New and have a few initial questions.

[Rcbs]

Firstly, hello, I am new to the forum so please treat gently! I also not a physicist but am fascinated with quantum theory and particle physics. I have a few questions...(sorry if they have been asked before, but having read various threads I am still confused!)

Here we go.

1. If a quantum system decoheres when it loses information to the environment, then how is it that an interferrence pattern can emerge at all? Surely the wave going through the slits would decohere when hitting the back plate collapsing the wave function and creating a particle?

2. I am still confused by the outcome of a single particle in the double slit experiment. Specifically whether a single particle/wave function creates an interference pattern or not. Of what I have read it seems not. But rather many single instances build up an interference pattern. What I fail to understand is why if a single particle is infact a wave it doesn't create an interference pattern on its own? One drop into a bowl of water creates a wave, we don't have to wait for many drops? (excuse the analogy).

3. What exactly is a quantum wave a wave in?

4. If the many worlds interpretation of qt is correct why is it that we would ever see an interference pattern at all? If two universes are created for slit A and slit B, and the particle exists in universe A and B going though a different slit each, then surely we would only perceive the outcome of the universe we were in? Would we not only ever see a dot? Or are we straddling multiple universes ourselves? Which would lead to a million follow up questions...lol.

5. What distances are required for a quantum system to decohere?

6. If the wave function is merely a mathematical device the what actually creates the actual interference pattern that we see?

Well that's it so far, look forward to your replies!

Thanks for your help,

Rcbs.

 

[bhobba]

Hi RCBS

All interesting questions

1. In the double slit experiment decoherence occurs at the detector ie the screen - prior to that the phase is still present and interference takes place.

2. A single particle does not build up a pattern - its a statistical thing precisely where a particle is detected and you need a large number of 'trials' like any statistical experiment for the precise pattern to emerge.

3. A quantum wave is not a wave in anything. Its simply a mathematical function used to calculate probabilities, but that function, in cases where it is called a wave function, is like a wave. In fact in interpretations based on decoherence, before decoherence occurs probabilities calculated this way are called pre-probabilities because until decoherence takes place it only has the potential to occur.

4. In the many world interpretation decoherence still occurs but instead of predicting a single result each result actually occurs but the observer and what is observed splits for each possible outcome - each observer experiences only one outcome - but there are many observers. Don't ask me for any more detail though because I only know the basics of it and I personally think it is mystical nonsense.

5. Its not a distance thing - its a time thing and usually occurs very very quickly - usually - but not always.

6. The wave function is simply a device to help calculate probabilities.

Thanks
Bill

 

[Rcbs]

Thanks Bill!

Here are some follow ups...

1. But when the wave hits the screen shouldn't the wave collapse regardless of whether it has interfered with itself?

2. Oh, I see, it doesn't right. Shouldn't it then? If a particle is a wave I still don't understand why it wouldn't produce an interference pattern on its own, in isolation?

3. Wow I'm lost! If an interference pattern is seen and that pattern suggests a wave created it, then surely a wave existed to create the pattern? If the wave is a mathematical function only then what created the very real interference pattern?

4. There may be many observers but we would only observe one outcome, so again why would we observe the multiple outcomes that are allegedly the cause of the interference pattern? Why would we not experience the one outcome of our particlular universe?

5. Oh I see. I hadn't read that it was a time thing, perhaps you could explain further? I guess time and distance are very closely related. So quantum computing relies on separating quantum systems in time?

6. Again I think I am getting very confused when there is clearly an interference pattern which I am told is the result of a wave. But the wave that created the pattern wasn't a real wave and exists in no medium. However the pattern is indeed real?

thanks, rcbs.

 

[Mark M]

It's not that a particle is literally some kind of wave. It's that, in quantum mechanics, the position of a particle is described by it's wavefunction. This gives the probabilities for finding the particle at different locations when you perform a measurement. Asking 'where is the particle?' prior to this observation is a meaningless question, you can only give the probabilities for certain positions. This wavefunction evolves like a classical wave. So, the probabilities of the particle's locations are such that, after enough land, an interference pattern will appear.

 

[Rcbs]

Thanks mark,

Yes I have read about Shrodinger and the Copenhagen interpretation. Perhaps I am getting hung up about the interference pattern and it's significance. I admit though that I still don't understand how something acts as a wave and creates a wave like pattern but isn't a wave.

