The Disappearance of Time
13 Let us consider the discovery of one of the simplest and most profound patterns found by ancient astronomers. The word "planet" comes from the Greek word for wanderer, but the planets don't wonder all over the sky. They all move along a great circle called the ecliptic, which is fixed with respect to the stars. The discovery of the ecliptic must have been the first step in decoding the records of planetary positions. A circle is a mathematical object, defined by a simple rule. What does it mean if a circle is seen in the motions in the sky?
Is this the visitation of a timeless phenomenon on into the ephemeral, time-boundworld? This might be how we would see it, but this is not how the ancients understood it.
The universe, for the ancients, was split into two realms: the earthly realm, which was the arena of birth and death, of change and decay, and the heavenly realm above, which was a place of timeless perfection. For them the sky was already a transcendental realm; it was populated by divine objects that neither grew nor decayed.
This was, after all, what they observed. Aristotle himself noted that “in the whole range of time past, so far as our inherited records reach, no change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts”.
If the objects in this divine realm were to move, these movements could only be perfect and thus eternal. To the ancients, it was evident that the planets move along a circle because, being divine and perfect, they could move only on the curve that was the most perfect. But the earthly realm is not perfect, so it might have seemed bizarre to them to describe motion on Earth in terms of perfect mathematical curves.
The division of the world into an earthly realm and heavenly spheres were codified in Aristotelian physics. Everything in the earthly realm was composed of mixtures of four elements: earth, water, air, fire. Each had a natural motion: the natural motion of earth, for example was to seek the centre of the universe. Change followed from the mixing of these four essences. Aether was the fifth element, the quintessence, which made up the heavenly realm and the objects that moved across it.
14 This division was the origin of the connection of elevation with transcendence. God, the heavens, perfection - these are above us, while we are trapped here below. From this perspective, the discovery that mathematical shapes are traced by motions in the sky makes sense, because both the mathematical and the heavenly are realms that transcend time and change. To know each of them is to transcend the earthly realm.
Mathematics, then, entered science as an expression of a belief in the timeless perfection of the heavens. Useful as mathematics has turned out to be, the postulation of timeless mathematical laws is never completely innocent, for it always carries a trace of the metaphysical fantasy of transcendence from our earthly world to one of perfect forms.
38 Doing physics in a box
We live in a universe that is always changing, full of matter that is always moving. What Descartes, Galileo, Kepler, and Newton learned to do was to isolate little pieces of the world, examine them and record the changes in them. They showed us how to display the records of these motions in simple diagrams whose axes represents the positions and times in a way that is frozen and hence amenable to being studied at our leisure.
Notice that to apply mathematics to a physical system, we first have to isolate it, and, in our thinking, separate it out from the complexity of motions that is the real universe. We couldn't get very far with the study of motion if we worried about how everything in the universe affects everything else.
The pioneers of physics, from Galileo to Einstein and up to the present day, could make progress because they could isolate a simple subsystem, like a game of catch, and study how the ball moves. In reality, though, a ball in flight is influenced in a myriad of ways by things outside the subsystem we defined. The simple description of a game of catch as an isolated system is a crude approximation of the real world - although one that has proved fruitful in discovering fundamental principles that appear to govern all motion in our universe.
This kind of approximation, in which we restrict our attention to a few variables or a few objects or particles, is characteristic of doing physics in a box. The key step is the selection, from the entire universe, of a subsystem to study. The key point is that this is always an approximation to a richer reality.
Boe: approximation - selection - Luhmann: system/environment - problems of Form.
It's easy to generalise our treatment of the game of catch to a large number of systems we study in physics. To study a system, we need to define what it contains and what is excluded from it. We treat the system as if it were isolated from the rest of the universe, and this isolation is itself a drastic approximation. We cannot remove a system from the universe, so in any experiment we can only decrease, but never eliminate, the outside influences on our system. In many cases, we can do this accurately enough to make the idealisation of an isolated system a useful intellectual construct.
