electrons travel faster than the speed of light

epkid08

Is it literally possible for them to be in two places at once?
Is this proven; How is this possible?

I mean, sure they travel very, very fast. Even if they travel faster than the speed of light, it would appear so that they are, but nothing can travel at a speed that literally freezes time [only apparently].

I think this hints more towards electrons traveling though another spacial dimension than traveling though time.

Mr Noblet

An electron is described by its wave function. The wave function is used to find the probability density of the electron, that is, the probability of it being at locations within a certain space. This is because an electron is not a point in the classical sense. It doesn't have an exact location, but a probability density. This can explain why it can be in two places at once. This means that the speed the electron must travel to be in these two locations irrelevant.

Crosson

No, that is a misconceived term that originates with the sensationalism in the newspapers of the 1930s.

ZapperZ

That is not exactly true. The "standard" interpretation for a quantum superposition is that the system has ALL of the states within that superposition before it is measured. This is the common view that has been described in QM (see Phillip Ball's article in May 1st 2008 issue of Nature).

An electron occupying several locations at once is what the wavefunction is describing in, for example, an H2 molecule, resulting in the bonding-antibonding state. Such a description is consistent with what is being interpreted in all of the Schrodinger Cat-type experiments (i.e. the Delft/Stony Brook SQUIDs experiment where they specifically describe the supercurrent flowing in both directions simultaneously).

So no, this isn't a "... sensationalism in the newspapers of the 1930s...."

Zz.

epkid08

Yes.

...and I'm aware of the Uncertainty principle, but just because its location is in a designated area, specifically unknown, doesn't mean it's in all places at the same time in that area.

Ciokko

have you read the other replies? o.O

Crosson

What do you mean in terms of the formalism, 'has all the states'? The state of the system is that superposition, its state is not equal to any of the individual states.

I looked at the Philip Ball decoherence article, and I have studied Josephson junctions and SQUIDS, but I do not interpret quantum mechanics the way you do; it doesn't make sense.

ZapperZ

The superposition of states where all the orthorgonal states are present in the description of the system has always been interpreted as having those states simultaneously. That's the "paradox" of the schrodinger cat system.

It is not my interpretation. I'm giving the prevailing view of what has been written as the description of superposition. If you look at all the papers, including the Leggett paper that I've mentioned several times, that is the standard interpretation of what superposition means. When someone who does not understand QM and ask such a question, that is what you have to provide.

Whether it makes any sense or not, that is no longer physics but a matter of tastes. I find it to make perfect sense if one abandons the notion of a "classical particle" that has definite physical boundary. So what does not makes sense to you can make perfect sense to someone else. This is what I meant as simply a matter of tastes, so arguing about something based on one's sense doesn't mean anything. Besides, since when has making sense been infallible?

Zz.

Crosson

No, that is the popularization of the paradox. If you read the original paper, Schrodinger is concerned with the transition from quantum superpositions to classical mixtures. He is not talking about how to interpret the superposition state, he is pointing out that quantum mechanics paradoxically predicts superposition states instead of mixtures.

You and I, with the benefit of 70 years of physics since Schrodinger, know that superpositions become mixtures because of decoherence, and so the paradox is resolved.

I agree that we should provide the standard answer. I don't see you referring to the Legget paper in this thread, so I searched google and of course your blog post on this topic came up:

Schrodinger Cat-type experiments

I followed the only link that leads to a freely accessible paper:

Detection of a Schroedinger's Cat State in an rf-SQUID

I read the entire paper, but did not find any evidence to support what you are calling the 'standard interpretation.' All of the wording in this paper is consistent with what I know about quantum mechanics, e.g.

"Here we present the first experimental evidence that a superconducting quantum interference device (SQUID) can be put into a superposition of twomagnetic-flux states, one corresponding to a few micro-amperes of current flowing clockwise, the other cor-
responding to the same amount of current flowing counterclockwise."

Great, they put it in a superposition of both states, (A + B). This is very different from saying they put it in state A and state B simultaneously (again, I wouldn't even know how to interpret the latter within the formalism).

