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The following passage has been extracted from the book Parallel Worlds, by Michio Kaku:

Because of uncertainty, the electron does not exist at any single point, but exists in all possible points around the nucleus. This electron “cloud” surrounding the nucleus represents the electron being many places at the same time...... Modern civilization would collapse, in fact, if electrons were not allowed to be in two places at the same time. (The molecules of our body would also collapse without this bizarre principle. Imagine two solar systems colliding in space, obeying Newton’s laws of gravity. The colliding solar systems would collapse into a chaotic jumble of planets and asteroids. Similarly, if the atoms obeyed Newton’s laws, they would disintegrate whenever they bumped into another atom. What keeps two atoms locked in a stable molecule is the fact that electrons can simultaneously be in so many places at the same time that they form an electron “cloud” which binds the atoms together. Thus, the reason why molecules are stable and the universe does not disintegrate is that electrons can be many places at the same time.)

If I am not wrong, the passage says that an electron (not the parts of an electron) can be found in many places at the same time. Is that right? A layman always wants to hear twice!

An electron carries the properties of mass, charge, etc. If it can be in different places at the same time, doesn't it violate conservation laws?

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    $\begingroup$ This is wrong: "represents the electron being many places at the same time". It is a probability cloud, a locus where it is probable to find the electron if one measures it. Outside that locus the probability is essentially zero. Suppose I know you have entered a building. I could draw a probability locus in the shape of the building (giving higher probability to toilets or information desks). This does not mean that you are spread all over the building. $\endgroup$
    – anna v
    Commented Oct 7, 2014 at 13:56
  • $\begingroup$ @annav: To be sure, are you claiming Kaku's statement to be false? $\endgroup$
    – Sensebe
    Commented Oct 7, 2014 at 14:06
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    $\begingroup$ Yes, fluffy bunny talk $\endgroup$
    – anna v
    Commented Oct 7, 2014 at 14:15
  • $\begingroup$ @annav: So, if we use any advanced "looking" device, we can look electron at a particular position. $\endgroup$
    – Sensebe
    Commented Oct 7, 2014 at 14:21
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    $\begingroup$ I have informed Kaku in Facebook guys. Stay tuned. $\endgroup$
    – Sensebe
    Commented Oct 7, 2014 at 15:34

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Like so many of his colleagues, Michio Kaku has written yet another "layman" book that you can safely dispose of without feeling bad. Modern physics doesn't deal in "electron clouds" any longer. That's an 80 year old paradigm that has outlived its usefulness. Today we are talking about quantum fields. A quantum field (more precisely THE quantum field) is an object that extends across the entire universe. An electron is a quantum of that quantum field, i.e. it can be thought of as a measurable state of this quantum field (in the free particle picture) and more generally, it's a representation of the discretized state change if this field from one of its (local observer dependent) states to another.

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    $\begingroup$ I've deleted the comment discussion. Please keep in mind that comments are not for extended discussion; you can continue in chat. $\endgroup$
    – David Z
    Commented Oct 10, 2014 at 2:12
  • $\begingroup$ Yes, we are all grateful! $\endgroup$ Commented Oct 10, 2014 at 10:16
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The thing is not that the electron is at all places at one time, but the probability to measure the electron at a certain time isn't localized at a certain point as it is with classical mechanics. The wave function of which the modulus squared gives the probability density of the electron being at a certain place is at first not much more than a mathematical tool to describe the weirdness of quantum mechanics. If you measure one single electron orbiting around a proton (i.e. in a hydrogen atom) you will find that is localized in a certain point. If you make this measurements lots of times you will see that you will find the electron at different places around the proton, and the relative probability of these measurements will be fully described by the Hydrogen wave function.

Indeed charge is still conserved in quantum mechanics, analogous to the example with the position, if you measure the charge of the smeared out electron cloud you will always measure the charge to be 1 elemental charge, the wave function simply gives a probability for where this charge is most likely to be found.

