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I don't understand how quantum mechanics (and therefore also quantum computers) can work given that while we work with quantum states, particles that this quantum state consist of cannot be observed, which is the most fundamental requirement.

If I am not mistaken, by "observed" we mean interaction with any other particle (photon, gluon, electron or whatever else). So my very important questions:

  1. Aren't the particles this quantum state consists of interacting with each other? Why doesn't that cause the state to collapse?

  2. Aren't all particles in the universe interacting with Higgs field and gravitons etc? Why doesn't that cause every quantum state to collapse?

I feel there is something very fundamental in quantum mechanics that I am not aware of, hence I would be very pleased to have these questions answered.

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The state is usually taken to be the state of the whole system, i.e., inclusive of interactions. The wavefunction collapses if someone "outside" the system performs and observation. – Sanath K. Devalapurkar Jan 14 '14 at 23:56
Related: "Quantum Zeno Effect" – dmckee Jan 15 '14 at 0:31
"If I am not mistaken, by "observed" we mean interaction with any other particle" - no, this is wrong. – Anixx Jan 15 '14 at 1:17
@SanathDevalapurkar What if we consider the whole universe as a quantum system? Or at least consider a quantum system that includes the observer. – Cameron Martin May 20 '14 at 0:57
@CameronMartin The universe is non-quantum, as is obvious. If the quantum system includes the observer, then I'm not sure. This is a philosophical question - I'd like it if you could email me, where we could continue this discussion (this post is over 4 months old - it's not right to bring it to the front page). For my email, see my profile page. – Sanath K. Devalapurkar May 20 '14 at 1:00

4 Answers 4

up vote 9 down vote accepted

Aren't the particles this quantum state consists of interacting with each other? Why doesn't that cause the state to collapse?

We have a mathematical model for the observations we can make of any system in the micro world. This model is quantum mechanics and its predictions have been verified experimentally over and over again.

Observables are quantities we can measure about the particles and fields in the micro world. A main postulate is that to every observable there corresponds a quantum mechanical operator. These operators enter the quantum mechanical equations whose solutions given the boundary conditions describe a system in the micro world.

It is true that a quantum system is continually interacting within itself as described by the quantum model, and there can be continual interactions with the boundaries but interaction is not a synonym for a measurement. The continuous interactions are off mass shell, virtual, and within the bounds of the quantum mechanical solutions of specific energy levels and allowed states and conservation of quantum numbers. They are not measurements.

Aren't all particles in the universe interacting with Higgs field and gravitons etc? Why doesn't that cause every quantum state to collapse?

Collapse is fancy terminology for measurement . Nobody is measuring the higg's field continuous virtual exchanges that give mass to the elementary particles, nor the gravitons either. In fact gravitons are hypothetical particle because we have never measured one, in the way we have measured photons. Also nobody is measuring the virtual photons that keep the electrons in their energy levels around the nucleus.

The basic misconception is identifying "interaction" with measurement. A measurement necessarily means an interaction. An interaction is much more than a measurement.

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Here's a nice short story which illustrates the philosophical problem nicely. Why our subjective experience of measurements is the way it is is a big mystery. – spraff Nov 4 at 9:57

Your question contains a false statement:

If I am not mistaken, by "observed" we mean interaction with any other particle

You are mistaken.

In different interpretations of quantum mechanics the definition of "measurement" is different. But I think it would be enough if I give just five of which you can choose yourself.

  • In Copenhagen/von Neuman interpretations the collapse of the wave function is triggered by the observer. This person has the special property which no other object in universe is capable of. In Copenhagen interpretation the collapse can be triggered by any system which is connected to the observer, including the measurement apparatus and external medium (if the observer is not isolated from it). All things can be arbitrarily divided into the observed system and the measuring system by so-called "Heisenberg cut" with the only requirement the measuring system include the observer.

  • The von Neuman interpretation is the edge case of Copenhagen interpretation where the Heisenberg cut is placed as close to the observer as possible. As such even the parts of his brain still be be considered the part of the observed system. In von Neuman interpretation the collapse of the wave function happens when the observer feels any qualia(feeling) depended on the measured value.

  • In Bohm interpretation the collapse of the wave function happens when the observer introduces into the measured system some perturbation, which is inevitable when performing the measurement. The difference between the measurement and any other interaction is in that the perturbation introduced by measurement is unknown beforehand. This is because initial conditions of a system containing the observer are unknown. In other words, the observer always contains information which is unknown and cannot be determined by any means due to self-reference problem. Thomas Breuer called this phenomenon "subjective decoherence". The philosophers believe that this unpredictability of the system containing the observer for himself, defines the free will.

  • In Relational interpretation the collapse happens when the interaction affects the ultimate measurement performed by ultimate observer on the universal wave function at infinite future. As such, for the collapse to happen the result of interaction should somehow affect the external medium, the stars, etc, either now or in the future, rather than being recohered and lost.

  • In Many-worlds interpretation the wavefunction collapse never happens. Instead what the observer perceives as the collapse is just the event of entanglement of the observer with the observed system.

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Let's first of all clear some things up about the fundamental postulates of quantum mechanics.

