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I read all the questions and responses related to determinism, quantum mechanics

I read all the questions and responses related to determinism, quantum mechanics and chaos theory that you have posted, but I am still unclear exactly how they relate. Supposedly, quantum mechanics and chaos theory refute any hard case for determinism, but I am still unclear as to how. Could anyone add to this or suggest some reading on the subject?

Determinism is the view that the state of the world at any moment, plus the laws of nature, determine (i.e., logically entail) the state of the world at any other moment. Quantum mechanics and chaos theory relate to determinism in rather different ways.

Chaos theory concerns systems whose development is exquisitely sensitive to their current state -- in that a very small change to their current state would produce enormous changes to their later state. A chaotic system is not incompatible with determinism as I have defined it above. But the existence of chaotic systems entails that any small uncertainty in our knowledge of that system's initial conditions (and some such uncertainty is always present, for grubby practical reasons) will quickly ramify into great uncertainty in our predictions regarding that system, even if we know all of the relevant laws of nature.

None of this threatens determinism as a view about prediction "in principle." But quantum mechanics does that. The complete state of a system, as quantum mechancs describes it, fails (when combined with the laws of nature given by quantum mechanics) to determine the outcomes of later measurements on that system. If quantum mechanics gives a complete description of the universe, then the universe is indeterministic.

Well, that's roughly right. It leaves out some important complications, such as (i) the fact that there are some deterministic interpretations of quantum mechanics, though those interpretations involve their own weird elements, and (ii) quantum mechanics is perfectly deterministic except insofar as it concerns measurement outcomes. That is, in a universe without observers but governed by quantum mechanics, determinism would hold. That observers (or measuring devices) have a special role in quantum mechanics is pretty weird -- arguably, a great deal weirder than indeterminism.

Could a newly discovered law of physics ever change/affect a law of logic?

Could a newly discovered law of physics ever change/affect a law of logic?

Very good question!

Let's begin by drawing an important distinction. By "changing a law of logic", you might mean (i) our changing our minds about what the laws of logic are, or (ii) the actual laws of logic changing -- one set of laws was in force at one time and another set is in force at another time. I will assume you had option (i) in mind, since the idea that the laws of logic change is at least as weird as the idea that the laws of physics change (which is to say: pretty weird), and in any case, the change would surely not be a result of something as cosmically inconsequential as our making a certain scientific discovery!

So, your question now is: Could we be justified in changing our minds about what the laws of logic are as a result of a discovery in physics? This is a controversial question. Some philosophers have said that we know the laws of logic a priori -- that is, independent of sensory input. In general, such philosophers do not think that we could justly change our minds about what the laws of logic are as a result of a discovery in physics. If a discovery in physics led us to recognize that, say, the distributive law of logic (i.e., "p and (q or r) if and only if (p and q) or (p and r)") is false, then we really recognized this fact independent of any particular observation made by scientists. The scientific discovery simply caused us to recognize something; it did not play any role in our justification for our new beliefs about the laws of logic.

On the other hand, some philosophers (Duhem, Poincare, Carnap, famously Quine, and Putnam at certain moments) have thought that our beliefs about the laws of logic are just as vulnerable to being overthrown by observations of the world as our strongly held scientific theories are -- which is to say, it would take some very remarkable observations to overthrow these beliefs, but that this sort of thing can happen, especially in a "scientific revolution." Some philosophers have even argued that discoveries in quantum mechanics have called into question the distributive law (mentioned above).

Did Einstein ever engage the "scientific method" of empirical investigation in

Did Einstein ever engage the "scientific method" of empirical investigation in the course of his work on special and general relativity; and if not, wasn't he more a philosopher of science (albeit an exceptionally productive and influential one) than a scientist? If Einstein simply engaged in a priori reasoning and conceptual analysis (using his famous thought-experiments) then I don't see why the physics community has any more claim to him than the philosophical community. After all, it seems that his methodolgy bore a much stronger resemblance to that of contemporary philosophical efforts than it does to anything going on in or commonly associated with physics departments. -Will Leonard

An excellent question!

Many of Einstein's most famous papers make shockingly few references to the details of previous empirical work by other scientists. To put the same point in another way, many of Einstein's most famous arguments arise largely from "philosophical" considerations. For instance, Einstein's 1905 special theory of relativity paper begins by noting a symmetry in electromagnetism: that the current induced by a magnet moving relative to a loop of conducting wire is the same, according to electromagnetic theory, whether the magnet is moving and the conductor is at rest, or vice versa, as long as their relative motion is the same in both cases. However, Maxwell's electromagnetic theory (as it was then understood) assigns the induced current different causes in the two cases. Einstein suggests that the current should be understood as having the same cause in the two cases, which leads him to suppose that there is no fact about whether a force is really electric or magnetic. Clearly, this argument invokes a kind of parsimony in explanation that has plenty of antecedents in philosophy. Furthermore, this argument is inspired by concerns about the reality of absolute motion, over and above relative motion, that go back at least to Newton and Leibniz.

