I want to give a computer lecture to freshmen. They don't know anything. What should I say? Not in the textbook? Practical. Non-computer major.

Seth Lloyd and Y. Jack Wu

In order to keep pace with the times, researchers can regard the laws of physics as computer programs and the universe as computers.

Black hole computer may sound ridiculous, however, researchers in cosmology and basic physics are proving that it is a useful conceptual tool. If physicists can create black holes in particle accelerators (which is expected to be possible in 10 years), they may actually be able to observe black holes and perform operations.

Is there a difference between a computer and a cosmic black hole? At first glance, this question sounds like the prologue of a Microsoft joke. However, it is one of the most profound problems in physics today. For most people, computers are specialized new inventions: streamlined desktop cabinets or fingernail-like chips in coffee pots. For physicists, all natural systems are computers. Rocks, atomic bombs and galaxies may not run Linux programs, but they also record and process information. Every electron, photon and other elementary particle stores a data bit value. Nature and information are intertwined, as john wheeler, a physicist at Princeton University, said, "It comes from bits."

Black holes may seem to be exceptions to all rules of calculation, and it is not difficult to input information into black holes. However, according to Einstein's general theory of relativity, it is impossible to extract information from black holes. The matter entering the black hole has been homogenized, and its composition and details have been irrevocably lost. In the1970s, Stephen Hawking of Cambridge University in England showed that when quantum mechanics is considered, black holes do have outputs: they burn like hot coal. However, in Hawking's analysis, this radiation is disordered and random; It doesn't carry any information about what entered it. If an elephant falls in, the elephant's energy value will leak out-but this energy will be a hodgepodge. It cannot be used (even in principle) or recreated.

Because the laws of quantum mechanics retain information, the obvious loss of information has caused a series of problems. Other scientists, including Leonard Susskind of Stanford University, John Preskill of California Institute of Technology and Gerard T. Hooft of Utrecht University in the Netherlands, believe that in fact, the emitted radiation is not random, but a process in which matter falls into a black hole. In the summer of 2004, Hawking turned to agree with them that black holes are also being calculated.

Black holes are just the biggest special case of the universal principle of registering and processing information in the universe. This principle itself is not new. In the19th century, the founder of statistical mechanics developed knowledge later called information theory to explain the laws of thermodynamics. At first glance, thermodynamics and information theory are two independent categories: one is to describe steam engines, the other is to optimize communication; However, entropy, a thermodynamic quantity, limits the ability of steam engines to do useful work. Entropy is directly proportional to the number of bits recorded by the position and speed of molecules in matter. Quantum mechanics in the 20th century put this discovery on a solid quantitative basis, which made scientists have a great concept of quantum information. The bits that make up the universe are qubits, or "qubits", whose properties are far richer than ordinary bits.

Analyzing the universe with the help of bits and bytes can not replace the conventional analysis of equal force and energy, but it reveals many amazing new facts. For example, it solves a paradox in the field of statistical mechanics called "Maxwell's demon"-this paradox seems to allow the existence of perpetual motion machines. In recent years, we and other physicists have been looking at cosmology and basic physics from the same point of view: the nature of black holes, the fine-scale structure of time and space, the behavior of dark matter in the universe and some extreme natural laws. The universe is not only a giant computer, but also a giant quantum computer. As Paola Zizzi, a physicist at the University of Padua in Italy, said, "It comes from qubits."

Gigabit is too slow.

Physics and information theory (from the central principle of quantum mechanics) have merged: in the final analysis, dispersion is the nature of nature; A natural system can be described by finite bit values. In this system, each particle behaves like a logic gate of a computer. Its spin "axis" can point to one of two directions, so a bit can be encoded and flipped to perform simple calculation operations.

The system is also discrete in time. The time taken to transmit a bit is the minimum. A theorem named by two pioneers of information processing physics, Norman Margolis of MIT and Lev Levitin of Boston University, gives an exact order of magnitude. This theorem is related to Heisenberg's uncertainty principle (uncertainty principle describes the internal trade-off when measuring two related physical quantities, such as position and momentum or time and energy), which claims that the time t required to transfer a bit depends on the energy e you apply, and the more energy you apply, the shorter the time may be. The mathematical expression is T≥h/4E, where h is Planck constant (the main parameter of quantum theory). For example, an experimental quantum computer uses protons to store information bits, and a magnetic field is used to flip the value of each bit. These operations take place in the shortest time allowed by Margolus-Levitin theorem.

Many conclusions can be drawn from this theorem, including the geometric limitation of time and space on the computing power of the whole universe. As a preview, try to consider the computing power limit of ordinary matter-in this case, take a kilogram of matter that occupies a liter of volume, and we will call it the "extreme handheld computer".

