ON TIME

1
ON TIME

• An Introduction into the theory behind Albert
  Einsteins Special Relativity

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Relativity in a nutshell

• Qn What would a beam of light look like if you
  were to race alongside it?
• According to Newton, one could catch up to any
  moving object if one could travel fast enough.
• Einstein realised that if that were to happen,
  the wave would appear to be frozen in time
• This is against the laws of physics.

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Relativity in a nutshell

• Einstein observed that the speed of light in
  vacuo appeared to be some sort of cosmic speed
  limit that nothing can surpass- a cosmological
  constant
• This is because the speed of light is absolute in
  all frames of reference - it always appears to be
  the same regardless of ones speed
• This led to the creation of the Special Theory of
  Relativity in 1905.

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Time Dilation

• Remember that the speed of light is constant in
  all frames of reference- but how does this work?
• Imagine an electron travelling at 0.8c racing
  alongside a stream of photons

Photons

• From your frame of reference, you would see the
  electron almost keeping up with the photons

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Time Dilation

• BUT from the electrons frame of reference, no
  matter how fast it can travel, the photons will
  seem to be racing ahead at their usual pace (c).
  This is because the speed of light is the same in
  all frames of reference.

Photons
???!

• This is the time dilation effect. Time itself
  had slowed down for the electron!

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Time Dilation

• The time dilation effect The faster an object
  travels, the slower time passes for it.
• Let us now take the path that an object at rest
  and a moving object trace through time. Time
  elapses slower for the moving object as compared
  to the object at rest.

OR
1s
OM
1s
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Time Dilation

• Because time now passes by more slowly for the
  electron (due to its high speed) as compared to
  the photons, from the electrons frame of
  reference it would then appear to be travelling
  much more slowly compared to the photons
• This is because light is not subject to time
  dilation. (Principle of non-invariance)

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Distance/Time comparison
Time comparison
1s
1s
. Due to time dilation, when 5s have elapsed for
the photon, only 3s have elapsed for the electron
travelling at 0.8c, from its frame of reference.
Distance comparison
D/s
D/s
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Time Dilation

• The time dilation factor, or Lorentz factor, can
  be calculated using the formula (1-v2/c2)-1/2
• E.g. For the electron travelling at 0.8c, the
  Lorentz factor would be (1-0.82/1.02)-1/2 1.67,
  i.e. when one second has elapsed for the
  electron, 1.67 seconds would have elapsed for the
  photon (or for any other object at rest, for that
  matter.)

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Muon Decay

• Muons are inherently unstable particles that
  decay in a matter of a microseconds
• Muons created by cosmic-ray impacts in the upper
  atmosphere can travel all the way deep
  underground. Their presence is recorded by Geiger
  counters.
• Yet, in the time taken for a muon to decay, even
  light travels less than a kilometre. So why are
  these muons able to travel such a great distance
  (20km) to ground level?

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Muon Decay

• This is because the time dilation effect results
  in the muons appearing to age slower than they
  should!
• When a few microseconds have elapsed for the
  muon, much more time would have elapsed for an
  observer at rest.

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Length Contraction

• The length contraction effect The faster an
  object travels, the shorter it appears to be to
  an observer at rest. The distance travelled by
  the object will also appear to be shortened from
  the objects frame of reference.
• The length contraction factor can be calculated
  using the formula (1-v2/c2)1/2, where the result
  would be the apparent length of the object in
  comparison to the actual length of the object.

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Length Contraction

• To demonstrate this effect, lets say a
  familiar-looking electron (0.8c!) wants to travel
  from Point A to Point B, 240 000m away.

From a stationary observers frame of reference
B
A
Distance travelled in one second

• The electron would have taken 1 second to travel
  from A to B since 0.8 X 300 000m (distance
  travelled by light in one second) 240 000m.

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Length Contraction

• But, due to time dilation, when 1 second has
  elapsed for the observer, only 0.6 seconds would
  have elapsed for the electron.
• Also, due to length contraction, the electron
  would have perceived itself to have only
  travelled (1-0.82/1.02)1/2 0.6 times the actual
  distance of 240 000m

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Length Contraction

• From its frame of reference, the electron would
  have travelled only 0.6 X 240 000 144 000m
• 144 000m/0.6s 240 000 m s-1 0.8c
• Hence, the resulting velocity would still remain
  unchanged. This is because velocity is an
  inherent property of an object and cannot be
  changed without the presence of an external
  force.
• This shows how time dilation and length
  contraction are interrelated.