 

[bhobba]

Here are some follow ups...

1. But when the wave hits the screen shouldn't the wave collapse regardless of whether it has interfered with itself?

2. Oh, I see, it doesn't right. Shouldn't it then? If a particle is a wave I still don't understand why it wouldn't produce an interference pattern on its own, in isolation?

3. Wow I'm lost! If an interference pattern is seen and that pattern suggests a wave created it, then surely a wave existed to create the pattern? If the wave is a mathematical function only then what created the very real interference pattern?

4. There may be many observers but we would only observe one outcome, so again why would we observe the multiple outcomes that are allegedly the cause of the interference pattern? Why would we not experience the one outcome of our particlular universe?

5. Oh I see. I hadn't read that it was a time thing, perhaps you could explain further? I guess time and distance are very closely related. So quantum computing relies on separating quantum systems in time?

6. Again I think I am getting very confused when there is clearly an interference pattern which I am told is the result of a wave. But the wave that created the pattern wasn't a real wave and exists in no medium. However the pattern is indeed real?

1. The interference pattern is caused by the mathematical nature of the function that describes the particle - it is called its state. It has the mathematical form of equations in other areas of physics that describe waves (specifically as explained later it uses complex numbers) but it is not waves in anything - it is simply a mathematical function. The physical interpretation of this function is that squaring it gives the probability of finding the particle in that position if you were to observe it, but because that function is wavelike you will not find it in certain places where its value is zero but in other places where its value is large - that is what builds up the interference pattern. At the screen interaction with the screen causes it to decohere which is a process where this very weird state of affairs where the particle is in fact literally in many positions at the same time becomes a single outcome - but we simply do not know which one.

2. Forget this thing the particle is a wave. The particle is not a wave - as Feynman says - its a particle pure and simple. The essence of QM is what is known as the superposition principle where if a particle can be in two states then it can be in a state where it literally is partly in either state. To understand this better have a read of the first Chapter Of Diracs celebrated book on QM:
http://www.informationphilosopher.com/solutions/scientists/dirac/chapter_1.html

Applying that to position means it can partly be in two positions at once. That can be extended where it can literally be in all the points in space at once - the wave function describes how much it is at that point in space. At some places it not at all at that point and at others it is more strongly at that point - this is because the mathematical functions describing the very weird state of affairs have the form of waves so you get interference effects. When the particle interacts with the screen processes happen in the screen, called decoherence, that change it from being partly in all these different positions to being in a particular position but the math only allows us to predict the probability of that position.

3. The particle is not a wave - the weird state of affairs where it is partly in all these different positions simultaneously is described by equations with a wave like form - but it is not a wave.

4. The cause of the interference pattern is not multiple outcomes - it is the mathematical nature of the weird superposition the particle is in where it is literally in all these different positions simultaneously. This is the essence of all quantum weirdness as Feynman says. Do not try to visualize it - it can't be done - if you do you will sink into a hole no one has ever escaped from.

5. What is there to explain - when decoherence occurs it normally occurs very very quickly - so quick it is nearly impossible to detect - but experiments have managed to do so.

6. The cause of your confusion is you have been told its a wave - it isn't - its a particle. But in the double slit experiment it literally is in many positions simultaneously and the equations that describe that weird totally unvisualizeable state of affairs have the form of wave equations found in other areas of physics. But it is not a wave - simple as that. The wave particle duality is a crock of rubbish.

For a much better explanation than the kiddy stuff you find even in some textbooks see the lectures Feynman gave about it:
http://vega.org.uk/video/subseries/8/

He states the truth outright - it is not a wave - it is a particle. However he does not analyse in terms of position where it is partly in all these different positions at once - but rather in terms of paths where it literally follows all possible paths at once. This is the raw essence of QM - where is can be in many positions simultaneously or follow many paths at the same time. The reason interference effects occur is not because it is waves - it is due to the mathematical nature of the equations that describe it - specifically it due to the fact the mathematics involves complex numbers so phase comes into it and cancellation and reinforcement can occur depending on if its out of phase or in phase. If you know complex numbers remember they can be represented on an argand diagram with a length and angle. Now the superposition principle I mentioned previously is described by complex numbers. If the superposition is in phase you get reinforcement and the particle is more strongly at that position - out of phase it cancels - and the particle is not at that position at all. That is the cause of interference effects - not that it is a wave - its because the superposition a particle can be in involves complex numbers.

