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Promises to keep

  1. Apr 5, 2006 #1
    "What I tell you three times is true."
    Lewis Carroll, The Hunting of the Snark​
    In the Pure and Mixed thread I gave three promises.
    1. vanesch suggested that I am refusing to make sense of quantum mechanics beyond the claim (which I endorse) that the quantum formalism is nothing but an algorithm for assigning probabilities to possible measurement outcomes on the basis of actual outcomes. In this post I promised to outline my way of making sense of quantum mechanics in a separate thread.
    2. In this post I claimed that to be able to conceive of the ontological entities I posit, one has to accept the quantum formalism as being fundamentally a probability algorithm. To which vanesch replied: "I wonder how you are going to do this, without introducing them as a mathematical object!" To which I replied in this post that the answer deserves a separate thread.
    3. vanesch wrote: "I don't see how you are constructing a conception of the quantum world which is strongly objective, if you START by saying that we only have an algorithm, and no description!" To which I replied in this post that "maybe I should explain this in a new thread. Maybe I will!"
    Here goes.
    • As said, I accept the following as true: The quantum formalism is an algorithm for assigning probabilities to possible measurement outcomes on the basis of actual outcomes. Its mathematical ingredients (state vectors, wave functions,…) are not (at the same time or instead of this) representations of reality.
    • I fully agree with Asher Peres that "there is no interpolating wave function giving the 'state of the system' between measurements." The quantum formalism allows us to calculate the correlations between measurement outcomes. It doesn’t say anything about mechanisms or processes through which outcomes are correlated.
    • I further believe that analyses of the quantum-mechanical correlations in a variety of setups have established beyond reasonable doubt that measurements do not reveal pre-existent properties (of objects or systems) or pre-existent values (of observables) but instead create their outcomes. Two examples can be found at my site: Mermin's illustration of Bell's theorem and the experiment of Greenberger, Horne, and Zeilinger.
    • I adopt the following interpretational policy: I do not assume the truth of any statement about a physical system that is not confirmed by a measurement, and I do not assume the falsity of any statement about a physical system that is not proved false by a measurement. If a statement is neither confirmed nor proved false by a measurement, then it is neither true nor false but meaningless.
    • Corollary: Whenever quantum mechanics instructs us to add amplitudes rather than probabilities, the distinctions we make between the corresponding alternatives are distinctions that "Nature does not make"; they correspond to nothing in the real world; they exist solely in our heads.
    • The first case in point is a simple scattering experiment. As simple as it is, it has far-reaching ontological implications.
    So much for starters.

    For those of you who think that discussions of philosophical/foundational issue are futile: take a look at this article by Lee Smolin. You can read the gist of it in this post.

    *************************************************​
    A koan (pronounced /ko.an/) is a story, dialog, question, or statement in the history and lore of Chan (Zen) Buddhism, generally containing aspects that are inaccessible to rational understanding, yet that may be accessible to intuition.
    Wikipedia​
     
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  3. Apr 5, 2006 #2

    Hurkyl

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    All measurements in this post take values in {0, 1}.

    Let M be the outcome of a measurement. If it makes sense to say that a measurement hasn't yet occured, let M be such.

    Let N be the outcome of a measurement. If it makes sense to say that a measurement has yet occured, let N be such.

    Let P be the outcome of a measurement. If it makes sense to say that P occured before N, let P be such.

    Which of the following statements do you take to be meaningful questions?


    Will the outcome of M be 1?
    What is the probability that M will be 1?
    What is the probability that M will be 1, given that N was 1?

    Was the outcome of N 1?
    What is the probability that N was 1??
    What is the probability that N was 1, given that M will be 1?
    What is the probability that N was 1, given that P was 1?

    What is the probability that P was 1, given that N was 1?
     
  4. Apr 5, 2006 #3
    Such as what? Sorry, I don’t understand this. Can you make yourself clearer?
     
  5. Apr 5, 2006 #4

    Hurkyl

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    I wanted to just say

    Let M be a measurement that hasn't happened yet.
    Let N be a measurement that's already happened.
    Let P be a measurement that happened before N.


    I just wanted to cover the case where you don't find the time ordering physically meaningful -- I still wanted to ask my question.
     