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Gravitational Timewarping

• Motion is not the only thing that causes time
  dilation to occur the effect of gravity can slow
  time down as well.
• The stronger the gravitational influence, the
  slower time passes by.
• This is in part due to Einsteins equivalence
  principle which states that the effects of
  acceleration are equal to the effects of
  gravitation.

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Gravitational Timewarping

• When a light-emitting body accelerates away from
  you, the light that reaches you will be
  continuously red-shifted (i.e. its frequency will
  be lowered) due to the Doppler effect.
• Replace the accelerating body with a
  gravitational body, and this would mean that
  light travelling away from the body will undergo
  a lowering in frequency as well.

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Gravitational Timewarping

• Since frequency is a measure of the number of
  waves per second, a lowering of frequency as a
  result of the gravitational red-shift would also
  mean a reduction in the number of waves per
  second.
• If the number of waves per second is reduced as
  light travels away from the gravitational object,
  this would mean that time itself is speeded up as
  the distance increases.

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Gravitational Timewarping
As the number of waves per second decreases with
increasing distance from the gravitational body,
a reverse time dilation effect occurs
1 s
the length of one second appears to get shorter
and shorter as time speeds up.
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Moving On

• So is the secret to outlasting your peers
  running around very fast in the basement?
• Anyway, now that were done with the key aspects
  of Special Relativity, let us now move on to more
  abstract ideas of time and space

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The Speed of Time A Theory

• Some of you might be wondering why is it that
  makes light so special? Why is the speed of light
  absolute in all frames of reference? Why isnt
  light affected by relativity?
• As for now, the answer is we dont know. But for
  the moment, heres our take on the matter.

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The Speed of Time A Theory

• Suppose that there is actually more than one type
  of time Time as the fourth dimension (or the
  time that we know it), and time as a temporal
  force that can travel alongside us as we trace
  out our passage through 4th dimensional time.
• Most of us would think that we experience the
  passage of time due to our movement forward in 4D
  time. The speed of our movement through time
  would depend on the speed of our motion through
  3D space.

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The Speed of Time A Theory

• But what if I told you that there exists a
  temporal force that also travels alongside us as
  we travel forward on our timeline?
• This temporal force would consist of particles of
  time known as temporons, which are 10-45s
  (quantum) units of time.
• We would then experience the passage of time due
  to the passage of these temporons through us.

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The Speed of Time A Theory

• Now, an observer at rest would experience the
  full effects of these temporons zipping through
  him
• Since he is not moving and the temporons are
  moving at a very high speed, time passes by
  quickly for him.
• But suppose he starts to move. The temporons
  would now pass by slower relative to him in his
  frame of reference, and thus, time would appear
  to be slowed down, or dilated!

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The Speed of Time A Theory

• As he moves faster and faster, time gets more and
  more dilated.
• According to the Lorentz formula, when one
  reaches the speed of light, time is dilated
  completely and thus time would then logically
  stop.
• This is where the magic of this theory comes in
  A potential explanation for the non-invariance of
  light!

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The Speed of Time A Theory

• According to the theory, we experience time
  passing by when temporons pass through us.
• If we travelled at the speed of light and if time
  were to stop, however, this would mean that no
  temporons are passing us by!
• Now suppose these temporons actually travel at a
  specific speed the speed of light.

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The Speed of Time A Theory

• This would mean that when WE travel at the speed
  of light, no temporons would then be able to pass
  through us since we are travelling at the same
  speed as they are! The result would be a time
  stoppage exactly the result predicted by time
  dilation!
• Nowwhat would happen if we then chose to travel
  faster than the speed of light???

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The Speed of Time A Theory

• According to the theory, we would theoretically
  be able to catch up with the temporons racing in
  front of us and experience time in reverse! This
  effect has also been predicted by the Lorentz
  formula!
• So, is it really possible to travel backwards in
  time? Could this theory in fact be the
  explanation for time dilation, and therefore, the
  principle of non-invariance after all?

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ONLY TIME WILL TELL.
Questions, anyone?