Do I understand Heisenberg?

[Renfield]

My understanding of Heisenburg is that it is possible to measure the position of a moving particle exactly, or the velocity of that particle exactly, but you can't measure both simultaniously.

It mainly applies to the subatomic world, not to everyday experience.

 

[Walter Wayne]

What about Schrodingers Cat?

I think Schrodinger's Cat is an unfortunate metaphor in that some people believe he was illustrating macroscopic phenomena as well as wave-particle phenomena. Basically it illustrates wave-particle duality and the affects of observation.

A thought experiment
(upon re-reading this I don't know if I explained this well, but what the hey)

Start off with the double-slit experiment. An electron-gun pointed at a double-slit and a phosphor screen on the other side. The screen lights up in an interference pattern caused by the double slit. We slow down the electron-gun until it is firing one electron at a time, and we still notice the electrons strike the screen in a pattern defined by the interference of the double slit. The electron is interfering with itself in a wave like manner.

That is the classical experiment. Now lets add two ideal electron detectors. We put a wire loop around each slit which detects electrons passing through it. What makes it an "ideal" detector is that I am going to neglect any transfer of energy from electron to detector which is necessary in a real system. Thus my imaginary detector doesn't perturb the electron in the traditional sense of slowing it or deflecting it.

With the ideal detector around each slit we now know which slit an electron passes through. How does this affect the experiment? Well, as the electron approaches the slits, it has a 0.5 probability wave function at each slit. In the old experiment, we didn't detect the electon, so this wave function didn't collapse the function. It proceeded through both slits and thus the wave-function could interfere with itself producing the interference pattern. In this experiment I do detect which slit the electron goes through, so it wave function becomes 1 over the area of one slit, and 0 over the area of the other. As a result as the wave function evolves towards the phosphor screen, NO interference pattern is produced. Instead the electron will look like it came from a single source at the slit, in terms of where it is likely to hit the screen.

Notice my detector where ideal, they did the impossible by detecting without adding or removing energy, but still they affected the electron. In the classical experiment the electron stays in an indeterminant state (the cats box stays closed) and we don't know which slit the electron passed through (we don't know if the cat is dead or alive), and we see an interference pattern on the screen. In the modified experiements the electron state is determined (we open the box) and can say the electron passed through slit A (yes, we killed the cat) and this measuring affected the outcome of the electron hitting screen.

I believe what Schrodinger's cat illustrates is the idea of the mere act of interacting (observation) affects the wave-particle itself, by collapsing the electrons (cats) wave function.

Walt

Edit: After reading Teabags post I blame John for all the times I got Schroedinger's name wrong.

 

[DaveW]

Lendri's answers to the HUP question are the best so far:
Heisenberg Uncertainty Principle

To put it in layman's terms, I can either know the momentum to fairly high degree of accuracy, or the poisition, but not both. I could also find some values of the two (know position and momentum) to some medium-level accuracy. The product of the uncertainties can never be below a certain value.

 

[Walter Wayne]

Lendri's answers to the HUP question are the best so far:
Heisenberg Uncertainty Principle

To put it in layman's terms, I can either know the momentum to fairly high degree of accuracy, or the poisition, but not both. I could also find some values of the two (know position and momentum) to some medium-level accuracy. The product of the uncertainties can never be below a certain value.

Dave, I'm not sure I agree with that page.

From the linked page
There is an uncertainty associated with each measurement, e.g., there is some dp and dx, which I can never get rid of even in a perfect experiment!!!. This is due to the fact that whenever I make a measurement, I must disturb the system.

It has been a while since I looked at the derivation, but I don't recall Heisenberg ever bring in a measurement. It has to do with defining things in terms of wave-functions and showing that it will never be physical defined to such precision, even without bringing into it perturbations caused by measurement.

Next time I have a chance, maybe I'll look at the derivation process again.

Walt

 

[Walter Wayne]

I also noted from that page,

We do not know if this indeterminism is actually the way the Universe works because the theory of Quantum Mechanics is probably incomplete. That is, we do not know if the Universe actually behaves in a probabilistic manner (there are many possible paths a particle can follow and the observed path is chosen probabilistically) or if the Universe is deterministic in the sense that I can predict the path a particle will follow with 100 % certainty.
[My Bolding]

We know for a fact the particle doesn't follow a deterministic path; otherwise photons, electrons and such would not produce interference patterns when passing through a double slit one at a time, they would only pass through one slit and produce no interference. As it is a single photon passes through both slits and interferes with itself.

