Its About Time

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Its About Time

• Ian Morison
• Gresham Professor of Astronomy

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Time is natures way of preventing everything
happening at once.

• John Wheeler

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Local Solar Time
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Sundials
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Water Clock
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Pendulum Clocks

• Whilst still a student, in 1602, Galileo
  observed the swing of a lamp in Pisa Cathedral
  and timed it with his pulse.

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Galileos Clock
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Huygens Clock
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Temperature Compensated Pendulums
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Local Time Across the UK
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Greenwich Mean Time

• As the Earths orbit is slightly elliptical and
  the Earths axis is inclined to the plane of the
  Solar System, the length of the day changes from
  day to day.

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Variation in the Length of the Solar Day
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• Clocks are set to run so that 24 hrs is the
  average length of the day over one year.
• This means that
• The Sun is not usually due south at midday.
• Sunrise and sunset are not equally spaced about
  midday.

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The Analema
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Equation of Time
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An observation.

• The earliest sunset is around December 12th.
• - 1552 (London)
• The latest sunrise is around December 30th.
• - 0806 (London)
• Evenings are getting lighter, but mornings
  continue to get darker after Christmas.

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A lunar problem

• The problem is that, over time, due to the tidal
  forces of the Moon, the Earths rotations rate is
  gradually slowing - this means that the length
  of time defined by the second is increasing!
• (But short term speeding up occurs too.)

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Ephemeris Time

• For a while, the definition of the second was
  tied down to the motion of the Earth around the
  Sun rather than the rotation of the Earth.
• This was known as Ephemeris Time (ET).
• In 1956 the IAU recommended that the second be
  defined as 1/31,556,925.9747 of a year as
  measured from one spring equinox to the next.

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Universal Time

• GMT was formally replaced by Universal Time (UT)
  in 1928.
• In fact, Britain has never legally moved from
  GMT to UT!
• But it doesnt matter as GMT is identical to UT.

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Atomic Clocks

• Actually Atomic Frequency Standards but, by
  dividing down by an appropriate amount, one can
  get one tick per second which can be counted to
  make a clock.

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Hydrogen Maser
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NPL Caesium Beam Clock

• Louis Essen (right)
• Jack Parry (left)

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Caesium Atomic Fountain

• Lasers are use to bring the caesium atoms to a
  virtual standstill.
• 5 parts in 1016 accuracy!
• 1 second in 60 million years.

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Atomic Time

• In 1967 the definition of the second was changed
  to one based on a Caesium Beam Atomic Frequency
  Standard
• The second is the duration of 9,192,631,770
  periods of the radiation corresponding to the
  transition between the two hyperfine levels of
  the ground state of the caesium 133 atom.

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Leap Seconds

• It may well be that the definition of the second
  was not quite right as, even though the rotation
  rate of the Earth is not changing much at the
  moment, we are having to insert quite a number of
  leap seconds.
• This is usually done on the first of January when
  the accumulated time difference between the time
  measured by the atomic clocks and the Sun differs
  by around a second, so bringing solar and atomic
  time back in step.

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• Since the time definition was changed, 22 leap
  seconds have had to be added, about one every 18
  months, but there were none between 1998 and 2005
  showing the slowdown is not particularly regular.
  
• Had Atomic Time been defined as 9192,631,937
  cycles instead of 9192,631,770, only six leap
  seconds would have been needed!

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Pulsars - the best natural clocks in the universe
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M1The Crab Nebula
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Rotating Beam
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The Crab Pulsar
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Globular Cluster 47 Tucanae
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• One of the best pulsar clocks known at the
  present time is 171307 which has been "spun up"
  by matter falling onto it from a companion white
  dwarf star.

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• It now has a pulse period of 4.57 milliseconds -
  spinning 218.8 times per second - and is
  currently slowing down at a rate of 200
  nanoseconds in 12 years. That is a precision of
  one part in 1,892,160,000,000 better than one
  part in 1013!

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Harrisons Clocks
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Corpus Clock

• Grasshopper Escapement

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Synchronising Time

• Not as easy as you might think!

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Edinburgh Castle One Oclock Gun

• At opposite ends of the Royal Mile.

