# The effect of wavefunction collapse on spacetime?

#### asimov42

Hi folks,

I'm not sure if it's best to ask this question here, or in the Special & General Relativity section - it's probably more appropriate for this forum.

I've been wondering about the following question: what effect does wavefunction collapse have on space-time? For example, if we measure, say, the position of an electron at some point in time, its wavefunction should collapse instantaneously. The collapse should localize the 'peak' of the wavefunction to a smaller region of space-time, and this should happen instantaneously.

Shouldn't this collapse have an effect on the space-time background? I.e. because the position of the electron is now localized in a smaller region of space-time, shouldn't the shape of space-time also change (due to gravity), albeit by a very small amount? If the collapse occurs instantaneously, does this imply an instantaneous change in space-time also? And if so, wouldn't this make space-time discontinuous?

Thanks all. As a final remark, perhaps the questions about can't really be answered until there is a workable theory of quantum gravity?

J.

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#### Dmitry67

In the most commonly accepted version of CI, neither wavefunction nor collapse are REAL. It is our 'knowledge' about the system, and it is observer dependent (for different observers there are different collapses - check Wigner's friend experiment)

After the discovery of the Quantum Decoherence (wiki it) there is no longer need in the mysterious 'collapse' as measurements can be explained using just pure QM without any additional assumptions about special role of measurements

For that reason MWI is more and more accepted and CI is no longer #1.

#### lalbatros

But then I doubt that it would be observer-dependent.

Before decoherence was a widely used word, the interaction of the microscopic system with the macroscopic world (measuring device) was also used for the interpretation. Long ago, this was the pov of Landau who probably did not consider the "measurement problem" was anything of interrest.

Since I have learned physics mainly in Landau book, this pov is my basic hypothesis, and I really prefer not discussing this question unless there is some prospect for real physics instead of lounge philosophy or even new mysticism.

It seems that today this has really become a laboratory topic and this make me very happy. I don't expect decoherence to have any relation with our understanding of spacetime.
But your question is not very clear in this respect.

#### Fra

Another personal opinon to add to your calculation.

I've been wondering about the following question: what effect does wavefunction collapse have on space-time? For example, if we measure, say, the position of an electron at some point in time, its wavefunction should collapse instantaneously. The collapse should localize the 'peak' of the wavefunction to a smaller region of space-time, and this should happen instantaneously.

Shouldn't this collapse have an effect on the space-time background? I.e. because the position of the electron is now localized in a smaller region of space-time, shouldn't the shape of space-time also change (due to gravity), albeit by a very small amount?
For me the best way of seeing it is that the wavefunction represents the observers information about it's own environment (spacetime is part of the structure of that information). But this information is local, to the observer. Thus the collapse is not non-local if you look at where the information is encoded. The collapse is merely a local information update. No mystery at all.

In this view, the question is then (IMHO) rather different: how an spacetime emerges in the sense that the different observer views are related exactly by the observer-observer transformations of SR and GR. At first glance this would suggest that each observer would see a totally different spacetime, unrelated to it's neighbouring observers. But this would be the case only if they didn't interact, but of course the do.

Ie. how can the disitributed observer images, by interaction synchronize as to be consistent with some global, or quasi-global(some local neighbourhoods) symmetries.

I think this is what the result of observers evolving together in ineraction results in. And how can we understand, how the interaction process itself, produces distributed images, but that are related by a symmetry. (IE. the logic of emergent symmetry.) But the details on an exact model is still missing.

Thanks all. As a final remark, perhaps the questions about can't really be answered until there is a workable theory of quantum gravity?
I think the the last questions I posed, won't be answered until there is a theory of QG.

/Fredrik

#### Ilja

In the most commonly accepted version of CI, neither wavefunction nor collapse are REAL. It is our 'knowledge' about the system, and it is observer dependent (for different observers there are different collapses - check Wigner's friend experiment)

After the discovery of the Quantum Decoherence (wiki it) there is no longer need in the mysterious 'collapse' as measurements can be explained using just pure QM without any additional assumptions about special role of measurements

For that reason MWI is more and more accepted and CI is no longer #1.
Decoherence needs some undefined "decomposition of the world into systems" (some tensor product structure).

Moreover, it is irrelevant for the measurement problem. If you have a superposition of a living and a dead cat, decoherence does not help you. Instead, it gives you only a superposition of a living cat + environment and a dead cat + environment.

The problem remains the same.

#### Dmitry67

Moreover, it is irrelevant for the measurement problem. If you have a superposition of a living and a dead cat, decoherence does not help you. Instead, it gives you only a superposition of a living cat + environment and a dead cat + environment.

