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Suppose I have some physical process to use in some experiment. For instance, let's consider just looking at an object to measure its position.

The basic modelization for this is to consider geometric optic : the light goes along a straight line from the object to the observer.

But this is of course not the actual situations. You can find gigantic laundry lists where this model breaks down with effects of various sizes :

  • The light does not move in a vacuum but in a continuous media, making its path not actually a straight line, its path depending on the local pressure, temperature, composition, etc, of the media it goes through.
  • The geometric approximation is only true in the limit of short wavelengths.
  • The light will get scattered during propagation due to various effects
  • The geometry of the underlying space may fail to be Euclidian

Those effects will all influence light propagation to some degree of various sizes. There are also effects on the measuring apparatus (vibrations, thermal dilation, etc) that can affect this modelization.

The question is, are there systematic ways of trying to predict such effects in a given experiment? I know that such effects are difficult to predict in such circumstances, but are there such things as listings of such effects to watch out for in experimental settings?

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For scientific purposes, there will always be conditions which have to be either assumed perfect or ignored for the purpose of simplification.

A humorous analogy to this are typical sentences such as "Assume the cow is spherical" in numerous textbooks. This should hint at first glance that, in many cases, trying to control for every single situation that can and will affect your experiment, you should take care of it. In many cases, you can also state "the effect of X is negligible due to ..." and explain why you neglect such effects.

The light does not move in a vacuum but in a continuous media, making its path not actually a straight line, its path depending on the local pressure, temperature, composition, etc, of the media it goes through. The geometric approximation is only true in the limit of short wavelengths. The light will get scattered during propagation due to various effects The geometry of the underlying space may fail to be Euclidian

While these are for the most part true and valid concerns to have, you have to first understand what you are trying to study and why it matters for that specific case.

  • First, while air is not necessarily vacuum, for most intents and purposes, let's say, in lab conditions (controlled temperature, small range e.g. an optical setup) you can say that the effects of temperature and pressure changes are negligible. However, for space telecommunications, these assumptions are not valid anymore, as temperature and pressure are no longer local and they will definitely affect the experiment: Scale is important.
  • It is true that geometric optics are valid for a few wavelengths. However, again, you have to think about the scale: Are you working with a laser? Then your wavelength of interest is limited so you can simplify some conditions (refractive index can be a scalar instead of a function of wavelength, etc.). Additionally, if you are working in laboratory conditions, your assumptions can be more closely controlled.
  • The other two points are a repeat of the former two statements

Here it is important to care for two things: Which variables you can control, and which ones you can't. If you are unable to establish laboratory conditions, then what are you able to control?

  • Maybe you don't have temperature control in your laboratory: Then, you have to measure the temperature and if the fluctuations are large, state that the laboratory conditions are unstable and uncontrolled.
  • Maybe you are planning a field application: In this case, you should first have controlled laboratory conditions, and then it is possible to understand better what fails (if so is the case).

A large part of scientific research is being able to control variable conditions and reduce the solution space as much as possible. If it is not possible to reduce the solution space, then most likely the experiment conditions are also not as well-defined and that will lead to unstable results. As soon as you can control certain variables (change temperature, change pressure, change the experimental conditions) you will be able to better understand the phenomena you are studying, and in the end find solutions to your problems that apply more broadly and in different conditions that may not have a large influence in your experimental data.

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