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What kind of universe do we need to live in for induction to work?
Posted: 30 November 2011 01:43 PM   [ Ignore ]   [ # 76 ]
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dougsmith - 30 November 2011 10:46 AM

To be clear, one doesn’t have to give up all of these.

Of course. That is what I meant. Thanks for clearing that up.

dougsmith - 30 November 2011 10:46 AM

I thought so, too, but the comparison chart on the wiki page you cited says there isn’t any observer role in Copenhagen. I suppose it’s in error?

Well, you only have to leave out one word (the italic one) and you are on the position that many people let feel oceanic…

According to the interpretation, the interaction of an observer or apparatus that is external to the quantum system is the cause of wave function collapse, thus according to Heisenberg “reality is in the observations, not in the electron”

dougsmith - 30 November 2011 10:46 AM

Sure, that’s from Heisenberg. I don’t think that’s a problem. If the model tells us that there’s a grainedness to reality, a smallest length/interval/etc. below which it’s either impossible to speak (the Planck length) or a finest accuracy beyond which it’s impossible to know, that’s OK.

That is not exactly right. From here:

The physical significance of the Planck length is a topic of research. Because the Planck length is so many orders of magnitudes smaller than any currently possible measurement, there is no hope of directly probing this length scale in the foreseeable future. Research on the Planck length is therefore mostly theoretical.

The insecurity of where an electron is can be light years. Suppose we have one single atom in an excited state. At some moment it falls back, and releases one single photon. If we wait one year before measuring it, then our uncertainty of the electron’s location adds up to two light years.

The uncertainty principle sets a lower limit to our certainty due to quantum effects that is much bigger than the Planck length. One can even estimate the size of e.g. a hydrogen atom using the uncertainty principle (see e.g. here). In its ground state the electron has the lowest possible energy state. But this cannot 0, otherwise we would know exactly where it is, namely exactly in the middle of the atom. Using the connection between momentum and energy one can derive the minimum size of the hydrogen atom, and I assure you it is many powers of 10 bigger than the Planck length…

Stephen, QM shows us that it makes no sense to ask for the exact location of quantum particles, independent of any interaction. Measurement is an interaction. The uncertainty therefore is not a limit of our knowledge, it is a limit imposed by nature.

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Posted: 30 November 2011 02:00 PM   [ Ignore ]   [ # 77 ]
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GdB - 30 November 2011 01:43 PM

Stephen, QM shows us that it makes no sense to ask for the exact location of quantum particles, independent of any interaction. Measurement is an interaction. The uncertainty therefore is not a limit of our knowledge, it is a limit imposed by nature.

How does it show us that?

Also when one says uncertainty is not just a limit of knowledge, what springs to mind is indeterminism which is not just due to limited knowledge.

Stephen

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Posted: 30 November 2011 02:47 PM   [ Ignore ]   [ # 78 ]
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GdB - 30 November 2011 01:43 PM
dougsmith - 30 November 2011 10:46 AM

Sure, that’s from Heisenberg. I don’t think that’s a problem. If the model tells us that there’s a grainedness to reality, a smallest length/interval/etc. below which it’s either impossible to speak (the Planck length) or a finest accuracy beyond which it’s impossible to know, that’s OK.

That is not exactly right. From here:

The physical significance of the Planck length is a topic of research. Because the Planck length is so many orders of magnitudes smaller than any currently possible measurement, there is no hope of directly probing this length scale in the foreseeable future. Research on the Planck length is therefore mostly theoretical.

The insecurity of where an electron is can be light years. Suppose we have one single atom in an excited state. At some moment it falls back, and releases one single photon. If we wait one year before measuring it, then our uncertainty of the electron’s location adds up to two light years.

The uncertainty principle sets a lower limit to our certainty due to quantum effects that is much bigger than the Planck length. One can even estimate the size of e.g. a hydrogen atom using the uncertainty principle (see e.g. here). In its ground state the electron has the lowest possible energy state. But this cannot 0, otherwise we would know exactly where it is, namely exactly in the middle of the atom. Using the connection between momentum and energy one can derive the minimum size of the hydrogen atom, and I assure you it is many powers of 10 bigger than the Planck length…

Yes, I’m aware of that. What I meant was that as regards knowledge of the facts Hesenberg’s uncertainty principle is like the Planck length in setting a well-defined boundary to knowledge. But you’re right in pointing out the difference as well.

