Having made these generalizations, we will now get down to the nuts and bolts of the language, how it is constructed and what features it must have.
Operational Definitions: An eloquent description of the essence of language is presented in the biography of Helen Keller, who because of blindness and deafness was denied most of the direct avenues for mimicry of the forms of language. For her it had to be built from its content. And because she was so mentally mature when this building began, unlike the case for most of us, she could remember and relate the process with a fully developed reasoning mind. Her first word was ``water'', singled out for experience by running a stream over her hand, and then represented as a word spelled in sign into the hand. In this way the word for ``water'' was created in her mind for the first time as the representation of something she could experience. The process of building such representations is called defining words. When a language is very complex, and words can be related to other words through long chains of association, it sometime can be forgotten that at bottom, every meaning for a word is somehow inherited from what one can do or what one can experience. The first important point about the languge of physics is that for all of its definitions, those associations are kept explicit. In other words, to say you have ``defined a word'' within the language of physics, you must mean that you have told precisely what actions or experiences that word will be used to represent. If you are describing something to do, the description must be complete and unambiguous enough to distinguish that action from other actions, and if you are describing something that you can experience, you have to also provide a way to distinguish that particular experience from the others that are possible.
In general, of course, since there are limitless slight variations on ways of acting and on experiences to be perceived, and since nothing is specified with limitless precision, any definition will have a degree of ambiguity that represents how precisely it specifies one action or identifies one experience. That ambiguity therefore also sets the limitations within which the word can even be assumed to have meaning. Thus there are words that one knows only specify actions with some imprecision, but then one also knows that those words do not even have a meaning in any sense of greater precision, until such can be provided by better specifying the actions.
The notion of Abstraction: There are times when it is very useful to refer to many different actions or experiences collectively, because one wants to ask questions or make statements about all of them, even when more precise words exist to refer to each of the individual cases. We will find that this is a very powerful way to use a little knowledge to understand a wide range of experiences, when we introduce the method of dimensional analysis in the next chapter. Any idea that is deliberately chosen to represent many such special cases, but not to restrict to any of them in particular, is called an abstraction. It is important to understand that an abstraction is not a kind of vagueness based on ignorance. Vagueness based on ignorance should be called that. An abstraction is a very carefully formed and concrete idea, the point of which is to encode what many things have in common, independently of whatever other ways they may differ. In physics, all the notions of dimensions, time length, mass, etc. are abstractions that tell how to compare things, clocks with other clocks or with heartbeats, metersticks with an amount of separation between people, and so forth.
The rôle of abstractions in physics is very important and very constrained. If you want to claim that an abstraction exists, you have to first make sure you have definitions of all of the special cases you want it to include, and you have to check to make sure: first, that all of the definitions make sense as real descriptions of things you can do, and second, that as such descriptions they really all have in common the thing that you want to denote with the abstraction. In other words, an abstraction is not somehow ``purer'' than all of the special cases to which it refers. Rather, it is ``as imperfect'' as the worst of them. This will be very important as we unravel the seeming paradoxes in relativity and the quantum theory. We don't start with ``time'' as ``an abstract'' which we approximate by citing cases in which we claim we recognize it. Rather we must first do the hard work of considering each of the cases, how we build a clock, who we choose to carry it around and read its ticks, how that person is moving, and so forth. After we have done this for all of the people we wish to describe, we go back and check each of the cases, and see if there is any universal notion that survives in each of them which permits us to create and name an abstraction that we call time. We will find that, depending what we would like to describe, there may be several or there may be none. It requires a fine sense of integrity to use abstractions in the language of physics, because one must first recognize that they are not assured even to exist, and one must then be constantly checking new applications of the word, to see if they really preserve its meaning and so grant the ability to use it.
Absense of a priori absolutes: We have now seen two ways in which the language of physics is very strongly a language of invention, in the fact that all definitions must be operational ones, so that one must always know how to reduce them to telling just what actions or experiences they describe, and in the fact that one literally builds abstractions from collections of underlying concrete definitions. Thus everything follows inevitably and traceably from experience, and abstractly defined words are no less operational than direct words; they are simply defined to refer to whole collections instead of narrowly specified individual cases. In this way also, one builds up complexity from simplicity, and not only does it take much greater care to define abstract ideas than directly experiential ones, there is no guarantee that a given level of abstraction or generality is even allowed by nature. Such was the case with certain assumptions about the nature of time as an abstract, held prior to the invention of relativity.
