Do I understand Heisenberg?

[Renfield]

Why not just look at it as a mathematical problem?

Position = x
momentum = mass*velocity = m*dx/dt
level.

This ihasn't been a problem since the invention of calculus. You can measure the volicity of a given object at any particular instant using the methods of calculus.

 

[Renfield]

I believe a lot of confusion results from the mathematicians' spectacularly obscure way of explaining the true meaning and importance of limits.

Well, its a really subtle and confusing thing to try and explain!

Really, I think people are too hard on math teachers.

 

[Renfield]

I haven't read Feynman so can't comment on that part, but I wonder if Schroedinger really intended the cat and all to represent what it really was, a whole bunch of particles. I was under the impression it was an illustration of the principles of quantum mechanics with an idea out of everyday life (OK, I realize most be don't drop poison, radiactive sources and a cat in to a box that often). I read the experiment as an illustration of indeterminant states and observation. But then I've never read the original.

Walt

Quantom physics is still pretty controversial and there's not a lot of agreement among physicists, I believe. It is a fact, everyone agrees about what's going on, but there's a lot of different interpretations out there. Some don't think that anything truly exists in a conventional way until there's an observer to collapse its wave function or whatever. That goes for starts, planets, galaxies, and even cats. Or people.

That's as I understand it anyway.

 

[Brian]

In quantum physics, all particles are waves to some extent, so any moving object travelling in one-dimension can only be said to be in an approximate location as a wave is always spread out over some area and a particle with a precise location at a single point would obviously not be a wave.

Heisenberg's uncertainty principle is about how the waves used to calculate things like position and momentum get bigger and smaller in relation to each other, and it isn't something which arises from problems with smaller and smaller increments.

Let's forget about Heisenberg for a second, I was obviously wrong in my conclusion.

An object moves at 1/10 of an inch per second. At any given second the object is somewhere between .1 and .10 of an inch of where it started?
You can go smaller and smaller. What happens if the distance travelled is smaller than the smallest unit of matter?

 

[Renfield]

Let's forget about Heisenberg for a second, I was obviously wrong in my conclusion.

An object moves at 1/10 of an inch per second. At any given second the object is somewhere between .1 and .10 of an inch of where it started?
You can go smaller and smaller. What happens if the distance travelled is smaller than the smallest unit of matter?

That's where limits come in. You can basically take a calculation using a number thats indefinably small. You use a symbol to stand for said number, since in can't be expressed with digits and decimals. What ends up happening is that this number gets canceled out when you plug it into an equation measuring rate of change (distance over time say for a moving object).

That's not an adequate explanation I suppose, but its the best I can do here. Kind of hard to explain in a bb post.

 

[Brian]

That's where limits come in. You can basically take a calculation using a number thats indefinably small. You use a symbol to stand for said number, since in can't be expressed with digits and decimals. What ends up happening is that this number gets canceled out when you plug it into an equation measuring rate of change (distance over time say for a moving object).

That's not an adequate explanation I suppose, but its the best I can do here. Kind of hard to explain in a bb post.

Eh, let alone a bb post, you'd be trying to explain it to someone who knows next to nothing about math. My first post is intuitive, is it right in the real world, if not on paper? I mean, is this an established principal ? Did I make the question clear, I'm just curious.

 

[Renfield]

Actually you're reasoning is pretty sound. You pointed out one of the limitations of mathematics before Newton and le Fermete came up with Calculus. Before then, scientists and maethematicians used to be stuck when they were faced with this kind of problem.

 

[rwald]

Actually you're reasoning is pretty sound. You pointed out one of the limitations of mathematics before Newton and le Fermete came up with Calculus. Before then, scientists and maethematicians used to be stuck when they were faced with this kind of problem.

Wait, who's le Fermete? Wasn't it Leibniz who developed the calculus cotemporally and independently of Newton?

 

[Ziggurat]

Quantom physics is still pretty controversial and there's not a lot of agreement among physicists, I believe.

Just to clarify, since I think casual readers might miss this and get the wrong impression: everyone agrees about the equations of quantum mechanics, everyone agrees about how wave functions behave. The confusion is only about what exactly the wave function means, not how the equations work.

 

[TeaBag420]

Quantom physics is still pretty controversial and there's not a lot of agreement among physicists, I believe.

Apparently the lack of agreement extends to spelling. I don't mean to attack Renfield specifically, but when I write in a non-English language, I spell words correctly. There's a lot of bad spelling in this thread, probably quite a bit from native English speakers.

