Are different interpretations of quantum mechanics empirically distinguishable? Are the different interpretations of Quantum mechanics just different viewpoints of the same physical reality? Or can experiments distinguish them? Are they empirically distinguishable or not?
I have read a paper in which Asher Peres states that quantum mechanics needs no interpretation and we can understand it by a minimum number of necessary postulates. Here is the last paragraph of the paper:

All this said, we would be the last to claim that the foundations of
  quantum theory are not worth further scrutiny. For instance, it is
  interesting to search for minimal sets of physical assumptions that
  give rise to the theory. Also, it is not yet understood how to combine
  quantum mechanics with gravitation, and there may well be important
  insight to be gleaned there. However, to make quantum mechanics a
  useful guide to the phenomena around us, we need nothing more than the
  fully consistent theory we already have. Quantum theory needs no
  interpretation.

This is the link to the paper (it is a paper with only two pages) Peres
Can you explain what he means when he says "quantum mechanics needs no interpretation"? i didn't get it from the paper!. Does he mean that we shouldn't try to assign any objective meaning to the wave function and consider it as reflection of our knowledge about the system? If yes, isn't it what Copenhagen interpretation says?!! (This is from wiki page of Copenhagen interpretation:"The wave function reflects our knowledge of the system") 
And finally, has anyone found that minimum number of postulates? 
 A: No, interpretations of quantum mechanics are not distiguishable in a physical experiment, otherwise they would be called theories rather than interpretations. 
It should be noted that there are some theories whom their authors call "interpretations" but they in fact are not. For instance the "objective collapse theories" often (wrongly) called "interpretations". These theories can be physically proven or disproven and predict different observations than the standard quantum mechanics (with all its interpretations).
That said, it is not that interpretations cannot be experimentally distinguished at all. Maybe they can be, but the experiment that would be able to distinguish between them would not be a physical (or scientific) experiment in the sense it would not satisfy the requirements for scientific method.
All scientific experiments regarding quantum mechanics should produce the same results as far as different interpretations concerned.
A: On paper, the difference between a theory and an interpretation is very clear. If two distinct sets of ideas/explanations generate experimentally distinguishable predictions, then they are two different theories. If they use different concepts but produce identical experimentally verifiable predictions, then they are two different interpretations of the same physical theory.
In practice, things are never so clear-cut. As a practical matter, we certainly do not currently possess either the theoretical or the experimental capability to unambiguously falsify either the many-worlds or Copenhagen interpretation in any experiment that can actually be performed in the real world. But as Count Iblis points out, there probably are some hypothetical experiments that distinguish them, which could be performed in principle but may never actually be feasible in practice. (I think the same is true of the de Broglie-Bohm interpretation, although I'm not familiar enough with that interpretation to say for sure.) For example, decoherence is defined to be the vanishing of all the elements of a system's reduced density matrix that are off-diagonal in some basis known as the "pointer basis". But perfect decoherence is an idealization; in practice the off-diagnonal elements will be exponentially small but never exactly zero. (Similarly, there will always be incredibly many-point tunneling terms connect different branches of the wavefunction that appear at zillionth order in perturbation theory.)
So as practical matter, the many-worlds and Copenhagen interpretations are equivalent as physical theories to within our current understanding. In principle, they are almost certainly distinguishable if one could perform arbitrarily precise experiments and had infinite processing power. I would argue that we do not yet understand the different interpretations well enough to judge whether they will ever be experimentally distingishable in practice with foreseeable technology.
So you could approach this situation in many ways, and take any of the following (defensible) perspectives:


*

*MWI's and Copenhagen's predictions are indistinguishable in practice, so they are different interpretations of the same theory.

*MWI's and Copenhagen's predictions are distinguishable in principle, so they are different theories but are equivalent in practice.

*We don't understand MWI and Copenhagen well enough to judge whether they will be experimentally distinguishable in the future. So we do not yet know whether they are different theories or simply different interpretations.