• Edinburgh Castle
• Holyrood House

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Edinburgh Castle One Oclock Gun

• Sound takes 5 seconds to travel one mile.

• Edinburgh Castle
• Holyrood House

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Edinburgh Castle One Oclock Gun

• Which is why the Queens clocks will be 5
  seconds slow!

• Edinburgh Castle
• Holyrood House

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Greenwich Time
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• In 1852 Charles Shepherd installed a new clock
  outside the gate of the Royal Observatory at
  Greenwich. This was an electrically operated
  clock, one of the earliest ever made, and it was
  controlled by a master clock mechanism inside the
  main building.

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The Bellvilles

• Rather than having people come to the observatory
  to set their clocks, John Henry Belville took the
  time go to the people. He would set the time
  daily on a John Arnold Son chronometer then
  travel around London giving the accurate time for
  a small fee.

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Maria Belvillein 1890

• John Bellville died in 1856 and the role - and
  the chronometer - were then taken over by his
  widow Maria, the first Greenwich Time Lady.

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Ruth Belvillle

• In 1892 Maria passed the family business to her
  daughter Ruth who became the most famous Time
  Lady.
• Every Monday, Ruth Belville visited the
  observatory and had the accuracy of the
  chronometer (which she called "Arnold")
  certified. She then walked around London selling
  on the time. She carried on this service until
  the 1930s.

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Greenwich Time Ball

• In 1833 the Observatory installed a Time ball
  which is dropped at precisely 1pm by an
  electrical system linked to the Master Clock at
  Greenwich.

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Lyttelton Time Ball
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Radio Controlled Clocks

• MSF Time signals are now transmitted from Anthorn
  in Cumbria

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Anthorn MSF Transmitter
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There is still a time delay

• Anthorn to London 480 km distance
• Time delay 480 / 3 x 105 seconds
• 0.0016 seconds
• 1.6 milliseconds

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GPS signals
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Cosmic Time

• How accurately can our clocks measure the time
  scale of the universe?

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Albert Einstein
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Time Dilation

• How might the fact that the Earth and hence our
  clocks are moving through space reduce the
  passage of time as compared to a clock at rest to
  the universe as a whole?

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• The Earth is Orbiting the Sun at 30 km/sec
• The Sun is orbiting the Galaxy at 220 km/sec
• The Galaxy will also be moving through space
  can we measure the combined speed?

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Penzias and Wilson

• Discovered the radiation left over from the Big
  Bang called the Cosmic Microwave Background
  (CMB).

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COBE

• Measured the temperature across the sky to great
  precision.

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• Penzias and Wilson
• COBE

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• We are moving through space at 650 km/sec in the
  direction of the constellation Leo.

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How much will this slow down time?

• Let us make a very simple clock and see what
  happens.

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A Photon Clock

• Our fundamental time period, t1, is given by
• t1 2d / c

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A moving clock
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• By Pythagoras l ((2d)2
  (vt2)2)1/2
• So the time interval between each tick, t2, will
  then be given by
• t2 l / c
  ((4d2 v2t22) / c2 )1/2
• Squaring both sides and cross multiplying gives
• t22c2 4d2 v2t22
• We can now relate t2 and t1 to v by
  substituting for d from above using
• d2
  t12 c2 / 4, giving,
• t22c2 t12 c2
  v2t22
• and so,
• t22 (c2 - v2) t12 c2
• so, finally,
• t2 / t1 c2 / sqrt (c2 -
  v22)

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t2 / t1 1 / sqrt(1 - v2 / c2)

• Only significant as v approaches c.

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• We can now enter our speed with respect to the
  universe, 650 km/sec, into this equation and get
  the ratio 1.0000023.
• This is exceedingly small so, to a very good
  approximation, our clocks can be used to measure
  the time scale of the universe.
• But we should not ignore a consequence of
  Einsteins General Theory of relativity

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Gravitational Time Dilation
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Photon Clock in a spacecraft moving at a steady
speed

• A photon clock in the spacecraft will run slow.

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A photon clock in an accelerating spacecraft

• The photon crosses the craft in a curved path.
• This will be longer than if the spacecraft were
  not accelerating.
• So there is additional time dilation caused by
  the acceleration.