 

[TeaBag420]

Let's forget about Heisenberg for a second, I was obviously wrong in my conclusion.
What happens if the distance travelled is smaller than the smallest unit of matter?

You raise an interesting question.

Does the smallest unit of matter have a center? If so, what is the distance traversed from the edge to the center?

If it has a center, does it have sides?

 

[Renfield]

Wait, who's le Fermete? Wasn't it Leibniz who developed the calculus cotemporally and independently of Newton?

Whoops. Its Pierre de Fermat I meant to refer to.

http://en.wikipedia.org/wiki/Pierre_de_Fermat

 

[Renfield]

Apparently the lack of agreement extends to spelling. I don't mean to attack Renfield specifically, but when I write in a non-English language, I spell words correctly. There's a lot of bad spelling in this thread, probably quite a bit from native English speakers.

Congrats.

 

[rwald]

Whoops. Its Pierre de Fermat I meant to refer to.

http://en.wikipedia.org/wiki/Pierre_de_Fermat

Fermat? "Last Theorum" guy? According to the link you provided, he is given "minor credit" for the developement of the calculus, but I think that Leibniz's contributions (to calculus) were more important than Fermat's.

Also, isn't it interesting how people often say "the calculus" when referring to it in a historical sense, but just "calculus" when using it in a mathematical one? You don't see textbooks on "The Multi-Variable Calculus" or "The Tensor Calculus." Or even "The Linear Algebra." Just an interesting linguistic note.

 

[pgwenthold]

This ihasn't been a problem since the invention of calculus. You can measure the volicity of a given object at any particular instant using the methods of calculus.

Nope.

Calculus is based on the concept of the limit.

You can talk about, "In the limit in which dx goes to zero" but that limit is never reached.

 

[garys_2k]

My knowledge of science can be best (only) described as Trivia. Do I have a handle on this?

If you say that a moving object is in a certain place between 12:00:01 and 12:00:02, what I'm saying is that it's at some point between

Here........and here

If I say it's in a certain place between 12:00:01 and 12:00:1.5 it's between

here....and here.

Downward into infinty.

In case I'm not being clear, the numbers are HH:MM:SS

Is that more or less why you can't say a thing is moving and that it has a certain position at the same time?

Not exactly. Heisenberg postulated a theoretical limit on how definable an object is depending on its position and momentum (which includes both speed and mass). Because it includes mass, the limit is different for different particles, whereas your post above doesn't have a mass dependency.

But regarding what I believe to be the more fundamental question you're asking, physics may have an ultimate limit, the Planck Length. This may be the shortest meaningful distance in the universe, at about 1.6E-35 meters. Distances shorter than this have no real meaning, so objects really can't be less than that distance apart, ever. Such distances fundamentally don't exist.

 

[hammegk]

Feynman's comments at the limits say, if a quantum entity knows where it is, it has no idea where it's going, and if it knows where it's going, it has no idea where it is.

Measurement as many mentioned is irrelevant.


rwald: reUR comment "The way I often like to think of it is that the box actually would need to be a light-cone for the superposition to be maintained. But is this correct? Could someone correct me here?" is not correct. That's what Bell's inequality points out.

 

[Renfield]

Nope.

Calculus is based on the concept of the limit.

You can talk about, "In the limit in which dx goes to zero" but that limit is never reached.

You are wrong, actually. You can talk about the velocity of an object at a precise instant. It doesn't matter that the limit never actually reaches zero. It becomes so small that it is negligable, and drops out of the equation. Any term that is a constant multiplied by this limit also will drop out.

Calculus enables us to find instantanious rates of change. You really can find the exact velocity of something at a particular instant. Trust me. Maybe others can explain it better, but I'm quite sure abou this. It is the exact velocity (or any other rate you want to talk about).

 

[Renfield]

Fermat? "Last Theorum" guy? According to the link you provided, he is given "minor credit" for the developement of the calculus, but I think that Leibniz's contributions (to calculus) were more important than Fermat's.

Also, isn't it interesting how people often say "the calculus" when referring to it in a historical sense, but just "calculus" when using it in a mathematical one? You don't see textbooks on "The Multi-Variable Calculus" or "The Tensor Calculus." Or even "The Linear Algebra." Just an interesting linguistic note.

Ah, you're right. I was reading something that referred to Fermet as the father of differential calculus. He developed calc a little further, but he was minor compared to Leibniz.

 

[Renfield]

Measurement as many mentioned is irrelevant.

I'm not so sure about that. Its by measuring (ie observing) the particle that it has to decide where it is, or what its momentum is. Until then it only exists in a sort of indeterminate state. We have to observe its momentum/position for its wave function to collapse.