Friday, June 9, 2023

4045 - EXPANDING UNIVERESE - god only knows this?

 

-    4045  -     EXPANDING  UNIVERESE  -  god only knows this? For the giant void to exist under  observations the giant void would have to be nearly spherical and our galaxy would have to be nearly in the center.  The void would have to be larger than we could detect and the Universe’s inhomogeneity would have to exist beyond our detection. And, it is expanding

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------------   4045   -  EXPANDING  UNIVERESE  - god only knows this? 

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-  In 1902 Hendirk Lorentz invented the equation for how mass would have to increase with velocity in order to keep the speed of light a constant, 300,000,000 meters / second.

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-------------  Mass moving  =  mass /  (1-v^2/c^2)^1/2

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--------------  where “v” is velocity and “c” is the speed of light.

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-  In1905 Einstein used Isaac Newton’s Binominal Theorem to expand the Lorentz Factor into a mathematical series.  (  See Review # 1078 “ My Favorite Equations”). 

 

-------------------     Mass moving  =  mass * (1-v^2/c^2)^-1/2

 

---------  E=mc^2 is a simplification of the Energy formula. It only applies to a mass at rest.  If a mass is in motion you need to include Kinetic Energy as part of total energy.  Normally the velocities are so slow relative to the speed of light the kinetic energy of mass in motion can be ignored.

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-   The energy of rest mass totally overwhelms it.  However, as the velocity increase and approaches the speed of light the Kinetic Energy becomes a significant factor in the total Mass-Energy formula. At the speed of light Kinetic Energy becomes half as great as Rest Energy.

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-----------------------  The binomial expansion of the mass in motion becomes:

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----------  Mass moving  =  mass ( 1 + 1/2 (v/c)^2  +  3/8 (v/c)^4  +  ........................

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--------  E = mc^2 with moving mass becomes:

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--------  E  =  mc^2 ( 1 + v^2/2c^2  +  3v^4/8c^4  +  .......................).

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--------  E  =  mc^2  + 1/2mv^2  +  3 /8mv^4/c^2  +  5/16mv^6/c^4  +  7/32 mv^8/c^6  +  9/64mv^10/c^8   .......................  mvc.

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-----------  where:  1/2mv^2 is the formula for Kinetic Energy.

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------------------------------  Substituting in the values for the constants:

 

- E  =  90,000,000,000,000,000m  +  1/2 mv^2  +  0.375mv^4/90,000,000,000,000,000    +  .................  You can see the rest mass energy is overwhelming unless velocity approaches the speed of light.  As velocity approaches the speed of light energy approaches infinity.

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-  Space-time symmetry requires the Conservation of Energy.  Total Energy as a function of momentum requires the square root be taken for this formula for total Energy. When you take a square root you always get two answers, positive and negative, because the square of a negative number is a positive number.

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-----------  E^2 =  p^2c^2  +  m^2c^4

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-----------  When you take the square root of this equations

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------------  There are two answers to this equation:

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-----------  E^2  = (pc-mc^2) * (pc+mc^2)

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-    If energy were negative, energy would decrease as momentum would increase.  This is not intuitive, so, E  =  pc - mc^2 is usually ignored.

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-    But, what if there were negative energy?

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-    What if the vacuum of space were filled with negative energy particles?

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-    We know that anti-matter exists.  Why not anti-energy?  Energy and matter are the -    same thing in different amounts.  Anti-matter is just like ordinary matter except it has the opposite charge.

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-    If a vacuum becomes a giant inert atom of neutral charge with all possible momentum states filled, then the loss of an electron leaves a hole which is equivalent to positive energy charge.  Therefore anti-electrons must exist.

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-    This particle was finally discovered n 1933 in a cloud chamber.  It was named the “positron” because it was just like an electron  but it had the opposite charge.  It was an anti-electron.  It was anti-matter.  Today scientists can produce all kinds of anti-matter in their laboratories.

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-    If anti-matter exists, why not anti-energy and anti-gravity?

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-    Anti-gravity appears to be accelerating the expansion of the Universe.  Something is causing it,  we do not know what.  We call it “Dark Energy“.  But, if we just assume it keeps doing what it is doing it will eventually rip everything in the Universe apart.  Everything.  Galaxies, stars, the Earth, even all the atoms.  Everything held together by gravity and the electromagnetic force will be ripped to pieces.

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-     We have known the Universe is expanding since 1929 when Edwin Hubble discovered that all the galaxies outside our Local Group were accelerating away from us.    In 1998 astronomers studying supernovae in distant galaxies determined that the rate of acceleration was actually increasing.

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-    There was something that interacts with the gravitational force but does not interact with the electromagnetic force and it counteracts the force of gravity.  It is some type of uniform negative pressure that is accelerating the expansion of the Universe.  The key here is “ uniform”.  If this negative pressure is uniform over time.  If it is invariant, then the Big Rip is bound to happen.