Thus we see that in the language of physics, everything is built and given meaning ``from the bottom up'', with ``the bottom'' being our carefully described experiences with nature. When one uses a language this way, the inheritence of words from eariler times or uses, or anywhere the literal operational descriptions are not included, carries with it no proper sense of ``meaning'', and consequently no confidence. Another way to say this is that there are no a priori absolutes in the language of physics. Such an absolute would be some word or notion that had inherited a meaning from something prior to specific experiences. Physicists simply refer to such an inherited word as ``undefined''.
It is good to recognize that a high degree of iconoclasty has developed in the physicist's relation to language (and to most everything else, as well). It does not matter how highly regarded an idea or notion or word is; it is always being scrutinized to see if there are any ways in which it predicts something definite about the behavior ot nature that is different from what is seen. Any such mistake requires that the word be re-analyzed, either restricted as merely an approximation to some better word, or thrown out altogether. Thus this language, with its operational definitions and its lack of icons, is active and alive. New parts are constantly being created as the range of human experience increases and more is seen, and old parts that are found to be wrong or misleading are eradicated when they can be found.
Why: A good observation to summarize the general attitude built on these premises concerns the way the word ``why'' is used in physics. ``Why'' is a tricky word, because it can mean two different things in two different contexts. People have desires, and they take actions in the hope of making certain things happen. In that context, one can observe a consequence of someone's action, and ask ``why'' something was made to happen, meaning ``with what purpose in mind?''. As noted, though, physicists have found it prudent not to be too prejudiced concerning the events of nature, because in expecting one thing, they can too easily overlook or misunderstand what really happens. Therefore, it doesn't fit the language of physics to ask ``with what purpose in mind'' something in nature happens, when one is having enough trouble describing the occurence by itself. Yet the central questions of physics still involve ``why'' one thing consistently happens, and not another. The point of the physicist's use of ``why'' is that this simpler notion can be asked, without inferring a human purpose behind the event. The physicist first tries to describe carefully what he sees. Then, simply describing a mechanism, he asks if there is anything simpler and more basic, a finer level of ``what'', that can account for the thing he saw originally. This ``sub-what'' is the physicist's notion of ``why''.
Logic: All we have said so far concerns the construction of words. But a language is made of more than the definitions of its words. All of the words, taken together, simply amount to a set of symbols in the mind for the parts of the world. In nature, though, there are not only parts that can be recognized, there are relations among them, which can be represented as rules for combining the words, so that the combinations mimic the actions of the things they represent in the world. These rules are called logic. They amount to a prescription for which ways of combining words are ``admissible'' if the resulting language is to represent the relations among the objects in the world as well as giving names to the objects themselves.
It is very important to understand that logic is as much a created entity as definition, and can also require modification or replacement if it turns out not to represent what is useful. Perhaps the best way to make this point is with an example whose derivation will be part of later chapters. One set of simple logical rules are the rules of arithmetic. 1+1=2, 3+4=7, and so forth. These rules require very few words on which to act. They require the numbers themselves, which are taken to represent some way of collecting things, like the fingers on a hand, and the notion of +, which means somehow ``bringing together'', as one does in no longer regarding a bunch of fingers as making up a group of 3 and a group of 4, but instead being considered together to make a group of 7. The rules of arithmetic are thus the rules that describe combining and dividing groups of things. It is easy to jump from counting fingers to counting miles, because you can lay miles end to end the same way you can lay fingers side by side. And from this jump, it is not hard to consider traveling those miles at different speeds, such as 3 miles in an hour, 4 miles in an hour, or 7 miles in an hour. From these steps it is very easy to conceive a logic by which one can ``add'' speeds, in miles-per-hour, the same way one adds fingers on a hand. The numbers and the rules already exist, so the logic is already complete and intact. And from walking back and forth on a train while the train is moving over the ground, it is ``easy to see'' how if you are moving and train is moving under you, you can cover more or less distance in the ``same time'' by walking with or against the motion of the train. Therefore, a natural use for arithmetic is to add speeds: 3mph+4mph=7mph. What could be easier? And, this addition is almost correct as a description of real trains (you have to be phenomenally precise to see anything wrong with it, moreso than we are able in most circumstances).