Walt

 

[DaveW]

Honestly, it has been a couple of years since my nuclear physics course, but I remember to some degree actually using that formula to estimate the expected uncertainties in measurements for a particle.

Another source discussing it similarly (not as much with the equation, though): http://www.aip.org/history/heisenberg/p08a.htm

 

[DaveW]

I also noted from that page,

We know for a fact the particle doesn't follow a deterministic path; otherwise photons, electrons and such would not produce interference patterns when passing through a double slit one at a time, they would only pass through one slit and produce no interference. As it is a single photon passes through both slits and interferes with itself.

Walt

Yeah, that is a very wierd statement. In order for us to have any chance of knowing with 100% certainty where the particle will path, we would have to know all the relevant factors about it.. which would then violate the uncertainty principle. The second link I provided seems to be better, though I chose the first for the presentation of the equation (guess I should have read it closer )

 

[DaveW]

Ugh, ok, that first link is rather bad, sorry. You are right, the uncertainty that Heisenberg was talking about was definitely not related to measurement errors at all (though they do still exist).

 

[rwald]

Schrodinger's Cat is a macroscopic quantum superposition state, and these MQS states only really exist only very, very briefly and in very, very small areas before decoherence eliminates them.

It's not that the cat is dead and alive until we open the box and thus measure it, all the particles in the cat get affected by the other particles of their environment (air molecules and radiation in the box) and in the tiniest fraction of a second the cat's state of quantum weirdness vanished, long before the box was opened.

Basically, these other particles "measure" the cat's particles.

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?

 

[wipeout]

Recent books on quantum paradoxes have taught me that decoherence from interaction with other particles in the surrounding environment destroys any possible macroscopic superposition state for the particles making up Schrodinger's Cat very, very quickly. I don't know how you could get a relatively big object like that into an MQS state.

Schrodinger's Cat paradox relies on trying to get all those particles into an "undecided" state which is like trying to go for a world domino-toppling record with countless millions of dominos balanced on end... but decoherence is basically that nature keeps throwing other dominos around the room all the time and knocking yours over before you get more than just a few balanced.

 

[wipeout]

I think Schrodinger's Cat is an unfortunate metaphor in that some people believe he was illustrating macroscopic phenomena as well as wave-particle phenomena. Basically it illustrates wave-particle duality and the affects of observation.

A thought experiment
(upon re-reading this I don't know if I explained this well, but what the hey)

Start off with the double-slit experiment. An electron-gun pointed at a double-slit and a phosphor screen on the other side. The screen lights up in an interference pattern caused by the double slit. We slow down the electron-gun until it is firing one electron at a time, and we still notice the electrons strike the screen in a pattern defined by the interference of the double slit. The electron is interfering with itself in a wave like manner.

That is the classical experiment. Now lets add two ideal electron detectors. We put a wire loop around each slit which detects electrons passing through it. What makes it an "ideal" detector is that I am going to neglect any transfer of energy from electron to detector which is necessary in a real system. Thus my imaginary detector doesn't perturb the electron in the traditional sense of slowing it or deflecting it.

With the ideal detector around each slit we now know which slit an electron passes through. How does this affect the experiment? Well, as the electron approaches the slits, it has a 0.5 probability wave function at each slit. In the old experiment, we didn't detect the electon, so this wave function didn't collapse the function. It proceeded through both slits and thus the wave-function could interfere with itself producing the interference pattern. In this experiment I do detect which slit the electron goes through, so it wave function becomes 1 over the area of one slit, and 0 over the area of the other. As a result as the wave function evolves towards the phosphor screen, NO interference pattern is produced. Instead the electron will look like it came from a single source at the slit, in terms of where it is likely to hit the screen.

Notice my detector where ideal, they did the impossible by detecting without adding or removing energy, but still they affected the electron. In the classical experiment the electron stays in an indeterminant state (the cats box stays closed) and we don't know which slit the electron passed through (we don't know if the cat is dead or alive), and we see an interference pattern on the screen. In the modified experiements the electron state is determined (we open the box) and can say the electron passed through slit A (yes, we killed the cat) and this measuring affected the outcome of the electron hitting screen.

I believe what Schrodinger's cat illustrates is the idea of the mere act of interacting (observation) affects the wave-particle itself, by collapsing the electrons (cats) wave function.

Walt

Edit: After reading Teabags post I blame John for all the times I got Schroedinger's name wrong.

That's basically the same as Richard Feynman's version of the two-slit experiment from his famous Feynman Lectures on Physics.

