Silly question about physics and quantum madness

[athon]

I hope this question doesn't get me laughed out of the club...

I have a biologist's grasp of physics; in other words, if I can't picture it in my mind I have difficulty understanding it. Obviously I have big problems with quantum mechanics, then.

Heisenberg's Uncertainty principle seems (to me) to imply a certain truly chaotic side of nature, where our expectation according to universal rules seems to falter. In other words, the laws of the universe nearly always work, but on a quantum level all bets are off.

Can this mean that on the macro level, the perceived laws are the sum average results of quantum effects? Hence laws are not steadfast and universal, but are a bias within the quantum chaos?

I really hope this isn't a silly question.

 

[geni]

Heisenberg's Uncertainty principle seems (to me) to imply a certain truly chaotic side of nature, where our expectation according to universal rules seems to falter.

No since:

1)Heisenberg's Uncertainty principle sets hard limits on the uncertianty

2)it only applies to certain conjugate quantities of single particles not to laws.

 

[athon]

Oh. Such a simple answer.

I feel decidedly stupid now.

So...if all laws are consistent even on a quantum level, does that mean there is a sort of fate for all actions? Hence knowing the near infinite number of variables in a universe would grant you knowledge of all actions prior to their occurance?

Sorry, getting kind of philosophical. I figured I'd put all my stupid questions into one thread and get it done with.

Athon

 

[Rob Lister]

I hope this question doesn't get me laughed out of the club...

I have a biologist's grasp of physics; in other words, if I can't picture it in my mind I have difficulty understanding it. Obviously I have big problems with quantum mechanics, then.

Heisenberg's Uncertainty principle seems (to me) to imply a certain truly chaotic side of nature, where our expectation according to universal rules seems to falter. In other words, the laws of the universe nearly always work, but on a quantum level all bets are off.

Can this mean that on the macro level, the perceived laws are the sum average results of quantum effects? Hence laws are not steadfast and universal, but are a bias within the quantum chaos?

I really hope this isn't a silly question.

Ditto your well expressed confusion.

I know it all works out in the macro average but it certainly is disconcerting.

 

[Ryan O'Dine]

Just a caveat.

Quantum randomness is not "pure" chance. There are bell curves of probabilities -- some states being much more likely than others. For this reason, in the macro world, the least likely states tend to wash out.

 

[Ziggurat]

So...if all laws are consistent even on a quantum level, does that mean there is a sort of fate for all actions? Hence knowing the near infinite number of variables in a universe would grant you knowledge of all actions prior to their occurance?

As far as we can tell, yes. Provided you knew the laws exactly, which there's no guarantee that we do. For example, Newtonian mechanics is a good approximation to special relativity in the low-velocity limit, and special relativity is a good approximation to general relativity in the low-gravity limit. It's certainly possible that quantum mechanics as we know it now is merely a good approximation to something more complete.

 

[geni]

Oh. Such a simple answer.

I feel decidedly stupid now.

So...if all laws are consistent even on a quantum level, does that mean there is a sort of fate for all actions?

We don't know what all the laws are yet (for example we don't have a theory of quantum gravity).

Hence knowing the near infinite number of variables in a universe would grant you knowledge of all actions prior to their occurance?

Only if you knew them to an infinite level of correctness (which you can't). Otherwise chaos thoery kicks in.

 

[Humphreys]

Can this mean that on the macro level, the perceived laws are the sum average results of quantum effects? Hence laws are not steadfast and universal, but are a bias within the quantum chaos?

I really hope this isn't a silly question.

I believe this is exactly right. I'm not sure where I read this, it may have even been in The Demon Haunted World, but it was suggested that you may wake up one morning to find out your car has passed straight through your garage door during the night, and appeared on the other side, fully formed.

It was also mentioned that a baseball could pass directly through a catcher's mitt, in theory, because everything is probabilistic at the quantum level, although the chances against are astronomical, obviously.

 

[DanishDynamite]

No since:

1)Heisenberg's Uncertainty principle sets hard limits on the uncertianty

Sure it set limits to uncertainty, but the revolutionary bit was that it made uncertainty an integral part of how the Universe functions, not some sort of nuisance due to inadequate technology or inadequate precision instruments. Heisenberg made it clear that no such precision instruments were possible, even in theory. The Universe simply functions with a built-in uncertainty.

 

[Number Six]

There's something about the HUP I don't understand. I'll explain things as I understand it and someone can point out my error.

Take momentum and velocity. The HUP says that the product of the errors in measuring those two things must always be larger than some number. The number if very small, but it is greater than 0. If the product must be greater than 0 then the error in measuring both momentum and velocity must also be greater than 0. And yet I hear it said that we can only measure one at a time exactly and not both. How can that be? It seems to me that can't measure either _exactly_ because the product of the errors is greater than 0. What am I missing?