*We don't understand MWI and Copenhagen well enough to judge whether they will ever be experimentally distinguishable in the future. But we should reserve the term "theory" to mean "something that we actually know how to distinguish in practice", and use "interpretations" to mean "ideas that we do not currently know how to distinguish experimentally". So the distinction between a theory and an interpretation is dependent on the scientific community's current knowledge of the subject. MWI and Copenhagen are currently just two different interpretations of the same theory, but way well eventually become two different theories as our understanding and/or experimental technology advance.


This distinction between actual experiments and "theoretical experiments" (a term with an interestingly semi-contradictory nature) comes up in other areas of physics as well. For example, Scott Aaronson's essay "Why Philosophers Should Care About Computational Complexity" puts a slightly different spin on some related ideas, and argues persuasively that philosophers should take seriously the practical limitations on what experiments and calculations could actually be performed in the real world.
A: I do not know that whether or not all interpretations can be distinguishable from each other. But after going through the link once, I thought Asher Peres probably implied that all the interpretations(De Broglie Bohm, MWI etc) will not have any effect on the probability of measurement outcomes (predictions of QM) i.e. the number of times detectors' clicks. In that sense, all the experiments with measurements (observables in QM) will give probabilistic outcomes and different interpretations are to explain the results, which are probabilistic in nature and all the interpretations are just various ways to rule out that probabilistic nature i.e different way to interpret the reasons for indeterminism which presents itself as one of the basic postulates in QM (as pointed out by Tom).
However experiments have been performed to Check whether or not QM is consistent with Local Hidden Variable Theory. One can measure joint probability and show that QM violates Bell's Inequality. In that sense, one can show that QM violates Local Hidden Variable Theory.(http://en.wikipedia.org/wiki/Bell_test_experiments). For other interpretations there are some thought experiments (as pointed out by @Count Iblis). But to my knowledge no such experiments has been performed till now.
A: It's not true that all the different interpretations are not (in principle) experimentally distinguishable. Let's consider the difference between Copenhagen Interpretation (CI),   De Broglie–Bohm theory (BT) and the Many Worlds Interpretation (MWI). BT assumes that under normal circumstances we have so-called quantum equilibrium and only then do you get the usual predictions of standard quantum mechanics that you get when you assdume CI. This means that you can try to detect small deviations of exact quantum equilibrium, see here for details.
If the MWI is correct then time evolution is always exactly unitary. The CI doesn't explain how we get to a non-unitary collapse, but it does assume that there exists such a thing. This implies that at least in principle there should be detectable effects. Systems that are well isolated from the environment should undergo a non-unitary time evolution at a rate that is faster than can be explained as being caused by decoherence by the residual interactions it still has with the environment.
David Deutsch has proposed a thought experiment to illustrate that MWI is not experimentally equivalent to CI. Suppose an artificially intelligent experimenter is simulated by a quantum computer. It will measure the operator A = |0><0| - |1><1|. The qubit is initialized in the state |1/sqrt(2)[|0> + |1>]. Then the CI predicts that after the measurement the state of the qubit undergoes a non-unitary collapse to one of the two possible eigenstates of A, i.e. |0> or |1>. The MWI asserts that the state of the entire quantum computer splits into two branches corresponding to either of the possible outcomes.
To decide who is right, the experimenter decides to let the computer perform the unitary time evolution corresponding to inverting the final state of the quantum computer (according to the MWI) to the initial state, but while keeping the record that a measurement has been performed. This transform to the modified initial state is still unitary and can therefore be implemented (all unitary transforms can be implemented using only the CNOT and single qubit rotations).
Then it is easy to check that if the CI is correct that you don't get that desired modified initial state back and the difference between the two states if the qubit you end up with, can be easily detected by doing measurements on it.