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Posted: 30 November 2011 04:40 PM   [ Ignore ]   [ # 79 ]
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http://en.wikipedia.org/wiki/Potential_energy#Relation_between_potential_energy.2C_potential_and_force

A thing to note about conservative forces is that the work done going from A to B does not depend on the route taken. If it did then it would be pointless to define a potential at each point in space. An example of a non-conservative force is friction. With friction, the route taken does affect the amount of work done, and it makes little sense to define a potential associated with friction.
All the examples above are actually force field stored energy (sometimes in disguise). For example in elastic potential energy, stretching an elastic material forces the atoms very slightly further apart. The equilibrium between electromagnetic forces and Pauli repulsion of electrons (they are fermions obeying Fermi statistics) is slightly violated resulting in a small returning force. Scientists rarely discuss forces on an atomic scale. Often interactions are described in terms of energy rather than force. One may think of potential energy as being derived from force or think of force as being derived from potential energy (though the latter approach requires a definition of energy that is independent from force which does not currently exist).
A conservative force can be expressed in the language of differential geometry as a closed form. As Euclidean space is contractible, its de Rham cohomology vanishes, so every closed form is also an exact form, and can be expressed as the gradient of a scalar field. This gives a mathematical justification of the fact that all conservative forces are gradients of a potential field.

Is this a description of a property of the universe at the Planck scale or is this even more fundamental?

[ Edited: 30 November 2011 04:45 PM by Write4U ]
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Posted: 01 December 2011 12:22 AM   [ Ignore ]   [ # 80 ]
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StephenLawrence - 30 November 2011 02:00 PM

Also when one says uncertainty is not just a limit of knowledge, what springs to mind is indeterminism which is not just due to limited knowledge.

That is the right spring in your mind. wink

Maybe this helps?
The phenomenon is mathematically seen the same as bandwidth spread in AM radio. See here:

one cannot simultaneously localize a signal (function) in both the time domain (f) and frequency domain (Fourier transform)

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Posted: 01 December 2011 12:25 AM   [ Ignore ]   [ # 81 ]
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Write4U - 30 November 2011 04:40 PM

Is this a description of a property of the universe at the Planck scale or is this even more fundamental?

What are you asking?
What you are citing is in simple terms that if you make a round walk in a mountainous landscape, you went just as much meters high as down, whatever the landscape.

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Posted: 01 December 2011 12:43 AM   [ Ignore ]   [ # 82 ]
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GdB - 01 December 2011 12:22 AM
StephenLawrence - 30 November 2011 02:00 PM

Also when one says uncertainty is not just a limit of knowledge, what springs to mind is indeterminism which is not just due to limited knowledge.

That is the right spring in your mind. wink

Ok, I thought you disagreed with that.

I don’t understand how you are a 100% determinist at the macro level and an indeterminist wrt to quantum particles.

one cannot simultaneously localize a signal (function) in both the time domain (f) and frequency domain (Fourier transform)

It seems to me like this. Because we can’t make a measurement without disturbing what we measure in some cases, there is certain stuff we cannot know.

But why that is supposed to objectively change anything, I’ve never understood.

Stephen

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Posted: 01 December 2011 03:32 AM   [ Ignore ]   [ # 83 ]
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StephenLawrence - 01 December 2011 12:43 AM

Ok, I thought you disagreed with that.

I don’t understand how you are a 100% determinist at the macro level and an indeterminist wrt to quantum particles.

That’s easy. In the macro world, quantum effects cancel each other out. That means in every system which is warm enough, where enough particles are around, etc quantum effects play no role. This is already the case for brain processes. So why bother?

StephenLawrence - 01 December 2011 12:43 AM

It seems to me like this. Because we can’t make a measurement without disturbing what we measure in some cases, there is certain stuff we cannot know.

But why that is supposed to objectively change anything, I’ve never understood.


In-Steven-Hawking,-2003.gif height=220px style=float : right;

No, that is just a way to make the idea digestible. The real reason is that particles have wave character. Maybe this illustration helps:

In the first graph we know the location of the particle rather precise, but then we cannot determine the frequency very precise (second graph). Exactly the opposite in graph 3: we can determine the frequency much better, but we cannot determine the location very precise (fourth graph).

 

 


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Posted: 01 December 2011 05:58 AM   [ Ignore ]   [ # 84 ]
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GdB - 01 December 2011 12:25 AM
Write4U - 30 November 2011 04:40 PM

Is this a description of a property of the universe at the Planck scale or is this even more fundamental?

