What's Dirac's Large Number Hypothesis ?

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In summary, Dirac's Large Number Hypothesis states that the ratio of the electrostatic force to gravitational attraction is equal to the ratio of the size of the universe to the size of an electron. This suggests that there is a connection between the size of the universe and the fundamental constants of nature. Additionally, the hypothesis proposes that particles may have a finite "horizon" or limit to their wavefunction, and that the observable universe is likely infinite or transfinite in volume. The equation m = (c^2/G)r shows a relationship between mass, the speed of light, and the Schwarzschild radius, providing further evidence for the hypothesis.
  • #1
Antonio Lao
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What's Dirac's Large Number Hypothesis ?

In 1938, Dirac noted that the ratio of the electrostatic force between and electron and a proton to their gravitational attraction was approximately equal to the ratio of the size of the universe to the size of an electron )[itex]10^{-20} [/itex] cm.

[tex] \frac{F_{elec}}{F_{grav}} \sim \frac{Size_u}{Size_e} \sim 10^{39} [/tex]

If we equate the gravitational acceleration of some mass, m, to the centripetal acceleration which depends on the velocity of this mass and as this velocity approaches the speed of light in vacuum then this mass is related to a large number product with radius of circular motion.

[tex] m = \left( \frac{c^2}{G} \right) r [/tex]
 
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  • #2
Could be that everything has a wavefunction limit, every particle has a finite 'Horizon', the limit of which is scale dependant?

The size 'apparent', of the Universe is not fully known. therefore the any ratio of Universe size must be governed by an actual particle, not by the actual Universe.

Particles may know the size of the Universe in relation to themselves?
 
  • #3
Olias said:
The size 'apparent', of the Universe is not fully known.

Based on the large number hypothesis, the size of the universe is roughly 10 billions light-years across. What is the corresponding increase in distance for a degree decrease in temperature?
 
  • #4
size considerations concern only the observable universe- the actual volume is almost certainly infinite/transfinite based on all the evidence we have-


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  • #5
The equation [itex] m = \left( \frac{c^2}{G} \right) r [/itex] implies that [itex]r[/itex] is equal to 1/2 the Schwarzschild radius, [itex]R[/itex].

[tex] R = \frac{2 G m}{c^2} [/tex]

The factor

[tex] \left( \frac{2 G}{c^2} \right) [/tex]

is a very small number.
 

1. What is Dirac's Large Number Hypothesis?

Dirac's Large Number Hypothesis is a theory proposed by British physicist Paul Dirac in 1937. It suggests that there is a fundamental relationship between the large dimensionless numbers in cosmology and the fundamental constants of nature, such as the speed of light and the gravitational constant.

2. How does Dirac's Large Number Hypothesis relate to the size and age of the universe?

According to Dirac's Large Number Hypothesis, the age of the universe is related to the size of the universe through a fundamental constant known as the Dirac number. This number is thought to be related to the ratio between the size of the universe and the size of the smallest particle, suggesting that the universe is expanding at a rate proportional to its size.

3. What evidence supports Dirac's Large Number Hypothesis?

There is no direct evidence that supports Dirac's Large Number Hypothesis, but it is consistent with current observations of the universe. For example, the hypothesis predicts that the universe is expanding at a rate that is proportional to its size, which is supported by observations of distant galaxies. Additionally, the hypothesis is supported by the fact that many of the large dimensionless numbers in cosmology are close to powers of the inverse of the Dirac number.

4. What is the significance of Dirac's Large Number Hypothesis in modern physics?

While Dirac's Large Number Hypothesis is not widely accepted in modern physics, it has influenced many theories and hypotheses in cosmology and particle physics. It has also led to further research and exploration of the fundamental constants of nature and their potential relationships.

5. Has Dirac's Large Number Hypothesis been proven or disproven?

No, Dirac's Large Number Hypothesis has not been proven or disproven. It remains a hypothesis and has not been widely accepted in the scientific community due to the lack of direct evidence. However, it continues to be a subject of interest and research in the fields of cosmology and particle physics.

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