There are two ways of doing research. Either we have some experimental observations (facts) we do not understand and therefore we are looking for an appropriate theory to explain them, or - contrary and less often - we have some theory and we are looking for its experimental confirmation, especially its predictions never investigated before. In both cases only the negative result is certain. The funny thing is that quite often we do not need high accuracy to see such negative result. Positive result, on the other hand, is never 100% certain, so it's better to say that "the experimental results are in agreement with such and such theory" or "don't contradict the theory" (but never: "confirm the theory"). If you are the experimenter, then your task is to present any obtained results with *reliable* estimates of uncertainties. Without such estimates the result is simply worthless, see this:

"The number pi (a ratio of circle's circumference to its diameter) is roughly equal to -1".

True or false?

If I gave you the answer (which I know!) could it be of any help to you? To me the question expresses nothing reasonable. But, perhaps, you only failed to make your point clear due to language limitations? Then a second attempt would be welcome.

The very beggining of your question asks about the -forever- difference between a controlled expmeriment and real-life results, along with the -again, forever- problem in scaling anything. The last of your question talks about variability and/or standard deviation. At least that's what I could understand. As dear Ulrich said before, rephrasing would be appreciated.

There are two ways of doing research. Either we have some experimental observations (facts) we do not understand and therefore we are looking for an appropriate theory to explain them, or - contrary and less often - we have some theory and we are looking for its experimental confirmation, especially its predictions never investigated before. In both cases only the negative result is certain. The funny thing is that quite often we do not need high accuracy to see such negative result. Positive result, on the other hand, is never 100% certain, so it's better to say that "the experimental results are in agreement with such and such theory" or "don't contradict the theory" (but never: "confirm the theory"). If you are the experimenter, then your task is to present any obtained results with *reliable* estimates of uncertainties. Without such estimates the result is simply worthless, see this:

"The number pi (a ratio of circle's circumference to its diameter) is roughly equal to -1".

True or false?

Any good theoretician will not believe his results, but will likely believe the experimental results, as he knows nature is more cleaver than he is. Any good experimentalist will not believe his experimental results and will not believe the theory either, as he knows nature is more cleaver than either! :-) Thus both will strive harder for facts and for falsifiable hypothesis (as opposed to verifiable ones which is very different).

http://en.wikipedia.org/wiki/Falsifiability

Marek Gutowski's answer remembers me the writings of the Nobel Laureate Richard P. Feynemann regarding theories, experiments and results. It's a good guide for all of the Researchers.

Dear Marek Gutowski and Kirk Flippo

Thanks for explanation.

@Dear Victor Ponce

Please write details about what u wrote in few lines.

The theory has its own limitations of having certain approximations and experiments have errors. Therefore a man will always be in an uncertain nature which he has to follow i,e he is in the limits of uncertainty. Therefore it is very hard to find a theory without any limitation.

To me, physics is done by succesive approximations with increasing precision. This applies both to theory and experiment. In particle physics, theorists struggle to compute ever more precisely the theoretical values (L.O, NLO, NNLO etc), whereas the experimentalists seek to reduce their error bars at a minimum.

The one challenges the other to improve precision.

However, we only know the 'truth' within our limited precision.

I'm not sure whether my following comment applies strictly to the current question, but at least I hope it does. Well, I cannot fully agree with Emmanuel's Chaniotakis point of view. Successive approximations, or rather better and better testing (polishing?) existing theories and measurement procedures, is important and indeed necessary. Fortunately physics also has another face, not related to this "better mouse trap" , purely technical approach. Think about electromagnetic induction law (by Faraday), discovery of superconductivity, creation of relativistic mechanics or even the simple observation of Brown's motion. None of those milestones were the result of successive approximation procedure (or the result of improved "resolving power"). Isn't it exactly this part of physics which makes it so fascinating and attractive?

It is the supposition or approximations or we can say some assumptions of a theory which are themselves the result of some other theory, philosophy or logic. Therefore if a theory gives accurate results, we have to believe on the assumptions already made. The assumptions could be wrong also but when it gives accurate results indicates itself the assumptions are accurate. These assumptions break the science itself into parts so as to understand a part of science. Therefore we can say science is infinite and we people on this earth initialize somewhere and stop somewhere.

Dear Dr.Gutowski,

In defence of my 'mouse trap' argument I would like to state these (and allow me to speak only for experimental physics with which I have larger experience than theory):

- To improve the precision of your experiment there are two ways: either wait till more sophisticated ecquipment is provided, or do a better experiment. e.g. if you want to do electron spectroscopy, you can use a conventional inorganic scintillator. But if you realise that an organic one has lower Z and therefore reduces the backscattering and bremsstrahlung contributions, then there you have it! To me this is BEAUTIFUL PHYSICS!!

- When measuring a quantity with its error , to reduce the error, you need to control your background and your setup the best way possible. As my old supervisor used to say, "If God controls the signal, the experimentalist controls the background" . This is the quintescence of the attempt of human itelligence to probe the innermost of nature. And to me this is thrilling!

