What is the Relation and Correspondence of Theory to Experiment?
As most of this discussion is widely known from the end of XIX century and later since the famous arguments of Einstein raised to Bohr and his "orthodox" Quantum Mechanics co-authors largely against the Quantum theory shaky basics.
What is the physical Value we are seeking in our experiment?
We won't restrict ourselves in this section of our website to the continuum mechanics disciplines presentations/definitions only. Some interesting draws can be said on atomic and particle physics endeavors. And we do this below in -
Maintaining this point of view, at the same time in our scope, of coarse, be the values, variables serving to the physical fields of different scales (as of a Bottom-Up and of Top-Down sequence).
We need to accept, to seriously stick to this fundamental idea -
That the point of measurement and the value of physical field (considered in continuum sense or within any volume or “dot” in the experimental apparatus for plasma, fusion, particle physics) at this point should correspond one to another within the brackets of the given, considered physical theory and its scales!
Those fiercely debated arguments of the first half of the XX-th century regarding the sense, applicability and meaning of measurement see, for example, - Born (*1 - 1956), Brilluoin (*2 - 1956), and a measured value (variable) we must see under different and as, seems much more, pleasurable angle of view.
That is, when we talk, design a measurement, and try to perform a one with the most accurate set up, we need to recognize the boundaries of acceptable (explainable) model definitions of this/that particular scales physics. Thus, there is no sense to talk, argue about the great accuracy of this/that measurement unless we circle more or less strictly - what are the possibilities for this scale physics to measure the most accurate value?
Does it have any sense to talk about the "greatest" accuracy for that meaning in distance measurement when we are inside of conventional continuum mechanics measuring environment ~(10^(-8) - 10^(-3))m? No sense to talk even on that. Does it have any good meaning when we will be discussing the accuracy in measurements being made within brackets of the conventionally taught Standard Quantum Mechanics (SQM) (atomic scale physics) scales ~(10^(-15) - 10^(-9))m as the one scale set-ups and know that everything in the measured sample(s) is moving all the time? Or appearing and disappearing! _____________________________
Meanwhile, in the string theory the values are being played down and up to the ~10^(-35) m scales. Does it further mean not a waste of time when we'll be talking about subatomic accuracy when measuring the variables pertaining to the solar system scales (10^(9) - 10^(15))m?
Further going, What about galaxy scales? Do we need to keep in mind the atomic scale (usually SQM) phenomena and then Jump to the Light Speed years scale, or million Light Speed years scale, as astronomers and astrophysicists do?
And talk about Conservation Laws? And be surprised when these Conservations Do Not occur?
And, by the way, mostly workers apply the same Governing Equations (GE) to the phenomena of the great misbalance of scales?
For all that XX-th century and this XXI era beginning the discussions do not include the sense of physics of definite scales, otherwise those arguments in and around quantum mechanics were almost useless, unless we know how to connect, communicate, relate the accuracy and measured variables even in varied different scales physics? Even for neighboring ones? Which we do not know exactly even now!
So, keep up studying within the assigned and elaborated definitions of the assigned scales physics. ________________________
For example, the most practically known and felt issue of water (or liquid) flowing through the soil (sand on a beach, for example) or any porous medium. Do we mean when we think or talk about that flow of water which is occurring inside, between "these two" sand particles or around of "this" grain of sand? Or we think, feel and measure the obvious flow rate (or velocity) within this piece of sand (soil) medium together with the inside water of the overall size as of approximately (1 cm^(3)) or (10 cm^(3)) and containing the millions of sand grains ? Or even of (10^(0) - 10) m^(3) scale when talking on oil exploration ideas.
Obviously, we think about these latter scales and their collective outputs (due to great number of separate pieces of matter involved). ____________________________
That is - we mean and should measure the Upper scale (10^0 - 10) cm^3 or (10^0 - 10) m^3 phenomena. Meanwhile, the point is that this problem is the Two Scale problem at least and as such should be addressed not with the ad-hoc models (even spoken as the heterogeneous), but with the HtVAT as we see in the subsection some text (just part of a substantial studies) -
I would like to remind readers that the concept of difference between the Homogeneous and Heterogenous Media Experiments, Experimental basics came first when our studies using the VAT had been exploring this area (see below in References the partial list of related studies). That was natural to set-up the procedures for experiment and its data reduction using the same theory, the same governing equations as were used for theoretical investigations.
As we mentioned many times in this website, there are numerous methods and theories having been developed for Heterogeneous medium studies, at the same time those theories used for experimental method set-ups are still based on the Homogeneous Physics definitions, models, data reduction procedures, rules "of engagement," etc. And that's quite incorrect and suffice for getting wrong results.
More of that, as we discovered through the model developments and the practical examples, the mechanisms, the physical characteristics those surfaced only via using the Heterogeneous models and Governing Equations can not be seen while using the lower scale Homogeneous statements and definitions.
This is quite a strong statement, I understand this and I am trying to illustrate this incompatibility with examples in few areas. Few of the most striking examples I had encountered being at NATO ASI-2004, see in the section "Urban Air Pollution" remarks on this kind of experiments -
see, also, the links therein.
