---------------------- 1995 - The Natural Constants
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- Run the clock backwards. Past when you were born, past when the Earth was born, past galaxies, back to when the Universe was interconnected at a single point. Reverse time and space again and that was the beginning of our Expanding Universe.
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- For the first 360,000 years the expansion of space and time only contained radiation and charged particles. When the expansion cooled to 3,000 Kelvin ( 5,000 degrees Fahrenheit ) protons and electrons formed neutral atoms. Cold, dark matter began to form. The matter had mass that bent and curved the fabric of expanding space-time. Light (radiation) followed a straight line at a constant speed but through curved space-time which is the same as gravity.
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- Gravity caused space and time to vary depending on its position in this expanding fabric. Gravity slows down time and shrinks space. (Think about that for a minute) Gravity was dominate for the next 7 billion years.
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- Then the repulsion force causing the vacuum of space-time to expand took over as mass became diluted in its expansion. For the next 7 billion years the universe’s expansion began to accelerate. Today it is still accelerating and at an ever increasing rate.
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- Today the Universe is 93 billion lightyears across. The galaxies at the edge are disappearing because there is so much expanding space-time between us the galaxies are receding so fast the light radiation will never reach us. Radiation can only travel at a limited, constant speed of 300,000 kilometers per second and no faster.
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--------------------------- c = 3*10^6 km/sec
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- This is one of the Natural Constants in the Universe. We believe that it is constant every where regardless of position or motion throughout the entire Universe.
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- The strength of gravity is another constant believed to be the same everywhere in the Universe, 0.0000000000667 m^3/kg*sec^2
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----------------------- G = 6.67259 * 10^-11 meters^3 / (kilograms * seconds^2 )
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- That is a very small number. Gravity is by far the weakest force among the 4 forces, Strong and Weak nuclear and electromagnetic.
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- Another Constant is Planck’s Constant of Action ( “h” ) representing the smallest energy change that can be observed, a quantum bit of energy. It is the amount of energy a single photon of electromagnetic radiation carries.
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- Electromagnetic radiation energy varies in direct proportion to frequency.
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------------------------- E = h * f
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- The higher the frequency the greater the energy from radio waves to Gamma Rays. “h” is the constant of proportionality to fit the units of measurement being used.
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------------------------ h = 6.625 * 10^-34 kilograms * meter^2 / seconds
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- We believe these constants of Nature are the same everywhere in the Universe. They are what they are. We have no fundamental laws or equations to derive them. We can only measure them. But, these constants show up in the equations we use to mathematically describe our physical world.
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- In order to measure these constants we need constant units of measurement. To measure the speed of light in meters per second we need a standard length of a meter and a standard duration of time for a second.
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- In 1905 science tried to define the meter as one millionth of a quarter of the Earth’s meridian. We defined the mass of a gram to be one cubic centimeter of pure water at zero degrees Centigrade. These are arbitrary standards and not very accurate depending on the measurement.
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-------------------------- Light speed = c = 299,792,458 meters per second
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-------------------------- Light speed = c = 670,633,500 miles per hour
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------------------------- Light speed = c = 186,282 miles per second
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- And , those speeds are always the same for every observer regardless of his relative motion. (Think about that for a minute) .
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- Time is in the best shape for having a standard of measurement. The kilogram standard became a platinum bar in a vacuum vault in Paris , France. There was also a platinum rod that was exactly one meter long. Thousands of transfer standards were spread around the world so we could communicate with common weights and measures. The time standard used a cadmium light . A green light exactly 6438.4696 Angstroms in wavelength. (643.8 nanometers ). It was used to define 10^-10 meters, 10 nanometers, as one Angstrom.
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- Science has made enormous progress measuring time with accuracy. Using light pulses lasting just 250 attoseconds ( 10^-18 seconds ) from high speed lasers. Time measurements with Cesium beam clocks. They sell for abut $50,000 today and are accurate to a microsecond a month, 5 parts in 10^13.
