What is Vacuum, in the 18th century and in the 21st century?
Leibniz's Second Letter and Fifth Letter
Leibniz: "..., for the more matter there is, the more God has occasion to exercise his wisdom and power. This is one reason, among others, why I maintain that there is no vacuum at all."
Here Leibniz mentions the concept of vacuum, and this is going to be discussed more in detail in subsequent letters. "Vacuum" is not an easy concept, however it may look obvious to laymen. Here, in the context of Clarke's and Leibniz' letters, "vacuum" means "empty space", i.e. a space in between chunks of matter which exist in the universe. The problem is: in what sense of "empty"? Absolutely, literally, nothing? But isn't absolute space, even without any matter, subsisting eternally and independently (see Newton's description of absolute space and time)? Then empty space is still something! Hence Newton's doctrine is often termed substantivalism of space and time.
In the 19th century, the concept of field is established thanks to Faraday and Maxwell. In order for electromagnetic forces to be transferred from here to there, there must be something called field for this transfer. As is well known by now, electromagnetism needs medium for communicating waves (e.g., light), and therefore there must be a field from here to there; so it is impossible that absolute nothingness reigns in between. The medium for electromagnetism was soon named ether. Many physicists in the 19th century believed that this ether filled space, even though there may be no ordinary matter (called ponderable matter), no particles, in a given region of space. As is well known, ether caused a lot of touble in the pre-relativistic era.
But in the beginning of the 20th century, Einstein proposed special relativity. And didn't this expell ether from physics? No uniform motion relative to ether can be detected, neither by mechanical laws, nor by electromagnetic laws; all inertial frames are on a par, and hence we cannot give any physical meaning to the ether at rest. Relativity needs no ether. Doe it follow, then, that empty space, vacuum, was recovered? Not quite. We still need electromagnetism, and this means we still need fields in otherwise empty space. Moreover, general relativity, Einstein's theory of gravity, also needs a field, a gravitational field. In other words, space (otherwise empty) must include, or depend on, these fields. And these fields are something, are they not? Thus, although it is a verbal matter whether or not you call space filled with these fields "vacuum", the vacuum so called is something (substantival), not absolute nothingness. Thus Leibniz' assertion dies hard.
In the latter half of the 20th century, the spirit of Einstein's dream of the unified field theory, and of the unification of all physics revived. The electromagnetic force and the weak force, two of the four fundamental forces of the nature, are believed to be unified by Grashaw, Weinberg and Salam. And soon, Grashaw and Georgi among others, proposed a grand unified theory (GUT) for the three forces except for the gravity. And such theories introduce Higgs fields (which are not experimentally confirmed yet), another species of field. Encouraged by the success of electroweak theory (i.e. the unified theory of electromagnetism and weak force), many physicists believe that the four forces can be unified in the following way: once upon a time, all forces were one when the temperature of the universe was incredibly high; but then the bigbang or some preliminary process began and the hot and dense universe began to expand and to cool down; then, according to the process called phase transitions (a good example is the water; a gas of water, if cooled, becomes liquid water, and then ice, and these qualitative changes are a phase transition), gravity was separated from the original at a certain temperature, next the force of colors, the ancester of the strong force (protons and neutrons are composed of quarks, and the quarks are governed by the force of colors; at a certain stage, this turns to the strong force), at still a lower temperature, and finally the weak and electromagnetic forces. All this needs Higgs fields, and the present universe must be still filled by them, or a cold relic of them.
But what's the point of assuming such weird fields? All right, by virture of some properties of Higgs fields, the notion of vacuum gets a nice meaning, and many physicists believe we can overcome several grave difficulties of the standard bigbang theory (first proposed by Gamov and others in 1948), thereby advancing the physical cosmology, getting still closer to the very beginning. How does the tiny universe get the tremendous energy for producing matter and a huge expansion? The answer seems to hinge on the notion of vacuum (or what Alan Guth calls "false vacuum") in Higgs fields in the early universe. The "vacuum" here is not a mere emptiness but has a rich content, quantum and cosmological. On this basis, the inflationary cosmology appeared. "Inflation" means a rapid, accelerated expansion; this is supposed to have occurred, in a very short time, at an ealiest period of the universe. Leaving out all the details, the upshot may be summarized in the following figure. "K" means the absolute temperature, Kelvin degrees.
And, although this has nothing to do with Leibniz, recent researches suggest the following picture for the overall history of the universe; the expansion of the universe seems to be accelerating again.
Getting back to Leibniz, he comes back to vacuum in the Fifth Letter:
The author objects against me the vacuum discovered by Mr. Guericke of Magdeburg, which is made by pumping the air out of a receiver, ... . The Aristotelians and Cartesians, who do not admit a true vacuum, have said in answer to that experiment of Mr. Guericke, as well as to that of Torricelli of Florence ... that there is no vacuum at all in the tube or in the receiver, since glass has small pores which the beams of light, the effluvia of the magnet, and other very thin fluids may go through. I am of their opinion, ...
Does this look stupid? Recall that the notion of fields appeared only in the 19th century, about 150 years later than Leibniz's correspondence. If Leibniz knew this, he would certainly have said, instead of "thin fluids", "subtle fields"; notice he refers to light and magnet which are treated mainly in terms of fields in the 19th century and on. And today, fields are regarded as a form of matter, in a sense. Thus Leibniz's assertion is far from stupid! In our contemporary physics, even particles without mass are admitted, i.e. photon and graviton.
References
Greene, Brian (2004) The Fabric of the Cosmos, Allen Lane.
Guth, Alan (1997) The Inflationary Universe, Perseus Books.
Last modified, June 6, 2005. (c) Soshichi Uchii