First, there are not two possible outcomes (interference patterns or not), but actually a continuum (perfect interference pattern, then decreasing contrast down to the point where no interference pattern is left). In simplistic terms: The stronger the interaction between your interfering particles and the environment, the smaller the contrast. Now Gravity has two problems:

1. Interaction with gravity is rather weak.

2. What matters is not the interaction with gravity, but the difference in interaction between your two slits. And this difference is much smaller than the total effect.

So as a result, Gravity would show up as a smaller one of all these dirt effects that distinguish an experiment from theory, but mandate no specific discussion.

Do you mean something like phase shift in COW experiment or a different phenomena?

The point is that you are in an external field, that of the earth. And external fields do not ``reduce the wavepacket''. For that you need interactions in which the coherent nature of the original wavefunction gets transferred to other objects (other degrees of  freedom, if you prefer).

Wave function collapse by measurement is defined as reduction of superposition of several eigenstates to a single eigenstate. This in my interpretation means that all the possible statistical outcome of the measurement process reduces to one definite outcome. This is due to the interference of light particle with the particles of two slits in the double slit experiment. So this one definite outcome is the wave interference pattern that you see. Wave function collapse does not mean no outcome at all. And as mentioned by Ulf, interaction with gravity is weak and its contribution is very small in the total effect.

Eventhough gravitational waves are discovered, there is no evidence for the existence of Graviton. So whether gravity is associated with a particle or whether gravity is a force at all, are debatable questions. We know that gravity is very weak at the present epoch in the history of the universe but it is generally accepted that interaction with gravity becomes critical near Planck epoch, 10^(-43) sec. after big bang. In following quantum gravity theory, gravity becomes so strong at Planck time that not only it collapses the wave function to a single eigenstate but it also collapses the wave associated with that single eigenstate leaving behind no mass gap at all.and the energy associated with this single eigenstate becomes perfectly motionless. So you cannot call this energy anymore because energy and motion coexist by definition.

Article Periodic quantum gravity and cosmology

First: I don't know the answer.

Second, I like the question due to its simple positively naive, though correct  projection of what is sometimes formulated as the von Neumann principle. The explanation that the weak interaction causes weak (i.e. some  intermediate) collaps is an opposite postulate. As an example of a rigorous model one can accept the reduced evolution, which is defined as the  evolution of  the partial trace of the unitarly (thus: determinstically) evolving compound system (the subsystem plus its environment). Some  already classical results related to this subject can be found within works devoted to open quantum systems.

Best regards

Because gravity is classical on those scales. So it doesn't define a superposition, but a single state, defined by the solution of Einstein's equations.

@ Stam Nicolis

OK, but if we modify the original question as follows:

Why does TheSeaOf_EM-waves  not lead to a collapse of the wave function in the double slit experiment for electrons?

1 - Does this question make sense?

2 - If yes, then does TheSeaOf_EM-waves  lead to collapse . . ? And WHY?

Regards,

Joachim Domsta

The classical electromagnetic field *does* lead to a classical result for the electron, because it's a solution of Maxwell's equations. The difference wit the gravitational field is that electrons couple more strongly to the electromagnetic field than to the gravitational field.

Incidentally, there's no such notion as a ``sea of EM waves''-and there isn't any notion as ``collapse of the wavefunction'' either. The statement is that a classical measurement can only lead to a classical result. A superposition isn't classical, so it can't be measured by a classical apparatus.

@ Stam Nicolis

Your answer contains too many unprecisely formulated  notions and relations. The content can be guessed, only.

For instance, it follows (probably) that your answer to the original question is:

there isn't any notion as ``collapse of the wavefunction''

But then I am justified to wonder if your answer

"Because gravity is classical on those scales. So it doesn't define a superposition, but a single state, defined by the solution of Einstein's equations."

was about the collapse at all;  which wouldn'd appear even in the case when  the gravity were not classical.

From your second answer:

"the electromagnetic field is classical, so it's not a superposition,"

Who is asking about the superposition of the field - the discussion is about the wave function of electrons (or elementary particles) interacting with the fields. One can treat them like a potential in the standard Schrodinger equations. Probably you have misunderstood the question since it contains this sentence

"Why is interaction with "Gravity" itself not a "measurement" which leads to a collapse of the wave function?"

If one selects  words "" interaction with "Gravity" itself ''"  , then in fact, one can think that the question is about wave collaps of the field, which - of course - is impossible due to its classicality, so to say.

Hopefully, your expected  valueable  answers explaining in more details the main question will appear soon.

Sincerely, Joachim Domsta

Interaction of charged particles, that are used in diffraction experiments,  with gravity is negligible, that's why. Interaction with classical electromagnetic fields isn't. 

So the gravitational field's contribution to any measurement is negligible. 

But there, still,  isn't any content to the expression ``collapse of the wavefunction''. It doesn't mean anything. What's measured is well defined.

OK, I agree that for ``collapse of the wave function''   a  commonly accepted definition is not given. However reading some papers one gets impression that there are many measurement theorists who use this notion keeping in mind such a structure of notions, where the collapse is understood as a phenomenon that the result of a measurement is a pure state - one of the eigenstates of some observable, mostly - of the Hamiltonian.  I think that the Author of the current question is trying to discuss this notion showing an intrisic inconsistency:  If a measurement were any interaction, than for instance interaction of the observed particles with outer field (say - em) would be a measurement, too. and as a consequence some particular pure states should a result, exhibiting the feature of the interaction. But the list of possible pure states varies from author to author, unfortunately for this interesting fashion. But if there were a well defined observable deciding about the list, one should see the influence of the perturbations independently of their strength. Seemingly, Stam votes for the obvious and reasonable point of view, that the efect must depend on the strength of the interaction.  To this point we are of the same meaning.