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- National Institute of Standards and Technology , NIST, has clocks accurate to 5 parts in 10^16. Clocks using lasers on aluminum ions are accurate to 10^18 range. 10^18 precision is less than ½ second over the 14 billion year age of the Universe, which contains 4*10^17 seconds
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- But, there is a limiting factor to time accuracy. Time is distorted by gravity and motion. Gravity is the curvature of space-time. Moving this accuracy from place to place becomes a dilemma . Time slows as gravity gets stronger. Time slows as speed increases. (Think about that for a minute)
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- Is there a better way to deriving true standards for time, mass, length and even temperature? Can it be done using these Natural Constants? Max Planck came up with an interesting way using ratios. Planck mass squared = Planck’s Constant * speed of light / Gravitational Constant :
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---------------------- (mass)^2 = h * c / G
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----------------------- h = 6.6*10^-34 kg *m^2 / sec
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----------------------- G = 6.7*10^-11 m^3 / (sec^2 * kg)
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----------------------- c = 3*10^8 m / sec
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---------------------- m^2 = (6.6 * 3 ) / (6.7) (10^-34) * (10^8) / (10^11) (kg * m^2 /sec) * (m/sec) * ((sec^2 * kg) / (m^3))
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--------------------- m^2 = 29.6*10^-16
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-------------------- m = 5.4 * 10^-8 kilograms
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- The Planck Mass is 0.000,000,054 kilograms, 10^-8 kg is small but a proton is 10^-27 kilograms, an electron is 10^-31 kilograms.
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- We can use the same technique to derive Planck Length ( “r” ):
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--------------------------- r^2 = G * h / c^3
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---------------------------- r^2 = (6.7 *6.6 / 27) (10^-11)* (10^-34 / 10^24) (( m^3 /(sec^2*kg)) * ((kg*m^2)/sec) * (sec^3 / m^3)
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--------------------------- r^2 = 16.4*10^-70 m^2
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-------------------------- r = 4 * 10^-35 meters
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- 10^-35 meters is the shortest distance that can exist. A very small quantum brick. If you counted off one Planck Length per second it would take 1,000 times the age of the Universe to measure the diameter of an atom . ( See footnote 1)
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- Planck Time ( “t” ) :
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--------------------- t^2 = G * h / c^5
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--------------------- t^2 = (6.7 *6.6) / (243) ( 10^-11)* (10^-34) / (10^40) (( m^3 /sec^2 * kg) * (kg * m^2) / (sec) * (sec^5 / m^5)
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----------------------t^2 = 1.82*10^-86 sec^2
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---------------------- t = 1.35*10^-43 seconds.
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- That is the smallest amount of time, a Planck Second. It is quantum time.
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- There is also a Planck Temperature that is really hot:
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---------------------- T^2 = h*c^5 /( G * K)
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---------------------- T = 3.5 *10^32 Kelvin
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- “K” is Boltzmann’s Constant which is a conversion from units of energy to units of temperature. This must have been how hot it was at the start of the Big Bang.
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- There is the Fine Structure Constant (Alpha) that links the speed of light to Planck’s Constant for electric charge governing the strength of electromagnetism.
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-------------------- Alpha = (137.035989561)^-1
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------------------- Alpha = 2 * pi * h / e^2
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------------------- “e” is the constant for electric charge
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------------------- e = 1.602*10^-19 ampere - seconds.
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---------------------ampere = 1.46*10^19 electrons per second.
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- The Cosmological Constant is the ratio of Dark Matter to Dark Energy. It is the energy density in the vacuum of space. It is the repulsive force opposing gravity and causing the Universe to accelerate in its expansion. (Think about that for a minute)
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- There are more constants in Nature. Most are so delicate that if they changed ever so slightly , even the Universe would not exist as we know it. Life to a computer scientist is the ability to process and store information. To a biologist it is the faculty to evolve by natural selection. To a chemist it is non-equilibrium energy flows. To a priest it is a mystery we turn over to God.
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- (Footnote 1) Diameter of an atom 10^-15 meters
------------------ 3.16 *10^7 seconds / year * 14 * 10^9 years = 44 * 10^16 seconds
----------------- One Planck length per second = 10^-35 * 4.4*10^17 = 10^-18 meters
----------------- 10^-18 to 10^-15 needs another 1,000 times , 10^3.
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- Other Reviews available upon request:
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- #1772 - Fine Structure Constant. A new standard for mass could be energy from atomic Cesium, E = h*f / c^2. Mass of an electron is 9.10938188*10^-31 kilograms. How accurate is the kilogram?
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- # 1336 - Mystery of the Fine Structure Constant.
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- # 938 - Gravity has by far the weakest coupling constant which is its strength of interaction.
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- #1108 - Forces of Nature: Strong = 1, , Electromagnetic = 1/137 = Alpha? = 0.007 . Weak = 10^-6 , Gravity = 10^-39.
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- #406 - Absolute zero temperature. T^2 = G * h / 2*pi*c^5
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- #368 - Time comes to us in particles 10^-43 seconds each.
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- #6 - Big Bang’s first creations.
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