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Why is anything measurable?

  1. Apr 9, 2010 #1

    ConradDJ

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    I want to argue that there’s something very basic about the structure of the physical world that’s taken for granted everywhere in physics, but isn’t actually described in any theory. The argument goes like this –

    What does it take for any physical parameter to be observable? Take the mass of a particle – there are several ways to measure that. For example, if we know its charge, we can watch how the particle’s path gets deflected as it moves through a magnetic field. To do that we have to measure its charge and observe its position at certain times, so we have to be able to measure distances and time-intervals, as well as the strength and orientation of the field.

    Very generally, every way that any physical parameter can be measured will always involve the measurement of several other parameters. There is no such thing as a simple isolated measurement. So the question is – in what kind of system is any kind of measurement possible?

    What I want to get at here has nothing to do with whether a human being is involved. It’s a question of what’s needed in the physical situation itself so that the value of a certain parameter can be meaningfully defined, in that situation. The mass of the particle can’t be meaningfully defined except by reference to other parameters, whose values must also be meaningfully defined.

    Now in the world we live in, there are obviously many observable parameters. For every one of them there are certain interaction-contexts through which they can be measured, all of which involve the measurement of other parameters, in other interaction-contexts. It’s not important to this argument exactly what a “measurement” or “observation” is. It’s enough that we know they’re possible... and that for anything to be in any way observable, there have to be other things that are also observable, in terms of still other things that are also observable.

    This isn’t an infinite regress – I assume there are only a finite number of basic physical parameters defining each other. But there has to be a certain closure or completeness to the structure of the observable world, as a self-defining system. It seems to me that this inter-referential completeness is a very remarkable characteristic of our universe, and one that no theory I know of takes into account.

    We tend to take it for granted that if something is real, then of course there will be some way to measure it. After all, if a particle has a certain property X that can’t be observed in any way, then it makes no difference to anything whether that property exists or not – it’s simply meaningless. That makes sense, but I don’t think it undercuts my argument.

    It’s easy to see that not just any physical system supports the measurement of its own parameters. Imagine a Minimal Newtonian Cosmos consisting of simple point-particles scattered through Euclidean space and time. Say each particle has a certain mass, and no other characteristics, and that they interact with each other only through Newton’s gravity.

    This seems like a mathematically well-defined system – but there’s no way actually to measure the distance between two particles, or how they move, or what their respective masses are. Interaction in this system may be lawful, but it doesn’t communicate any information about anything, since none of the parameters of the law are defined by the system itself.

    My point is that in physics, we don’t require that our theoretical models define all their own parameters in terms of each other. We try not to introduce parameters that are – in our universe – unobservable. But we don’t try to model what it is about the structure of our universe that lets anything be observable.

    I think this is probably why we haven’t come to any clear understanding about Relativity and Quantum theory, and the relationship between them. These theories both (in different ways) make measurement central, but we’re still building models that don’t consider what it takes to make any measurement possible.
     
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  3. Apr 9, 2010 #2
    I like it, but I'm a little confused. I see the underline - can you clarify what you are asking though?

    I will say that it all reminds me of arguments concerning language. How can we precisely define any word when we must use other undefined words to do so? Are we doomed to circular references and ambiguity? Is precision even possible?

    Anyways I don't want an answer. I just thought it was interesting parallel. But what exactly are you asking? Are you looking for a grounding to the circular definitions of properties in terms of other properties?
     
  4. Apr 9, 2010 #3
    See http://www.nyu.edu/gsas/dept/philo/faculty/block/papers/MentalSemanticHolism.html#anchor822217 (It's just a passing overview, so I'm sure there's better literature to find)
    Also:

    http://en.wikipedia.org/wiki/Confirmation_holism
    http://en.wikipedia.org/wiki/Semantic_holism
     
    Last edited: Apr 9, 2010
  5. Apr 9, 2010 #4
    in what kind of system is any kind of measurement possible?


