Quantum Mechanics: Explained for a Novice

[steersman]

I'm a physics novice who has a question for all you gurus out there. I've heard that following the laws of quantum mechanics, an event could occur twice while producing two different outcomes. How is this possible? Or mayby I've completely misunderstood. Can someone explain for me?

 

[selfAdjoint]

If you do a quantum experiment, that means you operate somehow on some quantum entity to produce a result in the form of some measured quantity. The nature of the quantum world is such that that measured quantity can come in more than one value. Which one you find is a question of probability, and if you did the experiment again, exactly the same, tomorrow, maybe one of the other values would show up on your meter.

Quantum Mechanics gives you the probability of each possible outcome, and if you did the same experiment thousands of times, the number of times each value came up, divided be the number of experiments, would approsimate to the quantum probability.

 

[steersman]

It sounds like quantum probability is really just an inability to measure events accurately at the quantum level. I should have known there's no such thing as randomness in a system.

 

[jcsd]

Originally posted by steersman
It sounds like quantum probability is really just an inability to measure events accurately at the quantum level. I should have known there's no such thing as randomness in a system.

No it's much deeper than this, quantum mechanics is trult stochastic, in other words it is truly random.

 

[steersman]

Can you explain why please?, I'm very interested

 

[FZ+]

Basically, the idea of HUP being a limit on measurement is really inaccurate. What HUP says is that there is no real absolute, distinguishable values of velocity and position, or time and energy on such small scales. It isn't just measurement - it is the reality of the situation. (someone should really go through the textbooks, and change Heisenberg's analogy of the photons bouncing off the electrons...)

But this is still somewhat open to interpretation, though the evidence does most point to the existence of such quantum randomness. (IMHO, of course)

 

[steersman]

Originally posted by FZ+
Basically, the idea of HUP being a limit on measurement is really inaccurate. What HUP says is that there is no real absolute, distinguishable values of velocity and position, or time and energy on such small scales. It isn't just measurement - it is the reality of the situation. (someone should really go through the textbooks, and change Heisenberg's analogy of the photons bouncing off the electrons...)

But this is still somewhat open to interpretation, though the evidence does most point to the existence of such quantum randomness. (IMHO, of course)

What is HUP?
I think I know what you're talking about. You're saying that the variables involved in quantum mechanics need to be measured to an infinitesimal degree before you can predict events - and since we can't do that the events are random.

Ok, here's my problem. Measurement is not a property of things, it's a tool we use. Therefore this stumbling block does not necessarily indicate that events on the quantum level are random. We may never be able to accurately depict them, but to say they are random seems to be a fallacy.

 

[chroot]

It is not a fallacy -- it is proven. Read up on the Bell inequalities and the Aspect experiment. It turns out that is it absolutely not possible for a deterministic quantum theory to agree with experiment. (Many people are stunned when they first learn of this -- you included, I'm sure -- but it is fact.)

Nor is it a stumbling block -- it's part of the fundamental character of microscopic things. There can be no advance in technology or technique that can allow us to find a precise position and a precise momentum for a particle simultaneously. The particles simply do not have precise positions and momenta at the same time. This conclusion was reached some 80 years ago now.

If you're looking for some way to understand the Heisenberg uncertainty principle (HUP) qualitatively, here's how Griffiths describes it:

Imagine that you're holding one end of a very long rope, and you generate a wave by shaking it up and down rhythmically. If someone asked you, "Precisely where is the wave?" you'd probably think he was a little bit nutty: The wave isn't precisely anywhere--it's spread out over 50 feet or so. On the other hand, if he asked you what the wavelength is, you could give him a reasonable answer: It looks like about 6 feet. By contrast, if you gave the rope a sudden jerk, you'd get a relatively narrow bump traveling down the line. This time the first question (where precisely is the wave?) is a sensible one, and the second (What is its wavelength?) seems nutty--it isn't even vaguely periodic, so how can you assign a wavelength to it? Of course, you can draw intermediate cases, in which the wave is fairly well localized and the wavelength is fairly well defined, but there is an inescapable trade-off here: The more precise a wave's position is, the less precise is its wavelength, and vice versa.