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-    In addition to Dark Energy we know there is Dark Matter.  We know there is something that interacts with the gravitational force but does not interact with the electromagnetic force.  Ordinary Matter only comprises 4.6% of the Universe.  Dark Matter is 5 times greater.

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-      Ordinary Matter  does interact with the electromagnetic force.  In fact, EVERYTHING we can see or communicate with, everything to do with the elements or atoms or chemistry, or biology interacts with the electromagnetic force.  That is our world, our known Universe.  There is another Unknown Universe that is 95% of what is out there.

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-    Astronomer’s tools have gone far beyond the optical telescope.  Astronomers today use a cluster of galaxies as a gravitational lens to see the Dark Matter that is in front of their image.  The massive gravity of the cluster warps space-time.  The light from a distant object follows the bent space-time which acts as a lens to allow astronomers to see what sits behind the galaxy cluster.  The luminous mass of the cluster is not enough to warp space.  The extra mass that is not luminous must be Dark Matter that we can not see.

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-    Another tool is measuring the microwave energy  of the Cosmic Microwave Background that is the after glow 380,000 years after the Big Bang.  These CMB measurements allowed astronomers to determine the percentage of mass-energy that is in the Universe.

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-    The ratio of energy to the critical mass-energy is 72%.  The critical mass-energy is that amount that is just enough to stop the expansion of the Universe at an infinite distance.  The ratio of matter to critical mass-energy is 27.6% with 4.6% being Ordinary Matter and 23% being Dark Matter.

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-    From these ratios astronomers can say the Universe will expand forever. The Big Rip will happen.   The geometry of the shape of the Universe is Flat, neither concave nor convex.  The temperature is 2.725 Kelvin.  The Age is 13,700,000,000 years.

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-     Three different methods were used to determine the ratios of the Universe’s composition.  The plot was made with the y-axis the Energy Density / Critical Density and the x-axis the Mass Density / Critical Density.  Using high redshift supernovae, and the Cosmic Microwave Background  and the slope of a Flat Universe the lines intersect at 72% Energy and 28% Matter.

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-    Type 1a Supernovae were used as standard candles to determine the expansion rate of the Universe.  The supernovae were White Dwarf’s at 1.4 Solar Mass so the absolute luminosity was known.  The distance was measured by the redshift of the light caused by the expansion of the Universe.  And, by the dimness of the light that had traveled that far.

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-    They determined that the rate of expansion is accelerating.  The supernovae that are further back in time, further away, are dimmer than expected.  Dimness is Apparent Brightness and it is proportional to Luminosity, the intensity of light at the source and inversely proportional to the distance away.

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-----------------  The Apparent Brightness  =  Luminosity  /  4 * pi * distance^2

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-    Type 1a Supernovae are known to be binary stars with one star a White Dwarf that goes supernova when its mass exceeds 1.4 Solar Mass.  We know the Luminosity of these explosions to be 10^10 Solar Luminosity.  We measure the brightness and calculate the distance.  The Apparent Brightness is called Flux.

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--------------  distance ^2  =  Luminosity / 4*pi*Flux

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------------ where:   the Flux measured is 0.23*10^-10 watts / meter^2, 0.023 billionths of a watt.  A watt is a joule*second, and, a photon is 6.625*10^-34 joule*seconds of energy.  Therefore, the Flux measured collected 3.47*10^18 photons per square centimeter.

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-----------  where:  the Luminosity of the Sun is 3.8268*10^26 watts.

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-----------  where:  a lightyear = 9.4605 *10^15 meters

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--------------  distance ^2  =  3.8268*10^26 *10^10 / 12.57*2.3*10^-11

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--------------  distance ^2  =  0.1324 *10^47

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--------------  distance   =  11.5*10^22 meters / 9.4605 *10^15 meters / lightyear

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--------------  distance   =  1.22/ 10^7  lightyear

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-------------  distance is 12.2 million lightyears

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-  The distance is also measured using the Doppler Shift of the spectrum lines, called Redshift.  The light shifts to the red end of the spectrum because the light moving away from us gets wider wavelengths as expanding space stretches it out.

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-------------  Redshift  =  (Wo - w) / w

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-----------  where:  Wo is the observed wavelength of 662.9 and 491 nanometers

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-----------  where: w is the actual wavelength from the source of 656.3 and 486.1 nanometers

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-------------  Redshift  =  (662.9 - 656.3) / 656.3  =  0.01

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-------------  Redshift  =  (491 - 486.1)  /  486.1  =  0.01

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-  486.1 nanometers is the wavelength of the hydrogen spectrum.  For velocities not approaching the speed of light the formula is:

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----------------- velocity  =  c * Redshift

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--------------  where:  c = speed of light  =  3*10^8 meters / second

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--------------  velocity  =  1 % the speed of light  =  3 * 10^6 meters / second

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---------------  velocity  =  1860 miles per second  =  6,696,000 miles per hour that the star is moving away from us.

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-    Hubble’s Constant is how fast the Universe is expanding.  The velocity is a linear function of the distance away the star is.

