A non-metaphysical interpretation of measurement in quantum mechanics

In quantum mechanics, measurement plays a fundamental role and to me, its role is usually described in a rather odd way. The Copenhagen interpretation states thus

When that device makes a measurement, the wave function of the systems is said to collapse, or irreversibly reduce to an eigenstate of the observable that is registered.

But I could not find any understanding of when is the observation happening. Does it happen when the event (such as the electron hitting the screen) happens, or when a person seeing the plate, (or when that person tells me!)

I have read about the multiverse explanation, a few explanations like the importance of consciousness etc. I understand that this is a very fundamental question, and my question is not what really happens. My question is what is wrong with the following interpretation:

The process of measurement is the development of some sort of coherence (I am afraid of using the word entanglement because I do not understand it) between the observed object and the observer. So, from the observer's perspective, the wavefunction has collapsed, without the wavefunction ever collapsing from the perspective of anyone who has not observed it.

This is not the same as the Copenhagen interpretation because there is no real collapse of the wavefunction, nor the multiverse interpretation because there is no real splitting of the universe. This interpretation also makes the "Wigner's friend" experiment intuitive to understand, and removes the distinction between the observer and the observed.

Added after the comment by Luke:

In fact, this interpretation defines measurement as the observer attaining coherence with the observed. Consciousness plays no part, and neither does the act of conducting an observation modify anything about the observed nor split the universe. Repeat measurements by the observer will yield the same result because of the coherence. Isn't this consistency the meaning of reality? This will look to the observer as a collapsed wavefunction. However, for any external agent (Mr. Wigner) who has not made the observation, there is no collapse.

I am more of a quantum mechanics enthusiast, reading mainly from popular science books on this subject. I would be glad if anyone helps me understand why this interpretation is wrong.

What you're describing is nothing more, and nothing less, than the everettian Many-Worlds Interpretation, when it is understood correctly and without any extraneous metaphysics.

At its core, MWI is just about taking quantum mechanics at face value, without any artificial lines to try and distinguish "classical" systems from quantum ones. As such, the observer is a quantum system made of atoms and molecules and other quantum bits and pieces, and if you have a particle in a state $|a\rangle_\mathrm{particle}$ and you measure it, then the observer will go from the state $|\mathrm{ready}\rangle_\mathrm{observer}$ to the state $|\mathrm{observed}\ a\rangle_\mathrm{observer}$, or in other words, the measurement implements the transformation $$|a\rangle_\mathrm{particle}|\mathrm{ready}\rangle_\mathrm{observer} \mapsto |a\rangle_\mathrm{particle}|\mathrm{observed}\ a\rangle_\mathrm{observer}.$$ Similarly, if the particle starts in the state $|b\rangle_\mathrm{particle}$, then the measurement will implement the transformation $$|b\rangle_\mathrm{particle}|\mathrm{ready}\rangle_\mathrm{observer} \mapsto |b\rangle_\mathrm{particle}|\mathrm{observed}\ b\rangle_\mathrm{observer}.$$ And now comes the weird quantum mechanical bit: if take QM at face value and without limits to its validity, then the linearity of the Schrödinger equation tells us that if we start in a superposition state like $\frac{1}{\sqrt{2}}(|a\rangle_\mathrm{p}+|b\rangle_\mathrm{p})$ then the state will evolve to the superposition of the individual outcomes, i.e. $$\frac{|a\rangle_\mathrm{p}+|b\rangle_\mathrm{p}}{\sqrt{2}} |\mathrm{ready}\rangle_\mathrm{o} \mapsto \frac{ |a\rangle_\mathrm{p}|\mathrm{observed}\ a\rangle_\mathrm{o} + |b\rangle_\mathrm{p}|\mathrm{observed}\ b\rangle_\mathrm{o} }{\sqrt{2}} .$$ Now, I commend you for your restraint in using complicated concepts without fully understanding them, but in this instance there is no need to mince words: the particle has become entangled with the observer.

And, as part of the standard package when it comes with entanglement, neither the particle nor the observer can be assigned a (pure) quantum state on its own; instead, there is only one big universal wavefunction. This is what Everett's interpretation really says (starting from the very title of his PhD thesis, The Theory of the Universal Wave Function). The additional baggage involved in things like

because there is no real splitting of the universe

is just additional mumbo-jumbo added in by monkey brains that have a hard time understanding what it would be like to be a conscious quantum system that's entangled with the rest of the universe.