In quantum mechanics, particles are considered (roughly speaking) by oscillatory probability waves. All particles obey the HUP.

Richard Feynman speaks at great length about these matters in his Lectures on Physics. If you're still unwilling to accept experimental fact, you might want to do some reading.

- Warren

 

[steersman]

I accept experimental fact, I accept the analogy you used.

My argument is logic based. I said: Measurement is not a property of things, it's a tool we use.

You said: The particles simply do not have precise positions and momenta at the same time. I understand this, but the problem is an artificial one. It has been created by attempting to quantify.

If you attempt to quantify - the events are not just random, they are inexplicable.

Without any sort of measurement, they are still theoretically deterministic even though they can never be determined.

What I'm espousing here isn't scientific, but it's still interesting.

 

[jcsd]

Originally posted by chroot
It is not a fallacy -- it is proven. Read up on the Bell inequalities and the Aspect experiment. It turns out that is it absolutely not possible for a deterministic quantum theory to agree with experiment. (Many people are stunned when they first learn of this -- you included, I'm sure -- but it is fact.)

Nor is it a stumbling block -- it's part of the fundamental character of microscopic things. There can be no advance in technology or technique that can allow us to find a precise position and a precise momentum for a particle simultaneously. The particles simply do not have precise positions and momenta at the same time. This conclusion was reached some 80 years ago now.

If you're looking for some way to understand the Heisenberg uncertainty principle (HUP) qualitatively, here's how Griffiths describes it:

In quantum mechanics, particles are considered (roughly speaking) by oscillatory probability waves. All particles obey the HUP.

Richard Feynman speaks at great length about these matters in his Lectures on Physics. If you're still unwilling to accept experimental fact, you might want to do some reading.

- Warren

Chroot, I disagree Bell's theorum most certainly rules out a local hidden variables theory, but it still allows a non-local hidden variables theory such as De-Broglie-Bohm theory (though as this predicts that atoms have electric dipole moments this is probably incorrect).

That said to me the ASpect experiments are compelling evidence that the Copenhagen Interpretation is the best current interpretation of quantum mechanics.

 

[chroot]

Originally posted by steersman
I understand this, but the problem is an artificial one. It has been created by attempting to quantify.

I have no idea what this means.

Without any sort of measurement, they are still theoretically deterministic even though they can never be determined.

Scientists are usually local positivists. If you can't measure it, even in principle, then it doesn't exist.

- Warren

 

[steersman]

I Said: I understand this, but the problem is an artificial one. It has been created by attempting to quantify.

I mean that the problem is created by attempting to impose an artificial process on a physical system.

Chroot said: Scientists are usually local positivists. If you can't measure it, even in principle, then it doesn't exist.

There's nothing new age or metaphysical about what I said. I called QM randomness a fallacy becuase my argument was based on logical reasoning, something used all the time in science.

 

[FZ+]

No... you don't understand. The Heisenberg uncertainty principle has nothing to do with measurement. It makes a statement as to what the particles actually ARE.

 

[Hurkyl]

I think what steersman is trying to say is that the randomness only appers when we try to pigeonhole the world into things like position & momentum.

IOW things really are deterministic, but cannot be described deterministically with position & momentum-like descriptions.

 

[steersman]

No... you don't understand. The Heisenberg uncertainty principle has nothing to do with measurement. It makes a statement as to what the particles actually ARE.