What are you asking?
What you are citing is in simple terms that if you make a round walk in a mountainous landscape, you went just as much meters high as down, whatever the landscape.

I was citing an excerpt from a substantial presentation in Wiki. Perhaps I should have edited out the last paragraph, which I believe you used for your simplified analogy, which I do understand.
Please forgive me if I posed the question in the wrong terms or if I am reading more into it than what is presented, but it seems to me that the greater part of the presentation deals with a more subtle method of movement than just a round walk in a mountainous landscape….. confused

What peaked my curiosity was the description that:

Scientists rarely discuss forces on an atomic scale. Often interactions are described in terms of energy rather than force. One may think of potential energy as being derived from force or think of force as being derived from potential energy (though the latter approach requires a definition of energy that is independent from force which does not currently exist).

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Posted: 01 December 2011 06:34 AM   [ Ignore ]   [ # 85 ]
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Write4U - 01 December 2011 05:58 AM

it seems to me that the greater part of the presentation deals with a more subtle method of movement than just a round walk in a mountainous landscape….. confused

Not really. Especially not if you realise that you move in a gravity field. Every time you climb a mountain, you also climb out of a gravity well, that costs energy. The net energy you gain and lose when you get back to the point where you started is exactly 0, because the gravity field is conservative.

Write4U - 01 December 2011 05:58 AM

What peaked my curiosity was the description that:

Scientists rarely discuss forces on an atomic scale. Often interactions are described in terms of energy rather than force. One may think of potential energy as being derived from force or think of force as being derived from potential energy (though the latter approach requires a definition of energy that is independent from force which does not currently exist).

Yes , you cannot define energy without the concept of force. Or the other way round. This is just what kkwan and I were discussing a while ago, but then about mass and force.

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Posted: 01 December 2011 12:29 PM   [ Ignore ]   [ # 86 ]
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GdB - 01 December 2011 03:32 AM
StephenLawrence - 01 December 2011 12:43 AM

Ok, I thought you disagreed with that.

I don’t understand how you are a 100% determinist at the macro level and an indeterminist wrt to quantum particles.

That’s easy. In the macro world, quantum effects cancel each other out. That means in every system which is warm enough, where enough particles are around, etc quantum effects play no role. This is already the case for brain processes. So why bother?

For most practical purposes I agree.

But the macro world is indeterministic unless the quantum effects cancel each other out completely.
Stephen

[ Edited: 01 December 2011 12:35 PM by StephenLawrence ]
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Posted: 01 December 2011 04:49 PM   [ Ignore ]   [ # 87 ]
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GdB - 01 December 2011 06:34 AM
Write4U - 01 December 2011 05:58 AM

it seems to me that the greater part of the presentation deals with a more subtle method of movement than just a round walk in a mountainous landscape….. confused

Not really. Especially not if you realise that you move in a gravity field. Every time you climb a mountain, you also climb out of a gravity well, that costs energy. The net energy you gain and lose when you get back to the point where you started is exactly 0, because the gravity field is conservative.

But what if the mountain is irrelevant, and your walk around consists of disappearing one one side and reappearing on the other, and no one can tell if you went around, over, or through the mountain?

[ Edited: 01 December 2011 04:55 PM by Write4U ]
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Posted: 01 December 2011 11:29 PM   [ Ignore ]   [ # 88 ]
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Write4U - 01 December 2011 04:49 PM

But what if the mountain is irrelevant, and your walk around consists of disappearing one one side and reappearing on the other, and no one can tell if you went around, over, or through the mountain?

Same. It is easy to see based on the law of conservation of energy. Otherwise you would have found a way to create energy from nothing, or destroy it without anything left.

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Posted: 01 December 2011 11:39 PM   [ Ignore ]   [ # 89 ]
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StephenLawrence - 01 December 2011 12:29 PM

For most practical purposes I agree.

But the macro world is indeterministic unless the quantum effects cancel each other out completely.

Free will is practical. And don’t forget: chance processes are an obstruction of free will. Determinism is a necessary basis for free will.

So even if some quantum fluctuations make it into the classical world (i.e. they do not cancel out completely) they are not relevant for free will, but disturb free will.

But now we are far away from induction…

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Posted: 02 December 2011 03:11 AM   [ Ignore ]   [ # 90 ]
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Again, thanks GdB for your excellent clarifications. It’s such a fascinating subject.

I’ll just.. zipper..for now….. smile

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