Latour Light Conjecture Confirmed
Remember the electromagnetic radiation spectrum from long, low energy radio waves through visible light to short, high energy gamma rays?
I wondered whether it went to infinity from both ends: infinitely long wavelengths across the universe and zero length infinite energy gamma rays.
My college physics book, Sears & Zemansky, University Physics, 1955, p719, shows scale Lmin <10-14 m, fmax >1023 cps and Lmax >107 m, fmin <10 cps. L*f = c = 3*108 m/s; L = wave length, m; f = frequency, waves/sec or cps. Visible f = 5*1014 cps, L = 6*10-7 m.
In 2005 I made the conjecture the answer was no. The span is finite. EMR is quantized, so the long wavelength is limited by the minimum Plank energy of photons and the shortest wavelength is limited to the minimum Plank distance.
If Lmin = Pl = 1.6*10-35 m,
fmax = 3*108 m/s /1.6*10-35 = 1.85*1043 cps. Fast!
Photon E, erg = h*f = hc/L, where h = Plank constant = 6.627*10-27 erg-sec.
Set Emin or fmin. If fmin = 1 cps, Emin = h and Lmax = 3*108 m.
Lmax could be size of universe, >8*1010 light years across = >7*1023 km.
Need photon Emin. Lmax = hc/Emin.
First a summary of what is light?
Light is massless, pure energy, electro-magnetic radiation waves or/and photons. A 100 watt light bulb emits 1020 photons/sec. Of all the energy emitted by the sun, only 2 photons in a billion warm Earth, the rest radiating uselessly into space.
One of the most important ideas of physics is the field, which maps the presence and magnitude of a force at different points in space. All electric fields represent stored energy. Light is an energy field coexisting in the space-time field that constitutes the universe.
Maxwell proved a changing magnetic field makes an electric field, electrons flow, electricity. Further a moving electric charge makes a magnetic field, magnets. Electromagnetic fields are magnetic fields perpendicular to electric fields. They are waves of electromagnetic radiation propagating with different wavelengths at fixed speed of light in a vacuum, c = 300,000 km/sec = 0.3 m/nanosec. Maxwell wrote the four partial differential equations that precisely and completely describe that energy field, everywhere, forever. That is one of the most elegant, profound and useful discoveries of the human mind!
Maxwell found the speed of EMR wave propagation is a constant, c = 1/sq rt(e*m)
e is electric permittivity of medium from Coulomb Law, force between 2 electric point charges, measured in lab = 4Pi*10-7 coul2/newton*m2
m is magnetic permeability from Ampere/Biot Law, strength of magnetic field due to electric current, measured in lab, 1/m = 4Pi*9*109 coul2 /newton*m2
So Maxwell derives speed of EMR = 1/(e*m)0.5 = 3*108 m/s.
Speed of light measured from Jupiter moons is = 3*108 m/s.
Conclusion: light is electromagnetic radiation and c is the conversion factor between units of space and time. The EMR field fills the entire space-time field of the universe. The only information we get from outside the solar system is light, captured by telescopes.
Light is also energy packets, particles called photons. Some have very little energy; some have enormous energy. Photons interact with matter; atoms and molecules absorb and emit them. Photons are encapsulated in electrons, affecting their energy level orbitals around protons and neutrons in each atomic nucleus. Photons are elementary particles. Two gamma ray photons can collide to make an electron + positron; this is how electrons are created from pure energy. Matter and energy are interchangeable according to E = Mc2.
How many photons in the entire universe?
Photon/proton = 2*109, big.
Protons/atom = 0.75(1) + 0.25(2) = 1.25 (assumes universe is 75{154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117} H, rest He)
Universe has 1070 atoms, very big.
So 2*109 x 1.25 x 1070 = 2.5*1079 photons, huge.
But a google = 10100, so photons in universe = 2.5*10-21 google, infinitesimal. It is all relative.
Energy spanning every electron to the universe, fastest thing going, converted to your mind by your eyes, light is a big deal. Just open your eyes and look around you. You are it.
My conjecture was confirmed in June 2013, Wikipedia.
F = frequency, cps = Hz
L = wavelength, meter
E = photon energy, eV
F*L = 3*108 mps, c
E*L = 1.24*10-6 eVm
Spectrum is not continuous; it has <1.9*1043 discrete wavelengths because photons are quantized.
Long wavelength gaps are set by min energy 4*10-15; short wavelength gaps set by min length 1.6*10-35. The wavelength gaps shrink with increasing frequency; the energy gaps grow with increasing frequency. The gaps in the visible range are determined by both. Quantum mechanics knows.
This means 1) the longest wavelength is one light sec = 3*108 meters, 300,000 km; lowest radio frequency is 1 cps; minimum photon energy is 4.1*10-15 eV and the shortest wavelength is 1.6*10-35 meter; highest frequency is 1.9*1043 cps; maximum photon energy is 7.7*1028 eV.
You can see EMR on a wall of the Children’s Museum Houston. US government licenses management rights to it to radio and TV broadcasters, cell phones and GPS. Religions, Sun worshippers and Nature lovers say Light is a manifestation of God The Holy Spirit. He is in those higher powers. That is Beautiful. That sheds some Light on Earth and puts an end to it.
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