If you look at the lectures of Feynman I linked to he explains it in terms of a turning arrow - that turning arrow is mathematically a complex number and is the root cause of interference. Basically what decoherence does is cause this phase encoded in complex numbers to leak out to the environment and you are left with a specific position or whatever the observational setup allows you to detect - its usually position but can be other stuff. This is a very crude explanation - if you want to know the nitty gritty you need to study the math.

Thanks
Bill

 

[Cthugha]

Forget this thing the particle is a wave. The particle is not a wave - as Feynman says - its a particle pure and simple. The essence of QM is what is known as the superposition principle where if a particle can be in two states then it can be in a state where it literally is partly in either state. To understand this better have a read of the first Chapter Of Diracs celebrated book on QM:

Two comments:
1) From a modern day perspective, Dirac's book contains some plain errors and misinterpretations. I would not suggest using it to understand modern physics.

2) Feynman's comment on the plain particle view probably did more harm than good. It is often quoted without further comments when people starting with qm have questions on the wave vs. particle questions. These people typically still have a classical notion of what a particle is and imagine it as similar to a bullet, localized, with well defined position. However, this is far from what Feynman had in mind. The modern physics meaning of particle is plain and simple that all interactions are quantized. You do not absorb half a photon. No bullet-like properties are implied.

Applying that to position means it can partly be in two positions at once. That can be extended where it can literally be in all the points in space at once - the wave function describes how much it is at that point in space. At some places it not at all at that point and at others it is more strongly at that point - this is because the mathematical functions describing the very weird state of affairs have the form of waves so you get interference effects.

It should be noted that this is an interpretation of what happens. The ontology of what happens between two measurements is quite unclear and not testable experimentally. One can interpret the experimental results and the equations governing them in a way that the particle literally is at several positions at once, but one does not have to. It rather seems like a minority opinion.

 

[nonequilibrium]

Rcbs, correct me if I'm wrong, but based on your statements it seems like you're not aware that if you shoot electrons individually you measure a discrete point at the detection screen, not a spread out wave-like pattern. The wave-like pattern only emerges when you shoot a bunch of electrons after each other: the wave-like property is statistical.

 

[bhobba]

It should be noted that this is an interpretation of what happens. The ontology of what happens between two measurements is quite unclear and not testable experimentally. One can interpret the experimental results and the equations governing them in a way that the particle literally is at several positions at once, but one does not have to. It rather seems like a minority opinion.

Well yes. But it should also be noted what the interpretation amounts to is interpreting what it means for something to be in a superposition ie partly in two distinct states. It is well known it can not mean it will sometimes be in state 1 and sometimes in state 2 - no it means something entirely different - that difference is encapsulated by saying it is in some sense in both states simultaneously where the meaning of this is given precision with whatever in interpretation you hold to. So I would update my explanation by removing the word literally and replacing it by in some sense.

Regarding Dirac it might be interesting if you could point out the errors in the first chapter - I can't spot them - but then again I am not quite as quick as I once was.

Thanks
Bill

 

[Rcbs]

Thanks for your replies.

mrvodka, yes I do understand that, however I was under the impression that the particle was an actual wave prior to decoherence, not just a mathematical one. I have now been informed it is not. Though I was also under the impression that a superposition was an attribute of a wave. Perhaps my confusion comes from not distinguishing between mathmatical and actual? However at the quantum level one can imagine the two are indistinguishable.

I thought the many world interpretation explained the superposition as single positions but in many, many universes. My point was that we would only be in one of the universes and thus would only see a single outcome or position not all of them.

My understanding of decoherence was that it is what happens when a quantum system loses info to the environment, perhaps through observation. I took this to mean that if you fire a photon at it, the quantum system is thus interfered with and decoheres. Therefore I assumed it was an act of physical violation to do with distance, as if a boundary had been crossed or a barrier.

So there is no wave particle duality? Better retract just about every pop science book on the subject!

I am a professional cgi animator so when you tell me not to visualise something my head explodes...

 

[Cthugha]

It is well known it can not mean it will sometimes be in state 1 and sometimes in state 2 - no it means something entirely different - that difference is encapsulated by saying it is in some sense in both states simultaneously where the meaning of this is given precision with whatever in interpretation you hold to. So I would update my explanation by removing the word literally and replacing it by in some sense.