  6. Apr 6, 2006 #5
    By definition, every measurement has an outcome, no matter whether it is in the past, the present, or the future relative to our spatiotemporal point of view. (By "measurement" I mean a successful measurement. An unsuccessfully attempted measurement does not qualify.)
    • Will the outcome of M be 1? – meaningful because there is an answer, we just don’t know it yet.
    • What is the probability that M will be 1? – meaningful since we can calculate it.
    • Was the outcome of N 1? – obviously meaningful.
    • What is the probability that M will be 1, given that N was 1? – meaningful since we can calculate it.
    • What is the probability that N was 1? – the answer depends on the assignment basis. There is no such thing as the probability of N. You can calculate it on the basis of outcomes of measurements performed later than as well as earlier than N using the Born rule, and you can calculate it on the basis of outcomes of measurements performed earlier and later than N using the rule of Aharonov, Bergmann, and Lebowitz. If you specify the assignment basis, the question is meaningful.
    • What is the probability that N was 1, given that M will be 1? – meaningful since we can calculate it. You are assuming an outcome for M. If the outcome of M is O, then the antecedent of your conditional statement is false, but not the conditional statement itself.
    • What is the probability that N was 1, given that P was 1? – meaningful since we can calculate it.
    • What is the probability that P was 1, given that N was 1?– meaningful since we can calculate it.
     
  7. Apr 6, 2006 #6

    selfAdjoint

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    Meaningful because we can calculate it? If this is your high falutin' philosophical sophistication, you can keep it.
     
  8. Apr 7, 2006 #7

    Hurkyl

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    Okay, but what about your philosophy allows you to prove it meaningful? Or is it simply assumed to be meaningful? (Same for M)


    What makes the two different?


    Are you just saying "the probability N was 1" is not meaningful, but "the probability N was 1 given M will be 1" is? Or is it something else entirely?


    How do we calculate it? For me to calculate it, I would need some assumption. Maybe to make an assumption on the state of the universe now, or maybe the state defined by a previous measurement (say, N=1). Either way, what I'm computing is:
    "The probability that M will be 1, given this assumption on the state"
    or
    "The probability that M will be 1, given N was 1"

    So I don't see how we can just compute "P(M)".

    Incidentally, would you say "The probability that M will be 1, given this assumption on the state" is meaningless since the assumption on the state corresponds not to a measurement, but to an "interpolation" between measurements?



    I guess I should also ask what "probability" means to you, in this setting. Are they fundamental things? Or is it more akin to the classical frequentist definition as the ratio of the frequency of the outcome to the number of experiments performed as the number of "identical" experiments goes to infinity?
     
    Last edited: Apr 7, 2006
  9. Apr 8, 2006 #8
    As the adorable Nicholson said in Anger Management, temper is the one thing you cannot get rid of by losing it. :biggrin:
     
  10. Apr 9, 2006 #9
    At this point assumed. Measurements have outcomes by their very definition, so it's meaningful to attribute to them any possible outcome, whether the attribution is true or false. (Meaningless means neither true nor false.) But at a later point I have to demonstrate the consistency of my interpretation. Having taken measurement outcomes for granted, I have to define them in terms of the formalism that correlates them. It can be done!

    It was careless of me to write that "What is the probability that M will be 1?" is a meaningful question since we can calculate it. The question is meaningful regardless of whether we are in a position to calculate that probability. What I meant is that in this case we may even have data that permit us to calculate it.
    As the question "What is the probability that M will be 1?" so the question "What is the probability that N was?" is meaningful. The difference lies not in the physics but in our habitual ways of thinking about it. It is usually taken for granted that later probabilities are calculated on the basis of earlier data. But when we speak of the probability of a past outcome, we had better specify whether we calculate it on the basis of even earlier outcomes or on the basis of later outcomes (in both cases using the Born rule) or on the basis of earlier and later outcomes using the ABL rule.
    It is incomplete rather than meaningless. When we speak of future measurements, there is little ambiguity about the assignment basis. When we speak of past measurements, we have to be more specific.
    Not an assumption but data. Probabilities are assigned to possible measurement outcomes on the basis of actual ones. There is no unique assignments basis, as one wrongly believes if one take the wave function for the assignment basis. One has to specify the measurement outcomes on the basis of which probabilities are assigned.
    We can't. We need data = measurement outcomes.
    I should think that the above answers this questions.
    I agree with Popper that a given type of event happens more often because it is more probable, rather than the other way round. Whereas relative frequencies are needed to (approximately) measure probabilities, they are not needed to define them.
    I'm no believer in potentialities (Heisenberg, Shimony) or tendencies or propensities (Popper), which strike me as ambiguous: sometimes they are taken for another kind of actuality and sometimes as just synonymous with possibility.
    The classical definition based on equiprobability has heuristic value, not least because it involves symmetry principles, but it is also potentially misleading, for expected symmetries may turn out to be actually missing.
    I certainly have no truck with the logical interpretation (conditional probability = degree of logical entailment, whatever that means), nor am I a fan of subjective interpretations (Bayes' degrees of belief or expectation). There is a clear sense in which quantum-mechanical probabilities are objective. The laws that correlate measurement outcomes are objective, and what gives the hydrogen atom (and every other composite object) its size is an objective fuzziness of relative positions and momenta rather than our ignorance of the exact position of the electron relative to the proton. (To my way of thinking, the proper way of dealing with a fuzzy observable is to assign probabilities to the possible outcomes of a measurement of this observable.)
    Finally, I'm no believer in absolute probabilities. I agree with Hans Primas that every probability is a conditional probability. I therefore prefer A. Rényi's alternative to Kolmogorov's probability theory, for the former is based on conditional probabilities whereas the latter is based on absolute probabilities. This is also why I consider propagators to be "more fundamental" than wave functions, for the latter, taken as fundamental, suggest the existence of absolute probabilities (defined by the wave function independent of measurements), whereas the former only involve conditional probabilities.
    More on the subject can be found here.
     