A: In the name "interpretations" it is implied that these are believed to not be empirically distinguishable. What everyone agrees on is how to calculate empirically testable predictions. That is essentially mathematics, and if you are very mathematically minded, you can propose to axiomize it, that is, find a minimum number of axioms (postulates) from which it follows. Obviously, as with any system of axioms, there is a bit of personal preference involved: Many call the time-dependent Schroedinger equation such a postulate. I personally prefer to only use de Broglie's matter-wave duality as a postulate and derive e.g. the (non-relativistic) Schroedinger equation for free massive particles from the non-relativistic impulse-energy relationship expressed for plane waves (which are one possible and hence sufficient choice for a basis system to express any wave in). I am afraid all one can summarily say is that there is no widespread consensus on what postulates/axioms to use; we physicists only agree on the (well-tested) outcome and perhaps that how exactly one gets there is at least as much a question of mathematics as of physics.
Whilst "interpretations" was certainly the correct word historically, one can make good arguments that some theories that carry the historical name "interpretation" can actually be tested, at least if you take a sufficiently broad approach to tests as to permit thought experiments. Most interpretations fail to resolve paradoxes, such as Schroedinger's cat, the EPR paradox, or how to determine what constitutes a measurement (or how a wave-function collapse is physically possible considering quantum mechanical evolution only permits unitary, that is non-collapsing, time-evolution). That means most "interpretations" do not pass the test of logical consistency since otherwise there would not be any such paradoxes.
Even with regard to experimental tests, we have at least two: The violation of the Bell inequality has been experimentally demonstrated, which is a test against hidden local variables, which would otherwise remain fair game for outlandish "interpretations." And a simplistic form of Schroedingers cat can be realized in a 2-qubit quantum computer, where modelling decoherence as interaction with an environment (that could be a real uncontrolled environment or simulated via more qubits) provides an experimentally verifiable detail theory of just how the cat would decohere out of its curious superposition. If you like, that constitutes an empirical test that the Schroedinger cat paradox is not really a paradox and any interpretation that is unable to resolve it must be an incorrect or at least incomplete theory.
Finally there is the issue of the recurrence time. Since quantum mechanics only allows unitary transforms, essentially rotations (and reflections) in a high dimensional Hilbert space, it predicts that everything repeats eventually, although most likely, due to the high dimensionality, only after a time that is mind-bogglingly huge even when compared to cosmological timescales. That is at odds with thermodynamics and relativity (at least if that is valid for ever expanding universes). There obviously must be tests for it, but finding them is surprisingly difficult. For example, even in theory waiting out the recurrence time is frustrated by the fact that if it exists as such, all notes and memories would have reverted, and we would again wonder if we should start the experiment for the first time ever! Yet on systems small enough that we can isolate them sufficiently from the environment to have short and observable recurrences (that experimentalists have come to call "revivals"), they demonstrably occur. At least to the extent that you consider this good enough to be at least a partial test of recurrence for the universe as a whole, this is of course at odds with any postulate of wavefunction collapse.
A: Regarding the interpretation of QM, there are several schools of thought. Apparently Asher belongs to the "just shut up and calculate" school.  He knows that classical intuitions do not suffice in trying to understand QA.  But your term "objective meaning" needs to be clarified since in QM, measurements of properties of an object (say an electron) cannot be independent of the system or observer doing the measurement when the measurement is made.  Can there be such a thing as an objective meaning when the meaning must necessarily, for humans, be a narrative saturated with the subject's own embodied metaphors? I submit that an understanding of any object, especially one that cannot be directly observed, cannot be entirely purged of subject.
Here are that minimum number of postulates I obtained from my on-line MIT course with professor Adams (which is really great): QM, lecture 3.


*

*The configuration or state of a quantum object is completely specified by a wavefunction denoted as $\psi(x)$.

*$p(x) = |\psi(x)|^2$ determines the probability (density) that an object in the state ψ(x) will be found at position $x$.

*Given two possible states of a quantum system corresponding to two wavefunctions $\psi_a$ and $\psi_b$, the system could also be in a superposition $\psi = \alpha\psi_a + \beta\psi_b$ with $\alpha$ and $\beta$ as arbitrary complex coefficients satisfying normalization.