    Those things which are known, and that we are capable of measuring through 'standards' we have set with the measuring tools we have created.
     
  6. Apr 9, 2010 #5
    The OP started with a empirical approach to measurement and then degenerated (in my evaluative opinion) into a philosophical discussion of logical propositions and necessary conditions/consequences.

    When I want to understand what measurement is and what makes it possible, I would start with a sample of concrete examples. To measure the mass of something, you place it on a scale where the fulcrum is exactly in between the end-points. Then you balance the scale with an certain amount of standardized mass-units on the other end, such as 1g weights. Measuring mass, thus, requires comparison based on the principle of a lever suspended in a homogeneous gravity context. One object going down is presumed to exert equivalent force to the opposite object being pushed up, hence the comparison becomes possible.

    So things are measurable not because they exist, but because they are manipulated to generate results according to the logic of certain assumptions, which may also be verified through repeatable testing. If you don't believe a scale works, you can measure one object and then another of the same mass and then balance the two objects with each other instead of counterweights. This demonstrates generalizability among different instances of applying the same comparative logic.

    If different things couldn't be compared in terms of the same comparative reference, they would not be measurable; or you would have to experiment until a stable reference was found.

    Measurement is based on the logic of regularity and comparability.

    Now my question is what the empirical facts are about this magnetic field used to measure particles. What is measured exactly and how?
     
  7. Apr 9, 2010 #6
    If I want to measure a length with a 1 mm accuracy, I need a stick 1 mm long, and I will count how many of those sticks will cover the length I want to measure. So all I need is a reference stick. In the past, the reference stick was defined by an actual physical stick. Today, the definition of length is a spectral one, from quantum mechanics. In principle, it does not require anything to be previously defined. It is a (pure) number times the wavelength of an atomic transition. We can have experimental definitions for units which are purely spectral, and only require a pure integral number times a fundamental constant throughout the universe. This is not done yet for every unit, in particular, the mass is still defined from a physical object (IIRC).

    On the theoretical side, we know the exact lists of parameters for our standard models of particle physics or cosmology for instance. Particle physics has 20 or so parameters. Speculations beyond the standard model amount to reducing this number of parameters, and this requirement is something explicit and well-understood in any serious research beyond the standard model of particle physics.

    Magnetic fields can be used to measure the ratio of charge to momentum for a particle. This ratio is directly related to the curvature radius of the trajectory of the particle in the magnetic field.
     
  8. Apr 9, 2010 #7
    well, you're going to have to wait just for a while until the 'magnetic field' is explained
     
  9. Apr 9, 2010 #8
    Empiricism and critical reason seems to be absent in these explanations of measurement. Are people capable of breaking these things down to the level of reviewable observations and reasoning, or is that too basic a level?
     
  10. Apr 9, 2010 #9

    1) yes

    2) no
     
  11. Apr 9, 2010 #10
    Wonderful, but you don't provide an example to go with it.
     
  12. Apr 9, 2010 #11
    what kind of example were you looking for?

    If your question is about the magnetic field, refer back to post #7
     
    Last edited: Apr 9, 2010
  13. Apr 9, 2010 #12
    To address a little more of the original question...

    In your minimal universe, if the only force is gravity, then that is what must be used for measurement. Introduce a third low-mass particle and see how it behaves. You can see the mass and location of the first two particles by observing what happens to your measuring device, the third particle.

    I know you wanted to avoid questions of measurement, but barring discussions of subjective knowledge, measurement just is interaction. Any system that undergoes an effect can be said to have measured whatever system it was that caused that effect. Measuring devices are physical systems designed to amplify effects to give us information about their causes.

    And units, of course, are arbitrary in terms of any underlying framework. We pick units that are useful because of their relationship to certain aspects of nature that we observe (or to other units that we decide are more basic).

    As to what generates observables from the void... who knows. In your example system, mass and location actually are observable because information about them can be communicated through gravity, which you allow for. Say your universe also has charge, though, but with no EM fields. Then you really would have a mathematically defined parameter with absolutely no method of being measured. There's no way to tell that there aren't such properties.

