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When the phrase "in principle" is used to explain a concept in physics, is a philosophical argument being made? If yes, what is the philosophical argument? If no, what is meant by "in principle" and what value does it add when it is used to explain a concept?

Some examples of the use of the phrase "in principle" (highlighted yellow):

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    $\begingroup$ I'm not sure this is a physics question. The usage means exactly the same thing it would mean in a text on any other subject. $\endgroup$
    – jacob1729
    Nov 3, 2020 at 15:49
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    $\begingroup$ I’m voting to close this question because it is not about physics. $\endgroup$ Nov 4, 2020 at 11:18

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The phrase "in principle" means that the action being described is hypothetical, usually assuming certain ideal conditions. It contrasts to an action performed "in practice", which refers to actually carrying out the task with all the real-world complications that arise.

The use of "in principle" implies that the task may be more difficult, or in fact practically impossible, when actually carried out.

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  • $\begingroup$ So would it fair to say "in principle" is synonymous with "hypothetically"? Could the above examples have "in principle" replaced with some form of "hypothetically" or would there be some meaning lost if that were to be done? $\endgroup$
    – Armadillo
    Nov 3, 2020 at 17:40
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    $\begingroup$ @Armadillo 'In principle' seems like a generally stronger version of 'hypothetically'. Like "In principle, we can enumerate all of the prime numbers." – that's true, in principle, if we had a computer with an infinite amount of memory and could wait an infinitely long duration. In my mind, 'hypothetically' is used more for (somewhat) plausible scenarios rather than (probably) impractical or implausible possibilities. $\endgroup$ Nov 4, 2020 at 0:44
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    $\begingroup$ As the old saying goes, "In theory, there's no difference between theory and practice, but in practice, there is a difference". $\endgroup$
    – PM 2Ring
    Nov 4, 2020 at 3:52
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    $\begingroup$ @Armadillo - 'hypothetically' is not quite right, as it implies that we're hypothesizing how something works, which is not the case. In the examples you gave the prerequisite understanding of physics or the logic of the experiment is already established - that's what is meant by "in principle". I.e., the phrasing "the approach is straightforward in principle" means that according to these principles just established/outlined, here's what the approach consists of - it's straightforward in itself, but in practice you may have to worry about extra things to actually get it done. $\endgroup$ Nov 4, 2020 at 4:20
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    $\begingroup$ @Armadillo - e.g., as an illustrative (but perhaps extreme) example, the principles behind the approach LIGO (gravitational wave detector) is based on were worked out throughout 1960s, but to actually make it happen, it took ~50 years to develop the necessary technology and work out all the kinks. $\endgroup$ Nov 4, 2020 at 4:32
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"In principle" things are things which can easily be derived from the fundamental principles of the model. This tends to get used in situations where the real life application of this is more complicated.

As an example from my computer science background, if given a matrix problem $Y=MX$, it is, in principle, possible to solve for $X$ given $Y$ by inverting $M$, so long as $M$ is non-singular. However, in practice, we often run into "almost singular" matrices which are mathematically proven to be not singular, but are incredibly close. As a result, sources of error tend to start to dominate the calculation of $M^{-1}$, yielding unwieldy results. (this is a big deal in computer science because we don't typically operate on real numbers, we operate on "floating point" numbers which are an approximation of real numbers, and those approximations add up in almost-singular situations)

One common usage of "in principle" in physics is when the test apparatus needed to collect all of the information is unrealistic. For example, in principle, one can predict the behavior of a macroscopic object by observing the state of all of its microscopic parts. However, in practice, this proves impossible because you can't cram enough test equipment in place... or because you can't convince your boss to buy just that much expensive hardware for a test!

Another common usage is in systems where the model is hand-waving away chaotic effects like turbulence. This can often be a very good model, but when you start trying to measure the data you need, you induce turbulence by accident.

Informally, "in principle" could be thought of as any system where the math says it should be easy, but the engineers' and technicians' eyes go wide when you suggest the contraption needed to test it!

As a fascinating contrast, consider predicting the weather. The weather is a famously chaotic system. For a long time, we thought that perfect weather prediction was possible in principle, just hard in practice. However, thanks to the work of Edward Lorenz, we discovered that weather was chaotic (indeed, discovered chaos theory as a whole). In fact, it turned out that long term weather prediction was not possible, even in principle.

Now there's a fascinating study into how one controls chaotic systems, perturbing them to keep them out of the chaotic regimes. Thankfully, nobody has done it to the weather, yet!

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    $\begingroup$ Edward Lorenz doesn't have a "t" in his last name, unlike Hendrik Lorentz. Thus we have Lorenz attractor, but Lorentz transformation. $\endgroup$
    – Ruslan
    Nov 4, 2020 at 9:21
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    $\begingroup$ This is especially important when discussing Lorentz-Lorenz equation ;) en.wikipedia.org/wiki/… $\endgroup$
    – Roger V.
    Nov 4, 2020 at 10:25
  • $\begingroup$ @Ruslan Thanks for that catch! Fixed! $\endgroup$
    – Cort Ammon
    Nov 4, 2020 at 15:07
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It's important to be aware that the phrase is by no means limited to physics, and it means the same thing there that it does in other contexts. It does not mean the same thing as "hypothetically". Instead, you use it when you have a simplified model for a situation, and the thing is possible in that model, even if it isn't possible in the more complicated realm of real life. You say it is true "in principle" because it follows from a set of principles. That can be valuable to illustrate the principles even if other complications make it impossible in practice.

When you say that something is hypothetical, by contrast, you are focusing on its presently unknown state. In fact, I would even go so far as to say this: You use "In principle" when something would work if a known valid model actually held in perfect generality. You say "hypothetically" when something follows from a model whose validity is still to be evaluated.

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In principle is the opposite of in practice. That is something may be easy/possible in principle, but hard/impractical to do in practice. For example, finding roots of a 4-th degree polynomial is possible in principle, but is is rarely done in practice as the expressions are cumbersome and it is often easier to resort to numerical procedures.

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Consider the following quote from Dirac,

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that the exact application of these laws leads to equations much too complicated to be soluble.

One could say that in principle, in order to describe any chemical reaction (for example), one merely needs to write down the Schrodinger equation describing all of the atoms in the system, and then solve it, et voila, all of chemistry has been reduced to physics. Of course in practice, even if one actually wrote down the equation (which is, again in principle, possible to do), actually solving it is entirely beyond our capability for anything more complicated than the Hydrogen atom.

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