Time for an Empirical View

1
Time for an Empirical View?

• Do the laws of physics suggest an arrow of
  time?
• Nature of time Newton vs. Einstein
• Unification What do the latest theories of
  physics
• suggest about the nature of time?

2
Does What We Know About Physics Suggest an
Arrow of Time?

• The laws of physics (mechanics, kinetic theory,
  nuclear theory,) are in general time symmetric
• Yet there are several important physical ideas
  which may be used to establish a temporal
  asymmetry - a direction of time

3
Times Arrows

• The Thermodynamic Arrow
• Entropy and the Second Law of Thermodynamics
• The Cosmological Arrow
• The Expansion of the Universe
• The Quantum Arrow
• The Collapse of the Wave Function
• The Radiative Arrow
• Expanding wavefronts
• The Psychological Arrow
• The relentless forward temporal progression

4
The Cosmological Arrow The Expansion of the
Universe

• Distinguishes between past and future - matter in
  the universe was more compressed in the past, and
  will be more dispersed in the future.
• Will the universe stop expanding?

5
The Thermodynamic Arrow - Entropy

• Heat always flows spontaneously from hot objects
  to cool ones - the reverse never takes place
  (without the input of energy)
• Heat flows in a particular direction
• This is one form of the Second Law of
  Thermodynamics

6

• The second law is one of the most general laws
  in physics
• - it can be expressed in many different, yet
  equivalent, ways
• - it applies to practically everything (matter
  in any form)
• General statement The entropy, S, of an isolated
  system never decreases
• or mathematically
• DS ? 0 where S k lnW

7

• D S ? 0 where S k lnW
• Reversible process DS 0
• Irreversible process DS gt 0
• k Boltzmanns constant (proportionality)
• W number of available microstates (possible
  arrangements)
• W 1 (S 0) ? a completely ordered state
• W ? ? (S ? ?) ? a completely disordered state

8
What have we here? An arrow of time!

• Weve found...
• increase in entropy ? increase in time
• The second law allows us to
• distinguish between future and past
• an asymmetry in time!
• Note! Nothing is said about the flow of time -
  only that the universe appears different in the
  two temporal directions

9

• Use of the word Law
• Second law tells us that if an isolated system
  undergoes a spontaneous process, its final state
  will be one in which the entropy (and also W) is
  a maximum
• BUT, it is NOT a fundamental law - Rather, it
  represents a statistical process

10

• For systems with a very small number of particles
  (with only a few number of available states),
  this lower entropy state is observed - e.g.,
  Brownian motion.
• But, for macroscopic systems (1023 particles),
  the probability that the entropy will actually
  decrease is exceedingly small.

11
(No Transcript)
12
Plot number of green squares vs move
For a 30x30 grid
13
Can entropy establish a physical arrow of time?

• Large scale fluctuations are unbelievably
  improbable. If large fluctuations did take
  place, the arrow of time would be lost
• The improbability of large fluctuations
  guarantees that the arrow of time will not
  disappear in the world around us
• The thermodynamic arrow of time may depend upon
  statistical averages, however it is very real.
  The arrow of time exists not only in the events
  that happen around us, but also in the universe
  as a whole - the direction of time is not a local
  phenomenon

14
Prices Criticism of Our View of Time

• Archimedes Point The view from nowhen
• Price double standard fallacy human
  perspective within time, distorts and exaggerates
  differences between past and future
• Must overcome our natural tendency to think about
  past and future differently by imagining a
  point outside time an Archimedean view from
  nowhen from which to observe time in an
  unbiased way

15
Newtonian ideas of space and time

• From Principia (1684)
• Time and space are separate, and form the
  foundation of science (unchanging backdrop)
• Time Absolute, true, and mathematical time, of
  itself and from its own nature, flows equably,
  without relation to anything external
• Space Absolute space, in its own nature,
  without relation to anything external, remains
  always similar and immovable

16
Einsteins ideas of space and time

• From 1905 papers
• Time and space are entwined and malleable
• Time NOT absolute depends on state of motion
• Space NOT absolute depends on state of motion