The problem remains the same.
Cat exchanges photons with the environment, and the enviroment get also decoherenced. So we get a superposition of:

living cat + happy observer

but not
superposition of both cats + confused observer

--> exactly what we observe.

#### Ilja

Cat exchanges photons with the environment, and the enviroment get also decoherenced. So we get a superposition of:

living cat + happy observer

but not
superposition of both cats + confused observer

--> exactly what we observe.
No. What we observe, is something describable by the wave function living cat + happy observer. Or, in other cases, by a wave function of dead cat + sad observer. And we have learned, in the beginners course of quantum mechanics,
that we should never never interpret a state psi1 + psi2 as being or in psi1 or in psi2. The superposition of them is something very different.

But my main objection against MWI is the missing of precise definitions. No definition of the decomposition into systems. No precise definition of the branches, nor of their evolution, nor of their splitting. Many words instead of many worlds.

#### Dmitry67

And we have learned, in the beginners course of quantum mechanics,
that we should never never interpret a state psi1 + psi2 as being or in psi1 or in psi2. The superposition of them is something very different.

But my main objection against MWI is the missing of precise definitions. No definition of the decomposition into systems. No precise definition of the branches, nor of their evolution, nor of their splitting. Many words instead of many worlds.
"beginners course" is based on CI for purely historical reasons. So many people start to assume that CI = QM and they even never learn about other interpretations.

MWI = pure (interpretation-less) QM + Quantum Decoherence (QD).
And MWI does not need any new axioms or assumptions, it is just a consequence of QD

Regarding "definitions, evolutions and spliiting" - there are all there:
http://en.wikipedia.org/wiki/Quantum_decoherence

#### Ilja

MWI = pure (interpretation-less) QM + Quantum Decoherence (QD).
And MWI does not need any new axioms or assumptions, it is just a consequence of QD

Regarding "definitions, evolutions and spliiting" - there are all there:
http://en.wikipedia.org/wiki/Quantum_decoherence
Your formula for MWI is wrong. Interpretationless QM gives a single state vector, and no containment relation between this vector and other vectors, which may appear in some decompositions.

Quantum decoherence needs a decomposition into systems to start. This decomposition is not provided by standard QM. Thus, you cannot even start with decoherence if you have only interpretationless QM.

I have not asked about definitions of decoherence, this is quite clear, but for the many worlds interpretation: branches, their evolution laws, any justification for the strange containment relation between the state and the branches, and the decomposition into systems you need to start decoherence.

#### Dmitry67

Your formula for MWI is wrong. Interpretationless QM gives a single state vector, and no containment relation between this vector and other vectors, which may appear in some decompositions.
However, decoherence by itself may not give a complete solution of the measurement problem, since all components of the wave function still exist in a global superposition, which is explicitly acknowledged in the many-worlds interpretation. All decoherence explains, in this view, is why these coherences are no longer available for inspection by local observers. To present a solution to the measurement problem in most interpretations of quantum mechanics, decoherence must be supplied with some nontrivial interpretational considerations (as for example Wojciech Zurek tends to do in his Existential interpretation). However, according to Everett and DeWitt the many-worlds interpretation can be derived from the formalism alone, in which case no extra interpretational layer is required.
Do you agree that QD explains measurements? Before QD was discovered MWI required some additional assumptions, like other iterpretations. QD made CI total BS: CI had invented the whole thing of 'collapse' just to explain measurements and the macroscopic behavior, and then oooops, we dont need collapse at all, we have QD! I wonder what CI guys do with both things.

On the contrary, MWI does not need any additional axioms. So CI is effectively cut by the Occams razor.

#### ueit

MWI = pure (interpretation-less) QM + Quantum Decoherence (QD).
And MWI does not need any new axioms or assumptions, it is just a consequence of QD
1. How does MWI account for the Born postulate?

2. How does MWI account for the observed reality (3d space, point particles)?

#### Dmitry67

1. How does MWI account for the Born postulate?

2. How does MWI account for the observed reality (3d space, point particles)?
1. http://en.wikipedia.org/wiki/Quantum_decoherence#Loss_of_interference_and_the_transition_from_quantum_to_classical

2.
As a consequence, the system behaves as a classical statistical ensemble of the different elements rather than as a single coherent quantum superposition of them. From the perspective of each ensemble member's measuring device, the system appears to have irreversibly collapsed onto a state with a precise value for the measured attributes, relative to that element.

#### ueit

The link does not address my questions. It does not explain how MWI (which accepts only the reality of the wave-function) is supposed to account for our observations consisting more or less of point particles in a 3D space. Only after this question is addressed we can speak about decoherence.