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  • $\begingroup$ "The thing is that not the electron is at all places at one time" so you are disagreeing the statement " electron being many places at the same time." $\endgroup$
    – Sensebe
    Commented Oct 7, 2014 at 13:39
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    $\begingroup$ @Godparticle Kaku is depending heavily on the word "represents". He says that the cloud that represents the electron exists everywhere. He does not say that the electron exists everywhere. At any rate, thinking of an electron as a particle in the everyday sense, as a perceivable object, is fruitless. We borrow the word "particle" to describe the thing, but we have to attach a different meaning to the word, a meaning prescribed by quantum physics. It's only a little bit like an everyday particle; in many ways it's different in ways that we can't comprehend. $\endgroup$
    – garyp
    Commented Oct 7, 2014 at 14:03
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    $\begingroup$ @Godparticle If we have a device which measures the position of an electron, then it will find the electron at some position. But we can't say exactly where. $\endgroup$
    – garyp
    Commented Oct 7, 2014 at 14:25
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    $\begingroup$ @Godparticle You'll have to ask your namesake. This is the way He made the universe. If it makes you feel any better, Einstein had the same question, and had a lot of trouble accepting the answer that, so far, has been unavoidable. $\endgroup$
    – garyp
    Commented Oct 7, 2014 at 15:04
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    $\begingroup$ @Godparticle 'Why can't we say where exactly it is?' Heh. If you want the members to teach you quantum physics, you should start a new topic. $\endgroup$
    – Spike0xff
    Commented Oct 7, 2014 at 19:41
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The following passage has been extracted from the book "Parallel Worlds-Michio Kaku":

Because of uncertainty, the electron does not exist at any single point, but exists in all possible points around the nucleus. This electron “cloud” surrounding the nucleus represents the electron being many places at the same time.

You say :" If I am not wrong, the passage says electron (not the parts of electron) can be found at many places at the same time. Isn't it? Layman always wants to hear twice!"

The 'wrong' part is combining "found" with "same time". It creates a picture of a spread out entity, which gives the impression that the electron has an extent in space. No. In all measurements the electron behaves as a point particle. Instead the measurements are fully described by quantum mechanical solutions of the problem "proton with an electron around", i.e. the hydrogen atom, combined with the Quantum Mechanical 'postulate/axiom': the square of the wave function represents the probability of finding an electron at (x,y,z) at a time t. All the measurements we have of elementary particles and atomic and nuclear physics are fully described by the QM model and its postulates.

"Electron carries the property of mass, charge, etc. If it can be at different places at the same time, doesn't it violate conservation laws? "

It cannot be in different places at the same time. In the classical sense yes, it would violate energy and momentum conservation to start with. But this is not a classical situation. If you look for it (do a measurement) you will find it in one place for a given time t. They have looked:

hydrogen orbitals measured

The First Image Ever of a Hydrogen Atom's Orbital Structure

This image was made by a special microscope and special analysis, but what I want to concentrate on is that it is made one point at a time, one electron at a time

Quote:

After zapping the atom with laser pulses, ionized electrons escaped and followed a particular trajectory to a 2D detector (a dual microchannel plate [MCP] detector placed perpendicular to the field itself). There are many trajectories that can be taken by the electrons to reach the same point on the detector, thus providing the researchers with a set of interference patterns — patterns that reflected the nodal structure of the wave function.

I hope this helps.

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"If I am not wrong, the passage says electron (not the parts of electron) can be found at many places at the same time."

An electron exists at many points at once, but we may only find it at one. That distinction is the paradox at the heart of quantum mechanics.

An experiment that explains this is the double slit experiment. When we fire electrons through a double slit, they create an interference pattern profoundly different from naively adding the results of 2 single slits. This shows that the electrons travel as waves and interfere. We see the same pattern when we fire those electrons individually (and then add up the resulting hits to make a pattern). To explain the patterns we see, the single electron must go through both slits (be in 2 places at once) and interfere with itself.

