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Large Number Hypothesis
Universal Constants
 In physics, many numbers that we believe do not
change with time, they are “universal constants”.
 4 so-called universal constants of nature:
1.
2.
3.
4.
speed of light, c
Gravitational constant, G
Planck constant, h
Boltzmann constant, k
•appear unchanged over time
•valid throughout the entire
universe
Speed of light, c
 c = 3.00 x 108ms-1
 Light is an electromagnetic wave, the speed of light is a
constant.
 When light travels through a medium, e.g., glass, its
speed is reduced according to the density of the glass.
Speed of light in air = c
Speed in medium (eg. glass) < c
Gravitational constant, G
 Any two objects attract each
other with a force proportional
to the product of their masses
divided by the square of their
separation.
 The constant of proportionality,
called G, is what is known as
the Gravitation constant.
 G = 6.67 x 10-11Nm2kg-2
 Einstein's theory of General
Relativity reinterprets the
meaning of G in terms of the
curvature of space-time around
the objects.
Planck constant, h
 Planck’s theory of quantized energy, which we now
called quantum theory.
 Electromagnetic radiation was not just a continuous
wave, radiations are emitted or absorbed in discrete
units called “quanta”.
 The energy of these quanta is proportional to the
frequency of the radiation. The constant of
proportionality called Planck constant.
 h = 6.63 x 10-34 Js
Boltzmann constant, k
 The product of the pressure and volume is
proportional to the number of molecules times
the temperature.
 The constant of proportionality is known as the
Boltzmann constant k.
 k = 1.38 x 10-23 JK-1
Large Number Hypothesis （LNH）
 It was first conceived and coined by the famous
physicist Paul Dirac 。
 Several very large dimensionless numbers of the order ~
「1039」 are constructible from certain physical
parameters of nature.
 Example：
The ratio of the Coulomb force (the force between
electromagnetic charges) to the gravitational force (the
force between masses in the universe) for a protonelectron pair is of the order of 1039.
 An example for contrast, the ratio of the Planck
constant and the electric charge is about 137.
 Dirac believes these large dimensionless
numbers are somewhat related to each other, e.g.,
a relationship exists between cosmological and
microscopic processes.
The ratio of the gravitational and the coulomb forces is not a
constant, but increases proportionally with the age of the
universe.
Are the universal constants (G、c、h、k) is not constant?!
Value of G
 Value of G which differs from the previous accepted
value by 0.1% to 0.7%.
 Two possibilities exist:
1. we underestimated the uncertainty in our
measurement of G;
2. G actually varies with time.
 Einstein's theory of relativity requires G to be a constant.
→ This theory have to be modified if G varies with time!
Fine Structure Constant
 the fine structure constant is a combination of electric
charge, Planck constant and speed of light. It measures
the strength of interactions between charged particles
and electromagnetic fields.
 Results from spectral analysis of “quasars” indicates
that this constant varies with time.
 Then, which constant varies with time：
the electric charge? the Planck constant? or the speed of
light?
Amount of Substance in the Universe
 Amount of Particles in the universe is
estimated to be about 1078, which is equal to
the square of the age of the universe.
 May the amount of particles in the universe
increase with the square of the age of the
universe?
In other words, may new matter be
continually being created?
Models of the Universe
 3 different models of the universe: the open, the closed and
the stationary model.
 The open model：the universe is forever expanding and
there will be no end of the universe.
The closed model：at some point in the future, the universe
will collapse into a point, denoting the end of the universe.
The stationary model：the universe neither expands nor
contracts, just remain as it is.
 From modern observation, the universe is expanding ;
 The maximum size of universe predicted by the close model
is not supported by the age of the universe；
 What remains is the open universe.
Conclusion
 Dirac conclude that there are two different time
evolutions in nature that are closely related to one
another:
The time evolution which governs
the motions of galaxies, planets, and
the evolution of the Universe.
The time evolution which
governs the periodic vibrations
of atoms and the atomic time
Appear in Einstein's theory of
gravitation, or the general
theory of relativity.
Appears in the theory of
atoms, or the quantum theory
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