One of the postulates is that all measurable quantities in a quantum system are represented mathematically by so called observables. An observable is thus a mathematical object, more specifically a real linear operator whose 'eigenstates' form a complete set. This essentially means that any quantum state can be expressed as a linear combination of these eigenstates of the observable.

A simple example of an observable is the spin operator. If we apply the postulate to this case it simply means that any spin state can be expressed as a combination of the eigenstates of the spin operator. If we are talking about the spin of an electron, for example, the eigenstates are 'spin up' and 'spin down' (naively one could think of an electron spinning counterclockwise or clockwise, respectively). So any spin state can be seen as a linear combination of these spin up and spin down states.

Now, when we do a measurement of the spin of a particular electron, we find out what the spin of the electron is at that moment. Another postulate states that the only possible outcomes of such a measurement is an eigenstate. So the only possible results of measuring the spin of an electron is either spin up, or spin down. After this measurement we thus know that the electron has one of these spins, it's previous spin state has 'collapsed' onto one of these states.

Now there are other postulates which explicitly tell us exactly how the state of a quantum system evolves with time. So if we wait a while after we measured the spin state of the electron, it's spin state might have changed if for example it interacts with some other particle. Using the laws of quantum mechanics, we can thus calculate the probabilities of measuring spin up or spin down at a later time.

So quantum mechanics really does not state anything about quantum states being constantly observed, or about observation apart from measurement at all for that matter. It is only concerned with measurements of states and evolution of states over time.

So to explain your particular question in terms of quantum mechanics, say that we have a complex quantum system consisting of many parts (particles, fields, etc). We can measure some properties of this system at the outset, providing us with a specific initial state of the system. These different parts of the system then might go on to interact with each other and evolve by the laws of quantum mechanics into some new state (i.e. by the Schrödinger equation or Dirac equation or by the equations of some quantum field theory etc). After this, we can do new measurements, and we can in principle calculate, exactly, the probabilities of the different possible outcomes of each of these measurements. When we do these new measurements, the probabilities stop being probabilities however and we get a new definite state, the previous 'probabilistic state' has 'collapsed' (the probabilistic state being a linear combination of eigenstates, and the collapsed state a specific eigenstate).

So I might have not answered your two specific questions, but hopefully I cleared some things up about quantum mechanics so that you now can see the inherent flaw in those questions.

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I just want to add something to the correct @annav answer, with a practical example in basic Quantum Field Theory. Imagine a particle process with $2$ initial particles and $2$ final particles, you have some initial state (say at t= $-\infty$), which is $|i\rangle =|1\rangle |2\rangle$, where $|1\rangle$ and $|2\rangle$ are the states (at t= $-\infty$) of the initial particles. This initial state $|i\rangle$ has a unitary evolution.

Practically, the non-trivial part of this evolution is due to the exchange of "virtual particles" (for instance you may imagine two initial electrons exchanging a "virtual photon", or a initial left-handed electron and initial right-handed electron exchanging a "virtual Higgs")

Now, the initial state $|i\rangle$ is evolving, so at $t = +\infty$, the final state could be written $|f\rangle = \sum\limits_{k,l} A_{1,2;k,l}|k\rangle |l\rangle$, where $|k\rangle$ and $|l\rangle$ represent some possible state for the final particles.

Until now, you see that there is a (unitary) evolution due to the interaction, but there is no "collapse". $A_{1,2;k,l}$, in the above expression, is simply the probability amplitude to find the final particles in a state $|k\rangle |l\rangle$, supposing the initial particles in a state $|1\rangle |2\rangle$.

However, if you make a measurement (at t=$+\infty$), you will have a "collapse", and you will find a final state $|k\rangle |l\rangle$ with the probability $|A_{1,2;k,l}|^2$

An other interesting point is that, considering here simple Quantum Mechanics, interactions between a particle and a measurement apparatus , may appear by entanglement. We may consider the example of the 2-slit experiment with photons. Without any measurement appararatus, the total state is $|\psi\rangle = |\psi_L\rangle + |\psi_R \rangle$, where $L$ and $R$ represent the two slits. If you bring a measurement apparatus potentially able to detect which slit has been used for the photon, but without doing explicitely the measurement, the new state is ;

$|\psi'\rangle = |\psi_L\rangle |M_L \rangle + |\psi_R \rangle |M_R \rangle$, where $|M_R\rangle$ and $|M_L\rangle$ are states of the measurement apparatus which are quasi-orthogonal ($\langle M_R|M_L\rangle = 0$). This is a pre-measurement state, we see that there is an entanglement between the states of the particle, and the states of the measurement apparatus. Because the states of the apparatus are orthogonal, this destroys the interference pattern. Now, you may really perform a measurement, in this case, you explicitely detect which slit has been used by the photon. After this, the final state would be $|\psi''\rangle = |\psi_L\rangle |M_L \rangle$, if the $L$ slit path is detected. More correct models would involve in fact entangled (pre-measurement) states between the particle, the measurement apparatus and the environment $ \sum\limits_i |\psi_i\rangle |M_i \rangle |E_i \rangle$.

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