Suppose we built an ingenious device that measures which slit the electron went through without changing its momentum too much. In such an experiment, we see the superposition of 2 single slit patterns rather than the double slit pattern. When we can measure which slit the electron goes through, it only goes through one.

"Does electron being many places at the same time violate Physics laws?"

There is no such thing as a point wave. An electron being in many places at once does not violate any laws, but simultaneously directly measuring it at many places would violate all the conservation laws you mentioned.

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  • $\begingroup$ Having not read the book, I cannot comment on it. I do have a profound distaste for the many-worlds interpretation as it is un-testable. $\endgroup$
    – user121330
    Commented Oct 7, 2014 at 17:03
  • $\begingroup$ I disagree with your interpretation of the two slit single electron. The quantum mechanical solution of "two slits and electron passing" gives a probability for the electron to pass through one or the other slit and that probability has a wave structure that is why we see it even one by one. $\endgroup$
    – anna v
    Commented Oct 8, 2014 at 6:57
  • $\begingroup$ @annav You are welcome to disagree, but theory and experiment disagree with you. If we place a detector that says which single slit the particle goes through, the interference pattern disappears. The theory gives a probability amplitude over space, there's no reason to expect that the electron isn't occupying the entire extent. $\endgroup$
    – user121330
    Commented Oct 8, 2014 at 13:15
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    $\begingroup$ When you put a detector you change the boundary conditions and the solutions of the prhttp://phys.org/news/2011-01-which-way-detector-mystery-double-slit.htmloblem change. Have a look at this experiment which shows what changes of boundary conditions do. $\endgroup$
    – anna v
    Commented Oct 8, 2014 at 13:43
  • $\begingroup$ @annav You are absolutely right - a change in boundary conditions changes the region of space an electron occupies. It is still a region of space and not a point. $\endgroup$
    – user121330
    Commented Oct 8, 2014 at 14:16
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Because of uncertainty, the electron does not exist at any single point, but exists in all possible points around the nucleus.

It is all a matter of interpretation. HUP:

\begin{align*} \sigma_x\sigma_p &\geq \frac{\hbar}{2} \end{align*}

states that you cannot know both position $x$ and momentum $p$ exactly, at an instant.

OK, say you want to know just the momentum, i.e. $p=mv$. Mass is a given in experiments conducted in colliders, so all you need to do is to find the velocity. How do you do that? You need to know how long it takes the particle to travel particular distance. Which means you need to find out ... particle's position - but not once, twice! - if you want to find out its momentum.

What does it mean for out problem? It's all quite simple and obvious, actually. Momentum itself is a property you cannot, by definition, determine for one position, for a point. So you can never know the momentum pertaining to one precise location in space, because momentum at an instant, and therefore at a point does not exist. Momentum comes from movement, and movement requires two different positions. Mystery solved! Without a concept of omnipresence and such. Mechanically, and not just mathematically ... :)

P.S. For more clarification on the subject, it is worthwhile to see juaranga's answer to the question: "Is the wave-particle duality a real duality?"

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Since the book is named "Parallel Worlds", it would not be inappropriate to give the Many World's Interpretion's view on this. A superposition of an electron being at different places should be interpreted as the electron being at all these places in different Worlds. So, there exists a World where the electron is in one position (but note that technically the position representation does not really exists, but let's forget about that detail here), another World where the electron is somewhere else, etc..

The observer also exists in all these Worlds, but he is exactly identical in all these Worlds. If the observer makes a measurement that locates the electron within some volume, then the set of initially identical observers will obviously split up into different groups, with observers from different groups finding a different outcome of the measurement.