About the discoveries you refered to , they are all most exciting!!Both the theoretical insight of Dirac which opened a brand new branch of physics and the observation of new phenomena are sources of pleasure in physics.

However what excites me most is the fact that using simple physics arguments one can explain phenomena and predict undiscovered ones! Take for example Feynmann's parton model - extremely simple in inspiration, but so succesful! Or Einstein's theory of specific heat- or even his realization that Planck's law can be applied at the photoeffect.

I heared many times the same argumentation that you described about theoretical and experimental specialists. I agree with you, it is an important problem in a lot of different fields of Physics. But in my opinion this situation mainly appears because generally theoretical and experimental groups works separately, by this way theoreticians do not have a clear idea about how experiment really works, while pure experimentalists do not know all details of the different theoretical models. Generally in the lucky group formed by experimental and theoretical staff the cited situation disappears. In fact a lot of times the experiments are proposed by theoretical part of the group with detailed description of the real possibility in measurements by using simulation tools. The only way to solve the question is to work together considering our limits in experimental observation and in theoretical estimation.

Just a small observation that always needs to be made regarding theory, experiments and reality. All theories are a simplification of the observed real world. They have validity within certain constraints. These simplified models allow us to think, use mathematical tools etc. and extrapolate into the unknown and consequently make experiments to test or disprove these extrapolations. But extrapolate to far and You are out on thin ice. If on a lake , You may actually fall trough the ice if You extrapolate to far. In my mind an efficient scientific process is iterative between experiment and theoretical modelling and extrapolations. But I agree that this is frequently poorly understood.

One point to discuss is that at present, there is a plethora of theoretical models about SUSY for example. The experimentalist doesn't really need to know all the background of each model. He should rather understand the main content and understand the signatures which he is searching for. He must optimize his tools and go for it.

This plethora is actually the reason I really don't like SUSY:P

1. Any theory is, in physics, a mathematical representation of the system which is studied. We expect that it is efficient, but also gives a sensible interpretation of what happens. This is a simplification, and there is no trouble about that, as long as we keep in mind that this a representation of reality, not necessarily the reality itself.

2. But that means that we need a model, starting in the step of measure, in order to decide what we want to measure, and how we will organize the measures. And this step, the model, is crucial. If a field is involved, you can assume that it is constant, and measure it in one point only, but doing so you loose the possibility to check your assumption. If you want to measure a function, you will at best get a statiscal estimation from a finite number of points. So for some problems uncertainty is unavoidable, but manageable.

3. The issue of models (meaning what lies between the data and their interpretation) is crucial. It can be proven that the usual "axioms" of quantum mechanics come from the way the models are built, including the Schrödinger equation. One can always assume that reality follows our model, but actually our models are not neutral in this.

4. To rebound on one example given in this forum : if a physicist claims that the ratio of the circonference of a circle to its diameter is a rational number, he can certainly provide very accurate experimental results to sustain its statement.

I wish the things were so obvious and easy: this is an experiment and that is a theory. Separate, but complementary. But now we have phonons. Where do they belong? You can't investigate ("see") them outside the sample - they simply do not exist in vacuum or in air. They are products of pure imaginations (theory, with math exceeding slightly familiar arithmetic operations on real numbers), yet they posses many directly measurable properties - like any true particle, or material object. Continuing: isn't it so that we are striving to purely imagined world, nicely following our theories, as numerous experiments seem to confirm? Is this still a reality? And if so, then to what precision??

Dear Mr Gutowski,

The key of a model is to define "variables" which are both linked to some physically measurable phenomenon, and mathematical objects meant to take place in some formal representation of what happens. This is not easy, and this is where all the talent of the physicist lies. And a theoretical model is usually required. But, once the theory has been chosen, the variables precisely defined, they provide the framework to organize the raw data which are the output of the measurement process. And this is the intermediary step - between measures and equations - that I have studied, and from there deduced the "axioms" of Quantum Mechanics.

A model is always a representation of the physical reality. It is usually a simplification. It can be pertinent or not. The variables which have been chosen, may not show the expected relations when the measures have been done,. But this is precisely the meaning of the experimental proof. A model depends on the tools available to make the measures, but also on the mathematical tools to express the variables, and pick up the right definitions. One of the main issue of the Quantum World is that we do not have these tools : continuing to represent a particle as a rotating solid with a momentum is certainly inaccurate, when we know that it can also behave as a wave. But - as far as I know - we do not not have the right variables to represent their dual features.

We must not be shameful of the idea that our models, and the theory which sustains them, is just a representation of the physical reality. What we must strive to do is to provide a theory and a model which are efficient (give accurate previsions), easy to use and easy to understand, at least by the workers in the field. The best example of such a model is the atomic representation in chemistry : a simple line such as :

H2+1/2O2->H2O + 286 kJ/Mol gives almost everything that we need, is closely related to the physical reality (even if this is a simplified one), and easy to use and understand.

The wrong answer is to state that the reality IS what our models prescribe. To say that we cannot measure simultaneously the position and the momentum of a particle because their observables do not commute is a violation of this basic rule (and at the macroscopic level, both variables can be observed simultaneoulsy).