Monthly Archives: February 2012

Scientific Hypothesis, Theory and Law

A class member recently asked me what the difference is between a theory and a law.  I believe this is a very common confusion, usually stemming from a popular view that a scientific theory is “just a theory”, implying it is less than likely to be true.  Similarly a “law” is loosely viewed as some form of universal and inviolable truth.

Here is my understanding (after some reflection) on what these terms mean.  Let us start with a sketch of what human knowledge is and the process by which it is accumulated.  I will preface what follows by saying that I am discussing what is commonly called “scientific knowledge”, that is, knowledge obtained through the observations achieved with our human senses, and then acted upon by human reason.  This statement does not exclude the use of instruments with which we may collect information, but we ultimately receive that information into our rational mind through our senses.

The senses present information to our minds. Our minds then group these sensory perceptions into clusters of similar observations.  When enough similar observations have been made to understand what they have in common, our minds replace the individual observations with a concept. A concept is a mental representation of a group of similar things which share common defining features. For example, after observing a series of objects which have four wheels, are self-propelled and carry individual or small groups of people over a paved surface, we will replace those observations with the concept “car”.

The detail of this process of concept formation is a major topic in itself which could fill many pages.  It applies not only to simple concrete objects, but also to ideas at all levels of abstraction.  Not only the concepts of “apple”, “dog”, and “house”, but ideas like “love”, “algebra”, and “gravitation” as well.  The concepts that are not directly reflected in objects we may refer to as abstract concepts.  The observations leading to these concepts are our recognition of other, lower-level, concepts.  So, for example, the concept of “fruit” comes from recognizing that the concepts of “apple”, “orange”, “banana”, and so on share common features.

When we start observing the relationships between concepts, and in particular relationships of cause and effect, we have reached the starting point for the creation of scientific theory.  A phenomenon is observed requiring explanation – the cause for the observed effect is sought.  After observing some number of occurrences of the phenomenon (A), we may find a common event that occurs at or before each occurrence (B).  From these repeated observations, we can form a hypothesis that B causes the occurrence of A.  At this level of development, we may have many different hypotheses attempting to explain the same phenomenon.

Here is an example.  A hot plate of glass dropped into cold water will shatter.  After observing this to occur for a small number of identical cases, we develop the following hypotheses to explain the breaking of the glass:  (A) Water breaks glass.  (B) The impact of the glass onto the surface of the water breaks the glass.  (C) A chemical reaction occurs between hot glass and cold water which breaks the glass.  (D) The difference in the temperature between the glass and the water causes the glass to break.  Each of these hypotheses is valid based on the observed events, as possible explanations for what has been observed.  They are, however, only hypotheses at this point because they have not been tested, nor compared carefully against the rest of our knowledge about the world.

We next perform some experiments to attempt to validate each of these hypotheses.  Experiment (1): We take a hot glass plate and drop it into cold gasoline; the glass shatters.  Experiment (2): We slowly pour cold water over a hot glass plate; the glass shatters.  Experiment (3): We drop a room-temperature glass plate into cold water; the glass does not break.  Experiment (4): We place a hot plate in a cold freezer; the glass shatters.

Experiment (1) makes hypotheses (A) and (C) unlikely.  Experiment (3) confirms that hypothesis (A) is not correct.  Experiment (2) makes hypothesis (B) untrue.  Experiment (4) indicates that (C) is even less likely, and confirms hypothesis (D).  Now, after a set of carefully designed experiments have been completed, hypothesis (D) can be considered to be a theory instead of a hypothesis.  The difference between a theory and a hypothesis is the observation of experiments which confirm the hypothesis, while eliminating alternative explanations.  Typically scientific experiments are designed and controlled to progressively narrow the number of alternative explanations by attempting to change one related variable at a time.

At this level of verification, we have a scientific theory, but not a law.  Comprehending the difference requires an understanding of how human knowledge is properly accumulated.  To be accepted as scientific knowledge requires that not only is the theory seen to be true experimentally, but that it is logically consistent with the current body of accumulated scientific knowledge.  This generally requires the completion of two processes.  The new theory must not be contradicted by the existing scientific knowledge, and it must be shown that either the theory fundamentally expands upon the existing knowledge –  it is not logically related to the existing knowledge – or it can be explained using the existing knowledge.