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  • $\begingroup$ That's back to front, I'm afraid. The Many Worlds interpretation is a consequence of quantum mechanics (subject to certain assumptions) rather than an explanation of it. Or, at least, I'm not aware of any way to explain QM in terms of "many worlds" that explains interference patterns. $\endgroup$ Commented Oct 8, 2014 at 3:01
  • $\begingroup$ But it is useful to consider how to interpret the superpositions in a physical way. So, if the electron has to be imagined to be both here and there, then the "here" and the "there" are actually positions in different Worlds, not the same World, which resolves the problem the OP had. $\endgroup$ Commented Oct 8, 2014 at 3:49
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    $\begingroup$ But if the "here" and "there" were in different worlds, there wouldn't be any interference patterns. $\endgroup$ Commented Oct 8, 2014 at 3:58
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The electron is not a particle. It's not a wave either. The fact that it seems to behave like one of those under certain conditions is pretty much irrelevant.

However, to understand this on a gut level, with the case of an electron in an orbital of an atom, it is very helpful to imagine the electron as a wave. The electron still has just the properties of any free electron - the same charge, mass etc. (ignoring relativistic effects, of course).

Let's say I send a sound pulse towards you. Where is this pulse located? It does not have a single precise location, instead, it's spread out somewhat over a certain area (and at the same time, it really is "infinite" in area, although it quickly drops in amplitude to almost nothing). If you try to measure it at different points, you'll get many different results for the "location" of the sound. Maybe your detector particle hit a through, maybe it hit a peak. Maybe it hit under a shallow angle, or not. As you can see, the ambiguity is not in the quantum at all - it's already there for any waves. Can you get the precise frequencies and amplitudes of all the constituent waves in a sound? Of course not, although you can do some educated guesses.

Before you even get to quantum field theory, have a look at fourier analysis of waves - it explores those themes quite deeply, and doesn't require as much prerequisite knowledge.

Ask yourself, what does it mean to observe the electron? You need to interact with it. Most likely using electro-magnetism. So you're trying to bounce one "wave" (a photon) off another "wave" (the electron). What does it even mean, when a photon is absorbed by the electron? Or scattered off it? Easy to imagine with particles, but how does a wave with momentum do it?

Popular science always has a problem with fitting so many questions into a format that will not bore the audience to death. It needs to simplify, and even outright lie. But in this case, it really is more about the fact that you can't stop thinking about the electron as some ball in some point around the atom - that's not the case. The only point where an electron is really behaving like a particle is in complete isolation from any other electrons and electro-magnetism - as soon as there are some interactions, the abstraction starts to break down.

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  • $\begingroup$ You might want to see juaranga's answer to this question: "Is the wave-particle duality a real duality?" $\endgroup$ Commented Oct 16, 2014 at 12:57
  • $\begingroup$ @brightmagus Thanks for that, that's a great answer. However, I don't think I'm in contradiction with that - I'm only showing the analogy, and I'm explicitly saying that quantum particles are neither classical particles, nor waves. I'm only using the wave analogy to give a gut understanding of e.g. certainty of position versus momentum on something you can actually play with easily - sound (which is a "real" wave, with all that entails). Where do you see the confusion? $\endgroup$
    – Luaan
    Commented Oct 16, 2014 at 13:06
  • $\begingroup$ Sure. Now, for HUP you might want to see my comment under Godparticle's question above :) (Sound is many particles, so they can be in many places at the same time without strain :) ) $\endgroup$ Commented Oct 16, 2014 at 13:25
  • $\begingroup$ @brightmagus That works great, but the wave packet example is IMO better in that it's obvious that the information just isn't there - it's not something that you could measure more accurately just by having better instruments, it just isn't there. Software that tries to decouple a bunch of different frequency/amplitude signals (and e.g. shift them) needs to do the multiple observation gig too (true, it doesn't modify the wave), and it needs to guess a lot. That's just basic fourrier analysis. $\endgroup$
    – Luaan
    Commented Oct 16, 2014 at 13:31
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    $\begingroup$ The measurement of momentum also cannot be improved so that we can know it for a particular point. Exactly as with your wave packet example, it's physically impossible, because such an information - or a property - simply doesn't exist. So your example is fine in itself, but what I said about momentum is true for both waves and particles (whether they show wave characteristics or not). $\endgroup$ Commented Oct 16, 2014 at 13:40

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