Einstein was quite familiar with philosophical work on scientific reasoning -- such as Duhem's view that scientific theories are tested as a whole, rather than each bit of a scientific theory being tested individually and therefore having to make empirical predictions all by itself. Einstein also emphasized that in undermining the traditional picture of space and time, he was inspired by the thought that all scientific concepts are free creations in response to evidence rather than compulsory in virtue of the fixed structure of the human mind. In this regard, he cited Hume and Mach as important influences.

All of that being said, I would still want to insist that Einstein was a scientist doing science. His goal was to account for various observations, and his "thought experiments" were always in the service of that goal. For instance, Einstein said that he got heart palpitations when his calculations revealed that the general theory of relativity could account for the longstanding anomaly in the motion of Mercury. Of course, Einstein was a theorist, not an experimentalist. (There is the famous episode in which Hubble gave Einstein a tour of the gigantic California telescope at which Hubble discovered that the universe is expanding; during the tour, Mrs. Hubble allegedly said to Mrs. Einstein that this was the place where her husband discovered the structure of the universe, and Mrs. Einstein replied that her husband did that on the back of an envelope.) But Einstein's theories were aimed at addressing problems arising from science.

It is often difficult to say where philosophy ends and science begins. I would not want to insist on a sharp line demarcating them. (This point extends beyond physics. Do investigations into the evolutionary origins of moral and aesthetic sentiments constitute philosophy or science?) And I would not be eager to embrace the questioner's presupposition that there is a distinctive "scientific method." But I do regard Einstein as a scientist -- one whose work continues to have great philosophical significance and shows great philosophical sensitivity and courage.

Do computers defy the law of conservation of mass? Because, if a computer can

Do computers defy the law of conservation of mass? Because, if a computer can copy a program there is twice the amount of space taken up. But how can you just duplicate an amount of space (MB, KB, GB,etc.) if you add nothing to it?

One way to think of why this might seem puzzling is in terms of the type-token distinction. To understand that distinction, consider the question how many words there are on the next line:

The The The The

You could answer "four" or you could answer "one", and both are correct. It's just that when you answer "four", you're talking about word-tokens, and when you answer "one", you're talking about word-types.

This distinction applies to lots of different kinds of things: words, sentences, musical compositions, and, indeed, computer programs. As we normally talk of computer programs, they are types. You and I might install the very same program on our computers, just as we might write the very same word. But there are also program tokens, and our computers have different tokens of the program sitting on their hard drives, or in memory, or what have you. When you copy a program, you create a new token of it, and so you do "add something", as it were, even though, in another sense, you do not create a new program, because you do not create a new program type but only a new token of an old type. So, indeed, twice the amount of memory is consumed, because what is stored in memory are tokens.

Quantum behaviour says that before a phenomenon is observed there may be a

Quantum behaviour says that before a phenomenon is observed there may be a number of possible outcomes. Once observed, the number of possible outcomes becomes one; what actually happened? Surely the present moment consists of an infinity of phenomena which, with the benefit of Quantum hindsight, may be seen to have *actually* been certainties. Uncertainty exists only in the mind of an imperfect observer; there’s no such thing as foresight outside of a limited, dry mathematical framework. This leads me to think the following; i) That everything is as it is because it could not possibly have been any other way. ii) All the things in the universe whose extremely improbable existence we marvel at and things which everything else depend on who, if they were any other way, lots of other things wouldn’t work either, were actually (in retrospect), absolute certainties. Is this a gross misunderstanding of Quantum theory, an obvious conclusion, or a line of thinking with some mileage? I can see it leading...

The problem you raise in your first paragraph is called the measurement problem: What happens when a measurement takes place?

Most physicists would not agree with your statement that "Surely the present moment consists of an infinity of phenomena which, with the benefit of Quantum hindsight, may be seen to have actually been certainties." The way most physicists interpret quantum mechanics, the uncertainty about the outcome of a measurement is not "only in the mind of an imperfect observer," but rather in the world itself. For example, before you measure the position of a particle, it simply doesn't have a position. It's not just that we don't know its position, it's that it doesn't have a position.