Part of the definition of a subsystem is a list of all the variables we need to measure in order to determine everything we want to know about it at a moment of time. The list of these variables makes up an abstraction we call the configuration of the system. To represent the set of all possible configurations, we define an abstract space called the configuration space.
Each point of the configuration space represents one possible configuration of the system.
The process by which the configuration space is defined starts with extracting the subsystem from the larger universe. Hence, the configuration space is always an approximation to a deeper and more complete description.
The configuration and its representation in a configuration space are both abstractions - human inventions that are helpful for the method of doing physics in a box.
44 We should be aware that this powerful method is based on some powerful assumptions. The first is that the configurations space is timeless.
It's assumed that some method can give the whole set of possible configurations ahead of time - that is, before we watch the actual evolution of the system. The possible configurations do not evolve, they simply are.
A second assumption is that the forces, and hence the laws the system is subject to, are timeless. They don't change in time, and they also presumably can be specified ahead of the actual study of the system.
The lesson here is as simple as it is terrifying. To the extent that the assumptions underlying the Newtonian paradigm are realised in nature, time is inessential and can be removed from the description of the world.
If the space of possible configurations can be specified timelessly, and the laws can as well, then the history of any system need not be seen as evolving in time. It is sufficient, for answering any question physics can pose, to see the whole history of any system as a single frozen curve in configurations space.
The seemingly most essential aspect of our experience of the world - its presentation to us as a succession of present moments - is missing from our most successful paradigm for the description of nature.
88 Time Reborn
103 The Cosmological Challenge
The great theories of 20th century physics - relativity, quantum theory, and the Standard Model - represent the highest achievements of physical science. They have beautiful mathematical expressions that result in precise predictions for experiments, which have been confirmed in many cases to great accuracy. And yet I argue that nothing along the lines of these theories can serve as a fundamental theory.
To support this claim, I can point to a feature that all established theories of physics share and which makes it difficult to extend them to the whole universe: each divides the whole world into parts, one that changes over time and the second assumed to be fixed and unchanging. The first is the system being studied, whose degrees of freedom change with time. The second is the rest of the universe; we can call it the background.
Boe: systemstheory: system/environment - fundamental assumptions.
104 The division of the world into a dynamical and a static part is a fiction, but it is an extremely useful one when it comes to describing small parts of the universe. The second part, assumed to be static, in reality consists of other dynamical entities outside the system being analysed. By ignoring their dynamics and evolution, we create a framework within which we discover simple laws.
The challenge we face when extending science to a theory on the whole universe is that there can be no static part, because everything in the universe changes, and there's nothing outside of it - nothing that can serve as a background against which to measure the motion of the rest. The invention of a way to surmount this barrier might be called the cosmological challenge.
105 The cosmological challenge requires us to formulate a theory that can be applied meaningfully to the whole universe. It must be a theory in which every dynamical actor is defined in terms only of other dynamical actors. Such a theory has no need of, and no place for, a fixed background; we call such theories background-independent.
We can see now that the cosmological dilemma is built into the structure of the Newtonian paradigm, because the very features responsible for success on smaller scales - including the dependence on fixed backgrounds and the fact that one law has an infinite number of solutions - turns into the reason for the paradigm's failure as the basis for a theory of cosmology.
107 We are ready to reverse the expectations that have guided physics from the time of Newton until very recently. Formerly, we thought of theories like Newtonian mechanics or quantum mechanics as candidates for fundamental theories that - if they succeed - would be perfect mirrors of the natural world, in the sense that everything true about nature would be echoed by a mathematical fact that is true of the theory.
The very structure of the Newtonian paradigm, based on timeless laws acting on a timeless space of configurations, was thought to be essential to this mirroring.
I am proposing that this aspiration was a metaphysical fantasy guaranteed to lead to the aforementioned dilemmas and confusions as soon as we tried applying that paradigm to the whole universe.
This stance requires a re-evaluation of the status of theories within the Newtonian paradigm - from candidates for fundamental theories to approximate descriptions of small subsystems of the universe. It is a re-evaluation that has already taken place among physicists and consists of two related changes of perspective:
1. All the theories we work with, including the Standard Model of Particle Physics and general relativity, are approximate theories, applying to truncations of nature that include only a subset of the degrees of freedom in the universe. We call such an approximate theory an effective theory.
