One needs contact to reality to check whether a theory is about this reality. But this is independent of my argument.PeroK said:How do you know what mathematical paths to follow? Unless experimental evidence tells you you are on the right track?
I literally could not have said this any better.A. Neumaier said:It is usually not very well defined, but in classical physics only for practical reasons, not for reasons of principle.
In classical physics you have complete control over the universe if a classical action for it is given. You can (in principle) define exactly what an observer is, by specifying which particles make it up. Then you can (in principle) define exactly how a proposed measurement of an observable X to be measure is done, by specifying which composite observable R - created solely from the observable making up the observer (a screen or a pointer) - defines the measurement result of measuring X. Then you can (in principle) analyze exactly to which extent the measurement result R agrees with the exact value of the observable X. It will never be exact, except by chance. But you can use statistical mechanics to work out (in principle) the mean (bias) and standard deviation (intrinsic uncertainty) of the error made. Then you can say with full mathematical clarity how accurate your measurement is.
Thus everything is well-defined in the classical theory - only practical considerations (keeping track of the atoms and doing the computations) prevent this for being actually done routinely. Instead one uses coarse approximations, like everywhere in physics, to simplify the burden. But there is no question of principle.
This is why deterministic classical mechanics does not suffer from the same philosophical problems as quantum physics. There are some with the stochastic version, due to the problem of saying what probability is, but this is no fundamental issue since classical mechanics is deterministic, and probability enters only through the approximation process.
Measurement is something an experimentalist is doing in the lab. It's not defined by mathematics but by real-world constructions in the lab! The observer's choice is as well defined by these real-world setups in the world. What's measured is due to the construction of the measurement device. Although the construction of the device indeed uses some theoretical input about what you want to measure to answer some question about phenomena finally the device defines what's measured.A. Neumaier said:I haven't seen any definition of measurement that is based on the mathematical formalism of QM alone.
It would have to be something that could be applied to a mathematical model of an imaginary world governed by the QM formalism, so that mathematical statements *theorems) are proved about measurements done according to that definition that tell that a particular multiparticle system actually measures what it is claimed to measure.
The observer's choice is also an activity of the physical system called observer, hence must be part of the model of the measurement process.
That's why there is a measurement problem. It consists in formalizing the concept of measurement in a similar way same way as we know how to formalize the concepts of force, energy, information, etc..vanhees71 said:Measurement is something an experimentalist is doing in the lab. It's not defined by mathematics but by real-world constructions in the lab!
I find that statement very strange. A was undr the impression that there is no difference between the experimental apparatus for a classic double slit experiment (which does NOT need QM at all for explaining) that for a QM one. Unless you consider dialing down the intensity of the light some sort of "real-world construction".vanhees71 said:Measurement is something an experimentalist is doing in the lab. It's not defined by mathematics but by real-world constructions in the lab! The observer's choice is as well defined by these real-world setups in the world. What's measured is due to the construction of the measurement device. Although the construction of the device indeed uses some theoretical input about what you want to measure to answer some question about phenomena finally the device defines what's measured.
Sure, but after all the quantities are defined operationally by real-world measurement devices. That's precisely what the metrological institutes do to define units for various quantities, and the basic definitions (representations by real-world measurement prescriptions) of the units change due to technological progress. E.g., the unit of mass, the kilogram, in the SI is not anymore accurately enough by the prototype kept in Paris, given the much better accuracy reached by redefining the unit via another measurement prescription, in this case by defining fundamental conversion factors like ##\hbar##, ##N_A##, etc.A. Neumaier said:That's why there is a measurement problem. It consists in formalizing the concept of measurement in a similar way same way as we know how to formalize the concepts of force, energy, information, etc..
Note that one can say the same about forces and fields as what you said about measurement. Forces and fields are something that experimentalists are measuring in the lab. It's not defined by mathematics but by real-world constructions in the lab!
But this describes the situation of 150 years ago.
In the mean time, forces and fields are defined by mathematics and not by real-world constructions in the lab! One needs the theoretical definition to find out what real-world constructions in the lab actually do measure, and how to calibrate the latter so that they measure as good as possible the quantities defined by the theory. One even changes the experimental meaning of basic procedures such as units of mass, time, and length in order that they fit better what theory predicts!
