Membrain

I think you might be misunderstanding what the wave actually is. It's not an "energy" wave as you called it. The electron doesn't become the wave and visa-versa. The wave is a representation of the probable locations of where the electron is. The best way to think of it is as a conceptual or mathematical tool that tells us where we can expect to find the electron when we try to measure its location. It's not actually there like a mechanical wave. What this means is that the electron has no definite location before the collapse of the wave. We call this "superposition". It's important to note that, although you'll hear superposition being defined as "being in more than one place at the same time", the most accurate way of understand it is "having equal probabilities of being measured in one place versus other places" (and even then, the probabilities aren't always equal).

Got it, thanks. That's interesting. So we know we have an electron in a specific location as we fire it from the gun (I'm assuming), and we have the same electron in a specific location on the target screen, but between those two locations the location of the electron is probabilistic?

I could visualize that.

Therein lies the most perplexing feature of quantum mechanics. The consensus is that this is non-deterministic. Some tried to fight this notion with the idea of "hidden local variables" but this was eventually disproved (I'm not sure how).

Hmm, dang. Can anyone confirm this?

To re-explain:

Here's a page with some images:

http://en.wikipedia.org/wiki/Double-slit_experiment

1. First, let's do this one electron at a time. Actually we only need to talk about one electron.

2. The electron goes through the double slits and is like a wave interacting with itself, yes?

3. When the self-interfering waves hit the target screen they show up as a single point.

4. There appears an "interference pattern" on the target screen made up of the accumulating points.

So my confusion comes from some apparent consistencies.

A: The electron seems to behave in at least one consistent way in that the self-interfering waves create a consistent "interference pattern". By this I mean, that after an electron goes through he slits, and a period of time passes where the electron has dissipated, the next electron comes, and when it passes through the slits it sets up the same interference pattern as the previous electron.

B. This implies that the waves from each slit are created at the same time for every electron, with the same "energy" (or whatever you want to call it) for each wave, in such a way as to accurately create the interference pattern. Because if the electron did something different, it would create a different interference pattern, yes?

C. Since the artists rendering of the self-interfering waves seems to show the waves bulging out towards the front, wouldn't that mean that the waves would collapse consistently at those most forward points? By that I mean, the waves to the left-most and right-most would never reach the target screen because the center "bulge" would always collapse the wave first.

That's about it. Another question is: if all the waves (for a single electron) "touched" the target screen at the same time, doesn't it make sense that the collapse points would appear random since you have all the waves collapsing at the exact same time?

Again, if the waves coming through the slits are consistent, and if they interact with the target screen at exactly the same time, wouldn't the apparent random collapse points make sense?

Perhaps I'm repeating myself too much, but I want to get as much out there as I could. Thanks!

The double slit experiment is decisive in clarifying how to interpret this uncertainty. Did you read swansont's post about this? You should read up on this. This double slit experiment shows that the only logical interpretation of its results is that a single electron is sometimes in two places at once - not that we don't know which of the two places it's in, but that it is in those two places at the same time.

Quick question on the double slit experiment for anyone to answer:

Do the electrons collapse back into a point on the target screen because they are in affect being measured?

If so, I also don't understand how the electron knows where to collapse. It seems to me that the illustrations show "waves" interacting with themselves and then creating this "interference pattern". I guess the way I'm looking at it is: if the electron wave did not collapse, would the target screen show the imprint of the entire "interference pattern" all at once, just getting stronger and stronger over time?

Thanks for the help. I searched and was unable to find this question answered.

There are experiments that have shown that information not known to us is, in fact, unknown. The concept is known as "local hidden variables"

 

Take, for example, a particle of spin zero, and let it decay into two particles, which must have complimentary spins (call them spin up and spin down) that must add to zero. This is known as entanglement. If we measure the spin of one of these particles, we also gain knowledge of the other. So we do a measurement, and find one particle to be spin up, and immediately know the other must be spin down. Now, one might think that the particle was spin up the whole time, and we just didn't know until we measured it, but experiments have been done that show this not to be the case. The spin orientation is actually undetermined. The classical notion must be discarded.