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------------  Hubble’s Constant  =  Ho  =  velocity / distance.

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-------------  Ho  =  47,000 miles per hour / million lightyears

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--------------  Ho  =  0.00734% *c / million lightyears

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------------  Hubble’s Constant  =  Ho  =  velocity / distance.

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------------  0.00734% c / million lightyears  =  1%*c / distance.

 

----------  distance  =  136 million lightyears.  This is how far the star is away from us using Hubble’s Constant.

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- If we measure a Redshift of 6, we can not use the formula  velocity =  c * Redshift.  Velocity  =  c*6 means the velocity is 6 times the speed of light.  We must use the formulas for Relativity for velocities approaching the speed of light.

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-------------  Redshift  =  (Wo - w) / w

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-------------  Redshift  =  Wo / w - 1

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------------  Redshift + 1  =  Wo/w  =  6 + 1  =  7,  which says that the distance to the supernova is 7 times greater than when the light left the supernova.  The Universe has expanded by 7 times and the temperature has cooled by 7 times.

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-  The blue light left the supernova at 486.1 nanometers wavelength.  We observed it here at 3,402.7 nanometers, in the far infrared wavelengths.

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-  The intensity of the luminosity of the supernova follows the Blackbody Curve which has a defined peak as a function of wavelength and temperature.

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------------- Wavelength Peak  =  2,900,000 nanometers  /  Kelvin

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-------------  Temperature  =  2,900,000 nanometers / Wavelength Peak

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-------------  Temperature  =  2,900,000 nanometers / 486.1 nanometers  =  5,967 Kelvin

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-------------  Temperature  =  2,900,000 nanometers / 3,402.7 nanometers  =  852 Kelvin

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-  The Universe has expanded by a factor of 7 and the temperature has cooled by a factor of 7.

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------------  Redshift + 1  =  Temperature / Temperature observed  =  5,967 Kelvin / 852 Kelvin  =  7

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-  These calculations are using Redshifts for the most distant supernovae we can observe.  The maximum Redshift we can observe is the Cosmic Microwave Background.  This afterglow of the Big Bang started out as Gamma Rays and today we see the radiation in Microwave wavelengths.  The peak wavelength of the CMB light curve is at 1,100,000 nanometers.  The temperature has cooled from 3,000 Kelvin to 2.73 Kelvin.

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------------- Wavelength Peak  =  2,900,000 nanometers  /  Kelvin

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------------- Wavelength Peak  =  2,900,000 nm  /  2.73 Kelvin  =  1.1*10^6 nanometers

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------------- Wavelength Peak  =  2,900,000 nm  /  3,000 Kelvin  =  970 nanometers

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------------  Redshift + 1  = 3,000 Kelvin  /  2.73 Kelvin  =  1100

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-    The Redshift is 1,100 and the expansion of the Universe has stretched wavelengths by a factor of 1,100 since the Cosmic Microwave Background first released its light 380,000 years after the Big Bang.

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-    If we are at the center of a giant void we could explain the Universe’s accelerating expansion without the need for the mysterious Dark Energy in space.  The Universe could be extremely big and look like Swiss cheese.  Uniform at the large scale and inhomogeneous at the smaller scale.

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-    Our calculations assume the Universe is homogeneous and isotropic.  But, it may not be a giant sphere.  It may be a giant blob, expanding different amounts in different directions.  We would have to be living in a truly giant void extending out past our Observable Universe.

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-    The void would have much less density than other parts of the Universe outside our view.  the less density would cause the attractive effect of gravity decelerating the expansion to be less.  So much less that the rate of expansion would be increasing inside the void.  It would be like the weak part of an expanding balloon forming a rapidly expanding bubble in one part out of the balloon.

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-    Contradicting this idea is the evidence that the Cosmic Microwave Background Radiation is uniform and homogeneous to one part in 100,000.  The CMB represents the Universe at age 380,000.  There is not evidence of giant voids in the CMB observations.

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-     Secondly the distribution of galaxies appears to be uniform in all directions.  Even the spaces in between galaxies seems to be uniform with small and equally sized voids.  For the giant void to exist under these observations the giant void would have to be nearly spherical and our galaxy would have to be nearly in the center.  The void would have to be larger than we could detect and the Universe’s inhomogeneity would have to exist beyond our detection. But, God only knows, the Universe might be this large.

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-    The other thought is that time is a variable.  The Redshifts can not distinguish form an expansion is space and a variation in time.  Velocity  =  change in space / change in time

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----------  v  =  ds / dt  =  (s2 - s1)  /  (t2 - t1). 

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-    If time is something you can count on and space is uniform and homogeneous then Dark Energy must exist and we should be able to discover what it is. God only knows.

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June 9,  2023       EXPANDING  UNIVERESE  - 1083,1084, 1085           4045

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--------------------- ---  Friday, June 9, 2023  ---------------------------------

 

 

 

 

           

 

 

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