Again from the article:

"Such a superposition would manifest itself in an anticrossing, as illustrated in Figure 1b, where the energy level diagram of two levels of different flux states (labelled
|0i and |1i) is shown in the neighbourhood in which they would become degenerate without coherent interaction (dashed lines). Coherent tunnelling lifts the degeneracy
(solid lines) so that at the degeneracy point the energy eigenstates are close to 1 √2
(|0i + |1i) and 1 √2(|0i − |1i) , the symmetric and antisymmetric superpositions."

In other words, they don't measure the superposition by measuring two currents going in opposite directions, they measure it directly by its properties as a superposition.

Making sense is not always infallible, but in contrast not making sense is always fallible. If a particle is in the state:

psi = a*v1 + b*v2

then it does not make sense to say that the particle is also simultaneously in the states

psi = v1

and

psi = v2

Since all three of these states are totally distinct. We already know exactly what state the particle is in:

psi = a*v1 + b*v2

And we can measure all the properties of the particle in this state.

That's fine, but then you must agree that it is sensationalist to say "the electron is in two places at once" since if it has no definite physical boundary then it has no definite location.

As for your abandoning the notion of a classical particle, this disagrees with the established standard interpretation in textbooks, e.g.

"In QED, the electron is point-like particle." -- Griffiths, Introduction to Elementary Particles

I also think the spread-out electron is untenable. In basic QM you could think of the electron as spread out in the form of the magnitude of its position space wave function, but what do you do in QFT?

reilly

Historically this is not true. See, for example, Kemble's QM text, which was very influential during the 30s. He, as do many other authors, simply uses the conventional interpretation of probability, given the probability measure W*(x)W(x) dV(x). So, interpreting, as you do, a superposition as representing a particle in many positions at once is, in fact, contrary to centuries of common practice in probability theory -- unless you are considering a statistical ensemble (sample space) in which case you can talk about two particles being at the same place at the same time.

How would you compute the probability of a particle being in two places at the same time?
Regards,
Reilly

ZapperZ

I still disagree that this isn't a standard view, since, again, I've read it way too many times beyond just want Phillip Ball had written. For example:

http://www.sciam.com/article.cfm?id=schrdingers-squid
http://physicsworld.com/cws/article/news/2815
http://physicsworld.com/cws/article/print/525

But to me, that is exactly saying the same current going in the opposite direction in the SQUID loop. The links I gave above (and I believe there is a News and Views article for one of the papers) interpreted it as such.

But that is the only way to detect such superposition, by either measuring the non-commuting observable, or the non-contextual observable. That's why this isn't a classical measurement where the "unknown state of our knowledge" has no physical manifestation that is measurable. This is also how we know the superposition description is valid. We don't detect an electron being localized at both H atom in the H2 molecule. We do, however, detect the effects via our measurement of the bonding-antibonding state. It's the same thing here.

Zz.

ZapperZ

But historically, an atom also looks like the Bohr atom.

I don't unless you consider the probability density of the wavefunction corresponds to such a quantity. This is no different than the smearing of the position of an electron in an atomic orbital. When 2 orbitals from two different atom hybridized, a single electron can localize itself at both locations when you have significant overlap of those orbitals. Tight-binding band structure calculations employ such a thing.

Look, I have ample problems with such interpretation and I can go on for pages on why I myself do not use such views. However, as I've mentioned in the previous post, it is THE prevailing view that when you have a "superposition of states", that ALL of those states are present simultaneously. The bell-type experiments is different from just a simple classical conservation of angular momentum case exactly because the superposition of the orthorgonal spin directions implies that the projection of the spin direction consists of all the possible spin states before measurement.

Zz.

Crosson

All three of these links are popularization articles. I agree that the first article supports your view, containing the following clear statement of what you call 'the standard interpretation':

In the new experiments, an electric current stood in for the cat and flowed both ways around a loop at the same time.

If you found a statement like this in a scientific article, or a graduate-level textbook, then I would be convinced. I too, however, have seen this kind of sensationalism in popularized articles, but I give infinitely more weight to the science I have learned from textbooks.