But for all of its internal consistency (what is better understood than arithmetic?), and the fact that the numbers all have names, it is not quite correct as a description of real trains, if you measure precisely enough. So, this lovely complete piece of logic turns out not to be applicable to the real world, and one has to invent another one. We will see in ch.(?) that, while the arithmetic of 1+1=2 is completely sound, it is not the only arithmetic possible, and in fact that the addition rule that we need for speeds can be written in such a way that, if one assigns numbers to the speeds in a convenient way, while 1/1000+1/1000 is almost equal to 2/1000, in this new kind of addition, 1+1=1.
This example is intended to caution against certain primitive notions, that ``pure reason'' can lead one to ``understand'' nature, and in fact that ``pure reason'' is even a meaningful expression. Such notions, in addition to probably assuming that words have some a priori meanings, seem to presume that somehow the rules for using them are equally or more ``self-evident''. Lessons with nature should have taught us better by now. It may have been a certain adherence to habit that led people to expect that the rule they could crudely measure for speeds, that 1/1000+1/1000 seemed to be about equal to 2/1000, along with the long traditions of counting fingers for which it worked so well absolutely (there is no trouble of precision in determining the number of fingers), that this rule in its pure form would be the ultimate rule for adding speeds to all precisions under all circumstances. Classically, this could be called a triumph of ``pure reason'' in predicting the bahavior of nature. It was conveniently shown to be what it was, an extrapolation from a narrow range of experiences, when it was found not to work well at all for things that are moving relative to each other at any noticeable fraction of the speed of light.
So it is important to understand that, no matter how long it has existed or how well it has served, logic is still something created by people, that may or may not be a useable set of rules for describing any particular case of interest. As such, it can at any time require revision, correction, supplementation with more complete or better rules, or replacement entirely.
Mathematics: This iconoclasty toward logic is all ventured with the highest respect, because it is all stated with the assumption that the logic is complete and consistent in the first place. That turns out to be remarkably difficult to achieve, because a langauge is a complicated construction with many places to make mistakes. It is often the case, because there are so many words and so many relations between them, that there is more than one way to ``reason'' from a question to an answer. If some set of rules makes it possible to start with the same question, but by different lines of reasoning to get to two different answers, then in fact it is not a sensible set of rules at all as regards that question or anything related to it. Therefore, it is probably best to call most of the rules of any language at any given time just ``rules'', because it will usually not be the case that they all fit together completely consistently.
Little by little, though, it has been possible to find particular small sets of words, and particular small sets of rules that apply to them, that can be shown to always produce the same answer from any question, no matter what lines of reasoning from the rules are used. These very limited sets of completely sensible language and logic are called Mathematics. Essentially, mathematics is that small part of language that is so well checked and so well understood that it can be trusted to always produce consistent results, no matter how and therefore no matter who uses it.
(Say more if or as there is a reason.)
Proof and Validation: One of the words that we will seldom use here is ``truth'', because it has been used so widely to represent so many different things that it is difficult to even say it has a particular meaning in general use. Perhaps the best way to approach the word is through what its etymology tells us was its intended use. Truth is that which can be trusted, so the intent is that it represent where one places one's confidence. Because that will be an important subject to us in its own right, we will discuss it in its own more careful terms later.
But there is another word, often associated with truth, for which we will have great need. That word is ``proof'', and unfortunately it has been abused in similar measure, because it has been as widely needed. (It is funny how those words for which there has been the greatest need are usually the most scarred and contorted, because they have passed through the most hands, and under the most circumstances of dire need that won't wait until a good use may be found. It is always the little words in a new language that will lose you.)
The wish to provide answers to questions that can be trusted imparts on us a need for two things. The first is a set of rules that even makes sense, and then the second is some justification that those are the right rules to apply to the situation under consideration. The first kind of trustworthiness comes from a kind of consistency checking that can take place entirely within the scope of the mind, because it deals only with the words and the relations established among them by the rules. The second requires a different kind of checking against experiences, to make sure that if the question is matched to one experience, the answer it predicts matches the associated ``resulting'' experience. Because these two kinds of trustworthiness are different, it is useful to have different words to refer to them.