Oh, and another thing:

helps me understand why this interpretation is wrong

If a given framework is an interpretation of quantum mechanics, in the proper sense of the term (i.e. it doesn't conflict with QM, in which case calling it an 'interpretation' is a good bit of a misnomer), then it can't be "right" or "wrong". Because interpretations of QM have no bearing on observed phenomena, their valuation lies strictly outside of scientific considerations, and you must necessarily use other, shall we say, more metaphysical criteria.

The process of measurement is the development of some sort of coherence (I am afraid of using the word entanglement because I do not understand it) between the observed object and the observer. So, from the observer's perspective, the wavefunction has collapsed, without the wavefunction ever collapsing from the perspective of anyone who has not observed it.

Entanglement is a consequence of quantum mechanics. If system 1 and system 2 interact so that their state has the form: $$\sum_a \alpha_a|\phi_a\rangle_1|\psi_a\rangle_2$$ and more than one of the $\alpha_a$ coefficients is non-zero, then system 1 and system 2 are entangled. The two systems then contain information about one another. If you measure the set of states $|\phi_a\rangle_1$ and get some particular value of $a$ then you can work out the state of system 2. If system 1 becomes entangled with the rest of the world, then you can no longer do interference between the different $a$ states and this explains the alleged collapse.

Now, if the word collapse is just a synonym for loss of interference, then you get the many worlds interpretation. If you want a collapse that produces just one state then you need some theory of the physical process of collapse. Those are the only real options. Either there is a physical process called collapse that reduces the number of states of a system to one state or there isn't.

If such a process takes place, then it will change the state of other systems that are arbitrarily distant from the measurement interaction. Eliminating all but one of the terms in the sum above affects both system 1 and system 2. If there is no collapse then the measurement process and all its consequences may be local if they are governed by local equations of motion. This is a substantive difference although many people like to pretend it isn't. This denial takes various forms such as denying that physics is trying to describe how the world works or saying that logic is no longer valid in quantum mechanics.

So, to summarise, the following options that are currently available: the MWI, non-locality and talking nonsense.

Why this is wrong is maybe the wrong question, because I cannot really prove you are wrong, but I can argue why this is highly problematic and bad for doing physics: Because it is an odd world view you obtain if you think that your conciousness influences the world so much.

1.) Physics has for centuries tried to understand nature. And we have seen that we get objective facts - whoever measures the speed of light in vacuum will get the same result, independent of your consciousness and whatever. The simplest and most compelling way to explain that was by asserting objective laws of nature that are just true and hold independtly of observations, measurements, and the human mind. (This can still be done in quantum mechanics, be it via collapse models, Bohmian mechanics, or something else.)

Your idea would part from that. Why do we all see the same if each mind collapses the wave function for itself? Where is the objective fact?

2.) You think that only the human mind can collapse the wave function? So does a cat see the quantum superpositions? Or do cats also collapse wave functions? What about rats? Bacteria? Where do you draw the line between not-collapsing and collapsing? Exactly like in the Copenhagen interpetation, you have to introduce an unnatural distinction between a measurement and a non-measurement or observer and non-observer, which cannot be made precise.

3.) Following John Bell, I would claim that a fundamental theory should be about simple constituents of the world described mathematically. Talking about "Well when I observe, something happens like ..." is not a good physical theory.

• Thanks for your response. I believe you have misunderstood. I am as uncomfortable about using conciousness at all. My interpretation places a 'concious human' making a measurement (observing) at the same level as a light sensitive diode, photographic plate, or a cat. The idea was: when a device makes a measurement, the measurer becomes coherent with the measuree. There is neither a collapse, and nor any role of conciousness either. Because the measurer attains a coherence, he/it will always see a collapsed wavefunction. Same for humans and diodes. Jun 8, 2017 at 11:13

What is a wave function?

It is a solution of a quantum mechanical equation with the approrpriate boundary conditions of the problem. This solution depends on (x,y,z,t) and is a complex function, and its square with the complex conjugate gives the probability distribution for the specific state to exist at an (x,y,z) when "measured" at time t.