2. In all our experiments and observations involving truncations of nature, we record the values of a subset of degrees of freedom and ignore the rest. The resulting records are compared with the predictions of effective theories.
Boe: Effecvtive theories - isolated systems - open systems; fundamental theories - Supertheory!
108 So the success of physics to this day is entirely based on the study of truncations of nature, which are modelled by effective theories. The art of doing physics at the experimental level is all about designing experiments to isolate and study a few degrees of freedom, ignoring the rest of the universe. The methodologies of theories are aimed at inventing effective theories to model the truncations of nature that the experimentalists study. Never in the history of physics have we been able to compare the predictions of a candidate for a truly fundamental theory - by which I mean one that cannot be understood as an effective theory - with experiment.
A subsystem of the universe modelled as if it were the only thing in the universe, neglecting everything outside it, is called an isolated system. But we should never forget that isolation from the whole is never complete. As noted, in the real world there are always interactions between any subsystem we may define and things outside it. To one extent or another, subsystems of the universe are always what physicists call open systems.
These are bounded systems that interact with things beyond those boundaries. So when we do physics in a box, we are approximating an open system by an isolated system. A great deal of the craft of experimental physics consists of turning open systems into all (approximately) isolated systems. We can never do this perfectly.
Nothing can be perfectly isolated.
Boe: approximations to truth: there are no timeless, eternal truths!
112 This may seemed disappointing. Physics is supposed to be about discovering the fundamental laws of nature. An effective theory is by definition not that. If you have too naive a view of science, you might think that the theory could not both agree with all experiments yet carried out and be considered at best only an approximation to the truth. The concept of an effective theory is important, because it expresses the subtle distinction.
The notion of an effective theory implies that progress in physics entails revolutions that completely change the conceptual bases of our understanding of nature while preserving the success of earlier theories. Newtonian physics can be considered an effective theory, applying to a domain in which speeds are much lower than that of light and quantum effects can be ignored. Within that domain, it remains as successful as it ever was.
General relativity is another example of a theory that was once a candidate for a fundamental description of nature but which is now understood to be an effective theory. For one thing, it leaves out the domain of quantum phenomena. General relativity is, at best, an approximation to a unified quantum theory of nature, and may be arrived at by truncating that more fundamental theory.
Quantum mechanics, too, is likely an approximation to a more fundamental theory. One sign of this is the fact that its equations are linear - meaning that the effects are always directly proportional to their causes. In every other example in which a linear equation is used in physics, the theory is known to arise as an approximation to a more fundamental (but still effective) theory that is nonlinear (in the sense that the effects may be proportional to a higher power of the cause), and the best bet is that this will turn out to be true of quantum mechanics as well.
The fact is that every theory we have so far used in physics has been an effective theory. It is sobering to realise that part of the cost of their success was the realisation that they are approximations.
Boe: non-linear theory: re-entry - non-trivial machines
We still may harbour the impression to invent a fundamental theory that describes nature without approximation. Both logic and history tell us this is impossible as long as we stay within the Newtonian paradigm. So as admirable as Newtonian physics, general relativity, quantum mechanics are, they cannot be the template for a fundamental cosmological theory. The only possible path to such theory is to take up the cosmological challenge and devise a theory not patterned on the Newtonian paradigm that can be applied to the whole universe without approximation.
114 Principles for a New Cosmology
We now begin our search for a theory that can truly be a theory of the whole universe such a theory must avoid the cosmological dilemma, and it must also be background-independent - not presuming a division of the world into two parts, one containing dynamical variables that evolve, the other containing fixed structures providing a background to give meaning to the evolving parts. Everything in the theory asserts its part of reality must be defined by its relationships to the rest of reality, in a way that renders it subject to change.
What must we require of a true cosmological theory?
Any new theory must contain what we already know about nature.
The new theory must be scientific: A real theory must imply specific testable predictions.