These conditions may seem to preclude revolutionary scientific advances – the Copernican revolution, or Einstein’s theory of gravitation for example.  It may similarly seem to contradict my conviction that the existing regime of “modern physics”, based upon the quantum theory and the Standard Model, will be overturned in the future.  However, this is not at all the case.  The presumption of the scientific method as outlined is that it has been consistently followed throughout the development of the existing body of scientific knowledge that the new theory appears to challenge.  But there have been large segments of scientific development that have failed to adhere to the scientific method.

The most common error within the historical body of scientific knowledge is the failure to base science solely upon observed facts and data.  Far too often some other, non-scientific, source of information has been used to set the groundwork upon which a scientific theory is constructed.  Historically, the most common non-scientific sources have been religious.

The geocentric theory to explain the motions of the celestial bodies was originally based upon a mixture of observation and assumptions about the nature of the astronomical objects involved.  Basic observations would suggest that the Earth lies motionless with the celestial objects rotating around it daily; however, when details of the motions of the planets and the Sun were measured with increasing accuracy, the defense of the geocentric theory rapidly turned from being based upon observations to being based upon mystical beliefs in the divinity, and therefore perfection, of the celestial objects.  Bruno, Copernicus and Galileo did not need to defend their theories against science, but against the Church.

The mystical thread in the development of astronomy did not end with Galileo.  Kepler accepted the Copernican system with great reluctance, and hampered his own success in determining the actual motions of the planets by adamantly insisting that the orbits were circular, because of the presumed divinity of the planets and the necessary perfection of their motions.  During his struggles to solve the problems of planetary motion he oscillated between difficult scientific investigations and lengthy whimsical fantasies based purely upon a quest for religious revelation.  Even Isaac Newton, inventor of calculus and the “law” of gravity, believed the planets to be living beings, and presumed the existence of a Prime Mover.

Einstein’s theories – both special relativity and general relativity (a new law of gravitation) did not invalidate prior science, but rather were revolutionary for dramatically expanding upon existing theory without creating contradictions.  The general theory of relativity in particular was a re-statement of existing theory from a completely new perspective, which then allowed an enormous expansion of the ability of science to explain phenomena which had been observed and had been difficult or impossible to explain within the existing framework of physics.

But modern physics is far from having removed the effects of non-scientific thinking.  Quantum mechanics, developed in the 1920’s and 1930’s, sought to explain recently observed facts and data, but did so starting from outside existing scientific theory.  The origins of the quantum theory lie in a new set of assertions not derived from existing science, and lying in direct contradiction to the most fundamental assumptions of physics.  The new theory is capable of explaining a vast variety of experimental observations – as such it does qualify as a theory using the definition I have stated earlier.  However, all attempts to resolve the enormous contradictions that quantum theory brings against the fundamental elements of science have ended in failure, or emphatic denial that the contradictions need to be resolved.

There are two core contradictions between quantum mechanics and the rest of established science; both are severe and extraordinarily fundamental.  Science presumes that every entity in the universe has definite and precise quantitative features.  An object has a location in space which it occupies.  An event occurs at a particular moment in time.  Man and therefore Science may be limited in its ability to know the values of these aspects of an object – and the limitation may even be a fundamental limitation which is physically impossible to overcome.  But quantum mechanics denies that there are specific values for some attributes (such as position and time), and that this lack of specificity is not a lack of knowledge, but that no specific values actually exist.

Science also presumes that all phenomena are caused by other phenomena – the law of causality.  Quantum mechanics explicitly denies this, and replaces the law of causality with probabilistic rules.  Quantum events are fundamentally uncertain and undetermined.  Attempts to develop interpretations for quantum mechanics that allow for the law of causality to be retained evolve into a variety of absurdities, the best known being the “many universes” interpretation, in which every event causes a divergence into multiple universes dependent on the actual outcome – many in this sense is an insanely large number.

Returning to our main topic, a theory that does successfully integrate into the existing body of (truly) scientific knowledge, is shown not to be in contradiction with that knowledge, and which is either explained within its context, or advances a new viewpoint which expands the basis for scientific knowledge will attain the designation of a scientific law.  A law in this sense implies that its falsification would entail a major disruption in our most fundamental understanding of the meaning of science, and is therefore scientifically impossible.

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