The double slit experiment one electron at a time is a good example.

The wave function is conseptually simple, it is the scattering of an "electron +2 slits" the momentum of the electron given as well as the distances and widths of the slits( the boundary conditions).

The measurement is the dot on the screen. Time is a parameter in sequential frames of the screen.

The dot is the footprint of the "collapsed" wavefunction for that one electron. It interacted with the screen once, and the wavefunction describing it from the first interaction with an atom of the screen changed and is unknown since the boundary conditions from then on are different for that electron and not accessible.

Analogous to one throw of the dice , the probability distribution builds up, electrons on slits, into the interference pattern seen. This tells us that indeed a wave equation must describe the behavior of electrons under these boundary conditions, as interference is footprint of wave behavior.

Measurements always "collapse" the wave functions, i.e. pick up one throw of the dice to build up the quantum mechanical probability pattern. For each individual electron a new wavefunction exists after hitting the screen and leaving its footprint.

• Thanks, Anna, for your reply. What you are saying is restating the Copenhagen interpretation that "Measurements always `collapse' the wave functions". This has a problem with the interpreting Wigner's friend experiment. The question is when does the wavefunction collapse happening. Jun 8, 2017 at 12:30
• In my experimentalist's view when the electron hits the screen atom and interacts with it, the boundary conditions of its wavefunction description changes once and for all at that time t1, recorded with the simple instrument of the screen. The experiment is still there and thousands if not hundreds of thousands of people have looked at it as recorded in this clever way. Looking at it does not affect the measurement. Jun 8, 2017 at 13:38
• No . The real detector is the geiger counter that triggers the release of the poison. The cat is just like the recording screen in the slit experiment. Whether you look or not if a decay has happened the cat is dead, otherwise it is alive. The same as whether you look or not the electron leaves a footprint on the screen. Jun 9, 2017 at 3:48
• For physics , it is a registration in real numbers that is a measurement. The dots on the screen have an (x,y) in real numbers. Once these are there permanently, thats it for physics. The rest is metaphysics. The same with the cat. Living is not a physical concept that can attributed with real numbers , at least with present knowledge of physics and the mathematical models we have. To introduce a cat in what is a counter of radiation measurement is cruel and unnecessary . What ever is controlled by a probability distribution calculable/modeled in physics has the need of statistical Jun 9, 2017 at 6:01
• accumulation. Where probability distributions are necessary as in quantum mechanics there is an "unknown" factor for the individual measurement. If it is recorded, when one looks at it is not in the quantum mechanical frame but the classical frame where we and our instruments measure. The trigger geiger counter that triggers the poison can trigger a clock reading to fix when the poison was released. Poison and clock are in the classical frame. S. cat is a confusion between classical and quantum frameworks and that can only happen in metaphysics, not physics., imo. Jun 9, 2017 at 6:06

What would a non-metaphysical interpretation of Quantum Mechanics be? By the very definition, an interpretation of Quantum Mechanics is some intellectual construction which makes the very same predictions as the Copenhaguen interpretation. Otherwise that would be a new theory, one that could be falsified by experimental means. So by definition, interpretations of Quantum Mechanics are metaphysical. This is the meaning of the word "metaphysical": the discourse about the language of physics.

I do not mean to use metaphysics as a demeaning word, "oh! this is just philosophy". Since the language of physics is math, metaphysics can also be discussed with mathematics. In the context of your question, as Emilio Pisanti pointed out, you are closer to MWI, I think, which Everett has mathematically conceptualised in his very seminal article, introducing concepts such as relative states and memory sequences. Another striking example, very different from the point of view you expressed, so I am only mentioning it for contrast, would be Bohmian mechanics, which also has a rich body of mathematically formalised concepts added to the Copenhaguen interpretation. But eventually, the mathematics of those metaphysics live in a different plane of existence than the Born rule, Schrödinger equation, etc.

Note of course, that you haven't expressed the core of your question with the required mathematical precision but I am not holding that against you as there are enough talented people around here to do just that, and as noted above, I think too that your statement can be likened to Everett's interpretation. It is just that your title made me jumped, and I wanted to make sure you do not fool yourself by blurring the line between metaphysics and physics here.