The word proof indicates that some set of totally consistent rules (in other words, a part of mathematics) lead to a particular answer from a particular question. Thus, statements are ``proven'' entirely within the mind, and can have a complete consistency there. But before answers, even if they are proven, can be given confidence, it is necessary to check that the rules used to prove them are suitable for describing the world. This step is called ``validation'' of the rules and hence of the answer. For instance, once we have the arithmetic of fingers, and we have some approximate notions of distance and time that seem to tell us that the addition rules for speeds are the same as the addition rules for fingers, we can imagine a kind of speed for which the arithmetic of fingers is always the correct one. Since the symbols and the rules already exist and are checked, this new application of the logic is consistent and things can be proved, such as that, if 1/1000+1/1000=2/1000, then 1+1 must =2. Such proof is a nontrivial thing, and statements that can be proven are rare and exceedingly valuable among the many for which such a definite conclusion is not even possible. But they are not enough to tell us anything about nature, because the step of validation tells that, while this arithmetic is consistent, a different one, also consistent, is required to describe nature. Thus validation can be seen as a check, not only of the integrity of the operational definitions, but also of the applicability of the rules.
In learning about operational definition and abstraction, we noticed a certain iconoclasty that arises within the language of physics, because the need for sound words is stronger than the reverence for language as an inheritence. In seeing the relation of physics to logic, mathematics, proof and validity, we find a certain essential humility, because everything is ultimately subordinate to nature to test its appropriateness and its useability. Proof is the highest level of logical confidence the mind can produce, and while mathematics is continually expanding, just the great difficulty of producing any completely consistent body of logic has made it impossible to build enough math to answer more than a tiny subset of the questions people would like to know how to ask. But in spite of its difficulty and its high quality, even the proof of mathematics provides no ultimate criteria, because it is always considered possible that it will be irrelevant.
Confidence: Understanding the nature of operational definitions and the physicist's notion of abstraction, and the different kinds of consistency-checking represented by the words proof and validation, we find that the language of physics, if it is used in a pure form, has a remarkable property, which is that, with enough work, it is always possible to figure out what a statement made within this language means. If the words are defined operationally and all of the abstractions have been properly checked to make sense, it is always possible to reduce every statement to its origins in what one does or what one sees, because these have been required to be kept explicit. Further, when something is claimed, it can be distinguished whether that claim is merely self-consistent (i.e., proven), or both proven and checked for validity of its assumptions. These are the key elements that make the language of physics one that it is always possible to understand. Certainly, there is nothing in the form of the words themselves that makes it necessary or inevitable to understand them, because language cannot have that power, but if one maintains the active relation to language of always pushing through this translation to actions, the language is promised to have the internal consistency to make that effort result in understanding. In this way the language of physics has overcome the first difficulty of communication, the conveyence of reliable meaning.
Now we turn to the second thing we require of language, the ability to bestow confidence. It comes from all the same features as the ability to be understood, but has more to do with the criteria for quality that are imposed on the language as it is created. If there ever was a point about the language of physics that was not adequately appreciated, it is the nature and degree of its confidence. Yet this point is of the formost importance, because all of the use of physics can be missed if a person thinks either that there is no reason to believe it, or that it is basically irrelevant to the events of his life. This kind of disbelief is encoded in a tragic oxymoron that hearkens to the days when words were used differently. It is expressed as a distinction between what is true ``in theory'' and what is assumed to be true (i.e., relevant or trustworthy) ``in the real world''. A similar use that applies more to the people than to the work is the dismissal of an issue as ``an academic question'', as opposed to one supposed to have useful relevance. The academicians will have to to clear their own reputations, but the word ``theory'' has come to be used in a particular way within the language of physics that needs to be appreciated.
