That a measurement problem exists was already clear in the first half of the 20th century. The question is how and why the quantum state wave, which is in fact a probability distribution, comes to an end. Probabilities are non-physical and therefore have the substance of a thought. Despite all the discussions, there is still no consensus between the physicists about the correct interpretation. Therefore I present here a very brief overview of the most common hypotheses each having their own club of supporters.
Hypotheses 1,2,3,4,5 and 7 try to save our image of an objective material universe. Hypothesis 6 is strongly inspired by virtual computer technology. The last two, 8 and 9, introduce the non-physical consciousness of the observer as an explanation. For the experimental proof that consciousness should not be ignored, read here. The order in which the hypotheses are represented is not an indication of their degree of acceptance by physicists.
1: Copenhagen interpretation of Niels Bohr and Werner Heisenberg
The quantum state wave is non-physical. This state wave collapses through a measuring instrument of sufficient size.
Criticism: Sufficient size has not been specified by Bohr. The double slit slide itself is undoubtedly a measuring device that is very large in relation to the quantum object but obviously does not collapse the state wave because then we would not see interference. Finally, every measurement system is always connected to the rest of the world.
The molecular unrest of the measuring device causes the state wave to collapse in such a way that only one of all these possibilities remains which then becomes the measured object. This is the reason that Qubits, the components of quantum computers, are cooled to near absolute zero and are mounted extremely vibration-free.
Criticism: Exactly the same objections as with the Copenhagen interpretation.
3: Hidden variables
The quantum mechanics would be incomplete. It is assumed that the quantum object always exists in material reality, but that we do not yet know the variables that would exactly describe its trajectory.
Criticism: The Bell tests have repeatedly shown that at least faster-than-light communication has to occur between entangled quantum objects. That is in direct conflict with Einstein’s relativity laws. Furthermore, the sophisticated nature of that supposed communication between quantum objects is still completely unknown. The fact that quantum mechanics is incomplete is also remarkable in view of its resounding success.
Everything that is possible also really happens. In this way we are rid of the wave of probabilities that is supposed to collapse into the measured object by a measurement . With every possible outcome of any event, such as the decay of a single radioactive atom, the physical universe splits into multiple physical universes, each containing a different possible outcome. A popular however rather anthropocentric variant of this is that the splitting into universes only happens with every decision we make, for example, whether or not to make a purchase.
Criticism: This hypothesis can neither be proven nor falsified. Assuming: 1 / the information content of the universe estimated by Seth Loyd, 1090 bits, and 2 / the smallest unit of time, the Planck time, of 5.4 x 10-43 seconds I arrive at a unlikely number of split-off universes per second. Furthermore, the recent findings in quantum biology, the still unexplained efficiency of the quantum phenomena in plants and animals, are a strong argument against these splits. See elsewhere on this site: Multiverse hypothesis disproved by quantum biology.
In super-selection it is assumed that super-positions of macroscopic different states do not occur, just like nature does not allow super-positions of different charges. Nature would then not allow a superposition of the quantum state of the quantum particle with the quantum state of the macroscopic measuring instrument.
Criticism: That nature does not allow something is not an explanation of the phenomenon in question but an explanation of not understanding. Here the workings of nature seem to be considered as an inherently closed box.
6: The Matrix
We are logged into a digital virtual reality world simulated in a computer of cosmic proportions. The laws of nature are nothing else but the rules of the software. This cosmic computer exists of course outside the physical universe, so it has to be a metaphysical computer. Logging out means dying (most of the time). This hypothesis provides an explanation for the digital nature of the quantum phenomena.
Criticism: It is unclear how we log in. Furthermore, this only moves the question about the nature of reality to the nature of metaphysical reality in which the cosmic computer exists. On the other hand, this is what physics always does, moving the question to the next perspective. Nothing really wrong with that.
7: Spontaneous collapse
The Schrödinger equation from which the quantum wave results is extended with a new natural constant making every physical system spontaneously collapsing the quantum state wave depending on the system’s size. The larger the system, the faster the collapse. This idea is one that could be measured by experiments with measuring instruments of increasing size. That is why this hypothesis seems falsifiable, for which it deserves to be tested.
Criticism: No system can exist absolutely separately from the rest of the world. A measuring instrument is not hanging in a vacuum insulated from the rest of the universe, but is attached to the laboratory table, to the floor, to the building, etc.
8: No collapse
The universe is one big entangled quantum wave that never collapses. The universe is therefore one large network of all possibilities in which every observer travels a possible trajectory and thus records his own history. This resembles the multiverse hypothesis of Sean Carroll rather closely. In this interpretation, however, there is no physical reality, only perceiving consciousness and a non-physical wave of chance.
Criticism: It is unclear how the interaction of the consciousness of the observer with that universal quantum wave takes place. Furthermore, it is a problem how two observers can agree on their observations. See Eugene Wigner.
9: Projection postulate by John von Neumann
Measuring instruments must also comply with the quantum mechanical laws, since they are composed of quantum objects, electrons, protons, neutrons, photons, etc. This implies that the measuring instrument should be still in the quantum wave state after the measurement. The instrument becomes entangled with quantum object. This develops into a chain of expanding quantum wave states. The human observer is the last in that chain of quantum states, but since man is ultimately also made up of quantum objects, his physical body cannot cause the quantum collapse. His body will be in an quantum wave state entangled with the total measurement chain. In fact, nothing that is in the physical material domain can collapse the wave state and therefore the quantum collapse should have a non-physical cause. The obvious candidate is our non-physical consciousness.
Criticism: Two non-red objects do not necessarily have the same color. The non-physical cause of the non-physical quantum collapse is just like this logical example not necessarily connected to the assumed non-physical consciousness. The deep question is whether something non-physical can have an effect on the physical since the non-physical must then have some physical components. Finally, the problem of several observers also arises here. See Eugene Wigner.
Read here on Quanta Magazine about a proposed – but not yet conducted – experiment that should provide clarity about the different hypotheses.
In short, so many minds, so many ideas. All these interpretations are still alive. The measurement problem is therefore still not satisfactorily resolved. Despite all those different interpretations, quantum mechanics is the most successful physical theory when you judge success based on its unrivaled accurate predictions. You can therefore permit yourself to ignore this problem in your laboratory. But from a philosophical point of view, the measurement problem is definitely an extremely important issue, namely about the nature of reality. We can try to formulate a hypothesis that contains and explains all phenomena. To do this we need first to formulate a strict set of principles.