planck

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planck

Postby papernuke » Wed Aug 16, 2006 9:34 pm

WHat is Planck Length? I read in this book (Hyperspace) that it was like -10^18ths of a cm.

ALso, what is Planck Energy? In the same book it said that it was 10^19 electron volts.
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Postby houserichichi » Thu Aug 17, 2006 12:56 am

Ignoring a factor of pi, the Planck mass is roughly the mass of a black hole with a Schwarzschild radius equal to its Compton wavelength. The radius of such a black hole would be, roughly, the Planck length.

The following thought experiment illuminates this fact. The task is to measure an object's position by bouncing electromagnetic radiation, namely photons, off of it. The shorter the wavelength of the photons, and hence the higher their energy, the more accurate the measurement. If the photons are sufficiently energetic to make possible a measurement more precise than a Planck length, their collision with the object would, in principle, create a minuscule black hole. This black hole would "swallow" the photon and thereby make it impossible to obtain a measurement. A simple calculation using dimensional analysis suggests that this problem arises if we attempt to measure an object's position with a precision of less than a Planck length.

This thought experiment draws on both general relativity and the Heisenberg uncertainty principle of quantum mechanics. Combined, these two theories imply that it is impossible to measure position to a precision less than the Planck length, or duration to a precision greater than the time a photon traveling at c would take to travel a Planck length. Hence in any theory of quantum gravity combining general relativity and quantum mechanics, traditional notions of space and time will break down at distances shorter than the Planck length or times shorter than the Planck time.

The Planck mass (which is equivalent to its energy) is the mass of a black hole whose Schwarzschild radius multiplied by pi equals its Compton wavelength. The radius of such a black hole is roughly the Planck length, which is believed to be the length scale at which both general relativity and quantum mechanics simultaneously become important.

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Postby papernuke » Thu Aug 17, 2006 1:10 am

Than how big is a blakc hole?
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Postby houserichichi » Thu Aug 17, 2006 1:46 am

There are at least two different ways to describe how big something is. We can say how much mass it has, or we can say how much space it takes up. Let's talk first about the masses of black holes.

There is no limit in principle to how much or how little mass a black hole can have. Any amount of mass at all can in principle be made to form a black hole if you compress it to a high enough density. We suspect that most of the black holes that are actually out there were produced in the deaths of massive stars, and so we expect those black holes to weigh about as much as a massive star. A typical mass for such a stellar black hole would be about 10 times the mass of the Sun, or about 10^{31} kilograms. (Here I'm using scientific notation: 10^{31} means a 1 with 31 zeroes after it, or 10,000,000,000,000,000,000,000,000,000,000.) Astronomers also suspect that many galaxies harbor extremely massive black holes at their centers. These are thought to weigh about a million times as much as the Sun, or 10^{36} kilograms.

The more massive a black hole is, the more space it takes up. In fact, the Schwarzschild radius (which means the radius of the horizon) and the mass are directly proportional to one another: if one black hole weighs ten times as much as another, its radius is ten times as large. A black hole with a mass equal to that of the Sun would have a radius of 3 kilometers. So a typical 10-solar-mass black hole would have a radius of 30 kilometers, and a million-solar-mass black hole at the center of a galaxy would have a radius of 3 million kilometers. Three million kilometers may sound like a lot, but it's actually not so big by astronomical standards. The Sun, for example, has a radius of about 700,000 kilometers, and so that supermassive black hole has a radius only about four times bigger than the Sun.

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