 

for further rading, you might want to read up on the Einstein Podolsky Rosen (EPR) paradox, and local hidden variables. But it is very much not elementary physics

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

OK, thanks. I looked at the EPR Paradox and have a question:

Concerning entangled electrons:

I have an interesting metaphor for the indeterminate positions of the entangled electrons involving flipping coins.

Let's say that two entangled electrons are created. My understanding is that they are in an indeterminate states until you measure one of them and then the other one takes on the opposite spin of the first.

This made me think about flipping a coin: when a coin is flipped it is in an indeterminate state until it stops moving, and then we can determine its state. I saw a similarity in that the electrons can be considered to be like coins endlessly flipping until we measure them, and then like a coin come to rest, we can determine a state. But prior to the measurement they are like coins spinning.

Does anything about this make sense when it comes to uncertainty, probability, and indeterminacy?

And forgive me if this is really dumb!

> To use your terms: Is the electron ambiguous?

 

Others may want to jump on me for this, but I would say, a little bit Yes, but not completely ambigous. Of course, "ambigous electron" is still ambigous itself I am still looking for a satisfactory formalism, meantime it's fuzzy.

 

/Fredrik

OK, thanks. Now I'll try to combine everything together:

Is the electron ambiguous to the degree that we are uncertain about it?

And is the ambiguity and uncertainty based upon measurement?

So if we are not measuring it, it is 100% ambiguous and 100% uncertain?

Or, are we even uncomfortable with making ambiguity and uncertainty the same thing?

(quoting Fredrik, but still addressing Membrain's query)

 

My main objection was to the phrasing that the electron collapsing to a point when you do a measurement, vs the wave function collapsing.

 

The wave function collapsing means you had a superposition of states in the basis and you've reduced that to one. That need not mean that you have localized the electron, though - the superposition could have been in an energy or spin state. You don't really know much more about the location of the electron after the measurement. The electron has not collapsed, per se, you have just forced it into a definite state.

Concerning the "uncertainty" of quantum mechanics: is the uncertainty referring to our uncertainty where the electron is between measurements? Or also, perhaps our uncertainty as to the electrons real "shape" and "movement" since when we try to measure, we influence the measurement?

To expand it... I would reprhase to say that

 

If we can't measure something, it existence is "ambigous".

 

Because I think non-ambigous and non-existent are quite different things.

 

Many things that exist are ambigous.

 

/Fredrik

OK, thanks. Now I'll try to work this into the original question: Does uncertainty refer to us being uncertain where an electron is.

To use your terms: Is the electron ambiguous?

> "If we can't measure something, it doesn't exist"?

 

If we can't measure something, what is the meaning in terms of effect, that this something does exist?

 

Logic is extremely important but I think the "new physics" of the last 100 years, and more important of the next 100 years will require some kind of fuzzy or probabilistic logic. Not merely new strange mathematics with the same old logic. Bring on the new logic and I am sure the new math will come, and in the light of the new logic it will seem very natural, and the old stuff will seem very simplistic.

 

This is how I personally see it. I think physicists have been too ignorant about philosophy for a long time. The new logic doesn't come without philosophy.

 

/Fredrik

Not to be pushy, but is there a definitive answer to the question?

Yes, No, Not Sure or Other?

Yes. If I write down your description and print out a picture of you on a sheet of paper, that sheet of paper is not you.

 

But it's QM. It can be confusing.

So is what you are saying:

The wave function is a description of the electron, but

the wave function is a not an electron

This makes sense, yes?

I think it depends on the approach, but normally I would for sure say that the exact wave does not have a definite physical existence in the old fashioned sense - like a water wave of sound wave.

 

In quantum mechanics the wavefunction is not measurable.

This is where it seems like there is sort of a philosophical question being answered. Are quantum mechanics physicists saying that, "If we can't measure something, it doesn't exist"?

If so, this to me seems like an ontological leap.

Please everyone, feel free to chime in on this question.

I think you're attributing the wave function collapse to some physical properties of the electron, and including the wave function in the so-called wave-particle duality.

 

The wave function is a description of the electron, not the electron itself. The electron exhibits both classical wave and particle properties. If the electron is in some undetermined state, you "collapse the wave function" when you measure it to be in one particular state, but that state may still exhibit wave properties, e.g. you may have a superposition of the spin states, but measuring the spin, which collapses the wave function, won't necessarily preclude the electron from demonstrating interference, which is a wave property.