  11. Apr 9, 2006 #10
    "If a statement is neither confirmed nor proved false by a measurement, then it is neither true nor false but meaningless."


    couldn't it also just be 'not proved' yet?
     
  12. Apr 9, 2006 #11

    Hurkyl

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    Oh good, I think I agree with you on these. (More or less) (though I still find wavefunctions and similar things a useful approach)

    The only substantial thing I have left to discuss is
    But I don't want to derail the intent of the thread, so I'll leave it alone.
     
    Last edited: Apr 9, 2006
  13. Apr 9, 2006 #12
    I was speaking of statements about physical systems or observables, which are of the form "system S has the property P at the time t" or "observable O has the value V at the time t". To prove or disprove such a statement is to verify or falsify it by means of a measurement. "Not proved" would mean "not measured".

    Regarding "yet". Statements within axiomatic systems can change from not proved (at an earlier time) to proved (at a later time). Statements of measurement outcomes include a time reference ("at the time t") and cannot change from one truth value to another. If the truth value of the proposition "system S has the property P at the time t" is ever established by way of a measurement, this proposition is timelessly true or false, as the case may be. If its truth value is never established by way of a measurement, the proposition is, has always been, and will always be meaningless.
     
  14. Apr 10, 2006 #13

    CarlB

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    This view eliminates free will.

    It's more intuitive to split "yet" into two uses of time, one giving the present age of the universe, the other being the temporal coordinate used to describe a patch of spacetime.

    Yes I realize that Einstein agreed with you (I read somewhere his statement on this from a few months before his death) on this, but my dog knows more about the difference between space and time than Einstein's relativity does. It's a pretty theory, but pretty and realistic are two different things. In your version, we are all both dead and alive and the obvious perceived passage of time is an illusion. Having me both dead and alive is as bad as MWI.

    Carl
     
  15. Apr 10, 2006 #14
    If its truth value is never established by way of a measurement, the proposition is, has always been, and will always be meaningless.


    I remember seeing a drawing in a book by Newton of a canon firing with incrementally increasing power from the top of a mountain.
     
  16. Apr 11, 2006 #15
    No doubt wave functions are useful. Given the motion and distribution of charges, we calculate the electromagnetic field tensor. Given this tensor, we calculate the Lorentz force (that is, the resulting acceleration of charges). Nobody denies the usefulness of the electromagnetic field tensor as a computational device. By the same token, given an actual measurement outcome, we calculate a wave function, and given a wave function, we calculate the probabilities of possible measurement outcomes. Nobody denies the usefulness of wave functions as computational devices.
    Then let's go on. As I said in the first post, I do not assume the truth of any statement about a physical system that is not confirmed by a measurement, and I do not assume the falsity of any statement about a physical system that is not proved false by a measurement. In other words, the properties of the quantum world are possessed on if, when, and to the extent that they are indicated by (can in principle be deduced from) an actual event or state of affairs (that is, by the outcome of a measurement in the widest sense of the word). The things whose existence I presuppose are property-indicating events or states of affairs. Eventually I will have to show (with the help of the quantum formalism itself) that their existence is consistent with the this formalism.

    As a first step in this direction, I want to explore what the formalism has to say on the substantial aspect of the quantum world. What do we mean by (a) substance? Aristotle did a fine job when he defined substance as that which cannot be the predicate in a sentence composed of a subject and a predicate. Such sentences are the staple of ordinary discourse. The grammatical relation between a subject and a predicate reflects a logical relation built into the way we think. If we think of an object as a substance with properties, then we project into the world a relation that primarily exists in our minds. A property is that in the world which corresponds to a predicate in a sentence composed of a subject and a predicate. A substance is that in the world which corresponds to a grammatical subject that cannot be the predicate of another such sentence.