FZ, I would like to know something of that statement. I have to disagree with you though on HUP and measurement. Consider this:

The uncertainty relations may be expressed in words as follows.
The simultaneous measurement of two conjugate variables (such as the momentum and position or the energy and time for a moving particle) entails a limitation on the precision (standard deviation) of each measurement. Namely: the more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa. In the most extreme case, absolute precision of one variable would entail absolute imprecision regarding the other.

from this site: http://www.aip.org/history/heisenberg/p08a.htm

Also, consider this:

Heisenberg realized that the uncertainty relations had profound implications. First, if we accept Heisenberg's argument that every concept has a meaning only in terms of the experiments used to measure it, we must agree that things that cannot be measured really have no meaning in physics. Thus, for instance, the path of a particle has no meaning beyond the precision with which it is observed. But a basic assumption of physics since Newton has been that a "real world" exists independently of us, regardless of whether or not we observe it. (This assumption did not go unchallenged, however, by some philsophers.) Heisenberg now argued that such concepts as orbits of electrons do not exist in nature unless and until we observe them.

from: http://www.aip.org/history/heisenberg/p08c.htm

I think people need to separate Heisenberg's uncertainity principal and Heisenberg's assumptions. The topic of discussion has resulted from a combination of the two.

 

[drag]

Greetings !

Originally posted by steersman
I think people need to separate Heisenberg's uncertainity principal and Heisenberg's assumptions. The topic of discussion has resulted from a combination of the two.

I think you need to separate what is being explained
to you from your own explanations...

What you are basicly saying, and that's understandable, is
that there is no real uncertainty. It is so because the
uncertainty is only a matter or measuremtn and when
it is not conducted the uncertainty in nature does not exist.

Well, basicly that idea is violated by even the simplest
and most basic of QM's experiments the Double Slit experiment:
Consider a single particle sent on its way towards
two slits with a small distance between them(small enough for
the wavefunction of the particle to "pass" through both).
Then position a screen behind the slits and measure the impacts
of many particles sent through the slits one by one.
You'll see a diffraction pattern - the impacts will show
that each particle(or wave-particle = wavicle) passed through
BOTH slits. On the other hand if you send a partcile
through a single slit with the other one closed OR place
a detector behind one of the slits and detect the partcile
OR NOT detect it behind THAT slit the wavefunction will
collapse and the particles will hit the screen around some
particuilar point - as a "normal" tiny ball like particle would.

In conclusion, you will SEE that nature itself, measured or not,
has wavicles and follows the HUP (for the quantized theories
and their particles).

Live long and prosper.

 

[chroot]

Listen, guy:

You obviously don't know quantum mechanics. You don't realize WHY the theory directly predicts that particles do not have precise positions and momenta simultaneously. You're reading a bunch of pseudo-technical prose descriptions of things, and thinking you understand it.

Learn the math of quantum mechanics, and you'll understand immediately why things have to be as they are. Until then, you simply don't know what the hell you're talking about. You'd do well to stop arguing with those who do.

- Warren

 

[FZ+]

Let's be a little gentler on steerman, shall we?

Steersman:
You have alas fallen into the no.1 public misconception about quantum mechanics - what uncertainty is actually about. It's probably not your fault, but the fault of Heisenberg's initial explanation of the effect which is hugely misleading, but still often reproduced.

Heisenberg's initial inspiration for the existence of the uncertainty effect was based on knowledge. True. But the mathematical derivation of this from fundamental facts is based on matrices, and from quantum laws of how particles behaved, not on the accuracy of the measurement. This is an essential point. Just as Einstein began with light clocks, Heisenberg's use of "measurement precision" is only an analogy for the real world significance of the HUP. The HUP, in it's useful form, in it's experimentally verified form, in the form we talk about when we say HUP, in the form we use it in most modern theories is based on it as a state of the actual existence of the particles, not of knowledge.

If I has my way, the analogy of the photons and the electrons shouldn't be used at all, but we should just go straight into no absolute position/momentum as a derived and confirmed physical fact.

 

[steersman]

drag:

I'm certain there is uncertainity. I'm not denying HUP or any experiment that has validated it. My question is: How can an event occur twice and produce two different outcomes while maintaining the exact same variables?

warren:

As I said in my first post to this board, I am a physics novice. I don't claim to understand the math involved in Heisenburg's theory as I believe it inconsequential to what I posit. I'm probably wrong. Forgive me if it seems I'm arguing with you.

