|
|
|
|
|
|
|
|
|
 Posted: Tue Jul 22, 2008 10:10 pm
The main problem I find with measurements is that the act itself affects what we try to measure. It introduces energy/movement.
|
 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Thu Jul 24, 2008 6:03 am
Quote: The main problem I find with measurements is that the act itself affects what we try to measure. It introduces energy/movement. What's strange is no direct interaction is necessary to perform a measurement.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Wed Sep 10, 2008 2:50 am
Well, in real analysis the consept of measurement is defined in what we call a metric in a metric space. In E^n the measure is the n-ary expansion of what you remeber from middle school, as derived from the Pythagorean theorem, as the distance formula for the Cartesian plane:  However, generally a measurement/measure can exist in any metric space. Here's another valid measure for E^n. p-norm distance In the general sense, a measure is a useful quanitization that obeys the following properties: 1. d(x, y) ≥ 0 (non-negativity) 2. d(x, y) = 0 if and only if x = y (identity of indiscernibles.) 3. d(x, y) = d(y, x) (symmetry) 4. d(x, z) ≤ d(x, y) + d(y, z) (subadditivity / triangle inequality). For all of you General relativity people, there's a metric tensor (note: there's a difference between what mathematicians call a tensor and what physicists call a tensor [physicists work with Cartesian tensors and tensor fields])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Mon Sep 15, 2008 10:29 pm
Err...you do realize that that's called a measure, and not a measurement, right? And that we're specifically talking about the quantum mechanical notion of measurement?
Besides which, analytical measure doesn't always have to be attached to a metric, especially when one isn't necessarily considering connected sets.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Mon Sep 15, 2008 10:53 pm
Layra-chan Err...you do realize that that's called a measure, and not a measurement, right? And that we're specifically talking about the quantum mechanical notion of measurement? Besides which, analytical measure doesn't always have to be attached to a metric, especially when one isn't necessarily considering connected sets. But all the things that we call measurements could be reduced to a measure provided that we constructed a metric space which models the physical space in which the measurement takes place.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Wed Sep 17, 2008 4:53 pm
Maguscrowley Layra-chan Err...you do realize that that's called a measure, and not a measurement, right? And that we're specifically talking about the quantum mechanical notion of measurement? Besides which, analytical measure doesn't always have to be attached to a metric, especially when one isn't necessarily considering connected sets. But all the things that we call measurements could be reduced to a measure provided that we constructed a metric space which models the physical space in which the measurement takes place. Not really. You can "measure" a property of an object by some physical means without using the results of those measurements to define a metric on the space. Nor do you need to assume that space has such a measure (which is less restrictive than a metric) to perform some types of unitless measurements.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Fri Sep 19, 2008 12:04 am
Swordmaster Dragon Maguscrowley Layra-chan Err...you do realize that that's called a measure, and not a measurement, right? And that we're specifically talking about the quantum mechanical notion of measurement? Besides which, analytical measure doesn't always have to be attached to a metric, especially when one isn't necessarily considering connected sets. But all the things that we call measurements could be reduced to a measure provided that we constructed a metric space which models the physical space in which the measurement takes place. Not really. You can "measure" a property of an object by some physical means without using the results of those measurements to define a metric on the space. Nor do you need to assume that space has such a measure (which is less restrictive than a metric) to perform some types of unitless measurements. No, you do not need to but that doesn't say that there is not a metric space which can be created to model and rigidly define what you are doing physically. I am going out on a limb by claiming that all physical measurements can be defined as measures. Actually I think someone here (Layra-chan) could think of something and disprove me with a counter example. That's kind of what I'm aiming for here. I'd like to say that fuzzy measurements (like early, late, further, closer, ) don't count ... but I wonder if that would work ....