17
Special Relativity

• Only notable at high speeds (v gt 10 the speed of
  light)
• Deals with the relative motions (at constant
  speed) between objects how observers in
  different states of motion will measure (NOT
  perceive) time and space
• INERTIAL FRAMES Frames in uniform motion
• No experiment can distinguish rest versus
  constant
• velocity

18
Special Theory of Relativity (1905)

• The special theory of relativity is based on two
  postulates  
• 1) No test of the laws of physics provides any
  way to distinguish one inertial reference frame
  from another. (Any frame moving at constant
  velocity is as good as any other as far as the
  laws of physics are concerned.)
• 2) The speed of light in a vacuum is a constant
  independent of the motion of the source or
  observer.

19
Relativity and Time
Observers in relative motion will see different
order for events
20
Relativity and Time
Each observer carries their own reference frame
of time and space which differs from that of
other observers who are in a state of relative
motion
So, which is the real time?
BOTH! There is no absolute time each observer
carries their own measure of space and time based
on their state of relative motion to other
observers
21
Does Physics Permit Time Travel?Does Philosophy?
Even philosophy must give way to the laws of
physics - Spock
Time flies like an arrow, fruit flies like a
banana - Marx

• Paradoxes of time travel and
• implications to our conception of causality
• Is time travel logically possible? (Lewis - The
  Paradoxes of time travel)
• Is backwards causation patently absurd?
  (Dummett - Bringing about the past)
• Can an event cause itself? (Horwich - Closed
  causal chains)

22
Is time travel logically possible? Lewis - The
Paradoxes of time travel

• Godel (1949) - Claims time travel backwards in
  time is possible
• Objections
• 1) Isnt time travel an oxymoron? (David Lewis
  frames his argument in terms of external time
  versus personal (proper) time)
• 2) Leibniz Law - (Personal identity) Identical
  objects have all the same properties
• 3) Backwards Causation - Disparity between
  personal and
• external time - causation runs earlier to
  later in personal time
• 4) Changing the past - Whatever has happened
  cannot be undone
• Autoinfanticide - Changing the past (logical
  impossibility) versus influencing the past (just
  because you didnt do something doesnt mean that
  you couldnt have done it)

23
Relativity and Quantum Mechanics
Both relativity, which deals with the very large,
and quantum mechanics, which deals with the very
small, treat time as individual points, which
join together to form a continuum ? Laws of
physics are based on continuous conception of
time Problem Relativity and quantum theory
cannot be united Search for a quantum theory
of gravity
24
(No Transcript)
25

• Is Time Discrete (Discontinuous)?
• The concept of a fundamental interval of time, a
  chronon, dates to antiquity
• So how is it that our conventional view is of a
  time continuum, why do we think time is
  continuous?
• Ordinary experience of time is that it is
  continuous we are not
• aware of any sudden jumps "in time" of the
  world around us
• Since the advent of mathematically formulated
  theories of
• mechanics, time has been modeled as a real
  valued parameter which
• takes all possible values in some interval -
  explicitly assuming that
• time is continuous
•  
• Although there have been suggestions that
  space-time may have a discrete structure I see no
  reason to abandon the continuum theories that
  have been so successful.
• Stephen Hawking

26
Towards a Quantum Theory of Gravity
Leading candidates String Theory Assumes
continuous nature of time Loop Quantum Gravity
Makes no assumptions about the nature of
time discrete time is a mathematical
consequence of theory
27
Loop Quantum Gravity
What is fundamental unit of space and
time? Smallest length Planck length 10-33cm
Related to strength of gravity, size of quanta
and speed of light Represents scale at which
geometry of space is no longer continuous Smalles
t time Planck time 10-43sec Gives scale for
smallest area (10-66cm2) and volume (10-99cm3)
(Note There are thus 1099 quanta of space in
one cm3)
28
Detecting Atoms of Time and Space
Given this small length scale, how can test
whether time and space are discontinuous? Loop
quantum gravity predicts that different
frequencies (colors) of light travel at slightly
different speeds
So, stay tunedwe may yet find the time!