Well, there are interpretations where when repeating the measurement, the particle will sometimes be in state one and sometimes in state two and there are interpretations like the ensemble interpretation where it is assumed that the wave function just applies to ensembles and not necessarily to single particles. Just like you said in post 2: its a statistical thing.

Returning more closely to the OP question, it is of course completely correct to point out the particle nature of whatever particle you use in the double slit. A single particle will not form an interference pattern because it will only lead to a single detection event. You need to repeat the experiment many times to see that many detection events form an interference pattern. The wavey thing is the probability amplitude. However, it cannot have more than statistical influence on a single event.

Regarding Dirac it might be interesting if you could point out the errors in the first chapter - I can't spot them - but then again I am not quite as quick as I once was.

Check Roy Glauber's take on Dirac's text in his Nobel lecture or more directly in Nucl.Phys. A774 (2006) 3-13 (also available at arXiv: http://arxiv.org/abs/nucl-th/0604021). I think the discussion starts somewhere on page 6.

 

[bhobba]

Check Roy Glauber's take on Dirac's text in his Nobel lecture or more directly in Nucl.Phys. A774 (2006) 3-13 (also available at arXiv: http://arxiv.org/abs/nucl-th/0604021). I think the discussion starts somewhere on page 6.

Yes Dirac's statement photons only interfere with themselves is simply wrong. Well picked up.

Thanks
Bill

 

[bhobba]

So there is no wave particle duality? Better retract just about every pop science book on the subject!

Indeed. Pop sci books are a problem. In trying to explain very complex and subtle concepts in simple language almost by definition of what you are trying to do leads to imprecision. They talk about de Broglie's insight but forget to point out once the full theory (called the transformation theory) was worked out and understood by Dirac, Von Neumann and others it was realized the waves weren't waves in any real sense - simply a convenient mathematical way of doing things for a lot of problems.

Thanks
Bill

 

[Maui]

It should be noted that this is an interpretation of what happens. The ontology of what happens between two measurements is quite unclear and not testable experimentally. One can interpret the experimental results and the equations governing them in a way that the particle literally is at several positions at once, but one does not have to. It rather seems like a minority opinion.

If the wavefunction isn't real(at least in some sense) but is just a statistical tool, how does decoherence of coherent states take place? I know you can explain it as the vanishing of the off-diagonal elements of the density matrix, i am referring to how it happens in the real world. What is decohering? There must be a process with real(in some sense) elements, otherwise we run into a logical contradiction.

 

[bhobba]

If the wavefunction isn't real(at least in some sense) but is just a statistical tool, how does decoherence of coherent states take place? I know you can explain it as the vanishing of the off-diagonal elements of the density matrix, i am referring to how it happens in the real world. What is decohering? There must be a process with real(in some sense) elements, otherwise we run into a logical contradiction.

Nothing real has to decohere. What a state represents is very interpretation dependant. It may simply be an abstract quantity representing the outcome of all the possible observations that can in principle be performed on the system. What decoherence does is leave a state with a very simple interpretation - one where it has a definite observational outcome in terms of whatever is doing the observing - but we only know probabilities of what the exact one it is. It resolves an issue with the ensemble interpretation. Because of the Kochen-Sprecker theorem you can not think of it as an ensemble of states with a known outcome ie having the property you are observing for sure - it needs be be more subtle than that - but with decoherence you can ie you can think of it being in an actual state before the observation that the observation reveals.

http://arxiv.org/pdf/quant-ph/0312059v4.pdf
'The reduced density matrix looks like a mixedstate density matrix because, if one actually measured an observable of the system, one would expect to get a definite outcome with a certain probability; in terms of measurement statistics, this is equivalent to the situation in which the system is in one of the states from the set of possible outcomes from the beginning, that is, before the measurement. As Pessoa (1998, p. 432) puts it, “taking a partial trace amounts to the statistical version of the projection postulate.”'

Einstein favored the ensemble interpretation I suspect because it whispered in your ear - something more is going on here and QM possibly incomplete - I believe that something more is decohrence - and QM is not incomplete.

