There is no measurement problem…

As there is an obvious lack of pertinent information about this subject and as I am relatively tired to do something else at this late time and because tomorrow I have a trip to a conference I will focus now on a relatively simple but very abused problem… The wanna be “measurement problem”. 

The people can be divided in physicists and non-physicists. This is not the only division but it makes sense at this moment. The non-physicists may be passionate about physics while having little technical knowledge about the subject. They listen to what physicists say and try to understand things assuming physicists know more… Sometimes this might be true, sometimes not and sometimes physicists simply have to profit from keeping anyone they can at a high level of ignorance. 

This might be the case with the so called “measurement problem”. Now, in order to understand what this is about one should go back some time, at the beginning of the past century when experiments of all sort started showing that questions assumed to have been formulated correctly were in fact ill-defined… These were the first years of quantum mechanics. 

One of the observations was that specific questions about a system and its parts were not perfectly definable in an absolute sense and all together, independently. Moreover, one observed that while single measurements were fundamentally unpredictable, there was some sense one could make out of the statistics of many measurements performed in contexts as similar as possible. 

At that moment it became clear that while for some questions a single measurement could in principle give a pretty much ok answer, in most of the cases, additional information was encoded such that it became visible only after performing many experiments and making a statistics. This happens because the questions themselves determine a part of the answer. For example, take a particle of spin 1/2. One knows from general laws that the spin of a particle is determined by some fundamental laws of nature. However, there might be another object that can in fact be observed, namely the projection of that spin on an axis. However, that projection can only take 2 values : +1/2 and -1/2 (of some units that I never care about)… Now, surely, the projection of a spin on an axis is a measurable outcome and it is observable but cannot be defined as a “state of the object” in the absence of a given axis. As the choice of an axis is arbitrary there is no law of nature to tell you what projection you will get, picking this or that axis every time. You can of course prepare the experiment such that your spin 1/2 particle will give always +1/2 when measured with a GIVEN axis but then, you are free to change that axis. The point is, there is no “a-priori” state of a “projection upon an axis” if there is no axis given. 

This principle must be really well understood: for example the question “what is the color of the night?” might sound poetical, even philosophical, but still, it is ill defined unless you specify something else… 

Ok, so, say, you pick an axis and with your experiment that doesn’t care about spin projections you start making measurements. Your statistics will show 50% of the cases with spin up and 50% with spin down (say). 

The experiment is completed and the problem is solved… 

Now come the “measurement problemists” into the debate. They that as long as they measure the spin with respect to their axis as being up the real physical state of the spin projection must have been up beforehand… Of course, stated in this way, their objection is meaningless… again, what axis? There is no axis on which to project unless you use an apparatus with an axis in it… But, they say, no, there was some spin that was like an arrow that was actually oriented the way I choose to put my apparatus… Really? Then let’s take another apparatus, somewhere further on the path of the same particle and rotate it with say, 23.4773 degrees to the left… What will you get? Well, according to the angle you will get either a spin projection up on the new axis or a spin projection down on the spin axis… there are no intermediate situations, that is the law of nature… The two outcomes will have different statistics in a probabilistic experiment but you don’t want to know about statistics… you want to know what the spin projection is in an “absolute sense” and get some idea what the “actual spin orientation of that thing” is… What you get is … well… one of the two situations: up or down… nothing in between… Was there a state before that measurement? well… it was a state defined with respect to the previous axis. The new axis changes the problem for the single electron… 

Ok, say you are a diehard skeptic or you just got a large grant allowing you to do “research” in this field and you want to keep the public opinion focused on the “mystery” because you want further funding for doing nothing… 

Then, the measurement pseudo-problem reveals itself in another “situation”… What these strange people say is that the wavefunction is a physical object that propagates through space etc. That wavefunction however is nothing like that… in fact, it contains all the information about all possible outcomes and all these outcomes are propagated in some perfectly local and deterministic way from one measurement to the next. Fact is, the wavefunction is an “expectation catalogue” as Schrodinger put it… it is the maximal set of knowledge we have about the system and it encodes all possible outcomes. When we measure the property of the system we give it physical meaning. Of course, some states of the system have physical meaning in any situation. For example electrons have spin 1/2 independent of measurement axes etc. So, the wavefunction (expectation catalogue) for that will be only 1/2 and that’s it… However, for the spin projection one has to consider the interference of more than one possible outcome. One locally propagates both and interfere the expectations through the statistics of the outcome. The answer quantum mechanics answered perfectly is “how do our expectations correlate?”… This is a very important question as there was a problem in deriving this via classical probabilities. 

The “measurement problemsists” say that the wavefunction is a “state of the system” and say they want to know what happens to the wavefunction “of an electron” when its spin projection is “measured”… See, there are already a few mistakes… the wavefunction is not of ONE electron… it is the wavefunction describing expectations for a statistics of outcomes involving many electrons… There is no “jump” in any sense in a physical substance when a measurement is performed… The measurement just adds the “little extra” that makes a question well defined… 

However, there were LOTS of experiments trying to measure the actual “physical” wannabe “process” in which the electron hops from a state of being “up and down at the same time” (lol) to a state of being only “up” or only “down”… these experiments were all failures and the laws of nature had a fun time laughing at the stupidity of the funding bodies of those “experimentalists” or “theoreticians”… 

I think that is all for this night… 


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