Wednesday, October 10, 2018

Let there be light, let there be photons



- 2113 -  Let there be light, let there be photons.  The photon is massless and only travels at one speed , the speed of light, 186,282 miles per second.  However, that speed is in a vacuum, light travels through transparent medium at lower speeds. -  When a photon hits an object it can be reflected or absorbed.  The transfer of energy from the photon to the object is proportional to its frequency.
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------------------  2113  -  Let there be light, let there be photons
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-  The photon is electromagnetic radiation having wavelengths and frequencies ranging from radio waves to gamma rays. 
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-  We normally do not think those are photons moving through the air powering your cell phone.  However, it is the photon of electromagnetic energy traveling over the airways that carries your voice conversations.  Those are photons cooking your food in the microwave.  Those are photons from distant stars that are lights in the night sky.
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-  The photon is massless and only travels at one speed , the speed of light, 186,282 miles per second.  However, that speed is in a vacuum, light travels through transparent medium at lower speeds.
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-   Light leaving the core of the Sun takes years to reach the surface.  Once at the surface it takes only 8.3 minutes to reach us.  The space shuttle is fast at 25,000 miles per hour but that is under 7 miles per second.  The frequency of yellow light is 5 * 10^20 cycles per second.  Or, a wavelength of 2*10^-21 seconds per cycle. 
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-  The eye blinks in 10^-1 seconds.  The camera shutter clicks in 10^-3 seconds.  The microprocessor has a cycle time of 10^-9 seconds.  A laser pulse is 4^-15 seconds. 
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-  The speed of light is the speed regulator, nothing can go faster than the photon.
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-  Massless particles MUST only travel at the speed of light.  And, likewise, particles with mass must slow down.  Mass becomes energy that has just slowed down enough for us to see it.
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-  When a photon hits an object it can be reflected or absorbed.  The transfer of energy from the photon to the object is proportional to its frequency.
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-------------------  A photon’s momentum = 6.6*10^-34 * frequency / 3*10^8. 
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------------------- Or, 6.6*10^-34 / wavelength.      p = h*f/c          p = h / w.
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------------------  The Energy in a photon = 6.6*10^-34 * frequency.     E = h*f. 
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-   So, the higher the frequency of a photon the more Energy it has.  X-rays have more energy than radio waves and blue light has more energy than red light.
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-  You would think that a massless object would have no momentum.  However, a photon does have momentum because it carries energy and energy is the same as mass.
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-----------------------E = mc^2.   Energy = 9*10^16 * mass.
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---------------------- Or, mass = Energy * .11*10^-16.
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---------------------- Energy = momentum * velocity. 
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-----------------------  E = m*v^2.
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-  Photons have both wave-like and particle-like behavior.   Or, better said, they have wave-like particle and particle-like wave behavior. 
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-  Albert Einstein in 1905 first proposed that light, and therefore all electromagnetic radiation, comes in quanta, or bundles of energy, called photons.  Photons have no electric charge.  They are a neutral particle.
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-   Whenever an electric charge is accelerated photons are emitted.  Whenever, an electron in an atom drops from a higher shell to a lower shell a photon is emitted. ( See Review 731 "The Electron").  Photons are emitted whenever matter and anti-matter come together and are annihilated ( See Review 730 - "Antimatter").
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-  Since the photon is massless you cannot use E = m*c^2, because you get zero energy.  For massless particles you have to use E = p*c.  Where “p” is its momentum.
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------------------------E^2  =  c^2*p^2 + m^2*c^4
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The Force is the rate of change of momentum with respect to time.  F = dp/dt
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-  In 1900 the electromagnetic energy radiation calculated from the temperature of an object was:
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-------------------  E  = 8*pi*f^2*k*T/c^3               , where k is Boltzman’s Constant.
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But, in 1905 the formula changed due to the discovery of Planck’s Constant:
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------------------- E = 8*pi*f^3/c^3 * (e^h*f/k*T - 1)    
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-------------------, where “h” = 6.6*10^-34 kilograms*m^2/sec.
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-  Photons can propagate with left-handed or right-handed rotation , or polarization.  That is what makes Polaroid glasses work as sunglasses.
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-   Photons have an integer spin = 1.  Therefore they are Bosons and obey the Bose-Einstein statistics in probabilistic behavior.
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-  In contrast, electrons have a spin = ½ .  They are Fermions and obey the Fermi-Durac statistics of probabilistic behavior and Pauli’s Exclusion Principle.
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-  All these formulas, give me a break, how does any of this stuff work and how can I use it?
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-  Answer:  Look up in the night sky and see a star. Use a wattmeter and measure the intensity of the light coming from that star.  The wattmeter peaks at 560 nanometers wavelength and the intensity is 1.6 * 10^-9 watts / meter^2. 
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-   560 nanometers is the color of blue-green light.   The light from that star has traveled over 1 billion lightyears and is therefore 1 billion years old.   In order to see that star how many of these old photons are entering your eye?
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-----------  The energy of one photon   =  E  =  h*f
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-----------   f = frequency = c / wavelength
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-----------   The intensity in watts is the number of photons times the energy of each photon.  
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-----------  N  =  I  / E
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------------  N  =  I * w / h * c
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------------  N  =  1.6 *10^-9 watts / m^2  *  5.6 * 10^-7 m     /     6.64*10^-34 kg*m^2/sec^2   *  3* 10^8 m
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-------------  N  =  .44  kg m/sec^2 * sec      /    kg*m^3 /sec^2  
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--------------  N  =  .44 * ^10 photons / m^2 / sec
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--------------  N  =  4.4 billion photons / meter^2 / sec
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-  The eye has a pupil that is ½ centimeter in diameter.
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-------------  Diameter = .005 meters 
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-  The area of the pupil   =  pi * r^2  =  3.14 * (2.5* 10^-3)^2 m^2
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---------------Area = 2 * 10^-5 m^2
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-  The number of photons entering the eye =  4.4*10^9 photons / m^2 * sec   *   2 * 10^-5 m^2  =  .9 * 10^5 photons / sec
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-------------  The eye is detecting 90,000 photons / second.
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-  The eye is capable of detecting 25 photons / second of red light.  That is enough energy to trigger the optic nerve in the retina.  With a night adapted eye, after 20 minutes in darkness, the eye’s chemistry changes and it is able to detect as few as 5 photons / second of starlight.
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-   In midday sunlight reaches 1400 watts / m^2. 
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---------------  N  =  1.4 *10^3watts / m^2  *  5.6 * 10^-7 m     /     6.64*10^-34 kg*m^2/sec^2   *  3* 10^8 m
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-----------------N  =  .39 * 10^22
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-----------------The number of photons entering the eye  in daylight  =  .39 * 10^22  photons / m^2 * sec   *   2 * 10^-5 m^2  =  .79 * 10^17 photons / sec.
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-----------------  79,000,000,000,000,000 photons enter the eye each second.
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------------------  The eye has a dynamic range of 18 powers of 10.  It truly is a remarkable instrument.
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 ---------------------   Wednesday, October 10, 2018   -------------------------
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