 

[TobiasTheViking]

There's something about the HUP I don't understand. I'll explain things as I understand it and someone can point out my error.

Take momentum and velocity. The HUP says that the product of the errors in measuring those two things must always be larger than some number. The number if very small, but it is greater than 0. If the product must be greater than 0 then the error in measuring both momentum and velocity must also be greater than 0. And yet I hear it said that we can only measure one at a time exactly and not both. How can that be? It seems to me that can't measure either _exactly_ because the product of the errors is greater than 0. What am I missing?

I think it is the combined error that must be between 0 and 1.
So, the closer you get to the exact speed, the more wrong the position will be, and vica versa.

But, i may be totally wrong.

 

[Yllanes]

There's something about the HUP I don't understand. I'll explain things as I understand it and someone can point out my error.

Take momentum and velocity. The HUP says that the product of the errors in measuring those two things must always be larger than some number. The number if very small, but it is greater than 0. If the product must be greater than 0 then the error in measuring both momentum and velocity must also be greater than 0. And yet I hear it said that we can only measure one at a time exactly and not both. How can that be? It seems to me that can't measure either _exactly_ because the product of the errors is greater than 0. What am I missing?

You can measure one of them exactly, but then you know nothing about the other (you could say, and this is quite horrible but maybe easy to understand, that you get an expression of the kind 0 · oo).

The real equation is

Where [A,B] = AB - BA is the commutator of the operators A and B (for position and momentum equal to i hbar) and psi is the state. If two operators commute, we say they are compatible and we can know both of them with exact precision at the same time. In QM we want to find a complete system of compatible observables, whose eigenstates (states for which the uncertainty is zero) will form a basis of the space of state vectors.

You can understand this if you know some basic linear algebra. Consider two matrices, A and B. If they satisfy certain properties (as is always the case with observables) we can change bases so that they adopt a diagonal form. Each matrix will have a set of eigenvalues and a set of eigenvectors. Now, if the two matrices commute, their eigenvectors will be the same, so they can be diagonalised with the same change of basis. If they don't commute, they will require different bases and will not be diagonalised at the same time. In QM the matrices are often infinite dimensional, but this reasoning also applies. Now the eigenvectors are the only states with uncertainty zero.

 

[wipeout]

Heisenberg's Uncertainty principle seems (to me) to imply a certain truly chaotic side of nature, where our expectation according to universal rules seems to falter. In other words, the laws of the universe nearly always work, but on a quantum level all bets are off.

Can this mean that on the macro level, the perceived laws are the sum average results of quantum effects? Hence laws are not steadfast and universal, but are a bias within the quantum chaos?

Quantum interference between possibilities can sum up and cancel out in many situations. This allows classical behaviour to emerge from the far-from-classical quantum laws.

So you're on the right track with this summing up idea, it's just the quantum laws are always there and consistent, it's the classical laws which are not steadfast and universal.

They're very useful approximations, though.

 

[Dilb]

There's something about the HUP I don't understand. I'll explain things as I understand it and someone can point out my error.

Take momentum and velocity. The HUP says that the product of the errors in measuring those two things must always be larger than some number.

It's not the errors in the measurement, it's the uncertainties in our description of a particle. To boil it down:

Suppose you have a proton nicely fixed in space (somehow). An electron is bound to the proton. You then measure the position of the electron perfectly accurately (somehow), and put it back. Repeat a hundred times, and you'll measure some average position, and a standard deviation. Even though you set up the experiment exactly the same each time, the electron is in a different position. The standard deviation is the uncertainty in where we think the electron is.

Similarly you can measure momentum and find an uncertainty, despite the setup being exactly the same each time.

This will apply in any setup, the uncertainty of some pairs of measurable values will always multiply to a certain value. For example, if you use a uranium nucleus instead of just one proton, the electron will be tightly bound, and will have a smaller uncertainty in position, but it's momentum will have a larger uncertainty. It's true in a crystal, in a liquid, in empty space.

There are no "hidden variables" that were missing, an electron just doesn't have a fixed position. When we describe the electron as fully as possible, we can predict the average position, and the average variance in a measurement of the position. The HUP says that for any complete description of an electron (or other particle), we will predict that the variance* in the position and momentum of an electron will be greater than some value.

*Variance is related to standard deviation, but I want to keep in mind that these are not uncertainties in individual measurements, but statistics which discribe a large number of measurements.

 

[wipeout]

So...if all laws are consistent even on a quantum level, does that mean there is a sort of fate for all actions? Hence knowing the near infinite number of variables in a universe would grant you knowledge of all actions prior to their occurance?