FZ:

In a previous post I wrongly interpreted what you termed as 'HUP' to be randomess based on an inordinate precision of measurement. I hope you see that what I assert now is completely different to that.



Even though HUP is solid and proven, I believe it is incorrect to assign the proprety 'random' to these particles. Hurkyl summed up my position , except when he said things were deterministic - this implies they can be found.

How can quantum particles be intrinsically random? I'll have a look at hidden variable theory and Bell's inequalities to see if they have relevance to what I'm saying.

For now though: God does not play dice!

 

[drag]

Greetings !

Originally posted by steersman
I'm certain there is uncertainity. I'm not denying HUP or any experiment that has validated it. My question is: How can an event occur twice and produce two different outcomes while maintaining the exact same variables?

Well, that's what uncertainty means - with the same
parameters you only have probabilities for the various
results - which means that according to uncertainty you
can get different results.

chroot, I think it's always a type of shock for people when
they start learning QM and understand its couter-intuative
and illogical (according to common logic) results. Don't be
so hard on him. It's one thing to argue and another thing to
express strong doubt and require some convincing, after all
people are here to learn (and teach).

Live long and prosper.

 

[jcsd]

Originally posted by steersman
drag:

I'm certain there is uncertainity. I'm not denying HUP or any experiment that has validated it. My question is: How can an event occur twice and produce two different outcomes while maintaining the exact same variables?

warren:

As I said in my first post to this board, I am a physics novice. I don't claim to understand the math involved in Heisenburg's theory as I believe it inconsequential to what I posit. I'm probably wrong. Forgive me if it seems I'm arguing with you.

FZ:

In a previous post I wrongly interpreted what you termed as 'HUP' to be randomess based on an inordinate precision of measurement. I hope you see that what I assert now is completely different to that.



Even though HUP is solid and proven, I believe it is incorrect to assign the proprety 'random' to these particles. Hurkyl summed up my position , except when he said things were deterministic - this implies they can be found.

How can quantum particles be intrinsically random? I'll have a look at hidden variable theory and Bell's inequalities to see if they have relevance to what I'm saying.

For now though: God does not play dice!

What you are basically proposing is a 'hidden variable theory' i.e. you are saying that there is some unobserved detirministic process going on. Bell's theroum and Aspect's experiments have shown that a local hidden variable theory is impossible. A local hidden variable theory is one in which, like in classical physics two objects (or an object and a field like in Bohm's hidden variable theory) separated by distance can't affect each other instaneously. A hidden variables theory must be non-local which is a big problem in physics as such a theory would be incompatible with relativity.

 

[steersman]

drag said:

Well, that's what uncertainty means - with the same
parameters you only have probabilities for the various
results - which means that according to uncertainty you
can get different results.

Yes, I agree with that - which means you don't understand what I am saying.

HUP, I have read, came about when it was realized that the only way to determine position and momentum of a particle was to affect the particle in some way. This makes position and momentum mutually exclusive (oversimplifying I know). As a concomitant to this the possible results are represented by a waveform.

Experiments of the quantum level will always yield unpredictable results becuase we have reached the limits of determination. It is a logical fallacy though to equate this with true randomness on behalf of the quantum particles.

I think the word 'random' is used becuase, from a strictly scientific point of view, it has the same meaning as indetermination.

Quantum particles ARE truly stochastic, just remember that this is a statistical term.

I am definitely NOT positing a hidden variable theory. Nothing about what I am saying needs to be deterministic.

 

[russ_watters]

Originally posted by steersman
HUP, I have read, came about when it was realized that the only way to determine position and momentum of a particle was to affect the particle in some way. This makes position and momentum mutually exclusive (oversimplifying I know). As a concomitant to this the possible results are represented by a waveform.

Thats an oversimplification often used (its in "A Brief History of Time") to explain HUP and it creates misunderstandings such as the one you refuse to accept.