You must admit that the article does not exaclt say this, they use language more carefully to say that the particle is in a superposition, and then they describe the states that make up the superposition, exactly consistent with what I have learned from textbooks.

As I said, these are popularizations. I appreciate you taking the effort to find and post them, but they are not definitive sources.

I totally agree with this statement, we both know this.

ZapperZ

But textbooks don't deal with such "interpretations". As I've mentioned many times on here, QM must be understood at the level of its formalism. Most of us who are in this field couldn't care less how such a thing is interpreted. I know I don't use such a thing in my daily work. However, when we describe it, this is where we invoke such interpretation. I know for a fact that Leggett himself has used the same words that I did in his seminars to describe what "superposition" implies. I will look again at his J. of Phys - Condens. Matt. paper when I get into work tomorrow and see if he has used it there as well.

Zz.

Crosson

I totally agree, which is why I asked you in post #7 of this thread:

" What do you mean in terms of the formalism, 'has all the states'? "

Now I see that you are contrasting the formalism with the interpretation, which I hope you will agree is not something that they do a very good job in the popularizations that you linked (which only matters because that general trend is responsible for the OP asking this question).

I agree that the phrase "in both states at the same time" does not have any effect on the calculations, and I am glad to hear that you (and, presumably, your colleagues) do not give much care towards what you call 'the standard interpretation.'

Why not just say 'is in a superposition state' ? Or do you mean when describing to someone who does not know the formalism?

I believe you. It disappoints me slightly, but only in a way that someones politics, etc can detract from my admiration for their accomplishments in science.

Zz, I really appreciate the effort you have put in to show me evidence of the standard interpretation. Being familiar with some of your other threads, I know you have an accurate picture of the mainstream thinking in condensed matter physics.

In the future I will give a different response to the OP's question:

This is a widely held interpretation of the mathematical formalism of quantum mechanics, but there is no experiment to date that can confirm or deny the claim. In my opinion, this interpretation does not convey the subtleties of quantum superposition, and is excessively sensational.

muppet

In case the OP as been left confused by that debate...
In orthodox QM we don't really talk about the electron "being" in two places at once. In fact, we don't really talk about it "being" anywhere. We say that it is described by a wave function [tex]\Psi[/tex], a mathematical function that we can coerce into telling us the probability that we will find the particle in a particular place, or moving in a particular direction. There are certain kinds of functions called eigenfunctions that describe the particle being in a state that is physically allowed. Arguably the most bizarre thing about quantum mechanics is that most of the time, a particle isn't described by an eigenfunction, but by a linear combination of eigenfunctions; its wavefunction is that function you obtain by adding one eigenfunction to another, each function being multiplied by appropriate numbers so that you don't get probabilities greater than one. A particle described by such a linear combination of "allowed" states is said to be in a "superposition of states", and this is the origin of loose phrases such as "is in two places at once".
That much isn't really controversial (which you may find suprising!). What is controversial is whether or not nature really behaves in the way our maths seems to describe when we aren't looking; whether an electron really exists as some fuzzy, smeared-out field that decides to adopt definite values only when we decide to look for it. The part to which there are the most serious objections is the transition between a superposition of states and the particle we actually measure, a process known as the collapse of the wavefunction. Some people think it is physically real, but argue over what constitutes a measurement- some say it has to be carried out by a conscious observer, wheras some say any thermodynamically irreversible interaction with the environment will do. Some, however deny it, and instead claim that rather than the superposition of the particle collapsing, the observer instead is in a superposition of having measured all the possible values! This is the origin of talk you may have heard of the "many-worlds" interpretation. In one "world" the particle goes through one slit, in another it goes through the other, and the poor observer is split into two duplicates of himself, each identical in every detail except that memory corresponding to whether he believes the photon went through the left slit or the right one.
This may all seem deeply, deeply wierd. It is. Unfortunately (or interestingly, depending on your point of view) the experimental facts are so wierd as to necessitate a wierd explanation!

lightarrow

If this were true, the electron should be detected in the two places simultaneously, for example the two slits. This doesn't happen.
Another possible interpretation is that the electron "is not" here, or there, or in both places, before detecting it: it "is" where and when you detect it.