortened as they approach the point of collision. The later pictures show the nuclei merging to form a hot soup, in which experimenters hope to observe a new form of matter.
Also Simultaneity can be disagreed upon
• Different observers can disagree on the simultaneity of events
• http://www.scivee.tv/node/3025– Above video.. Train example
You and Jackie disagree on the simultaneity of
the red and green light
flashes
What would happen if you were travelling close to the speed of light?
As you get closer to ‘c’ mass increases… as defined by E=mc2
Therefore the amount of energy required to accelerate you becomes huge, at ‘c’ it would become infinity
Traveller moving at a speeds close to ‘c’ would be red-shifted if travelling away from stationary observer
Would be blue-shifted if travelling towards stationary observer View in front of traveller would be pulled into small porthole, blue towards the center….
red towards the edges http://www.youtube.com/watch?v=Uy7rrrCQh2w&feature=related Carl Sagan
Family Guy spoof of Carl Sagan http://www.youtube.com/watch?v=DI9ImScQGAo http://www.youtube.com/watch?v=JQnHTKZBTI4 weird optical effects
General Relativity• http://www.youtube.com/watch?v=0rocNtnD-yI
General Relativity
Special Relativity was an incomplete, only dealt w/ the ‘special’ case of constant motion
Einstein sought to create a theory of the universe that explained all types of motion and (ie the accelerated motion caused by gravity)
1916 Theory of General Relativity General Relativity explained acceleration’s and gravity’s role
in his earlier notions of space-time
This combined w/ Special Relativity threw out Classical Mechanics (Newton stuff) and ushered in the era of “Modern Physics”
General Relativity
Many consider to be the greatest scientific discovery OF ALL TIME **Gravity and acceleration appear to be same phenomenon
Einstein’s Elevator No difference between inertial effects in hypothetical accelerating elevator and the
feeling of gravity *In short, Gravity is not a force at all and is instead the curvature of space-
time around a large mass Curvature demonstrated
“spacetime tells matter how to move; matter tells spacetime how to curve” This curvature has many consequences
Time dilation near large masses Slower clocks when experiencing more gravity Faster clocks when experiencing less gravity
Black Holes Explanation of Big Bang and acceleration of an expanding universe
• http://www.youtube.com/watch?v=DbhuRcmSkMg&feature=related
Uncurved Space-Time
Curved Space-Time
Confirmation of General RelativityNewton vs. Einstein Throwdown with
the Sundown … May 29, 1919The Story
In order to confirm GR, scientist needed to prove this somehow… but how
They figured… if true, light should bend when travelling by a huge object… like for instance the sun.
So needed to observe stars that are behind the sun to see if their position was shifted from normal
Only time that you can see stars with sun in the sky is during a Total Solar Eclipse
After several failed attempts and measuring this another occurred 5/29/19
The path of the famous eclipse through South America
Amount of shift in the stars around
that sun is represented in Red
After this confirmation (over
3 years after GR was theorized)
Einstein became an instant
celebrity and world renowned
scientist
After the eclipse Einstein instantly became a worldwide celebrity both in the science world and in
pop culture His redefinition of the universe was now complete Sits as what many consider to be singly the greatest scientific discovery of all time
Other Proof of General Relativity• Orbit of Mercury
• Einstein’s Theory was able to accurately predict the orbit of Mercury whereas no previous notion of gravity was able to
Black Holes
Consequence of General RelativitySo weird that Einstein himself doubted their existence, even
though his theory predicted themWhat they are?
Remnants of a collapsed star Shrunk to such a small size, that its gravity became infinitely strong….
So strong its escape velocity is faster than the speed of light One of the most interesting objects in the Universe Nothing can escape a black hole Creates an infinitely deep hole in Space-Time,
How a black hole forms• Large star runs on nuclear fuel
(fusion)– Star was previously held together by
balance of outward pushing fusion and inward pulling gravity
– Outward force gone, so gravity takes over
– Star will go into a supernova on outside but inside pulls together
– If star is big enough it will keep shrinking until black hole forms
– Becomes infinitely dense w/ incredible amounts of gravity, escape speed is larger than speed of light
Parts of a black hole
• Event Horizon– “opening” of a black hole– Point of no return– Beyond this point not even light can escape
• Singularity– “bottom” of a black hole– No one knows what happens at the singularity– Where all the ‘stuff’ is
Different things stars can turn into upon collapse…
White dwarf Star with an original mass of about 0.4 to 3.4 times the mass of our Sun will collapse to a white dwarf If the mass of the star is less than about 1.2 solar masses after collapse, then will turn into a white dwarf A ball of dead slag gradually cooling down as it radiates away its thermal energy radius is on the order of 5000 km, and the density is about 1 ton per cubic centimeter. Eventually become a black dwarf… universe is not old enough to have any black dwarfs in existence Inside is thought to be one massive diamond…. Solid carbon
Neutron Star Stars with an original mass of about 4 -20 solar masses will collapse to this If mass of star left over after supernova is between 1.4 and three to four times as massive as our sun, it