Thanks
Bill

 

[DrewD]

RCBS, the idea of wave-particle duality is a nice way to visualize something that can't be visualized (if that makes sense). To imagine a quantum particle as a wave at some points and a classical particle at others may be easier than imagining a whole new idea which is a "quantum particle" that behaves in a way that is a lot like a wave in some ways, and a lot like a classical particle in others. If you find it easier to imagine it this way, weird things have to happen since the screen in the double slit experiment can only measure particle attributes. You can imagine that there is a wave interfering with itself, but no interference can be measured because only a single point will show up. You could imagine that the wave propagates and interferes with itself and then collapses at the screen, but the interference has already happened.

If you choose to think of it this way, I don't think you will be doing yourself any harm (unless you go back to school for physics). There is a reason that popsci books talk about it this way, just remember that it is a crude way of imagining a much richer mathematical model.

If you have a strong background in linear algebra and a moderate background in differential equations, you might hunker down and learn the real theory behind it, but your cgi experience will probably not come in handy:)

 

[Maui]

Nothing real has to decohere. What a state represents is very interpretation dependant. It may simply be an abstract quantity representing the outcome of all the possible observations that can in principle be performed on the system. What decoherence does is leave a state with a very simple interpretation - one where it has a definite observational outcome in terms of whatever is doing the observing - but we only know probabilities of what the exact one it is.

But to leave a state with a definite observational outcome the system must interact with its environment in a thermodynamically irreversible way. Do you view this environment as statistics as well? Is your monitor, the room etc. statistics? I assume not.

Nothing real has to decohere.

Yet if you islate a system from its classically real environment, it exhibits quantum behavior. Why isn't this a hint of more going on than statistics?

 

[Rcbs]

If you have a strong background in linear algebra and a moderate background in differential equations, you might hunker down and learn the real theory behind it, but your cgi experience will probably not come in handy:)

Exactly! Lol. Just when I thought I was asking the right questions...

 

[bhobba]

But to leave a state with a definite observational outcome the system must interact with its environment in a thermodynamically irreversible way. Do you view this environment as statistics as well? Is your monitor, the room etc. statistics? I assume not.Yet if you islate a system from its classically real environment, it exhibits quantum behavior. Why isn't this a hint of more going on than statistics?

QM is not 'statistics' - it is a model like Euclidean Geometry is a model based on the concept of state - not 'statisics' per se. Exactly what it is modeling is interpretation dependent. The environment is modeled as a state as well. I believe it models the outcomes of observations - but only probabilities can be predicted. A state encodes the outcome of observations and it is decoherence that is the mechanism for explaining how it changes from a superposition to a state observation reveals ie explains the measurement problem for all practical purposes.

And no, it does not answer the measurement problem because it does not say how a particular outcome is selected - merely for all practical purposes.

Thanks
Bill

 

[Maui]

QM is not 'statistics' - it is a model like Euclidean Geometry is a model based on the concept of state - not 'statisics' per se. Exactly what it is modeling is interpretation dependent. The environment is modeled as a state as well. I believe it models the outcomes of observations - but only probabilities can be predicted. A state encodes the outcome of observations and it is decoherence that is the mechanism for explaining how it changes from a superposition to a state observation reveals ie explains the measurement problem for all practical purposes.

And no, it does not answer the measurement problem because it does not say how a particular outcome is selected - merely for all practical purposes.

Thanks
Bill

I'd say that the C60 molecule not only exists between source and detector, but that it exists as a worldline all the way from source to detector and the act of decoherence+measurement brings out a classically looking result.

I don't agree that QM in its standard form is not a stastical tool. On the contrary, it's statistic pe se as only probabilities of large ensembles of 'particles' can be assigned and predicted. This of course doesn't inform us what happens between measurements but the traces left on the detector screen suggest something real went through(assuming there is no conspiracy on the part of particles to act as if they went through when in fact they didn't - Wheeler had such an idea with the DCQE of particles creating its own past during detections)

 

[Darwin123]

Firstly, hello, I am new to the forum so please treat gently! I also not a physicist but am fascinated with quantum theory and particle physics. I have a few questions...(sorry if they have been asked before, but having read various threads I am still confused!)

Here we go.

1. If a quantum system decoheres when it loses information to the environment, then how is it that an interferrence pattern can emerge at all? Surely the wave going through the slits would decohere when hitting the back plate collapsing the wave function and creating a particle?