Recall that mathematics is a body of words and rules that has been checked for complete internal consistency. Therefore, if the words are taken to represent things in the world, the rules and statements of mathematics become a sort of model in the mind for things that happen in the world. All of physics is a process of trying to build and use such mathematical models, which is the concrete version of the notion of ``understanding'' nature. But like anything else that people try, this model building is not always successful, and most of the time is only partly successful and partly flawed. But sometimes, it is possible to actually build a model in which all of the steps are consistent, so that one knows how to use the words to ask questions, and knows how to use sensible rules of logic to answer them. Such a model is then properly a part of mathematics. In the parlance of physics, a consistent, predictive mathematical model of some part of nature is called a theory. The idea that it should predict correctly what happens is a guard against vacuous ``correct'' statements like ``whatever happens happens''. In some sense, this is a correct statement, but only because it has been made so poor that, in an operational sense it describes everything without distinction, so it has essentially no meaning or utility. Thus to a physicist a ``theory'' is nothing like the kind of vague speculation suggested by conventional connotations of the word.
Here a certain caution is required, because even in physics the words tends to be used in two ways, though it is always possible to distinguish them. In its most general sense, ``theory'' is used to describe any predictive mathematical model, which may or may not have yet been checked completely for validity. In a more restrictive use, the term ``theory'' denotes something that is not only internally consistent, but has also been well checked for validity and found to be extremely reliable at predicting correct answers, as in ``The Theory of Relativity''. Because of the physicist's notion of confidence, these different uses represent differences of degree rather than differences of principle, which is why a single word gets applied to both extremes.
Even in its completely unchecked sense, as ``nothing more than'' a completely consistent and predictive mathematical model, a theory is a tremendously useful thing, because it is definite enough that its claims can necessarily be shown to be either right or wrong. For this reason a theory is the kind of object that will either eventually become trustworthy because it has been well checked and successful, or be abandoned because it has been found to predict other than what happens, unlike a vague or muddy speculation which can never be pinned down and thus never laid to rest one way or another. This use of the word ``theory'' (as in ``a proposed theory for high-temperature superconductivity'' or ``a theory of cosmogenesis'') is usually found among working physicists, as a name for various models that people invent in attempts to explain phenomena (such as superconductivity at high temperatures or conditions very early in the universe that are necessary to account for the way things are now), and which are submitted so that their predictions can be checked against experiments. Such theories do not tend to live long, because it is more common to guess wrong answers than right ones, but among circumspect people they are also not advertized as conveying confidence. They are merely possibilities.
At the other extreme are such mathematical models as ``The Theory of Relativity'' or ``The Quantum Theory''. The extent that these predictive models have been checked both for internal consistency and for validity in describing nature is new in all of human history, and should be appreciated, because it is the origin of the confidence of physics. By the time they can even be called theories, it has already been required that all of their statements are so definite and well understood that they can be unambiguously tested against what can be seen as the behavior of nature. Then the testing begins, and it is the harshest testing possible. Every time a theory predicts something that is actually seen to occur in nature, it gains a little more confidence as being possibly valid. But if it ever predicts anything that contradicts what is observed, it is called wrong, and loses all validity. Sometimes a theory can be patched or revised, because there is a degree of error in what the words tell us to look for, which make it possible for the theory to still predict correct answers reliably, but only within a restricted range of validity.
It is good to make this point with an example. One of the first theories that we will discuss is Newton's formulation of a model for gravity. It is increadibly important because it was so predictive and so good at generating correct answers that it was the first truly effective demonstration that there was a method for describing nature that promised to make the world a ``knowable'' place. The introduction of this theory coincided with the beginning of the wildfire called physics that has swept the world in the three hundred years since. The ideas behind this method, and what it enables us to describe and predict, are the subjects of chapter 3.
At the time Newton's predictive model for gravity was introduced, it was not known what were its limitations, and when every answer that it predicted coincided with what was seen, to as great a precision as the measurements could yield, it was even speculated that it had no limitations, that this predictive model would describe all gravitational phenomena to arbitrary precision. If the theory is taken as that kind of an ultimatum, it turns out that it is wrong, and even catastrophically so. Before the beginning of this century it was known that, while Newton's description predicted the motions of all other the planets and all the stars as far as people could overcome the complexity to make such predictions, it predicted a definite behavior for the orbit of Mercury that was different from what could reliably be measured. This appears to have been the first ``mistaken'' prediction of Newton's theory for gravity which required Einstein's general theory of relativity to correct, though there has been a wealth of evidence added since that time which supports the same requirement. The problem that makes Newton's theory catastrophically wrong as an ultimate description, once one has evidence that General Relativity is right, is that Relativity requires the complete destruction and reconstruction of the concepts of time and distance, in ways that are incompatible with the expression of Newton's rules and would invalidate them completely as an ``ultimate'' description.