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Thu Sep 25, 2008 11:10 pm
Maguscrowley Swordmaster Dragon Maguscrowley Layra-chan Err...you do realize that that's called a measure, and not a measurement, right? And that we're specifically talking about the quantum mechanical notion of measurement? Besides which, analytical measure doesn't always have to be attached to a metric, especially when one isn't necessarily considering connected sets. But all the things that we call measurements could be reduced to a measure provided that we constructed a metric space which models the physical space in which the measurement takes place. Not really. You can "measure" a property of an object by some physical means without using the results of those measurements to define a metric on the space. Nor do you need to assume that space has such a measure (which is less restrictive than a metric) to perform some types of unitless measurements. No, you do not need to but that doesn't say that there is not a metric space which can be created to model and rigidly define what you are doing physically. I am going out on a limb by claiming that all physical measurements can be defined as measures. Actually I think someone here (Layra-chan) could think of something and disprove me with a counter example. That's kind of what I'm aiming for here. I'd like to say that fuzzy measurements (like early, late, further, closer, ) don't count ... but I wonder if that would work .... Momentum, energy, etc. should all be good counterexamples, since they have not much to do with the space itself. Then again, that would all be tied in to precisely how you measure such properties in the first place, but any close-to-direct measurement procedure would give you a property which cannot be used to define a measure/metric.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Sat Sep 27, 2008 6:39 pm
Swordmaster Dragon Maguscrowley Swordmaster Dragon Maguscrowley Layra-chan Err...you do realize that that's called a measure, and not a measurement, right? And that we're specifically talking about the quantum mechanical notion of measurement? Besides which, analytical measure doesn't always have to be attached to a metric, especially when one isn't necessarily considering connected sets. But all the things that we call measurements could be reduced to a measure provided that we constructed a metric space which models the physical space in which the measurement takes place. Not really. You can "measure" a property of an object by some physical means without using the results of those measurements to define a metric on the space. Nor do you need to assume that space has such a measure (which is less restrictive than a metric) to perform some types of unitless measurements. No, you do not need to but that doesn't say that there is not a metric space which can be created to model and rigidly define what you are doing physically. I am going out on a limb by claiming that all physical measurements can be defined as measures. Actually I think someone here (Layra-chan) could think of something and disprove me with a counter example. That's kind of what I'm aiming for here. I'd like to say that fuzzy measurements (like early, late, further, closer, ) don't count ... but I wonder if that would work .... Momentum, energy, etc. should all be good counterexamples, since they have not much to do with the space itself. Then again, that would all be tied in to precisely how you measure such properties in the first place, but any close-to-direct measurement procedure would give you a property which cannot be used to define a measure/metric. Momentum() is a vector, so that's easy. Energy would be tough though. I suppose it wouldn't work for anything that's dimentsionless. There's a mathematical definition of measurement in Dimentional Analysis in Identification of Mathematical Models [kasprzak, lysik, & Rybaczuk] in chapter 1.2 elude to a classic theory of measurement, but the actual text is beyond my comprehension. Then there's Berka K., Measurement and it's Concepts, Theories, and Problems D. Reidel Publ. Comp Dortrecht Holland, Boston Studies in the Philosophy of Science.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Sun Sep 28, 2008 3:50 am
The problem here isn't about whether you can turn a particular measurable property of system into a metric space, but rather what does it mean, physically, to take an individual measurement.
We can define a distance between two values of the relevant property and thus create a metric space easily enough; the problem is that quantum objects tend to spend the bulk of their time outside of that metric space, and somehow measuring them (in the physical sense) forces them into the metric space in a what that seems at least somewhat probabilistic, although the probabilities themselves are deterministic. We can assign a metric to the space that the quantum objects do reside in, sure, but we still have to ask what it means for observation to act as essentially a non-deterministic orthogonal projection operator, since classical observation is nothing of the sort.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Wed Oct 22, 2008 5:52 pm
Well it's still and abstract construct of thought created by the consequence of senses and a knowledge of difference and size. We then project that onto the things we can observe through our senses. But this creates the philosophical world mind disconnect and I wanted to make reduction more feasible by keeping the definition mental rather then letting the elements of the knowledge of measurement go into the trap of sensory verification before we got a definition thought side. If our definition is tangled up in the sensory its a pandora's box of issues the least of which not being the reductionist arguments.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Thu Oct 23, 2008 12:49 am
It's not even a sensory problem at all; the problem is that to the best of our understanding, a particle cannot have a definite position and momentum at the same instance, and we have no idea what physical principles underlie this. We have no idea what physically occurs during superposition collapse.
A measurement is defined in two ways:
1: the classical sense of determining a quantity associated with a property of an object or system;
2: orthogonal projection from a waveform into an eigenspace associated with an operator acting on the Hilbert space
The problem is that we have no canonical way to reconcile these, perhaps because we can't actually see the projection happening. If we could muddle our perception with our theory, we'd probably actually be better off. But we can't, and that's the issue.
We're not trying to interpret physical reality in terms of our intuitive theory as you seem to think we are, we're trying to interpret our non-intuitive theory in terms of physical reality.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Posted: Thu Oct 23, 2008 8:17 am
I'm sorry I didn't realize that this was a discussion on a specific principle in physics. I thought it was something much more abstract in nature. My apologies.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Reply