Experiments of the quantum level will always yield unpredictable results becuase we have reached the limits of determination. It is a logical fallacy though to equate this with true randomness on behalf of the quantum particles.

Yes, that is a logical fallacy for some experiments, but coincidentally it is also something experimentally proven by others.

I think the word 'random' is used becuase, from a strictly scientific point of view, it has the same meaning as indetermination.

No.

I think you're hearing us, you're just choosing not to accept it because you are uncomfortable with the idea. There is really nothing wrong with that - Einstein didn't like it either. But Einstein eventually came to accept it because there is a mountain of evidence to support it. You should too. You don't have to believe us - read up on it some on your own.

 

[FZ+]

"Anyone who is not shocked by quantum theory has not understood it."

Niels Bohr

 

[jcsd]

Exactly, remeber quantum physics cannot be derived from classical physics (bar canonical quantization, etc. which is a much less than perfect procedure), so assumptions taken from the calssical world won't necessarily hold in the quantum world.

 

[steersman]

Yes, that is a logical fallacy for some experiments, but coincidentally it is also something experimentally proven by others.

Mayby, but could you name these experiments?, or, if possible, describe them to me?

I think you're hearing us, you're just choosing not to accept it because you are uncomfortable with the idea. There is really nothing wrong with that - Einstein didn't like it either. But Einstein eventually came to accept it because there is a mountain of evidence to support it. You should too. You don't have to believe us - read up on it some on your own.

No, all I'm trying to do is coax an exoteric answer out of one of you eggheads (that's not offensive is it?). I don't mind being wrong, I probably am.

Exactly, remeber quantum physics cannot be derived from classical physics (bar canonical quantization, etc. which is a much less than perfect procedure), so assumptions taken from the calssical world won't necessarily hold in the quantum world.

Well then, it seems that either classical physics is local, or quantum physics is local.

 

[drag]

Greetings !

Originally posted by steersman
Yes, I agree with that - which means you don't understand what I am saying.

HUP, I have read, came about when it was realized that the only way to determine position and momentum of a particle was to affect the particle in some way. This makes position and momentum mutually exclusive (oversimplifying I know). As a concomitant to this the possible results are represented by a waveform.

Experiments of the quantum level will always yield unpredictable results becuase we have reached the limits of determination. It is a logical fallacy though to equate this with true randomness on behalf of the quantum particles.

First of all, here's a link you may find useful:
http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html#quacon

Second, apparently you did not read quite carefully my
example with the double slit experiment:
Suppose that indeed it was only our uncertainty that
was at work here - in that case, the particles - when
not detected closely after the slit but allowed
to proceed and be detected on the screen - would NOT
produce a diffraction pattern ! Instead, they would
still hit the screen in the proximity of the points
that are opposite each slit ! But, the results of seeing
a diffraction pattern after sending many particles through
the double slit ONE BY ONE AT A TIME indicate that it
is every single particle itself that passed through BOTH
slits - which clearly shows us that the WF is not merely
our knowledge's limmitation - it is the way nature itself
acts - not as particles but as wavicles - spread through
space in what we mathematicly describe as a WF and able to
appear - be detected ANYWEHERE according to the probability
of that happening in every particular point in space (btw,
calculated as the square of the WF).

Live long and prosper.

 

[steersman]

drag said:

which clearly shows us that the WF is not merely
our knowledge's limmitation - it is the way nature itself
acts - not as particles but as wavicles - spread through
space in what we mathematicly describe as a WF and able to
appear - be detected ANYWEHERE according to the probability
of that happening in every particular point in space (btw,
calculated as the square of the WF).

You make a point about wavicles but it might help if you use the word random in your answer.

I have a book, More Big Questions, which is an interview with Paul Davies. This is how he describes a random event:

In other words nature is repeatable and dependable. But at the atomic level this is no longer so. You can set up identical systems in identical states and they will do different things. For example, you can fire an electron at a target and it bounces left, then repeat the experiment with identical circumstances and it will bounce to the right!

