Although people gain much information from their impressions, most matters of fact depend upon reasoning about causes and effects, even though people do not directly experience causal relations. What, then, are causal relations? According to Hume they have three components: contiguity of time and place, temporal priority of the cause, and constant conjunction.

In order for x to be the cause of y, x and y must exist adjacent to each other in space and time, x must precede y, and x and y must invariably exist together. There is nothing more to the idea of causality than this; in particular, people do not experience and do not know of any power, energy, or secret force that causes possess and that they transfer to the effect. Still, all judgments about causes and their effects are based upon experience.

To cite examples from An Enquiry Concerning Human Understanding (1748), since there is nothing in the experience of seeing a fire close by which logically requires that one will feel heat, and since there is nothing in the experience of seeing one rolling billiard ball contact another that logically requires the second one to begin moving, why does one expect heat to be felt and the second ball to roll? The explanation is custom. In previous experiences, the feeling of heat has regularly accompanied the sight of fire, and the motion of one billiard ball has accompanied the motion of another. Thus the mind becomes accustomed to certain expectations. "All inferences from experience, therefore, are effects of custom, not of reasoning." Thus it is that custom, not reason, is the great guide of life. In short, the idea of cause and effect is neither a relation of ideas nor a matter of fact. Although it is not a perception and not rationally justified, it is crucial to human survival and a central aspect of human survival and a central aspect of human cognition.

Regularities, even when expressed mathematically as laws of nature, are not fully satisfactory to everyone. Some insist that genuine understanding demands explanations of the causes of the laws, but it is in the realm of causation that there is the greatest disagreement. Modern quantum mechanics, for example, has given up the quest for causation and today rests only on mathematical description. Modern biology, on the other hand, thrives on causal chains that permit the understanding of physiological and evolutionary processes in terms of the physical activities of entities such as molecules, cells, and organisms. But even if causation and explanation are admitted as necessary, there is little agreement on the kinds of causes that are permissible, or possible, in science. If the history of science is to make any sense whatsoever, it is necessary to deal with the past on its own terms, and the fact is that for most of the history of science natural philosophers appealed to causes that would be summarily rejected by modern scientists. Spiritual and divine forces were accepted as both real and necessary until the end of the 18th century and, in areas such as biology, deep into the 19th century as well.

Certain conventions governed the appeal to God or the gods or to spirits. Gods and spirits, it was held, could not be completely arbitrary in their actions; otherwise the proper response would be propitiation, not rational investigation. But since the deity or deities were themselves rational, or bound by rational principles, it was possible for humans to uncover the rational order of the world. Faith in the ultimate rationality of the creator or governor of the world could actually stimulate original scientific work. Kepler's laws, Newton's absolute space, and Einstein's rejection of the probabilistic nature of quantum mechanics were all based on theological, not scientific, assumptions. For sensitive interpreters of phenomena, the ultimate intelligibility of nature has seemed to demand some rational guiding spirit. A notable expression of this idea is Einstein's statement that the wonder is not that mankind comprehends the world, but that the world is comprehensible.

Science, then, is to be considered in this context as knowledge of natural regularities that is subjected to some degree of skeptical rigor and explained by rational causes. One final caution is necessary. Nature is known only through the senses, of which sight, touch, and hearing are the dominant ones, and the human notion of reality is skewed toward the objects of these senses. The invention of such instruments as the telescope, the microscope, and the Geiger counter has brought an ever-increasing range of phenomena within the scope of the senses. Thus, scientific knowledge of the world is only partial, and the progress of science follows the ability of humans to make phenomena perceivable.

The first entanglement of three photons has been experimentally demonstrated by researchers at the University of Innsbruck. Individually, an entangled particle has properties (such as momentum) that are indeterminate and undefined until the particle is measured or otherwise disturbed. Measuring one entangled particle, however, defines its properties and seems to influence the properties of its partner or partners instantaneously, even if they are light years apart.

In the present experiment, sending individual photons through a special crystal sometimes converted a photon into two pairs of entangled photons. After detecting a "trigger" photon, and interfering two of the three others in a beamsplitter, it became impossible to determine which photon came from which entangled pair. As a result, the respective properties of the three remaining photons were indeterminate, which is one way of saying that they were entangled (the first such observation for three physically separated particles).

The researchers deduced that this entangled state is the long-coveted GHZ state proposed by physicists Daniel Greenberger, Michael Horne, and Anton Zeilinger in the late 1980s. In addition to facilitating more advanced forms of quantum cryptography, the GHZ state will help provide a nonstatistical test of the foundations of quantum mechanics. Albert Einstein, troubled by some implications of quantum science, believed that any rational description of nature is incomplete unless it is both a local and realistic theory: "realism" refers to the idea that a particle has properties that exist even before they are measured, and "locality" means that measuring one particle cannot affect the properties of another, physically separated particle faster than the speed of light.

But quantum mechanics states that realism, locality--or both--must be violated. Previous experiments have provided highly convincing evidence against local realism, but these "Bell's inequalities" tests require the measurement of many pairs of entangled photons to build up a body of statistical evidence against the idea. In contrast, studying a single set of properties in the GHZ particles (not yet reported) could verify the predictions of quantum mechanics while contradicting those of local realism.

Excerpt from the Encyclopedia Britannica without permission.