From: Henry Baker <hbaker1@pipeline.com>
To: math-fun <math-fun@mailman.xmission.com> Sent: Monday, May 28, 2012 5:34 PM Subject: Re: [math-fun] math-fun Digest, Vol 111, Issue 28
Perhaps "black holes" should be called "red holes"; after all, as time slows down close to the event horizon, all emitted light becomes red-shifted into the long wave radio spectrum; Mary no longer "sees" Joe, so much as hears him on her radio.
Don't count photons; count energy. The number of photons actually goes up dramatically as the frequency goes down.
No, the total number of photons is conserved under propagation and Doppler shift (or red shift). Astronomers denote redshift by z, where the wavelength is multiplied by 1+z. The energy per photon reduced by a factor 1/(1+z). Also the time duration of a pulse lengthens by (1+z), so that the rate of arrival of photons is reduced by the factor 1/(1+z). Thus the beam power goes down by 1/(1+z)^2. In our little story, the last photon that Mary receives is the last photon that Joe emitted before crossing the event horizon. Joe cannot tell of his adventures once he has crossed the horizon, though his final report may well arrive in the RF band.
Photons merely count the number of Planck lengths in a single wavelength of "light". Photons are merely the smallest units of a "transaction" in the "transactional >interpretation of quantum theory".
This is wrong. An electromagnetic wave at frequency ν has quantized energy levels, just as an atom does, and these allowed energies are nhν, where n is a nonnegative integer and h = 6.6e-34 J/Hz is Planck's constant. When the excitation energy is nhν, we say there are n photons present. When the wave interacts with a material system, it exchanges energy in multiples of hν, i.e. an integral number of photons are created or annihilated. Actually, the energy levels are (n + 1/2)hν, but I'm trying to avoid a digression into the issue of zero-point energy. The Planck length is the unique expression having dimensions of length formed from c = the speed of light, h = Planck's constant, and G = gravitational constant. It turns out to be about 1e-35 m. The similarly defined Planck time is about 1e-45 s, and Planck mass is a very tangible 20 μg. A particle of mass m, if confined to successively smaller volumes will need to be described by quantum mechanics when the confinement length approaches the Compton wavelength h/(mc), and by general relativity when the confinement length approaches the Schwartzchild radius Gm/c^2. The two limits are concurrent for a Planck mass particle, and the corresponding length is the Planck length. It is conjectured that in a full quantum theory of gravitation, which does not yet exist, the smooth structure of space-time breaks down on the Planck length scale. Space becomes foamy and subject to quantum umcertainty on that scale. -- Gene