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Constant Speed

• Astronaut is weightless.

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Accelerating

• Astronauts feet will rest on the floor and
  become aware that he has weight.

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• If the acceleration of the spacecraft was the
  same as the value of g (the acceleration due to
  gravity) at the surface of the Earth your
  apparent weight would be exactly the same and you
  could not tell the difference between being in
  the spacecraft or standing on the Earth.

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• Einstein pointed out that there is no way of
  distinguishing between the two scenarios. The
  acceleration due to gravity that we experience
  due to the mass of an object like the Earth is
  exactly equivalent in its effects to those
  experienced by those within an accelerating frame
  of reference.
• This observation became the basis of his General
  Theory of Relativity.

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• If so, we should thus expect that, in the
  presence of matter
• light will follow curved lines through space, not
  straight ones.
• the passage of time will be slowed.
• This is Gravitational Time Dilation.

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• Due to this effect, clocks on the Earths surface
  run slow compared to a clock in free space by
  700 picoseconds per second which is the order of
  1 part in 10-9. This is a far smaller effect
  than caused by our passage through space and can
  thus be ignored when we measure cosmic time.

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NIST, Boulder,at 1650m altitude

• NIST-7 will gain 15.6 nsec per day relative to a
  clock at sea level.

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The Global Positioning System

• GPS

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Atomic Clocks in GPS satellites

• As the Satellites are moving with respect to
  those on Earth they will appear to lose 7.1
  microseconds a day BUT ..

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Atomic Clocks in GPS satellites

• The atomic clocks on the satellite are in a
  gravitational field that is only ¼ of that on
  Earth and so they will run faster by 45.7
  microseconds per day.

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GPS

• Taking account of the 7.1 microseconds slowdown
  relative to clocks on Earth due to the Special
  Theory of Relativity the GPS clocks would gain
  38.6 microseconds a day.
• This would give an error of 10 km after one day!

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Spacetime

• The bringing together of space and time into a 4
  dimensional universe.

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Flat two-dimensional space

• d is a vector that has a length and a
  direction.
• d2 x2y2
• Given a length d, then, if the component in
  the y direction is increased, then that in the x
  direction must be reduced.
• d is said to be invarient.

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Combining Time and Space

• To make things simpler (without changing the
  basic idea at all) let's reduce the number of
  space dimensions to one so we have just one
  dimension in space (say x) along with one in
  time.
• This causes a problem!

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• The problem is that we cannot mix different
  "dimensions" such as length and time. This is
  easily got round converting time into length by
  multiplying time by a speed.
• So, instead of time, we multiply the time by a
  constant speed, let's call it c, so the resultant
  has the dimensions of length.

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• This should not seem too alien as we use "light
  years" all the time as a unit of length, this
  being a length given by multiplying the speed of
  light by the number of seconds in a year.

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Spacetime Vector, s.

• As seen by different observers who may be moving
  relative to one another, s is invariant but the
  distance and time each measures may well be
  different.

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How can one calculate s?
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• It turns out that there are only two possible
  ways of combining ct and x to give the magnitude,
  s, of the spacetime vector
• s2 (ct)2 x2
• or
• s2 (ct)2 - x2.

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• The first is just Pythagoras again, but if this
  is used to define the length of s, it turns out
  that some observers would actually see the person
  arrive (event B) before he had left (event A).
• A problem with causality.

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• The classic example of a problem involving
  causality is the "grandfather paradox" what if
  one were to go back in time and kill one's own
  grandfather before one's father was conceived?

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This leaves s2 (ct)2 - x2.

• This then, only leaves the second option.
  However, this allows the possibility of breaching
  the requirement of causality unless there is a
  maximum limit to the value at which one can
  travel through space - a cosmic speed limit if
  you like.

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Your friend goes on a rail trip
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• As observed by your friend his position in space
  will not have changed.
• The time interval that he measured on his
  wristwatch will be t1. So, as observed by him
• s2 (c t1)2

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• As measured by you, he will have traveled a
  distance given by vt2 in a time t2. Your
  measurement of the spacetime vector is thus
• s2 (ct2)2 - (vt2)2

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• As the spacetime vector is invariant, these must
  be equal so that
• (c t1)2 (ct2)2 -
  (vt2)2
• This finally gives
• t2/ t1 1 / sqrt(1 - v2/c2) .
  