However, it is still not quite clear what is the theory of measurement for those who exclude the ''wave function collapse''.  My point with respect to this is that the only consistent  with standard quantum mechanics  model is the following: an observation is any evolution a compound system SYS  consisting at least of two subsystems - the observer  OBS  and the object  OBJ, ventualny the third one, i.e. the enviroment ENV. A result of the observation (vel measurement) is based on the reduced evolution of OBS any information about the evolution of SYS, in particular - about the reduced evolution of OBJ. The commonly accepted way of understanding the reduced state is the corresponding to OBS partial trace of the density matrix of  SYS (in some notation denoted by Tr_{OBJ \otimes ENV} ). There are many examples showing that in this fashion is appropriate due to the following basic features: the information about the system is the greater, the longer in duration the observation is performed and  the stronger the interaction holds. Moreover, depending on the interaction Hamiltonian the maximal information about the outer compound subsystem  OBJ \otimes ENV  may happen to be just the diagonal of their initial density matrix. One can call this decoherence. Although, there is no decoherence of the state, only (in the exemplary case) the information about the state of  OBJ  is reduced to its diagonal in a representation determined strictly by the interaction. I have tried to propagate this point of view, withot any success, yet.

Returning to the question of this thread, according to the above model no wave collapse can be observed. Instead the result will be perturbed if compared to the lack of outer fields, and negligible if the time of observation is shorter. Thus the result can give us additionaly information not only about the slits, but also about the perturbing fields, if their interaction is strong enough.  Everybody interested in more detailed explanation of my point of view is kindly asked to look at a conference presentation on my RG page

https://www.researchgate.net/publication/308595613_Quantum_Systems%27_Measurement_through_Product_Hamiltonians?ev=srch_pub

Best regards,

Conference Paper Quantum Systems' Measurement through Product Hamiltonians

There isn't any conceptual problem with describing the interaction of a quantum particle with an external field and computing the transition probabilities-it's done all the time. 

Nor is there any conceptual problem with computing what happens after such a measurement. 

Obviously there is no problem with evaluating the reduced states and  accepting the reduced evolution as everything what the subsystem "knows"  about the system. The new concept is to accept this as an ultimate model of quantum measurement, without any collapses and/or decoherence. The system evolves its own way, and the subsystem is just a reduced evolution of the system, THAT'S ALL.  The problem however is, that most researchers discuss the measurement problem introducing pointers, classical observer/device, immolition measurements etc.In my opinion all such adds should be excluded from considerations  unless build they are expessable in terms of evolution of compound systems.

Besides, my material's aim is to show, that under suitable circumstances (= interacting Hamiltonians) the observer can restore the evolution of the system in all details; moreover, in anothe cases, only restricted information is available. And just for making this way interesting, the examples are chosen in such a way that the diagonal of the observed subsystem becomes the upper bound of the available information fo the observer. And it is not just incidentaly consistent with the popular interpretation, that the (observed) system after measurement is found in the mixture of pure eigen wave-functions of some observables. My examples show which operator(s)  is/are responsible for the choice of the  so called preferred basis: namely those related to the observablse which commute with the factors of the interacting Hamiltonian (suitably expressed if the Hamiltonan is  of the product form).  I think that this point of view is juast  a little bit more fixing the notion of quantum observation/measurement, although substantially different if compared to commonly spread interpretations, the one of von Neumann included.

I hope the above comments expalin why I am again  kindly asking Stam for his definition of the quantum measurement. Obviously statements like "What's measured is well defined" is not sufficient for this discussion, at least due to existence of many different definitions in the literature.

Regards 

``If a measurement were any interaction, than for instance interaction of the observed particles with outer field (say - em) would be a measurement, too.''

Yes, unfortunately the premise is incorrect. Measurement, however defined, always involves at some stage some kind of loss of coherence. This means that the measured system is somehow entangled with an environment which we cannot (and do not wish to) observe. This leads to loss of coherence and may lead to measurement. For this, you need an interaction with an environment which is capable of getting entangled with the system of interest. You therefore need a system with a (preferably large) number of degrees of freedom. An external field, whatever its nature, does not give this possibility.

Of course it does; that's exactly what an external field is. Its backreaction can be neglected.

Even though I agree with some of the points, let me present more precisely the way the proposed model of measurement is related to the decoherence.

Firstly, any changes experienced by the system are due to its unitary evolution, perturbed however by the interaction between subsytems.

Secondly, the decoherence apprears only as the information about the outer system obtained from the reduced evolution of the observer (by taking the partial trace of the whole system's state).

Thirtly, if the interaction is commuting (in a way explained in the above referred file), then the result of the observation (i.e. everything readable from the reduced evolution) is the diagonal of the state of the outer system - this models the decoherence, which in fact does not follow.

Fourthly, other examples presented in the conference paper show, that if the interaction is suitably built of non-commuting factors, then from the reduced evolution of the observer the evolution of the whole system is completely restorable

Fifthly, the only losses are due to the perturbation of the dynamic of the whole system caused by obviously unremovable interaction, which means that in this model there is no place for non-demolition of the measured system, if compared to the freely evolving outer part(s).

Thank you for your attention.

Best regards, Joachim Domsta

There's no reason to make vague proclamations, when the rules for performing the calculations are well defined and in all the textbooks.Just compute the transition amplitude, by any method-solving the Schrödinger equation, or by the path integral.  Take the square of its absolute value to compute the transition probability. 

 Gravity is negligible, for the two slit experiment, that's all. It's a standard exercise to introduce an external field and compute its effects on the transition amplitude. 

Of course, gravity is negligible for the two slit experiment. And the definition of the quantum measurement is an issue for other discussion.