Among important features of HSP-VAT are that it allows specific medium types and morphologies , lower-scale fluctuations of variables, cross-effects of different variable fluctuations, and interface variable fluctuations effects, etc. to be considered. It is not possible to include all of these characteristics in current homogeneous models explicitly using conventional theoretical approaches.It is worth to poin out in this section that - it can be said that the HSP-VAT only gives such desirable features as:
1) Effects of interfaces and grain boundaries being accounted directly.
2) Inclusion of effects causing by morphology of phases. Morphology description directly involved in physical fields equations.
3) Separate and combined fields description and their interactions mathematically and physically described exactly. No guessing about effective coefficients - those nobody knows how to calculate exactly if taking a one scale model.
4) Effective coefficients correct mathematical description - those ''theories'' used right now for that purpose, are only approximate description - often simply wrong.
5) Correct description of experiments in Heterogeneous Media - again, right now for this purpose is used the homogeneous presentation of the medium properties and explanation of experiments are done via bulk features. Those bulk features describe the field as by classical homogeneous medium differential equations.
6) Purposeful design and optimization of materials via hierarchical physical descriptions which use the VAT governing equations and further can be used to connect properties - morphology - component features. There are exist the first models provided for that purpose in fluid mechanics and thermal physics.
*1 - Born, M., Physics in My Generation: A Selection of Papers, Pergamon, New York, (1956).
*2 - Brillouin, L., Science and information theory, Academic Press, New York, (1956).
Travkin, V.S. and Catton, I., "Porous Media Transport Descriptions - Non-Local, Linear and Non-linear Against Effective Thermal/Fluid Properties", in Advances in Colloid and Interface Science, Vol. 76-77, pp. 389-443, 1998.
V.S. Travkin, V.S., Catton, I., Hu, K., Ponomarenko, A.T., and Shevchenko, V.G., "Transport Phenomena in Heterogeneous Media: Experimental Data Reduction and Analysis", in Proc. ASME, AMD-233, Vol. 233, pp. 21-31, 1999.
Travkin, V.S., Catton, I., Ponomarenko, A.T., and Gridnev, S.A., "Multiscale Non-local Interactions of Acoustical and Optical Fields in Heterogeneous Materials. Possibilities for Design of New Materials", in Advances in Acousto-Optics'99, abstracts, SIOF, Florence, pp. 31-32, 1999.
Travkin, V.S. and Catton, I., "Local and Nonlocal Thermal Transport in Superstructures - Modeling, Experiments and Combined Electrical - Thermal Conductivities Optimization," in Proc. 5th IUMRS-Int. Conf. Advansed Materials'99, abstracts, Beijing, Vol. 2, p. 342, 1999.
Travkin, V.S. and Catton, I., "TRANSPORT PHENOMENA IN HETEROGENEOUS MEDIA BASED ON VOLUME AVERAGING THEORY", in Advances in Heat Transfer, Vol. 34, pp.1-144, 2001
Travkin, V.S. and Catton, I., "Heat and Charge Conductivities in Superlattices -- Two-Scale Measuring and Modeling," in Intern. Mech. Engin. Congress and Exposition (IMECE'2001), IMECE/HTD-24260, pp.1-12, 2001.
Travkin, V.S., Hu, K., Rizzi, M., Canino, M., and Catton, I., "Revising the Goals and Means for the Base-to-Air Cooling Stage for Semiconductor Heat Removal - Experiments and Their Results," in Proc. 17th IEEE SEMI-THERM Symp., IEEE, pp. 85-94, 2001.
Rizzi, M., Canino, M., K. Hu, S. Jones, V. Travkin, I. Catton, (2001), "Experimental Investigation of Pin Fin Heat Sink Effectiveness," in Proc. 35th ASME National Heat Transfer Conference, Anaheim, CA, June 10-12, 2001. CD-ROM.
Travkin, V.S. and Catton, I., "Analysis of Measuring Techniques of Superlattices Thermal Conductivity," in Intern. Mech. Engin. Congress and Exposition (IMECE'2001), ASME, IMECE/HTD-24348, pp.1-12, 2001.
Travkin, V.S., "Relating Semiconductor Heat Sink Local and Non-Local Experimental and Simulation Data to Upper Scale Design Goals," in Proc. Intern. Mech. Engin. Congress and Expos ., IMECE-2001/HTD-24383, pp. 1-12, 2001.
Travkin, V.S., Sergievsky, E.D., Krinitsky, E.V., and Catton, I., "Integrated Heterogeneous Design of Semiconductor Heat Sink via Scaled Direct Micro-Modeling, Upper Scale VAT Simulation and Experiment. Comparison and Verification of Properties," in Intern. Mech. Engin. Congress and Exposition (IMECE'2001), IMECE/HTD-24380, pp.1-6, 2001.
Travkin, V.S., Catton, I., Ponomarenko, A.T., and Kalinin, Yu.E., "Bottom Up and Top Down, from Nano-Scale to Micro-Scale, Hierarchical Descriptions of Electrodynamic, Thermal and Magnetic Fields in Ferromagnets and HTSCs", in Proc. DOE 20th Symposium on Energy Engineering Sciences, Argonne National Laboratory, pp. 296-304, 2002.