Astronomy and Cosmology week 5 – Tuesday 6 May 2003 LIGHT Star Date Light lecture Workshop: calculate Planck mass (Univ.5e Ch.28) break Minilectures Thursday: Ch.6, Telescopes Friday: quiz on Ch.5 (not Ch.6) Next week: spectra and spectrometers

Calculating the Planck length and mass: 1. You used energy conservation to find the GRAVITATIONAL size of a black hole, the Schwartzschild radius R. 2.Next, use the energy of light to calculate the QUANTUM MECH. size of a black hole, De Broglie wavelength. 3. Then, equate the QM size with the Gravitational size to find the PLANCK MASS M p of the smallest sensible black hole. 4. Finally, substitute M into R to find PLANCK LENGTH L p 5.and then calculate both M p and L p.

1.Gravitational size of black hole (BH): R = event horizon The Schwarzschild radius, inside which not even light (v=c) can escape, describes the GRAVITATIONAL SIZE of BH.

2. Quantum mechanical size of black hole The deBroglie wavelength,, describes the smallest region of space in which a particle (or a black hole) of mass m can be localized, according to quantum mechanics.

3. Find the Planck mass, M p If a black hole had a mass less than the Planck mass M p, its quantum-mechanical size could be outside its event horizon. This wouldn’t make sense, so M is the smallest possible black hole.

4. Find the Planck length, L p These both yield the Planck length, L p. Any black hole smaller than this could have its singularity outside its event horizon. That wouldn’t make sense, so L is the smallest possible black hole we can describe with both QM and GR, our current theory of gravity.

5. Calculate the Planck length and mass These are smallest scales we can describe with both QM and GR.