I will answer with what I remember from decoherence theory. This is an alternative to the Copenhagen interpretation. Basically, it is a "waves only" theory. In this theory, a measuring instrument is a complex superposition of waves with many unknown phases. The wave interaction between the measuring instrument and the object being measured causes the collapse.
The quantum system can only decohere to a complex environment. The complex environment has to have many degrees of freedom. In particle terms, the environment has to have a lot of loosely connected particles in unknown positions. In wave terms, the environment has to have a superposition of waves with many unknown phases.
The back plate is not complex. The plate is a rigid body on the time scale of the experiment, meaning that it is made of many atoms that are held in place by large internal forces. The wave corresponding to the different atoms are in phase. The forces that hold the plate together are hypothesized to be so strong, the electrons do not disturb them in the slightest.
When you shine a laser beam on the electron, you are introducing a complex system. There are no internal forces holding the photons in place. So the laser beam can cause a collapse.

2. I am still confused by the outcome of a single particle in the double slit experiment. Specifically whether a single particle/wave function creates an interference pattern or not. Of what I have read it seems not. But rather many single instances build up an interference pattern. What I fail to understand is why if a single particle is infact a wave it doesn't create an interference pattern on its own? One drop into a bowl of water creates a wave, we don't have to wait for many drops? (excuse the analogy).

The single particle is not a wave. It corresponds to a wave. However, the single particle is not localized. It can be anywhere within the wave.
Think of it this way. The particle forms from the wave after the wave interacts with a complex object (see the answer to question 1). The particle doesn't exist until after the wave decoheres.
A localized particle is a superposition of waves where each wave has the same phase. The complex object that causes the wave collapse forces the phases to be equal.

3. What exactly is a quantum wave a wave in?

A field. Fields are another abstraction.
A field is usually associated with a type of particle. The electromagnetic field is associated with photons, the strong force field is associated with gluons, the electron field is associated with electrons, the quark field is associated with quarks, the gravitational field is associated with gravitons, etc.

4. If the many worlds interpretation of qt is correct why is it that we would ever see an interference pattern at all? If two universes are created for slit A and slit B, and the particle exists in universe A and B going though a different slit each, then surely we would only perceive the outcome of the universe we were in? Would we not only ever see a dot? Or are we straddling multiple universes ourselves? Which would lead to a million follow up questions...lol.

I don't think the many worlds interpretation is correct, but this isn't the main problem.
One doesn't see an interference pattern that forms from anyone particle or event in anyone universe. The interference pattern comes about because of an accumulation of events.
Even when a photon interferes with itself, the interference pattern isn't apparent from the one photon. One has to wait for many photon detections in your own universe before the interference pattern builds up. The majority of universes contain versions of you that have the most likely interference patterns. However, there is a small minority of universes that don't see an interference pattern at all for that experiment.

5. What distances are required for a quantum system to decohere?

It depends on the complexity of the environment. Notice that it doesn't only depend on size of environment.
Decoherence theory hypothesizes that the environments has to have many "parts" with many "random phases". A "measuring instrument" is by definition a superposition of waves where many of these waves are incoherent with respect to each other.
Many scientists who developed quantum mechanics thought that there was a size boundary between classical and quantum mechanical systems. Currently, it now appears that complexity is the real boundary between quantum and classical systems.
Here is my conjecture. I often use this when analyzing a problem. However, I have no reference.
My conjecture is that there is a thermodynamics connection. Supposedly, systems have to decohere before entropy is created. So a "measuring instrument" can be considered an object with lots of entropy. Wave forms that have a lot of random phases in their component parts have a lot of entropy, due to the randomness. So an environment is fundamentally a wave with lots of entropy.
In any case, here is my take on decoherence theory. If you see a system where there are many moving parts in random motion relative to each other, that is a "measuring instrument". The motion of those random parts causes the probed "wave" collapse. The randomness in the motion also makes the environment act classical.
I lost my book on "decoherence theory". Sorry I can't cite anything.

6. If the wave function is merely a mathematical device the what actually creates the actual interference pattern that we see?

Reality?
Come on, now!

Well that's it so far, look forward to your replies!

Thanks for your help,

Rcbs.

 

[nonequilibrium]

Darwin, I'd like to clarify that decoherence is not a separate interpretation but rather that it's a part of all interpretations. Decoherence is simply a mathematical phenonemon (which, however, was not observed from the beginning of quantum theory and is hence not as well-known by all physicists) and requires no interpretation. (However, some physicists do claim that decoherence solves some outstanding problems in quantum theory, and if that were the case it would indeed seem to be an interpretation on its own. However, such claims are unfounded.)