His version has a lightbulb after the slits and the photons from the lightbulb either scatter off the electrons (or not), and you see a flash (or not) and a particle is detected (or interference pattern emerges) at the screen.

Decoherence is the answer which has emerged in the last 30 years (and well after Feynman's Lectures) as to why the interference pattern gets "washed out" (as the terminology I've seen calls it) when something interacts with electrons and the interference pattern disappears.

The relationship of this two-slit experiment to Schrodinger's Cat is that in the case of the cat paradox, it's obviously a whole lot more particles making up the cat, the air, the box and space itself and interacting with each other, but decoherence is involved here as well.

The cat can never be made into a wave-like state like the electron because too many things interact to allow that, hence no paradox anymore. It's just a cat in a box all the time.

I'm still learning the subject and figuring out the details myself, though.

 

[Dancing David]

On the measurement issue,

I am not an expert but certain things in physics rely on the fact that the energy partyicle's position is a wave function and not a mechanistic ball rolling in space time.

I thought that for hydrogen to fuse into helium there has to be the indeterminancy. A proton can not approach another proton because of the Coulumb effects, they repluse each other the stronger they get. But because the protons are actualy wave forms and indeterminate, the probability that one will end up next to another incraeses as temperature and pressure rise. So for the sun to shine we have to have indeterminancy.

So it is not just an issue of measurement, it is also an issue that an energy particle is defined by a wave form occupy-ing an indeterminante region of space time.

 

[pgwenthold]

Why not just look at it as a mathematical problem?

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

In order to know momentum, you have to have a quantity dx = x2 - x1. However, if you have dx, then how do you define the position? All you can say is that it is somewhere between x1 and x2, because dx > 0.

OTOH, if you try to specify the position exactly, then dx = 0 and you don't have any momentum information. Basically, given zero-point motion, in order to define x, you have to look at a point in time, which means that dx/dt is undefined.

I like to use snapshots of a ball flying through the air to demonstrate it. If the ball is moving sufficiently slow and you have the shutter speed, on the picture it will look like the ball is floating in mid-air:

I ask the class, ok, now which direction is the ball moving? Without seeing any context, you can't tell which way the ball is moving. However, we can specify perfectly where the ball is.

OTOH, if the ball is moving fast and/or the shutter speed is slow, you see a blur. For example, in the picture of Barry Bonds shown below, you can see the blur of the ball between the pitcher and home.

Given the blur, you have a pretty good idea of the path of the ball. However, if I ask you "What is the position of the ball in that picture?" you are stuck. All you can say is that when the picture was taken, it was in that section of the blur. Hence, when you have information on the path, by definition you lose information on the position.

Now, the uncertainties that result become most significant at the subatomic level, but the concept works pretty well even at the macroscopic level.

 

[Walter Wayne]

The relationship of this two-slit experiment to Schrodinger's Cat is that in the case of the cat paradox, it's obviously a whole lot more particles making up the cat, the air, the box and space itself and interacting with each other, but decoherence is involved here as well.

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

 

[wipeout]

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.

I think the overall point was that quantum concepts like indeterminate states and observation would be amplified to macroscopic scales and have macroscopic effects but that we don't see them so something, somewhere is missing.

 

[Brian]

So, is there a name for what I described in my original post?

 

[wipeout]

I was pondering the problem of the meaning of velocity and acceleration at a point of time last year in classical physics, never mind quantum.

I concluded that the mathematicians mean something slightly different from scientists and engineers when it comes to the difference between delta x and dx and that this mathematical meaning does indeed allow for precise values of velocity and acceleration at a point in time.

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

Epsilon-delta-epsilon-delta-epsilon-delta....zzzzzzzzzzzzzzz....

 

[wipeout]

So, is there a name for what I described in my original post?

Zeno's paradoxes are rather similar and well-known, and are worth looking up. They relate to motion in both classical or quantum physics and cut time and distance into smaller and smaller bits. They also often lead people into longer and longer arguments too.

 

[Brian]

Zeno's paradoxes are rather similar and well-known, and are worth looking up. They relate to motion in both classical or quantum physics and cut time and distance into smaller and smaller bits. They also often lead people into longer and longer arguments too.

I know about Zeno's Paradoxes. If I'm not mistaken that'd take us to the .3333....*3=1 thread.
Am I more or less right though? In any given increment of time a moving object can only be said to be somewhere between two points.

 

[wipeout]

Am I more or less right though? In any given increment of time a moving object can only be said to be somewhere between two points.

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.