#### Ilja

Do you agree that QD explains measurements?

No. It needs a decomposition of the universe into systems. This decomposition is not defined.

See my paper arXiv:0901.3262

#### Dmitry67

The link does not address my questions. It does not explain how MWI (which accepts only the reality of the wave-function) is supposed to account for our observations consisting more or less of point particles in a 3D space. Only after this question is addressed we can speak about decoherence.
On the contrary, QD explains why you observe 'particles'
Say, you register 1 photon using your photocamera. Photon (wave) hits the matrix, and it splits/decoherenced into 4000000 branches (for 4Megpixel camera). Then you say: look,photon is particle, it is almost a point, it hit just one pixel!

#### ueit

On the contrary, QD explains why you observe 'particles'
Say, you register 1 photon using your photocamera. Photon (wave) hits the matrix, and it splits/decoherenced into 4000000 branches (for 4Megpixel camera). Then you say: look,photon is particle, it is almost a point, it hit just one pixel!
Yeah, but you have already assumed the 3D classical world with ready-made 3d objects (the 4Megpixel camera for example). First, you need to explain how these objects are supposed to appear from your universal wavefunction. Then you have to explain how to ascribe probabilities for different branches and so on.

#### Dmitry67

QM explain the existence of complex systems: atoms, moleculs, crystalls from the first principles without any additional assumptions. There is nothing new.

#### lalbatros

What about entanglement as the fabric of space-time?

#### bg032

Regarding "definitions, evolutions and spliiting" - there are all there:
http://en.wikipedia.org/wiki/Quantum_decoherence
In the above link I have not found an answer to the following simple question: let $$\Psi(t)$$ be the wave function of the universe at a suitable time t. According to MWI+decoherence, it is split into n branches or worlds:

$$\Psi(t)=\Psi_1 + \ldots + \Psi_n$$

What is the criterion defining this splitting? Can some expert in MWI+decoherence answer this?

Note 1: if the criterion requires to split the universe into subsystems, the criterion for this splitting is also required.

Note 2: of course the criterion must be mathematical; thus a criterion of the type

$$|\hbox{cat alive}\rangle + |\hbox{cat dead}\rangle$$

is not acceptable.

#### Ilja

QM explain the existence of complex systems: atoms, moleculs, crystalls from the first principles without any additional assumptions. There is nothing new.
QM explains it, but not from first principles. Instead, one needs some classical background, or something else which replaces this classical background. Say, the configuration of pilot wave theory.

#### Dmitry67

Wait, lets take for example hydrogen atom (lets assume that proton is elementary)
Hydrogen atom can be calculated from the first principles using QFT

Or are you talking about some phylosophical issues like 'yes, we have a result, some numbers, but what we have actually calculated'?

#### Dmitry67

In the above link I have not found an answer to the following simple question: let $$\Psi(t)$$ be the wave function of the universe at a suitable time t. According to MWI+decoherence, it is split into n branches or worlds:

$$\Psi(t)=\Psi_1 + \ldots + \Psi_n$$

What is the criterion defining this splitting? Can some expert in MWI+decoherence answer this?

Note 1: if the criterion requires to split the universe into subsystems, the criterion for this splitting is also required.

Note 2: of course the criterion must be mathematical; thus a criterion of the type

$$|\hbox{cat alive}\rangle + |\hbox{cat dead}\rangle$$

is not acceptable.
Whats about density matrix approach in the same article?

#### LaserMind

Hi folks,

I'm not sure if it's best to ask this question here, or in the Special & General Relativity section - it's probably more appropriate for this forum.

I've been wondering about the following question: what effect does wavefunction collapse have on space-time? For example, if we measure, say, the position of an electron at some point in time, its wavefunction should collapse instantaneously. The collapse should localize the 'peak' of the wavefunction to a smaller region of space-time, and this should happen instantaneously.

Shouldn't this collapse have an effect on the space-time background? I.e. because the position of the electron is now localized in a smaller region of space-time, shouldn't the shape of space-time also change (due to gravity), albeit by a very small amount? If the collapse occurs instantaneously, does this imply an instantaneous change in space-time also? And if so, wouldn't this make space-time discontinuous?

Thanks all. As a final remark, perhaps the questions about can't really be answered until there is a workable theory of quantum gravity?

J.
My view is that the electron does not collapse into a tiny heap when observed but the observation gets a snapshot at one time only. I don't know why we call it 'collapse' come to think of it - what collapses?

#### bg032

Whats about density matrix approach in the same article?
This approach requires to take the partial trace of a density matrix, which requires the decomposition into subsystems, and this decomposition is not mathematically defined.

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