    From QM we know that things like mass and spin are not consistently defined properties belonging to particles. It is very reasonable to question whether these properties can even be said to exist, or if there is some other basic layer that these manifest out of. The properties we have probably aren't even basic, but because they are measurable, they are all we have to work with. Since we can't investigate anything beyond the observable, we're really just stuck here. I think at this point the question reduces to why is there something rather than nothing? - what reason is there for anything to appear as an observable. That's a tough question, but at least there's been a lot of investigation into it.

    So to answer why is anything measurable? I would refer to discussions of why is there something rather than nothing? I really think they reduce to the same question of why observables exist, or rather, why anything is observable. There is a technical difference on the matter of unobservable properties, but unobservable properties aren't what anyone is asking about when they ask why there's something rather than nothing. That technicality isn't a concern for any of the arguments.

    Unless, of course, your issue is with the holism of scientific theories and properties. Then see above :smile:.
     
    Last edited: Apr 9, 2010
  14. Apr 9, 2010 #13
    What I'm looking for? You answered my question that "yes, people are capable of breaking these things down to the level of reviewable observations and reasoning."

    You shouldn't have to explain how a magnetic field works to explain how it can be applied to measure something else. You don't have to explain how gravity works to postulate that downward movement on one side of a scale is equal to upward movement on the other, and that the two balancing each other out means mass-equivalency.
     
  15. Apr 9, 2010 #14
    well, if you don't explain how a magnetic field works or you don't explain how gravity works, then any results will be flawed to some extent, in the same way as if you don't know how a yardstick works (how to use it), it can only be used in a comparative sense, like the balance beam scale.
     
    Last edited: Apr 9, 2010
  16. Apr 9, 2010 #15
    Mass and spin are precisely the constants required to define a particle in modern QM. Mass and spin define the representation of the proper orthochronous Lorentz group to which the particle belong.
     
  17. Apr 9, 2010 #16
    Can I ask if you agree with the argument that "why is anything measurable?" is functionally equivalent to "why is there something rather than nothing?" See above, but to recap, it's something like:

    Why is anything measurable?
    Why is anything observable?
    Why is anything an observable?
    Why do observables exist?
    Why do observables exist rather than not existing?
    Why is there something rather than nothing?

    If you disagree that the above are equivalent, or at least equivalently motivated (and therefore analyzed), at which step do you think they differ and why?
     
  18. Apr 9, 2010 #17
    And neither mass nor spin are persistently defined on a particle. There are particles with indefinite mass. There are particles with indefinite spin. Neither mass nor spin can therefore be an essential property of a particle, so the argument goes.*

    If there are basic properties essential to the existence of particles, we haven't found them yet.

    This conversation probably belongs somewhere else though. It wasn't terribly important to my argument.

    (*Similarly, no other properties that we use in physics can be essential properties of particles.)
     
  19. Apr 9, 2010 #18
    the comparative sense is all that is entailed in measurement. Measurement is nothing more than comparison of comparable things in terms of standardized units. You can measure length in terms of anything else, if you can keep moving one across the other without losing track of where the end of it was before you put it at the point again as a beginning. You can measure volume using any comparison if both can be submerged in the same fluid. The foundation of measurement is to understand the mechanics of the instrumentation.
     
  20. Apr 9, 2010 #19
    The title of the thread is "why is anything measurable," but it sounds like it should be "is measurability proof of existence?"

    It's not. You can measure an imaginary unicorn with an imaginary yardstick and arrive at an imaginary length, but it doesn't mean the unicorn or the yardstick existed outside of your imagination.
     
  21. Apr 9, 2010 #20
    Yeah, you can't measure imaginary things. You can pretend to, but that's totally irrelevant to anything we're discussing.

    I'm trying to keep this on track here. I think we'd all appreciate a little effort.
     
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