But obviously the rules are not useless, because it took more than 250 years even to find decisive evidence that there was anything for which they predicted wrong answers. And, accordingly, they are still used for almost every calculation involving gravity in everyday circumstances where their errors are smaller than anything that is measured or that affects the engineering of machines. What has happened, then, in the process of understanding not only Newton's theory, but also General Relativity which followed it, is that both Newton's rules and their answers have been shown to arise as consistent and correct rules to describe certain kinds of measurements which are not precise enough to distinguish among certain differences. Thus the words ``time'' and ``distance'' as used by Newton's formulation turn out to be, not true abstractions that are consistent with everything that has been experienced, but approximations which have the necessary properties of the better definitions under certain circumstances, and for which the accuracy of the approximation is now known, because the error from it has been provided by General Relativity.
In this way, Newton's theory of gravity has become something like the application of arithmetic to the addition of speeds. It can exist as a completely consistent internal model in the mind, and is now ``complete'' in a sense that it could not be when Newton invented it, because along with the rules for using the words comes a definite understanding of the intrinsic limitations within which the words can be taken to have a meaning. In other words, the theory now not only tells what behevior it predicts, but also tells which phenomena it can and cannot be used to describe. Taken in this more complete sense, Newton's theory survives as a `correct' theory, because there is no case ever measured which it claims to describe for which it has predicted an answer different from what is observed.
In any other environment than the language of physics, a set of predictive rules that had been tested throughout the world for generations, by the most suspicious of people, and never found to be wrong in any case, would presumably be deemed worthy of ``total confidence''. Having said as much as we have about the relation of physics to its words, the notion of ``total confidence'' clearly violates their basic rôle. Thus even Newton's theory of gravity, with its known limitations of validity, is never taken as an absolute, but only gathers more and more confidence as it works correctly more and more times. But, in the practical sense of what deserves trust as important and useful, this is clearly the most nearly absolute confidence that has ever existed, and in day to day life any physicist would more readily doubt the health of his mind at this point than expect a violation of these laws. It deserves to be said, though, that the whole point of the way in which experiments are done is intended to get around even the possibility of such things as the failure of a mind, and if an experiment were to reliably show that Newton's laws did make a wrong prediction, they would have to retrench further in their validity or be abandoned as a source of confidence.
Compared against Newton's theory of gravity, General Relativity is now the theory for which the limits are not known. The stature of this theory is truly amazing, because not only does it include intrinsically every correct prediction of the Newtonian theory and go beyond it to specify its limitations, but so far there has never been anything observed that contradicted a prediction of General Relativity. There are certain circumstantial suggestions, mostly provided by the Quantum Theory but somewhat within its own structure, that it too will not be an ``ultimate'' theory, but these objections can only be found to apply to such exreme circumstances that it has not been remotely possible to perform tests under these conditions to suggest what form the next improvement might have.
The case is even more extreme for the Quantum Theory, which not only has no wrong predictions or suggested internal difficulties, but which it has also been possible to test to far greater precision and in a wider variety of cases than has General Relativity, because the special properties it predicts for the parts of nature tend to be more drastic and more accessible than those that distinguish Einstein's from Newton's gravity. To give a sense of scale, it is worth mentioning that the most precise of these tests of the quantum theory is a measurement of a certain magnetic property of the electron, which agrees within the accuracy of the prediction. But that accuracy is phenomenal, because if this were instead a prediction of the distence from Los Angeles to New York, a similar agreement would require that the prediction be correct to within the width of a human hair (assuming, of course, that the notion of a ``distance'' between two cities were given a meaning at that level of precision). The only thing that suggests the incompleteness of the current form of the Quantum Theory is the fact that it has not been possible to absorb General Relativity into itself, which is more a caution about its completeness than about its ultimate correctness.