• This is exactly the formula we derived earlier
  but only if we interpret c as the velocity of
  light.

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The Twin Paradox
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• One twin leaves Earth and travels away at a high
  speed and then comes back.
• But in the point of view of the space twin, the
  twin on Earth could be said to be moving away at
  high speed.
• Why should one be older than the other?

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Acceleration?

• Many authors state that the situation is not
  symmetric as one twin has had to accelerate,
  decelerate, change direction, accelerate and then
  decelerate to get back home.
• Others say that acceleration need not be invoked.

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Clocks travels at 0.6c
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Is Time Travel Possible?
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A Wormhole a shortcut from one part of the
universe to another
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My Space Trip

• I decide to go to the Andromeda galaxy in my Mk10
  spaceship which is parked on the lawn outside my
  lounge. My wife does not like space travel, but
  would like to see what Andromeda is like. We
  make a very short wormhole that goes from our
  lounge into the spaceship.

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• Though this, she can see what is going on as I
  accelerate away to a speed of 99.99999999999999999
  9 of the speed of light and reach (as measured
  on my watch) Andromeda in 4 hours!

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• You might think that the wormhole has to stretch
  - it doesnt. Amazingly, general relativity
  allows it to remain the same length throughout
  the voyage - the further away I am, the better a
  shortcut it is!

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• My wife is able to see Andromeda as the opening
  of the wormhole is conveniently located besides a
  porthole in the spaceship.

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• I turn the spaceship round and head home arriving
  on my lawn 4 hours later and so just 8 hours
  since I left. But everything is different, my
  house can no longer be seen through the porthole
  of the spacecraft.
• I know that by travelling so close to the speed
  of light on my journey I will have travelled just
  over 5 million years into the future. (Andromeda
  is 2.5 million light years away so, as measured
  on Earth, had I travelled at the speed of light
  my return journey would have taken 5 million
  years.)

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• I take a look around and leave the spaceship door
  open. But remember I still have my link
  through the wormhole to my lounge. It is time
  for the supper, so I crawl through the wormhole
  and greet my wife. In doing so I travelled back
  in time 5 million years!

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• My journey has turned a wormhole - a tunnel
  through space - into a tunnel through time and it
  has become a time machine!
• People who lived 5,000,000 years into the future
  at the location of my house could enter the
  spaceship, crawl through the wormhole and travel
  back to the present.

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A significant point
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• It is probably apparent that a significant
  limitation of such a time machine (and all others
  so far proposed) is that it is only possible to
  go as far back in time as the initial creation of
  the worm hole. This means that using such a
  machine will not allow you to go back to a time
  before it was created.

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• As such a time machine has yet to be constructed,
  tourists from the future cannot reach this far
  back in time - which perhaps explains why we do
  not come across them!

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When did time begin?

• When was the origin of our Universe

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Edwin Hubble

• Showed that the
• Universe was
• expanding.

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The Hubble Diagram

• V H0x R where H0 Hubbles Constant

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An Expanding Universe
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The Hubble Time

• 1/ H0 is the age of the universe if we make
  the (incorrect) assumption that the expansion has
  been constant.
• From Hubbles value of his constant (500
  km/sec/Mpc) he got an age of 2,000 million
  years.
• Current best value is 72 km/sec/Mpc.
• This gives 13.6 Billion years

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A quandary

• We actually believe that the universe is 13.6 to
  13.7 Billion years old.
• So our uniform expansion calculation is giving
  the right answer!
• But the Universe has NOT expanded uniformly.
• So why is our result right????

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More by luck than judgement!
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The Origin of Time

• Assuming, as St Augustine said The universe
  began with time, not in time. Our clocks should
  read 13.7 billion years.
• But some cosmologists believe that our
  universe was created by the coming together of
  two branes moving in a higher unseen dimension
  and, if so, time existed before the Big Bang and
  the cosmos (that is the totality of everything)
  could be far, far older.

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We may never know!
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My time has run out.