Sort of, yeah. As the most extreme example, the initial state of the universe contains all the possibilities for the universe but the chance nature of quantum theory means while we'd know everything which could happen, we wouldn't know what will happen.

As the Nobel laureate Murray Gell-Mann jokes to his friend Jim Hartle about his work with Stephen Hawking on this: "If you know the wave function of the universe, why aren't you rich?"

 

[athon]

It's not the errors in the measurement, it's the uncertainties in our description of a particle. To boil it down:

Suppose you have a proton nicely fixed in space (somehow). An electron is bound to the proton. You then measure the position of the electron perfectly accurately (somehow), and put it back. Repeat a hundred times, and you'll measure some average position, and a standard deviation. Even though you set up the experiment exactly the same each time, the electron is in a different position. The standard deviation is the uncertainty in where we think the electron is.

Sorry to post and run here (I'm researching something at work and probably shouldn't be posting here...but, ah, screw it).

Is the uncertainty the result of being uncertain, or because the particle itself has no certain position? For example, I count the leaves on a tree. I then put them back on, and count them again. There are a certain number of leaves on the tree, and my counting is accurate, however I get a narrow range of numbers. Am I to then assume that there are not a certain number of leaves on the tree? Or am I to assume that my counting has not been as accurate as I would have liked?

I'll get back to some of the other posts later. Thanks for those who replied; I might be able to grasp this yet!

Athon

 

[thaiboxerken]

Is there any weight behind the claim that "quantum physics shows that consciousness affects reality?"

This lady, with a major in physics, claims that it does.

http://freedomofreligion.myfreeforum.org/sutra507.php#507

 

[epepke]

I hope this question doesn't get me laughed out of the club...

I have a biologist's grasp of physics; in other words, if I can't picture it in my mind I have difficulty understanding it. Obviously I have big problems with quantum mechanics, then.

Heisenberg's Uncertainty principle seems (to me) to imply a certain truly chaotic side of nature, where our expectation according to universal rules seems to falter.

I wouldn't use the term "chaotic" to describe this, because "chaos" has a particular meaning. It describes extreme sensitivity to initial conditions, even though deterministic systems. The systems have positive feedback and can usually be modeled by coupled differential equations.

In other words, the laws of the universe nearly always work, but on a quantum level all bets are off.

The mathematics at the quantum level are just as solid as any other mathematics, and they're also pretty simple. They're just so different that they can be hard for people to grok.

Can this mean that on the macro level, the perceived laws are the sum average results of quantum effects?

You could say that. The decoherence people, whom I think have a lot of good ideas, say this a lot.

At a macro level, light goes through a vacuum in a straight line (or a geodesic in gravity).

At a quantum level, the highest probability of a photon's path is along amplitudes that are so similar that they reinforce each other, resulting in a path that is a straight line (or a geodesic in gravity).

At a macro level, light slows down when going through glass.

At a less naive macro level, it slaloms around the stuff in the glass, so while it doesn't slow down, it has to take a longer path.

At a quantum level, the amplitudes of the photons interfere with the amplitudes of electrons in such a way that the maximal probability path resembles a slalom (albeit a slalom in many possible directions).

 

[joller]

Just a caveat.

Quantum randomness is not "pure" chance. There are bell curves of probabilities -- some states being much more likely than others. For this reason, in the macro world, the least likely states tend to wash out.

My understanding is that the underlying random variables are in fact 'pure chance'.
Every random variable is pure chance. it the correlation between the variables etc. that creates the bell curve.
Say for example, if you throw a six sided dice, the chances of each side facing up will be the same (for a theoretical perfect dice, which of course doesnt exist), but if you throw 2 such dice and sum the result, the bell curve will start appearing.
But then again the random variables are just a way to mathematically express certain systems/ processes

 

[Dilb]

Sorry to post and run here (I'm researching something at work and probably shouldn't be posting here...but, ah, screw it).

Is the uncertainty the result of being uncertain, or because the particle itself has no certain position? For example, I count the leaves on a tree. I then put them back on, and count them again. There are a certain number of leaves on the tree, and my counting is accurate, however I get a narrow range of numbers. Am I to then assume that there are not a certain number of leaves on the tree? Or am I to assume that my counting has not been as accurate as I would have liked?

I'll get back to some of the other posts later. Thanks for those who replied; I might be able to grasp this yet!

Athon

The deviation of a particle's position is intrinsic to the particle. A measurement can measure a precise position with less error. It's like tossing coins.

If I toss 10 coins, I expect to get heads 5 times. Over many tosses, I expect a deviation of 1.58, so I would say the result is 5 +/- 1.58 heads. But I can toss 10 coins and measure exactly 4.