# Abstract

A new explanation of the spectrum of black-body radiation is presented based on finite precision computation

instead of statistics.

## Black Hole of Classical Physics

The starting point of modern physics was that classical physics failed to explain black body radiation:

**black body**

**absorbs**all incoming light of

**all frequencies**, but

**only emits low frequencies**with a

**cut-off**

**of high frequency**depending on

**temperature.**This is illustrated in the following figures showing

This is why the Earth absorbing light from the Sun of all frequencies from low to high, does not itself glow like the Sun, but only radiates low frequency infrared light:

predicted that the Earth would shine like the Sun, with no cut-off of high frequencies as indicated in the following figure:

But the Earth does not glow like the Sun and the question to be answered was (and is):

**Why is formally reversible wave mechanics, in reality irreversible with cut-off of high frequencies?**

To answer this question Planck used a form of statistical mechanics, where the high-frequency cut-off was explained as an effect of smaller probability of high-frequency quanta. But Planck was not happy with his resolution, which he believed was only a mathematical trick without physical meaning, and Planck became a revolutionary against his will.

## Finite Precision Computation as Explanation of Cut-Off.

## The above question is the question of **i****rreversiblity in a formally reversible Hamiltonian system**, which is answered by the new version of the second law of thermodynamics based on **finite precision computation instead of statistics. **The answer is the same because wave mechanics of absorption and emission of light is an example of a formally reversible Hamiltonian system. The answer is developed in computational black-body radiation [1]and in concentrate reads:

**a black-body can be seen as a network of interacting atomic oscillators which are excited by incoming waves and can emit waves by coordinated oscillation****irreversibility arises from finite precision computation and not from statistics****cut-off of high frequencies occurs because the required coordination of atomic oscillations cannot be met by finite precision computation****physics is a form of analog computation of finite precision****the cut-off frequency increases with temperature because the amplitude of oscillation increases which increases relative precision****a black-body transforms coordinated high-frequency input into low-frequency infrared heat radiation****cut-off of high frequencies is a well-known phenomenon in computational wave propagation arising from finite precision and not from statistics.**

## A Classical Model of Black-Body Radiation

**wave equation**for the deflection

**U**of a vibrating string of temperature

**T**subject to a distributed forcing

**F**and radiating energy to the surrounding medium:

**U_**

**tt**

**– U_xx**

**- R U_ttt**

**- H^**

**2**

**U_txx= F for 0 < x < 1, t > 0**

**T_**

**t**

**= integral (F**

**2**

**– R u_**

**tt**

**u_**

**tt**

**) dx for t > 0,**

**R > 0**is a coefficient of radiation,

**H**

**= h/T**is an effective mesh size representing the

**cut-off wave length**, where

**h**is a nominal mesh size representing Planck’s constant, and the subscript denotes differentiation with respect to time

**t**or space

**x.**

**H2Utxx**modeling

**diffusion from computation causing computational dissipation H2UtxUtx entering the energy balance of incoming energy from forcing and outgoing radiating energy, generating heat increasing the temperature.**