Please allow me to parse your language a bit to see if I can't gain some understanding. Some of what you say confuses me not so much due to jargon as much as perhaps what appears to be contradictions.

For example, the sentence "The wave function is a description of the electron, not the electron itself". I paraphrase this to say:

The wave function is a description of the electron, and

the wave function is a not a description of the electron

Confusing, eh? So am I interpreting something incorrectly?

Thanks again for patience. The questions come from a lack of understanding and nothing more.

No, I disagree and here's why: Take an electron or photon, for example, and send it toward a double slit. It will pass through both slits, and intefere with itself, as long as you have no device to measure it going through one particular slit. It is not true that the particle has a well-defined path that we just can't measure precisely enough. i.e. if you don't explicitly measure which path it takes, it takes both. That's not behavior consistent with the particle having a definite existence and putting the uncertainty into the measurement.

I thought the particle was considered to be an un-collapsed wave, and as such behaves like a wave (which ripples through both slits and interferes with itself on he other side).

Doesn't a wave have a definite existence? Like a water wave?

Thanks everyone for your responses. Please pardon me for not answering each post individually, but I think I've come up with another question that gets closer to my goal:

Two things:

One, it sounds like "uncertainty" has something to do with "probability" in that since we can't accurately measure sub-atomic wave/particles we have to take a probabilistic, statistical approach which leads to scientists being "uncertain" as to what the sub-atomic particles are doing at any one time. The sub-atomic particles are not themselves "uncertain"; they have a definite existence within reality, we just can't measure them with certainty.

And two, since science only gives validity to things that are provable and measurable, scientists have take the extra step of saying, "Since sub-atomic particles are inherently not measurable (at least not accurately), they can be considered to be inherently indeterminate".

To clarify: I think scientists think that to assert a determinacy about sub-atomic particles is something that is unmeasurable, and that it is only "philosophical" to talk about it. This is apparently almost heretical in science. Saying that something is "philosophical" seems to be comparable to saying that something is non-scientific.

So is the close® to the truth?

OK, this is my second post!

After learning a thing or two about "probability" on my first thread, I wanted to ask about "uncertainty".

For starters, when it came to probabilities, it seems clear that the electron was in an uncertain place. Is this what is meant by "uncertainty" within quantum mechanics?

Thanks for your patience in advance.

Yes that's true. The conservation of probability that is considered important requires that the electron must not dissappear.

 

But this is in basic QM. In the generalizaiton with particle-antiparticle interactions there may be fluctuations to this.

 

But yes, "summing over all possibilities" you are always 100% right so to speak. That is sort of by construction.

 

/Fredrik

OK thanks very much (all). I will now start a thread called "Question about Uncertainty".

Thanks again.

I think what membrain is asking here is whether the precise number of electrons is a function of probability. I don't think so. If it's a silver atom, and it's not ionized, then there are exactly 47 electrons (AFAIK). Fredrik's point that we can't know with absolute certainty whether they are in the vicinity of the atom is still true, but it is certain that 47 of them exist. It is an odd concept, isn't it - that an electron can have no definite position yet still definitely exist.

Yes! I think we are getting close.

So where I was headed was: when it comes to probabilities, is it true that we are not talking about probabilities of an electron's existence, but probabilities that it is located "over there" as opposed to "over here"?

I'm not sure if it was the answer you were looking for, but it's an attempt to explain how come the uncertainty is not because of plain ignorance, but rather the definition of variables. Or put another way, some variable just aren't independent, and that's how determining one, does affect that other one, or at least our knowledge of the other one, and there is btw, no difference in this case. Because there is no other way to know that to interact.

It sounds like you're talking about measurement. I'm OK with an electron being not measurable with any accuracy. I just wanted to make sure that we consider there to be 47 electrons in a silver atom. This means that there is no probability to the electrons' existence within the atom, right? It's certain isn't it?

I have to add this.

 

> In a gas, we don't know the position of every single molecule.