Nowdays we can do real-world double-slit experiments with single photons or particles, and these experiments cannot be described by classical particle or field theories but only by quantum theory, confirming the predictions of this theory with high accuracy. Physics is an empirical science, and theories are modified or even completely new ones (but that's very rare; it happened only twice since Newton with the discovery of relativity and QT) due to newly discovered observational facts.Boing3000 said:I find that statement very strange. A was undr the impression that there is no difference between the experimental apparatus for a classic double slit experiment (which does NOT need QM at all for explaining) that for a QM one. Unless you consider dialing down the intensity of the light some sort of "real-world construction".
What is measure is the very same "macroscopic/classic" thing. The real-world realization comes when quantum object are "resolved" one by one. Can't we say that the measurement problem comes from the fact that QM has zero power of prediction for one event, and start having more and more sense only to connect the "in between" behaviors of "identically prepared quantum" ?
Isn't the measurement problem the fact that reality is not made of ensemble (those exist only in the theory and your mind) but only of individual events ?
A. Neumaier said:In the mean time, forces and fields are defined by mathematics and not by real-world constructions in the lab!
What I meant to say is that even 200 hundred years ago all double slits experiments were already done with "individual" photons, we just didn't knew it.vanhees71 said:Nowdays we can do real-world double-slit experiments with single photons or particles,
Of course, only QT can explain how all these individual events coalesce to some ensemble behavior, and also explains so many other "spooky" ones. Nobody is disputing that.vanhees71 said:and these experiments cannot be described by classical particle or field theories but only by quantum theory,
Isn't that THE measurement problem ? That you need to add an "s", an unspecified number of "s" before the measurements reach any significant accuracy.vanhees71 said:confirming the predictions of this theory with high accuracy.
Indeed, and the only new observational fact is that some part of nature "comes in packet". And QM brilliantly describe an ensemble of measurements. But observational data are made of series of events/facts. I may understand your view about when an ensemble measurement start, but not when it ends. I need a number of events, and "infinite" is not something I would accept without calling it a "problem".vanhees71 said:Physics is an empirical science, and theories are modified or even completely new ones (but that's very rare; it happened only twice since Newton with the discovery of relativity and QT) due to newly discovered observational facts.
and in addition they are defined theoretically by the theory. One does not replace the other. Both aspects must be present for a complete understanding.vanhees71 said:the quantities are defined operationally by real-world measurement devices.
(quoted from here) and Gerard t'Hooft,Steven Weinberg (in 2017) said:The development of quantum mechanics in the first decades of the twentieth century came as a shock to many physicists. Today, despite the great successes of quantum mechanics, arguments continue about its meaning, and its future. [...]
It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means.
(quoted from here).Gerard t'Hooft (in 2015) said:When used correctly, it was found that the outcome of an experiment can be predicted precisely, but the answer often comes in a statistical form: upon repeating the experiment many times, statistical distributions will be found, and only those can be predicted by the theory, not the outcome of a single observation. Finally then, one could ask: what is the cause of all these observed statistical fluctuations?
No, 200 years ago there were no one-photon sources available. It's not easy to prepare Fock states of photons!Boing3000 said:What I meant to say is that even 200 hundred years ago all double slits experiments were already done with "individual" photons, we just didn't knew it.
I didn't say anything about Fock State. Maybe you mean that the Taylor experiment of in 1909 is all about Fock state ?vanhees71 said:No, 200 years ago there were no one-photon sources available. It's not easy to prepare Fock states of photons!
Boing, is there a ODE that describes light composed of entagled photons? If so, can you give it here?Boing3000 said:I didn't say anything about Fock State. Maybe you mean that the Taylor experiment of in 1909 is all about Fock state ?
I am quite sure that you are not saying that light is not "made of" individual photons (meaning un-entangled), so the only conclusion I can draw here is that QM predict a different interference pattern between ensemble of photons only being able to interfere with themselves (in a path integral way), or being able to interfere with some non-Fock "companion" in some more classical way (something I am unaware of, thus my "individual" photon statement).