will become a dense neutron star (a neutron star is about 11 kilometers in diameter Almost a black hole Super dense Teaspoonful weighs a billion tons
Black Hole Stars an original mass of about 20 solar masses or greater will form into black holes If star remnants after supernova has more than about 2.5 solar masses, gravity wins and the neutron star
collapses into a black hole
Multiwavelength X-ray, infrared, and optical compilation image of Kepler's Supernova Remnant, SN 1604. ( Chandra X-ray Observatory)
This is a mosaic image, one of the largest ever taken by NASA's Hubble Space Telescope of the Crab Nebula, a six-light-year-wide expanding remnant of a star's supernova explosion. Japanese and Chinese astronomers recorded this violent event nearly 1,000 years ago in 1054, as did, almost certainly, Native Americans. Located at a distance of about 6,500 light-years (2 kpc) from Earth, the nebula has a diameter of 11 ly (3.4 pc) and is expanding at a rate of about 1,500 kilometers per second. At the centre of the nebula lies the Crab Pulsar, a rotating neutron star
Light bending around a black hole… animation
• “gravitational lensing”
Classifications of Black Holes
• Stellar-Mass Black Holes– “Regular” size black holes– Formed from death of star and haven’t grown to
be significantly larger• Supermassive Black Holes
– Believed to be at the center of every galaxy
Proof of black holes • Stars orbiting very fast around “nothing”• Binary systems
– Star and black hole in a dance together• Accretion disk around a black hole• Bursts of x-rays
Paths of stars orbiting around an
empty point in space, once orbital data
calculated the only object that could be causing objects to move
like this is a black hole. “empty” space objects are
orbiting
• http://www.youtube.com/watch?v=tJxUHCndt4Y&safe=active
An artists concept of a microquasar, like V404 Cygni. The black hole is stealing gas from
a companion star (left). The gas forms a thin, hot disk (accretion disk) around the black hole. When enough gas builds up there is a bright flare-up of X-rays, and jets of charged particles squirt away at close to the speed of light. [ESA]
X-rays that can be
detected
X-ray image of Cygnus x-1
Videos• http://fora.tv/2008/02/19/Neil_DeGrasse_Tys
on_Death_by_Black_Hole#fullprogram• http://www.youtube.com/watch?v=D3AfNXdg
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• Morgan Freeman – Through the Wormhole
Swartzchild Radius• The radius to which an object will need to shrink
to in order to turn into a black hole
• Anything can ‘technically’ get turned into a BH if made small enough
• In actuality, only appropriately large enough stars will when they die
• Found with equation– R = 2GM/c2
Key Properties of Main Sequence Stars
Mass/MSun Luminosity/LSunEffective Temperature (K) Radius/RSun
Main sequence lifespan (yrs)
0.10 3×10-3 2,900 0.16 2×1012
0.50 0.03 3,800 0.6 2×1011
0.75 0.3 5,000 0.8 3×1010
1.0 1 6,000 1.0 1×1010
1.5 5 7,000 1.4 2×109
3 60 11,000 2.5 2×108
5 600 17,000 3.8 7×107
10 10,000 22,000 5.6 2×107
15 17,000 28,000 6.8 1×107
25 80,000 35,000 8.7 7×106
60 790,000 44,500 15 3.4×106
Evolution of StarsClouds of Hydrogen begin condensing into more dense
clusters due to gravitation. Eventually the density gets high enough that the Hydrogen
begins fusing into Helium. This fusion releases energy, mostly in the form of electromagnetic radiation. Our sun is currently in this phase. Note that the gravitational attraction of the matter of the star is trying to make it smaller; this is balanced by the radiation pressure that is trying to push the matter outward making the star bigger. photograph of a birthplace of stars; http://www.seds.org/hst/M16WF2.html.
After about a billion years the Hydrogen fuel is exhausted. It starts fusing the Helium into heavier elements. The temperature of the star goes up, causing it to become much bigger. In this phase the star is called a "red giant."
When this "fuel" is exhausted, there are three possible outcomes, depending on the total mass of the star:
If the mass of the star is less than about 1.2 solar masses, the star becomes a spinning ball of dead slag, gradually cooling down as it radiates away its thermal energy. It is called a "white dwarf." Its radius is on the order of 5000 km, and the density is about 1 ton per cubic centimeter.
If the mass of the star is greater than about 1.2 solar masses but less than about 3 solar masses, it goes through the white dwarf phase, but the gravitational attraction is so strong that the protons and electrons get fused into neutrons. Thus we end up with a spinning ball of neutrons, a "neutron star." The radius is on the order of 10 km, and the density is about 100 million tons per cubic centimeter. Astronomers believe that they have discovered many of these neutron stars; one of the best known is in the Crab nebula and is the remnant of a supernova that was seen on Earth in year 1054 of the current era. They "see" them because as they spin they emit a sweep of radiation, which we observe has having a regular periodicity. Thus before we knew they were neutron stars they were called "pulsars."
If the mass of the star is greater than about 3 solar masses, it goes through the neutron star stage and keeps collapsing. In this case, the gravitational attraction is so intense the neutrons are literally crushed out of existence. We call the object a "black hole."
Life Cycle of Stars• http://www.redorbit.com/education/reference_lib
rary/universe/stellar_evolution/246/index.html