    What use is this projection? There is a difference between an imagined bundle of properties (say, a dragon) and an actually existing bundle of properties. What distinguishes the latter from the former is that it is substantial (or material). It exists by itself, independently, rather than by virtue of our imagination or by virtue of being the property of something else.

    How many substances (independently existing things) does the physical world contain?

    Consider the following scenario. Initially there are two incoming particles, one (N) heading northward and one (S) heading southward. We want to calculate the probability p with which these particles scatter at right angles, so that in the end there is one particle (E) heading in a direction we shall call "eastward" and one particle (W) heading "westward." (We assume that the total momentum is zero, and that the scattering is elastic). If the particles lack distinguishing properties (identity tags) then p is the absolute square of the sum of two amplitudes A1, A2 corresponding to two possibilities:
    • W is the same object as S and E is the same object as N
    • W is the same object as N and E is the same object as S
    Every known particle is either a boson or a fermion. If there are no preferred directions (owing to external fields, particle spins, and such) then for bosons A1 = A2 while for fermions A1 = -A2. The boson amplitudes interfere constructively (meaning that p is larger than it would be if what really happens were either of those possibilities). The fermion amplitudes interfere destructively (meaning that p is less than it would be if what really happens were either of those possibilities). So what really happens can be neither of those possibilities. The question

    "Which incoming particle is identical with which outgoing particle?"​

    is meaningless. The challenge here as elsewhere in quantum mechanics is to learn to think in ways that do not lead to meaningless questions. The question arises because we assume that initially there are two things, and that each remains identical with itself and distinct from the other. It does not arise if we assume, instead, that initially there is one thing moving both northward and southward, and that in the end there is one thing moving both eastward and westward. In the meantime there is one thing doing nothing, for no properties can be attributed to a physical system when none are measured. The number of substances in this particular scenario is one.

    In the approximate, non-relativistic theory, the number of components that a system has, is (or can be) a constant. In the correct, relativistic theory, the number of components is an observable (and hence a property) like any other: it can be attributed to a system only if, when, and to the extent that it is measured. This disposes of the atomistic fantasy that a material object (or the world, for that matter) is made up of a fixed number of distinct and unchanging "ultimate constituents."

    The bottom line: the number of substances (independently existing things) in the physical world equals one.

    …in the fall of 1940, Feynman received a telephone call from John Wheeler [Feynman's thesis advisor] at the Graduate College in Princeton, in which he [Wheeler] said that he knew why all electrons have the same charge and the same mass. "Why?" asked Feynman, and Wheeler replied, "Because they are all one and the same electron."—Jagdish Mehra​
     
  17. Apr 11, 2006 #16
    Hi Carl,
    I don't see how. Given the little I have so far assumed in this thread, there is no basis for your conclusion. If you read my papers (as you said you would and I hope you still intend to) then you will see that I have argued extensively in favor of free will.
    It appears to me that you are making a very common mistake. The coexistence of the spatiotemporal whole is not a simultaneous but a tenseless or atemporal existence. You are right that an already existing future cannot depend on a free choice made right now, but an "already existing future'' is a contradiction in terms. The spatiotemporal whole may very well be what it is because of the choices that are freely made in it. The only thing that could preclude free will is the possibility of foreknowledge: if the future were as accessible as the past, I could know my choices before I make them, and so I could not entertain the belief that I made them of my own free will. But the future is a well-kept secret, as we all know.
    For reductionists of the Platonic-Pythagorean variety, qualities are nothing but quantities and hence illusory qua qualities. For me, quantities are nothing but means of manifesting or realizing qualities, which are what really matters. Quantities play a merely instrumental role, and this is what physics is concerned with. The fact that the world constructed by physics has no room for qualia therefore doesn’t mean there are no qualia. By the same token, the fact that the world constructed by physics has no room for the experiential now or an absolute present does not mean that there is no such thing. There is, and IT MATTERS.
     
  18. Apr 12, 2006 #17
    I have a question. How do you reconcile the apparent contradiction ? First you explain that each known substance in the "physical world" has two "independent" identities (boson or fermion). Then you use relativistic logic to conclude that the number of independent existing things (e.g., either bosons or fermions ) equals one. Thus, are you not forced to conclude that bosons and fermions are in fact always intermingled in the physical world ? Now, consider this example from the macroscopic scale. Let [NP] represent deuteron composed of two independent nucleon fermions called proton and neutron, [PNP] a fermion (also called helium-3), and [PNP] a fermion (also called triton). Now, from this equation 3 [NP] = 1 [NPN] + 1 [PNP] we reach a conclusion that you seem to predict above--that is, that "bosons" and "fermions" when viewed as clusters of nucleons are but "one" substance. Is this a correct view of what you are saying about bosons and fermions being "one substance" ? Thanks for clarification you can provide.
     