This interpretation seems to be forced on us by experiments like the famous two-slit experiment. In this experiment, particles are fired at a barrier with two slits in it, and then their positions are recorded when they strike a screen behind the barrier. These positions form an interference pattern, similar to the interference pattern that would result from waves coming through the two slits and then interfering with each other. However, if you cover one of the slits, then the interference pattern goes away. If each particle went through one slit or the other, then you might expect the observed pattern to be a combination of the patterns you get with one slit or the other covered, but that's not what is actually observed. It seems as if each particle somehow goes through both slits--and therefore doesn't have a single precise position when it goes through the barrier. However, when it strikes the screen its position is measured and it is found to be at a particular position. Thus, on this interpretation of quantum mechanics, measurement is a mysterious process in which something that was indeterminate somehow becomes determinate.

However, there are other interpretations of quantum mechanics, sometimes called hidden variable interpretations, in which particles do have precise positions at all times. One such theory is David Bohm's theory. In this theory, the outcome of a measurement is predetermined, and uncertainty exists only in the mind of the observer. One advantage of this theory in my opinion is that it completely solves the measurement problem: A particle has a precise position at all times, and when you measure its position you find out where it is. There is no mysterious process of a position that was indeterminate becoming determinate. (The way Bohm's theory deals with the two-slit experiment is that the particle goes through only one slit, but there is also a wave that goes through both slits and then forms an interference pattern that guides the trajectory of the particle.)

Even in a deterministic theory like Bohm's, I'm not sure I would go along with your statement that "everything is as it is because it could not possibly have been any other way." In a deterministic theory the outcome of an experiment is determined by the initial conditions. The outcome could have been different if the initial conditions were different, so I wouldn't say that no other outcome was possible. It depends on what you mean by "possible", but if different initial conditions are considered to be possible, then different outcomes are possible as well.

A good reference for Bohm's theory: J. S. Bell, Speakable and unspeakable in quantum mechanics, Cambridge University Press, 1987.

Is it possible to determine whether the laws of Physics as they are currently

Is it possible to determine whether the laws of Physics as they are currently perceived will last indefinitely? Is there anything to prevent the nature of the universe changing so much tomorrow that reality as we know it breaks down?

Kant thought he had a strong answer to Hume, but this answer requires embracing a strange metaphysical doctrine of transcendental idealism that few have found palatable. Kant' s best discussions of this occurs in his Critique of Pure Reason.

Suppose, however, that we reject "strange" answers like Kant's idealism, and suppose we also admit that we cannot prove that the laws of physics will remain unchanged in the future. There may still be strong reasons why we ought to believe that the laws of physics will be invariant, for example because this belief is necessary for motivating people to be moral or for motivating humans to conduct scientific investigations of the world.

There are strands of both strands of argumentation--the "strange" idealistic one and the "practical" one about human motivation--in Kant's discussion of the systematicity of nature and the regulative use of reason in the first introduction to the Critique of Judgment.

Why is the Big Bang theory the most widely accepted theory of the creation of

Why is the Big Bang theory the most widely accepted theory of the creation of the universe?

The Big Bang theory nicely explains the expansion of the universe (discovered by Hubble in the 1920's). Obviously, that the universe is expanding suggests that it was a good deal smaller in the past. Likewise, the Big Bang theory nicely explains the cosmic microwave background radiation (detected by Penzias and Wilson in the 1960's, and predicted by Wilkinson and Dicke before that). This pervasive, pretty uniform, low-temperature radiation suggests that the universe was considerably hotter in the distant past. The rival "steady state" model of the universe has difficulty explaining these observations.

However, the "Big Bang theory" is no longer a single theory. Various alternative Big Bang models have been developed (such as the "inflationary" Big Bang theory) to account for additional facts that have been discovered (such as the value of omega, the ratio of the universe's total kinetic energy of expansion to its gravitational potential self-energy, which tends to slow down the expansion). At the moment, there is no serious rival to some sort of Big Bang model.

Finally, the Big Bang theory fits nicely with the general theory of relativity, according to which space and time are not some sort of unvarying stable stage on which the acts of the universe's history play out, but rather are themselves dynamic actors. The Big Bang is supposed to be the "creation of the universe" where the "the universe" includes space and time.

Science states that space is endless, and ever expanding. But, if we are inside

Science states that space is endless, and ever expanding. But, if we are inside the planet earth, the planet earth is inside the galaxy, the galaxy is inside space, then what is space inside? What is it expanding in? And if space is endless, how can it expand?

Space is not expanding "in" anything else. The distances between points in space are increasing, but not because they are moving through some "superspace" that contains space.