So the sense of confidence of physical statements can be summarized as follows. While the notion of confidence in physics is, because of the nature of the field, never accorded the status of an absolute, a ``theory'' that has come to be well validated as ``correct'' or ``trustworthy'' or ``true'' contains the most confident predictions that it has ever been possible to make. The theory is required, first, to be so clear, so definite and so consistent, that all of its statements can be definitively tested against experience with the real world, and for the theory to be valid such tests have to have been made widely, precisely, and must never have been found to be wrong. That is why it is an oxymoron to distinguish between ``theory'' and ``practice'' or ``experience in the real world''. When it is possible to create a valid one, a theory is the most checked and the most reliable description of the real world that it has ever been possible to make. And that is why, if there is anything known by people that deserves the effort to understand and to use, it is the content, attitude and methods of physics.
Experiment, Thought Experiment: The ability to test and check, over and over again, and so to establish confidence, has come with the appreciation that nature's events are truly repeatable. This has led to a refinement of peoples' ways of observing, known as ``experimentation''. The power of experimentation is that it frees people from second-hand reports about one-time occurences, and that it gives them better control over what they see. An experiment (from the French word ``experiment'', meaning simply ``experience'') is nothing more nor less than an attempt to arrange some piece of nature so that the desired phenomenon happens where you can see it, and to have enough control over the circumstances that can draw conclusions, reliably, about what you have seen. Technically, this has become a highly refined discipline and even art, but the principle is so simple, it is hard to appreciate how fundamental it is, as the progenitor and basis of every claim made in physics.
While experiments, by definition, are made of experiences, books, conversations and arguments are only made of words. The fact that we have begun to learn how to speak, though, has led the lanuage to take on some of the consistency of the natural phenomena it describes. This has been very useful because talk, unlike experience, is cheap. A good language, well used, can be very powerful in leading people to look for physical answers in fruitful places. If experiments had to be performed at random, the cost of learning new things would be frightfully high. Therefore, a certain very careful way of arguing has arisen, and come to be known as ``thought experiment''. Unlike real experiment, thought experiment bestows no fundamental confidence. However, effectively used, it can encompass the results of many real experiments in organizing the mind, keep people from pursuing many badly formed notions with expensive experiments that lead nowhere, and suggest clever new experiments that would never have been imagined at random. In these chapters, we will present many things in the language of thought experiment, because there is only so much that words can do, and also for another reason. Thought experiments can bring effects that occur at the fringes of experience into the realm of the familiar, without losing their logical order, if they are used carefully.
The essence of a thought experiment, that distinguishes it from any line of ``argument'', is this: Drawing on experiments that actually have been performed, one can imagine new experiments that could consistently be performed, and what their answers should be, even when they have not been. Many examples of this will be generated in the chapters on relativity. We will talk about what people in fast spaceships would see, hear and feel. Humans have never built such spaceships. They have, however, done very closely controlled experiments with elementary particles. Elementary particles cannot see, hear or feel, but they do age in predictable ways, respond to accelerations, and so forth. In many ways, particles have told us enough that we can accurately constrain what a person should feel under similar circumstances. This is because everything about the experiments indicates that there is no impediment to performing the same activities with people that have been performed with particles, apart from horrendous expense.
In a similar manner, we can imagine combinations of real experiments which happen, for one reason or another, never to have been performed. The only requirement is that our imaginations refer entirely to parts of experiments which have been performed, in such a way that nothing about the previous experiments indicates that they should work differently when we put them together.
The reason this point is raised here is that the reader is about to be exposed to some wild examples. Many of the activities we propose (building scaffolds around black holes, for example) are strange enough that it is unlikely anyone will ever do them. The thing to understand is that, despite their strangeness, these examples have been carefully chosen to respect all of the experiments that really have been done. As such, they are actually less cavalier than almost any claims that can be made, and the conclusions drawn from them are intended very seriously. The color of hyperbole is used, because sometimes extreme stories make their points more obvious, and because, in very real terms, most everything that is described, as far as we know, could really be done.
