I heard all 'interpretations' of quantum mechanics give exactly the same answer to every measurement so they are all equally correct.

It is common for physicists to say that the interpretations all give the same results, but they are wrong.

The interpretations fit into a couple of different categories. One interpretation takes the equations of motion of quantum mechanics, e.g. - the Schrodinger equation or Heisenberg equations of motion. That interpretation is called the many worlds interpretation of quantum mechanics (MWI). That term is used because it predicts the existence of structures each of which approximately resembles the universe as described by classical physics:

https://arxiv.org/abs/quant-ph/0107144

https://arxiv.org/abs/quant-ph/0104033

The MWI is experimentally testable, false claims to the contrary notwithstanding:

https://arxiv.org/abs/1508.02048

Some other interpretations are distinct physical theories that make different predictions and might in principle be distinguished from quantum mechanics by experiment, such as the grw collapse theory and the pilot wave theory:

https://arxiv.org/abs/0911.2823

https://arxiv.org/abs/1204.4325

The other interpretations, the Copenhagen interpretation (CI) and statistical interpretation (SI), are just bad philosophy dressed up as physics.

The CI claims that quantum mechanics should be used to calculate some stuff but is incomprehensible so you have to describe other stuff in terms of classical physics. But this position is deemed by fiat somehow to be equivalent to quantum mechanics, i.e. - the MWI. However, since any experimental result is an explanation of what happened at a particular place and time, not just some figures arbitrarily written on a page, the claim that quantum mechanics is incomprehensible rules out making any experimental predictions using the theory. If it is not possible to explain what events are taking place in an experiment, then it is not possible to tell whether the experiment is working. As such, the CI makes no experimental predictions.

The SI claims that quantum mechanics just makes predictions about probabilities. In reality, the quantities that are commonly described as probabilities only obey the rules of probability in some specific situations and break those rules in many experiments:

https://arxiv.org/abs/math/9911150.

So the SI appears just to be contradicted by reality. The SI's adovcates like to claim science is just about predicting experimental results. This strategy is not viable since experimental results have to be explanations not just stuff some guy wrote down for reasons explained previously.

oooohhkaaaayyyyyyyyy thanks for answering alanf ^-^ – BCLC – 2017-06-05T09:20:45.267

The MWI comes into being pretty late in the life of quantum dynamics for you to claim it is the basic theory. In fact it was largely dismissed as a model for decades. QFT is the rationalized version of CI, which you can give as much strife as you like for just being incomplete because it was first. But it, and not MWI, is what the current stable interpretation grew out of. – None – 2017-06-05T17:32:25.540

@jobermark The MWI is a consequence of the equations of motion of QM. The fact that people refused to acknowledge says more about them than the logic of the situation. QFT is not any kind of version of the CI since the CI makes no claims about reality beyond QM somehow being unsatisfactory. But, as with QM, the existence of the multiverse is a consequence of the theory https://arxiv.org/abs/0909.2673.

– alanf – 2017-06-05T20:22:20.837Aside from not answering the question of comparing interpretations of probability and quantum mechanics, this post is filled with personal opinions misrepresented as established facts. The opinion about MWI goes too far to be shared even by its supporters, like Sean Carroll, and those about CI and SI are just out there. It is regrettable that the OP hastily accepted this non-answer. IEP has an article on major interpretations of quantum mechanics, which should be consulted instead.

– Conifold – 2017-06-05T22:45:27.097@Conifold okay unaccepted. Forgot this isn't maths se lol thanks I guess – BCLC – 2017-06-06T04:22:55.410

The relevant issue is whether the interpretations of qm give the same answers to all questions. They do not as I explained. Also, what I said here does not go much beyond this http://www.daviddeutsch.org.uk/many-minds-interpretations-of-quantum-mechanics/, which describes the CI correctly as nonsense. I made the rather milder observation that it just doesn't make any experimental predictions.

– alanf – 2017-06-06T06:25:03.930