Does the electron bounce both left and right at the same time?

 

[FZ+]

By Copenhagen, ghost electrons go left and right, you collapse the wavefunction of the one you measure. How this is decided is random.

By Everett, yes. But which universe "you" are in is random. ie. there is no single special you.

 

[steersman]

Ok, I think we're getting into the guts of this thing now.

 

[jcsd]

Originally posted by FZ+
By Copenhagen, ghost electrons go left and right, you collapse the wavefunction of the one you measure. How this is decided is random.

By Everett, yes. But which universe "you" are in is random. ie. there is no single special you.

No, in the Copenhagen interpretation the wavefunction is a purely mathematical construct, you don't get 'ghost electrons'. In David Deutsch's variation of Everett's MWI you have 'shadow electrons' which travel both paths.

 

[steersman]

By Copenhagen, ghost electrons go left and right, you collapse the wavefunction of the one you measure. How this is decided is random.
By Everett, yes. But which universe "you" are in is random. ie. there is no single special you.

Just to clarify, is the phenomona you described the reason these particles are random/produce random effects?

If it is then we need to go back a bit,

Why were the interpretations of Copehagen and Everett needed? What are they explaining? What was wrong with the status-quo?

How do you know both electrons go left and right if the universe breaks off and only one event is observed?

 

[selfAdjoint]

Originally posted by steersman
Just to clarify, is the phenomona you described the reason these particles are random/produce random effects?

If it is then we need to go back a bit,

Why were the interpretations of Copehagen and Everett needed? What are they explaining? What was wrong with the status-quo?

How do you know both electrons go left and right if the universe breaks off and only one event is observed?

You don't. This is an interpretation. The problem is that quantum mechanics has two parts to it. The evolution part which is nice and smooth and analytical, and the "wave collapse" or "reduction" part which is as unsmooth as can be and paradoxical besides. Many physicists agonized over Collapse of the Wave Function, aka the Measurement Problem. Everett saw a way to avoid the problem by assuming that the wave function doesn't collapse to some eigenvalue, rather the world splits into enough copies to hold it with each of the possible eigenvalues. This leaves the wave function always smooth and analytic - i.e. always usable for calculations, but spread over many "branches" of the world.

 

[steersman]

selfadjoint said:

Everett saw a way to avoid the problem by assuming that the wave function doesn't collapse to some eigenvalue, rather the world splits into enough copies to hold it with each of the possible eigenvalues.

I still don't see what's wrong with collapsing to a single value. What are these interpretations explaining away?

 

[steersman]

Besides, what degree of measurement would it take to collapse the function - especially when speed and position can not be known?

 

[FabioF]

... a small addition to the discussion ...

Hi,
the main problem physicists have in front of them is NOT to explain "why" things happens, but "how" they do. In this sense, having a perfectly working, purely probabilistic theory to explain the behaviour of electrons, or whatever, should be just enough for a physicist.
Tring to find some hidden reason behind that thery or, even worst, behind its mathematical representation (which is basically the most convenient tool to expose the theory using a shared language), it's matter of philosophy, not physics.
I think this discussion'd better placed in www.phylosophyforums.com[/URL] :)
What do you think?
bye
Fabio

 

[selfAdjoint]

Like it or not, interpretation is one of the things physicists do. "Shut up and calculate" is good advice but it only works as long as you are calculating. Many physicists - and some of the best of them - concern themselves with questions of interpretation, and we can't just delegate that job to the physicsits.

What I wish is that somebody would lay out the consistent histories approach, not the dumbed down version for the public but the one with the details that impresses some of the finest minds in physics.

 

[steersman]

FabioF:

I know for a fact that the questions I'm asking can be answered by the "how" branch i.e. science. I'm not interested in interpretations so much as I'm interested in the facts that lead to problems that lead to interpretations. I'm all for sticking to the facts until I can understand them.

Just on a side note, there is no branch of thinking that can adequately deal with the "why", not even philosophy - unless you completely discount causality.