Its battery energy is the substance itself, which is directly converted into energy by Einstein's famous formula E=mc*2. If all these energies are put into the flipped bits, the computer can perform 10*5 1 times per second; With the decrease of energy, its operation gradually slows down. The storage capacity of a computer can be calculated by thermodynamics: when a kilogram of material is converted into energy in a liter of volume, its temperature is 65.438+0 billion Kelvin. Entropy is proportional to energy divided by temperature, corresponding to 10*3 1 bit information. The "extreme pocket computer" stores information in the microscopic motion and position of elementary particles, which move around in their volume, so every bit of information allowed by the laws of thermodynamics is put into use.

Limit calculation

What is a computer? This is a very complicated problem. No matter how accurately you define it, it is not just what people usually call a "computer", but any object in the world. Objects in nature can solve generalized logical and mathematical problems, although their input and output may not be meaningful to human beings. Natural computers are inherently digital: they store data in discrete quantum states, such as the spin of elementary particles. Their instruction set is quantum physics.

Whenever particles interact with each other, their orientations will be reversed. This process can be imagined with the help of programming languages such as C or Java: particles are just variables, and their interaction is an operation such as addition. Each bit of information can be flipped 10*20 times per second, which is equivalent to the clock speed of 100GG Hz. In fact, the system changes too fast to be controlled by the central clock. The time required to flip a number is approximately equal to the time required to transmit a signal from one number to an adjacent number. Therefore, the extremely convenient PDA is highly parallel: it does not run like a single processor, but like a huge array composed of multiple processors; Each processor works almost independently and transmits its operation results to other relatively slow processors.

In contrast, a conventional computer flips its information bits about 10*9 times per second, stores about 10* 12 bits of information, and contains only a single processor. If Moore's Law can be maintained, it is possible for your descendants to buy an ultimate PDA in the middle of the 23rd century. Engineers will find a way to accurately control the interaction between particles in plasma, which is hotter than the core of the sun, and controlling computers and correcting errors will take up a lot of communication bandwidth. Engineers may also solve the encapsulation problem of some nodes.

In a sense, if you recognize the right person, you can actually buy such equipment. One kilogram of matter is completely converted into energy-this is the working definition of a 20 million-ton hydrogen bomb. The exploded nuclear weapon is processing a lot of information, its initial structure provides input and its radiation provides output.

From nanotechnology to semiconductor technology *

If any substance can be regarded as a computer, then a black hole is a computer compressed to the smallest size. As the computer shrinks, the mutual attraction between its components increases until it finally increases until nothing can escape. The size of a black hole (called schwarzschild radius) is directly proportional to its mass.

The radius of a black hole with a mass of one kilogram is about10 *-27m (the radius of a proton is10 *-15m). The compressed computer has not changed its energy content, so it can perform 10*5 1 times per second as before. Only its storage capacity has changed. When gravity can be ignored, the total storage capacity is proportional to the number and volume of particles. When gravity plays a leading role, it connects particles, so they can store less information as a whole. The total storage capacity of a black hole is proportional to its surface area. In the1970s, Hawking and Jacob Bekenstein of Hebrew University in Jerusalem calculated that a black hole with a mass of one kilogram could record about 10* 16 bits of information, much less than before compression.

A black hole is a faster processor because it stores less information. It takes 10*-35 seconds to transmit a bit, which is equal to the time it takes for light to travel from one side of the computer to the other. Therefore, compared with a highly parallel extreme handheld computer, a black hole is a serial computer, and it behaves like an independent unit.

How does a black hole computer actually work? Input is not a problem: just encode the data in the form of matter or energy and throw it into a black hole. By properly preparing the materials to be put into the black hole, the hacker will be able to write any required calculation program for the black hole. Once matter enters a black hole, it disappears forever-the so-called "event horizon" divides the line that will never return. Particles falling vertically interact and perform operations for a limited time before reaching the center of the black hole. This center is the gravitational singularity, where particles no longer exist. What happens when matter is squeezed together at the singularity depends on the details of quantum gravity, which is unknown at present.

The output of the black hole computer appears in the form of Hawking radiation. If a black hole with a mass of one kilogram emits Hawking radiation, its mass will rapidly decay and disappear completely within 10*-2 1 second in order to maintain the radiation energy. The peak wavelength of radiation is equal to the radius of the black hole. For a black hole with a mass of one kilogram, this wavelength is equal to the wavelength of extremely intense gamma rays. Particle detectors can capture and decode this radiation for human use.

Hawking's research on black hole radiation associates his name with this radiation. He overthrew the traditional view that nothing can escape from a black hole. The emissivity of a black hole is inversely proportional to its size, so the energy loss of a big black hole (such as the black hole in the center of a galaxy) is much slower than the speed at which it swallows matter. However, in the future, experimenters may create some tiny black holes in particle accelerators, which will explode with the explosion of radiation. A black hole can't be regarded as a fixed object, but a short-lived collection of substances that perform operations at the maximum possible rate.

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