The new theory should answer the “Why these laws?” question.
The new theory should answer the “Why these initial conditions?”.
115 These are minimal requirements. The explanations such a theory gives of features of our universe must depend only on things that exist or occur within the universe. No chains of explanation can point outside the universe. So we must demand a principle of explanatory closure.
To be scientific, a theory needn't give the precise answer to any question you can conceive of, but there should be a great number of questions we believe we could answer if we knew more details about the universe. Leibniz’s principle of sufficient reason postulates that there should be an answer to any reasonable question we might ask about why the universe has some particular feature. An important test of the new scientific theories where the rate increases the number of questions we can answer. Progress occurs when we discover reasons for aspects of the universe that were unexplained by earlier theories
116 Leibniz’s principle has some consequences that should constrain a cosmological theory. One is that there should be nothing in the universe that acts on other things without self being acted upon. All influences of forces should be mutual. We can call this the principle of no unreciprocated actions.
This principle, then, forbids any reference to all fixed-background structures - entities whose properties are fixed for all time, regardless of the motion of matter. These background structures are the unconscious of physics, silently shaping our thinking to give meaning to the basic concepts be used to imagine the world. We think we know what “position” means because we are making unconscious assumptions about the existence of an absolute reference.
Several of the fundamental steps in the evolution of physics have consisted of recognising the existence of a fixed-background structure, removing it, and replacing it with a dynamical cause within the universe. This is what Ernst Mach did when he refuted Newton by suggesting that we feel dizzy when we spend because we move relative to the matter are in the universe rather than to absolute space.
If we insist on reciprocal action and rule out fixed-background structures, what we are saying is that every entity in the universe evolves dynamically, in interaction with everything else.
This is the essence of the philosophy of relationalism, which is usually attributed to Leibniz. We can extend this idea to assert that all properties in a cosmological theory should reflect evolving relationships among dynamical entities.
118 We now come to the most important question about the unknown cosmological theory: What will it have to say about the nature of time?
Will time be dissolved, as in Einstein's theory of general relativity?
Will time disappear and emerge only when needed,? Or will time play an essential role, unlike any of the theories since Newton?
I believe that time is needed for any theory that answers the Why these laws? question. If laws are to be explained, they must evolve. This was argued by Charles Sanders Peirce:
To suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational, is hardly a justifiable position. Uniformity is precisely the sort of facts that need to be accounted for…Law is par excellence the thing that wants a reason. Now the only possible way of accounting for the laws of nature and for uniformity in general is to suppose them results of evolution.
121 We conclude that the only way to have a scientific cosmological theory that can make falsifiable predictions is if the laws evolved in time. (The prediction of a theory is falsifiable if it could be contradicted by a doable experiment). Roberto Mangabeira Unger puts this more elegantly: Either time is real or it is not. If time is not real, then laws are timeless - but then the choice of laws is inexplicable, for reasons we have already discussed.
If, on the other hand, time is truly real, then nothing, not even the laws, can last forever. If the laws of nature act forever, we are in the Newtonian paradigm, and you could use them to reduce any property of the world at a later time to a property at an earlier time. So time being real means laws don't last forever. They must evolve.
The notion of timeless laws also violates the relational principle that nothing in the universe acts without being acted on. If you choose to except the laws of nature from this principle, seeing them as something outside the universe, you put them outside the realm of rational explanation. To make laws explicable we must consider them as much a part of the world as the particles they act on. This brings them into the purview of changing colours at it. They become explicable only when they participate in the dance of change and mutual influence that makes the world a whole.
Boe: dance of change –becoming (Hegel); mutual influence – interaction, communication! - Tales of Time and Change
123 The Evolution of Laws
The main message so far has been that the cosmology to progress, physics must abandon the idea that laws are timeless and eternal and embrace instead the idea that they evolve in real-time. This transition is necessary though that we can arrive at the cosmological theory - one that explains the choices of laws and initial conditions - that is testable and even vulnerable to falsification by doable experiments. The theory in which laws evolve is called cosmological natural selection.