  19. Apr 13, 2006 #18
    Imagine that in front of you there are two exactly similar objects. Because they are in different places, they are different objects. But is the fact that they are in different places the sole reason why they are different objects? Or is there another reason? For the moment I stop here. I would like to know what you think. But I will definitely get back to your question.
     
  20. Apr 14, 2006 #19
    No, the reason they are two different objects is due to the presence of constraint in degrees of freedom of their movement--it has nothing to do with being in different places. Thus,[NP] is an object with 6 degrees of freedom of movement in a three dimensional space (here N = proton, P = proton). We know [NP] is an object because its 6 degrees of freedom is less (that is, constrained) than the sum of its parts, which has 12 degrees of freedom of movement (e.g., 6 for N, 6 for P). Now, to your example, consider two [NP] [NP] in front of us. Do we have one object or two ? Clearly, if superposed as {[NP]+[NP]} we have only six degrees of freedom of movement, thus one free object. But, if not superposed as {[NP} + {[NP]} we have two objects, each with 6 degrees of freedom. In summary, the essence of being an "object" (a unity), rather than a collection of parts, corresponds to there being the presence of constraint in degrees of freedom of movement between unity and parts. Using this reasoning, the electron is not an object, neither the quark, the reason being that neither has constraint in degrees of freedom of movement. This is how I see it, but I am here to learn.
     
  21. Apr 15, 2006 #20
    Rade: To clarify what I was trying to say (and what you are trying to ask) permit me to get back to my question (post #18). I'll formulate it differently. Imagine two objects that differ in exactly one property. You may think classically of two exactly similar billiard balls in different places, or quantum-mechanically of the two electrons in the ground state of helium. Is the fact that these objects differ in one property the sole reason why we think of them as two different objects? Or is there another reason? This is a philosophical question, which is as deep as it is old.

    If you decide that it's the sole reason, I will point out that the distinguishing property is relational—two positions defined relative to each other (or relative to something else), two spins pointing in opposite directions (whenever measured)—and I will ask you to think of these objects as they are by themselves, regardless of the relations that exist between them. You are then thinking twice of one and the same object rather than of two objects. (You may point out that a system consisting of two bosons in exactly the same state has twice the mass than either boson, but this doesn’t answer the question as to whether there are two things of mass m or there is one thing of mass 2m.)

    If you say there is another reason, you need to point it out. Since the difference between the objects cannot concern their properties, it has to be a difference between their substances. To solve this problem, some philosophers defined matter (or substance) as that which is different in things with identical properties. But how can one substance—conceptually divested of its properties—differ from another substance? How can there even be another substance? On the other hand, imagine two objects with completely different properties. Isn't there something that is the same in them? Aren't they ultimate made of the same matter? Thus matter came to be defined all over again as that which is identical in things with different properties. Funny, isn’t it?

    Not until the advent of quantum mechanics was that ancient philosophical conundrum settled.
    I didn't say that. Being a boson or a fermion is a particle property. As I tried to explain, the function of the concept "substance" is to betoken independent existence. Classically we can attribute to every material object an independent existence, which means we can think of them as a multitude of substances. By symmetrizing or antisymmetrizing multi-particle states, quantum statistics disqualifies "substance" from serving as an identity tag. It does not allow us to conceive of a multitude of substances. It does not allow us to conceptually interpose a multitude of individual substances between the one substance that betokens existence and the multitude of existing bundles of properties. Hence ultimately there is only one substance. If you nevertheless want to attribute a substance to each bundle of properties, you must consider the substances of all things material as identical in the strong sense of numerical identity: they are one and the same thing, and all the multiplicity we perceive belongs to its properties.
    OK, but this makes no difference. The constraints are properties of hadrons just like positions.
    What do you mean by this "superposition"?
    ? A collection of parts is a unity. Recall Cantor's definition of a set: "a Many that allows itself to be thought of as a One."
    What you are addressing here is the difference between free and bound states, which is a different issue.
    An interesting conclusion with which I can agree. The so-called "ultimate constituents" are instrumental in the manifestation or realization of objects, rather than objects themselves. One could also argue that ultimately all properties are relatively defined. Disregard the relations between quarks and leptons and you are left with, not a multitude of substances without properties, but a single substance. It is because of the multitude of its self-relations that it appears to be a multitude of objects.
     
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