 

A fundamental difference is of course, is that in classical statistical mechanics, the reason we don't know the position of every molecule can technically be kind of said to be due to "ignorance" of the observer.

 

This is not so in quantum mechanics, where the reason we don't know everything is an intrinsic uncertainty, that is beyond even a "superobserver".

 

/Fredrik

How is our being unable to measure all of the electron in the electron shell not a limitation of measurement? Didn't we just agree that our method of measurement collapses the electron?

What about the electron are you measuring? "measure the electron" is pretty wide-open. There are a lot of measurements you can make.

Mass and velocity I believe are the common ones. Are there any measurements that we make where the electron does NOT collapse?

OK, so it sounds like the electrons (47 of them) are considered to exist within each silver atom.

So that if one had an ingot of silver, all of the atoms would be considered to have 47 electrons.

Now my understanding of "probabilities" is that when you measure the electron you can't measure the whole wavy/liquidy/smeared-out thing; you can only measure it once it is collapsed into a point.

Is this where the probability comes in? I can see how the electron can seem probabilistic since the electron is in all places within the shell at the same time.

OK thanks.

 

Concerning electrons going around the nucleus of atoms:

 

Via the periodic table, we define atoms by how many electrons (and protons and neutrons) they have, right? Well, lets take silver: atomic weight 47, five energy levels, with electron quantities-per-level being 2,8,18,18, and 1.

 

My understanding is that when we measure the electrons, the wave collapses and we are able to measure them, and that's how we know have many electrons there are at each energy level.

 

Before I go on, can I get some affirmation that I am on the right track here? I want to continue with probability as it refers to measurement and as it refers to reality, but I'd better make sure I'm on track first. Thanks.

Getting back to this question:

Does anyone consider this to be untrue?

I think first of all one has to let go of the concept that the electron is a little ball. Sometimes it behaves like one, but sometimes it does not.

 

And when dealing with sensitive details. Small things for example. The differece between reality and the observed reality is blurred.

 

To me the world is fundamentally fuzzy. It's chaos. Our minds and biology all suggests that there is sponatenous formation of associations. I haven't figured it out yet... but as far as quantium mechanics goes... and your electron case I'd say that... your presupposition that the electron is some kind of ball is probably what causes you to wonder "where it is" - assuming that a ball by definition has a definite position. Wich is a meaningless question until something interacts with it. And the type of interaction affects it's position too. If it's not a "ball" after all... maybe the question of "where is it" is simply wrong.

I have let go of the electron being "a ball".

The question of "where it is" seems crucial. I'm attempting to learn whether the electron is considered to be localized at all.

Hey Membrain,

 

I've got an account on http://www.ilovephilosophy.com as well. What's your username there?

"Membrain"!

It's always probabilistic, it's just sometimes that the probability wave is over a very small area (depending on the accuracy of your detector).

 

1. Probability wave around the orbital of the energy level that the electron is in.

2. There is an uncertainty about both it's x and y positions, it will have a quite well definined x, wavefront though.

3. When it is in a slit if it is double slits, it has a probability that it is in both slits.

4. A probability function based on what is around it. Other charge carriers.

OK thanks.

Concerning electrons going around the nucleus of atoms:

Via the periodic table, we define atoms by how many electrons (and protons and neutrons) they have, right? Well, lets take silver: atomic weight 47, five energy levels, with electron quantities-per-level being 2,8,18,18, and 1.

My understanding is that when we measure the electrons, the wave collapses and we are able to measure them, and that's how we know have many electrons there are at each energy level.

Before I go on, can I get some affirmation that I am on the right track here? I want to continue with probability as it refers to measurement and as it refers to reality, but I'd better make sure I'm on track first. Thanks.

To clarify: I'm looking for when the electron is considered to be probabilistic (and from what I've heard, it is never probabilistic when it is measured, so I supposed that we are talking about non-measured events).

I'll list a few and ask "Probabilistic or Non-Probablistic?"

1. An electron in a shell around a nucleus

2. An electron being fired towards a slit

3. An electron going through the slit

4. An electron "just sort of floating around in the air", not attached to a nucleus, not being fired towards nor going through a slit.

Is the electron considered probabilistic in all four of these (unmeasured) conditions? And if not, why not?