Intellectual Independence: It is no accident that everything that has been described here carries so strongly the inference toward the individual. The nature of the definitions and the way they are translated into actions, the suspension of reverence for tradition and the constant subordination to the experiences with nature, and the fact that a single observation can invalidate the most triumphant theory or cause its modification, all hint at the extreme power of individual actions and observations, not only in extracting use from the language but also in determining how it will be formed. This highly individual nature of the relation to the physicist's language is probably principally responsible for the success of physics and the rapid pace of its progress, and it carries a special implication for the way the results of physics can be learned and should be afforded confidence.
When ``knowledge'' or ``truth'' are taken as dogma that have to be accepted in part on faith from some authority, the acceptance robs the individual of a certain power to either create or change what is ``known''. But the needs of individuals for useful knowledge are as varied as their circumstances, and when the knowledge cannot be criticized as often as it needs to be used, groups of people become more like strange animals with many arms and legs and very few minds, than like real collections of whole people. Such an arrangement, created by an authoritative relation to knowledge, is a waste of resources, because every opportunity to use something that has been learned constitutes an opportunity to test its integrity, and the relation of people to knowledge should exploit and make the most possible use of this opportunity. It is probably true that, by making language for the first time completely translatable into action, and so completely the domain of any person, physics has first made it possible to make use of whole large populations of people, rather than small or isolated priesthoods of erudition, to check for mistakes.
In much the same way as it is easy to make mistakes, it is truly difficult to create insightful and useful, let alone completely consistent descriptions. In providing a relation to ideas through which it ceased to matter who was responsible for their creation, because it was only their efficacy at describing nature that required or withheld validation from them, the language of physics for the first time made it possible for people, as a group, to take real advantage of the creative efforts of many individuals, because no authority was required to determine what was correct, once the notion of correctness came to be understood as something that could be established equally and independently by every person who used the knowledge, and in fact that any notion of correctness that lacked this relativism also lacked content. In that way, the absolute repeatability of our experiences with nature replaced meaningfully the coordination and organization that it was never possible to provide with authorities for validation, and further unlike the authorities, to provide it for as many people as desired with equal efficacy. This is probably how, in such a short fraction of human history, the knowledge base of physics has come to include so many remarkable and powerful descriptions, and to be so very effectively cleaned of mistakes and wrong assertions. It exploits the power of people's desires and abilities, not only their wish to create, but also their desire to eliminate mistakes from the knowledge they want to trust, and even their hostility to any foreign or competing ideas. Once the criterion of correctness ceases to depend on any one person's endorsement, the most hostile of people toward an idea become some of the most valuable, because they are most driven to find any mistake it may have. An eloquent occurence that is common nowadays is also that the most hostile of people to an idea often become its strongest adherents if the idea turns out to be truly good, and their best efforts to find mistakes only validate it further instead. This represents a new achievement also of the ability to value correctness even over prejudice and initial incentive.
These same features that have made the language and the relation of physicists to it successful indicate how it should be used. The whole reason physics is important is that it describes the world we live in, and so should describe what we experience and what we choose to do within that world. It therefore represents the greatest misunderstanding of everything about the subject to approach it as something to be inherited from authorities or accepted on faith, when everything about the structure of the language begs that it be compared against the events of life. Thus in most instances, even if the claims of physics had not been tested as well as they have, it would be possible to decide whether to accept and act on them or not, simply by applying them to what you see around you and seeing if they work. This is the process of creating confidence which has been its whole source in physics all along.
The constant process of understanding, applying, testing and using everything one hears against the touchstone of one's own life, and of elevating individual experience with nature as the ultimate judge of validity, creates in the individual what could be called Intellectual Independence. This trait is of inestimable value, and trying to develop it seems to be a natural thing for people to do, as evidenced by the persistent probing and testing of very young children of everything they are told against their day-to-day experiences. Unfortunately, when knowledge is regarded as intrinsically authoritative, the acceptance of the terms of ``knowledge'' suppresses the independence of the intellect, and the simple weight and inefficiency of trying to use an authoritative knowledge structure eventually suppresses any incentive even to question. Thus while a desire for intellectual independence seems to be a feature of uncorrupted humans, the simple fact that it has been so little rewarded has suppressed it in the culture before now.