Large Number HypothesisLarge Number Hypothesis

Universal ConstantsUniversal Constants

In physics, many numbers that we believe do not In physics, many numbers that we believe do not change with time, they are change with time, they are “universal constants”“universal constants”..

4 so-called universal constants of nature:4 so-called universal constants of nature:

1.1. speed of light, c speed of light, c

2.2. Gravitational constant, G Gravitational constant, G

3.3. Planck constant, h Planck constant, h

4.4. Boltzmann constant, kBoltzmann constant, k

•appear unchanged over time

•valid throughout the entire universe

Speed of light, Speed of light, cc

c = 3.00 c = 3.00 xx 10 1088msms-1-1

Light is an electromagnetic wave, the speed of light is a Light is an electromagnetic wave, the speed of light is a constant.constant.

When light travels through a medium, e.g., glass, its speWhen light travels through a medium, e.g., glass, its speed is reduced according to the density of the glass. ed is reduced according to the density of the glass.

Speed of light in air = c Speed in medium (eg. glass) < c

Gravitational constantGravitational constant, , GG Any two objects attract each otAny two objects attract each ot

her with a force proportional to her with a force proportional to the product of their masses divithe product of their masses divided by the square of their separded by the square of their separation.ation.

The constant of proportionality,The constant of proportionality, called G, is what is known as t called G, is what is known as the Gravitation constant. he Gravitation constant.

G = 6.67 G = 6.67 xx 10 10-11-11NmNm22kgkg-2-2 Einstein's theory of General ReEinstein's theory of General Re

lativity reinterprets the meaninlativity reinterprets the meaning of G in terms of the curvature g of G in terms of the curvature of space-time around the objectof space-time around the objects.s.

Planck constantPlanck constant, , hh

Planck’s theory of quantized energy, which we now callPlanck’s theory of quantized energy, which we now called quantum theory.ed quantum theory.

Electromagnetic radiation was not just a continuous waElectromagnetic radiation was not just a continuous wave, radiations are emitted or absorbed in discrete units cve, radiations are emitted or absorbed in discrete units called “alled “quantaquanta”.”.

The energy of these quanta is proportional to the frequeThe energy of these quanta is proportional to the frequency of the radiation. The constant of proportionality callncy of the radiation. The constant of proportionality called Planck constant.ed Planck constant.

h = 6.63 h = 6.63 xx 10 10-34-34 Js Js

Boltzmann constantBoltzmann constant, , kk

The product of the pressure and volume is propoThe product of the pressure and volume is proportional to the number of molecules times the temrtional to the number of molecules times the temperature.perature.

The constant of proportionality is known as the The constant of proportionality is known as the Boltzmann constant k.Boltzmann constant k.

k = 1.38 k = 1.38 xx 10 10-23-23 JK JK-1-1

Large Number HypothesisLarge Number Hypothesis （（ LNHLNH）） It was first conceived and coined by the famous physicisIt was first conceived and coined by the famous physicis

t Paul Dirac t Paul Dirac 。。 Several very large dimensionless numbers of the order ~ Several very large dimensionless numbers of the order ~

「「 10103939 」」 are constructible from certain physical paramare constructible from certain physical parameters of nature.eters of nature.

ExampleExample ：：The ratio of the Coulomb force (the force between electrThe ratio of the Coulomb force (the force between electromagnetic charges) to the gravitational force (the force bomagnetic charges) to the gravitational force (the force between masses in the universe) for a proton-electron pair etween masses in the universe) for a proton-electron pair is of the order of 10is of the order of 103939..

An example for contrast, the ratio of the Planck cAn example for contrast, the ratio of the Planck constant and the electric charge is about 137.onstant and the electric charge is about 137.

Dirac believes these large dimensionless numberDirac believes these large dimensionless numbers are somewhat related to each other, e.g., a relatis are somewhat related to each other, e.g., a relationship exists between cosmological and microsconship exists between cosmological and microscopic processes.opic 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 GValue of G

Value of G which differs from the previous accepted Value of G which differs from the previous accepted value by 0.1% to 0.7%. value by 0.1% to 0.7%.

Two possibilities exist:Two possibilities exist:

1. we underestimated the uncertainty in our measur1. we underestimated the uncertainty in our measurement of G;ement of G;

2. G actually varies with time. 2. G actually varies with time.

Einstein's theory of relativity requires G to be a constant.Einstein's theory of relativity requires G to be a constant.

→→ This theory have to be modified if G varies with time!This theory have to be modified if G varies with time!

Fine Structure ConstantFine Structure Constant

the fine structure constant is a combination of electric cthe fine structure constant is a combination of electric charge, Planck constant and speed of light. It measures thharge, Planck constant and speed of light. It measures the strength of interactions between charged particles and e strength of interactions between charged particles and electromagnetic fields.electromagnetic fields.

Results from spectral analysis of “Results from spectral analysis of “quasarsquasars”” indicates th indicates that this constant varies with time.at this constant varies with time.

Then, which constant varies with timeThen, which constant varies with time ：：the electric charge? the Planck constant? or the speed of the electric charge? the Planck constant? or the speed of light?light?

Amount of Substance in the UniverseAmount of Substance in the Universe

Amount of Particles in the universe is estimaAmount of Particles in the universe is estimated to be about ted to be about 10107878, which is equal to the sq, which is equal to the square of the age of the universe.uare of the age of the universe.

May the amount of particles in the universe May the amount of particles in the universe increase with the square of the age of the unincrease with the square of the age of the universe?iverse?

In other words, In other words, may new matter be continualmay new matter be continually being created?ly being created?

Models of the UniverseModels of the Universe 3 different models of the universe: 3 different models of the universe: the openthe open, , the closedthe closed and and tt

he stationaryhe stationary model. model. The open modelThe open model ：： the universe is forever expanding and thethe universe is forever expanding and the

re will be no end of the universe. re will be no end of the universe. The closed modelThe closed model ：： at some point in the future, the universe at some point in the future, the universe will collapse into a point, denoting the end of the universe.will collapse into a point, denoting the end of the universe.The stationary modelThe stationary model ：： the universe neither expands nor cothe universe neither expands nor contracts, just remain as it is.ntracts, just remain as it is.

From modern observation, the universe is expanding ;From modern observation, the universe is expanding ; The maximum size of universe predicted by the close model The maximum size of universe predicted by the close model

is not supported by the age of the universeis not supported by the age of the universe ；； What remains is the What remains is the open universeopen universe..

ConclusionConclusion Dirac conclude that there are two different time evolutioDirac conclude that there are two different time evolutio

ns in nature that are closely related to one another:ns in nature that are closely related to one another:

The time evolution which governs the motions of galaxies, planets, and t

he 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 the

ory of relativity.

Appears in the theory of atoms, or the quantum theory

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