Mathematicians distinguish between two different approaches to defining geometric properties of a space: the extrinsic approach and the intrinsic approach. The extrinsic approach involves relating the space to some larger space that it sits inside; the intrinsic approach makes use of only the space itself, and not some larger space that it sits inside.

For example, suppose we want to study the curvature of the surface of the earth. One way to see that the surface of the earth is curved is to image a flat plane tangent to the surface of the earth at some point. We can detect and measure the curvature of the surface of the earth by noting that the surface deviates from the tangent plane, and measuring the size of this deviation. But this deviation takes place within the 3-dimensional space that the surface of the earth is embedded in, so this is an extrinsic measure of the curvature. The curvature can also be detected by making measurements that take place entirely on the surface of the earth. For example, if you lay out a large triangle on the surface of the earth and measure the angles of the triangle, you will find that they add up to more than 180 degrees. This measurement makes no reference to a larger space containing the earth's surface, so it is an intrinsic measure of the curvature of the surface.

Cosmologists use only the intrinsic approach when discussing the geometry of spacetime. Thus, none of this discussion involves any reference to a larger space that spacetime sits inside. Although they may use words that seem to suggest such a larger space, such as "expansion" or "curvature", those words are always being used to refer to some intrinsic property of spacetime itself, and not some relationship between spacetime and a larger space.

It is often said that the the phrase "before the BIG BANG" is meaningless

It is often said that the the phrase "before the BIG BANG" is meaningless because the BB is the beginning of things, time included. My question is "Is the phrase truly meaningless?" I take it as axiomatic that a real event occurs only if it were already a possible event. If the BB did indeed happen then it must have been the fruition of an antecedent possibility - some entity 'before the BB'. ERIC STOCKTON, ORKNEY UK

I, too, have heard it said that the phrase "before the Big Bang" is meaningless. One analogy I have heard drawn is between the phrase "before the Big Bang" and the phrase "more northerly than 90 degrees north latitude". Just as the latter phrase refers to no real location on Earth, so the former phrase is supposed to refer to no real location in time. According to cosmology's current picture of the Big Bang (as I understand it), the analogy is apt. (Of course, that doesn't rule out the possibility of further scientific developments resulting in corrections to the theory of the Big Bang.)

It may seem unsatisfying to you that a scientific theory could just rule out as "meaningless" a notion that seems pretheoretically to be perfectly sensible. Intuitively, it seems like the question "What happened before the Big Bang?" ought to have an ordinary answer, rather than a cop-out answer like "There is no such time." However, the history of science is full of examples of questions that were once thought to have ordinary sorts of answers but later were discovered not to do so. These were not cop outs. Rather, they were consequences of well-confirmed scientific theories. For example, it was once believed that in order for a body to keep moving at a constant speed in a constant direction, something must continually be acting upon it; otherwise it would slow down and eventually stop. That seems like a sensible idea, based on our everyday experiences. However, Newton discovered that the question "What keeps this body moving in a constant speed in a constant direction?" has no answer because it is based on a mistaken view. According to Newton's first law of motion, a body that is acted upon by no force at all will keep moving uniformly; forces cause accelerations, and motion in a constant speed at a constant direction involves no acceleration. Consequently, that motion could be maintained indefinitely, and would be in the absence of anything acting to change it. Perhaps science has discovered that the question "What happened before the Big Bang?" is in this respect like the pre-Newtonian question "What's keeping this body moving in a constant speed in a constant direction?"

I believe that it is assumed that the 'laws of physics', as we know them, apply

I believe that it is assumed that the 'laws of physics', as we know them, apply throughout the universe. Is this a reasonable assumption or is our concept of cosmic reality an error?

I agree with Alex that our best hypotheses may well not capture the actual laws of nature, and that physicists strive for unification, and I think there is a third aspect to this question. In spite of what the 20th century philosopher of science Karl Popper maintained, science depends on induction, on making inferences about the unobserved on the basis of the observed. And as the great eighteenth century philosopher David Hume observed, this depends on some kind of assumption of the uniformity of nature. Hume notoriously argued that we can have no good reason for this assumption, and that is very close to the point that we have no good reason for assuming that the laws of physics are the same in those parts of the universe we have observed as they are in those parts we have not observed. But without making something like that assumption, science would be impossible.

To put it differently, to leave open the possibility that laws might be different elsewhere is, if taken to an extreme, not just to abandon science's preference for unity: it is to abandon science. As the great physicist James Clerk Maxwell put it, we had better hope that nature is more like a book than a magazine.