The Role of Completeness in the Discoveries 
in Particle Physics

Sakir Kocabas
 
Istanbul Tecnhical University, Dept. of Space Engineering,
Maslak 80626, Istanbul, Turkey.
uckoca@itu.edu.tr

Symposium on Computational Discovery of Communicable Knowledge,                 1
Stanford University, March 24-25, 2001

	Abstract

	In this work, we focus on the role of completeness in theory development in particle physics. 

	In the early 1930s, physicists were puzzled by certain observations about  elementary particles, which they could not explain. 

	They had an incomplete theory of particle physics at hand, and this led them to introduce new hypotheses into the theory.

	This completeness-driven process, together with other processes driven by symmetry and consistency, resulted in the development of the theory of particle physics. 

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	Based on our discovery model BR-4, we focus on two episodes in this process: The discovery of neutrino, and the discovery of the quantum property called baryon number. 

	Our exposition will be in terms of :

	- A general problem statement that the physicists were faced with prior to the discoveries, 

	- The knowledge that was available at the time, general  principles and scientific data about the elementary particles themselves and their reactions, 

- And how the theory was developed after the discoveries.

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 	Introduction

	Research in scientific discovery started with modeling historical discoveries that took place in classical physics and chemistry. 

Early discovery models were based on the then current theories – such as the phlogiston theory and the oxygen theory in the 18th century chemistry – favoured by groups of scientists.  

Scientists use their favorite theory to communicate their observations and discoveries. 

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Theories

Theories serve four main purposes in scientific research:

	1)   As a framework for explaining phenomena within the scope of the theory.
	2) For predicting events by the methods of calculation embedded in the theory.
	3) As a language by which scientists communicate their ideas, discoveries, and criticisms with interested scientists in the community.
	4)  Since they are used as standart tools for testing the results of the calculations with observations, they also serve as tools for the systematic development of domain knowledge.

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	Early Work

	Early work on scientific discovery in AI focused on modeling historical discoveries in the 17th and 18th century physics (Langley, Simon, Bradshaw & Zytkow, 1987) and chemistry (Zytkow & Simon, 1986; Rose & Langley, 1986). 

Recent research turned towards building systems that can assist scientists in original discoveries in chemistry (Valdes-Perez, 1995), and astrophysics (Kocabas & Langley, 2000). 

The common feature of all these historical and actual discovery systems that they operate within a particular theory, and hence, present their inputs and outputs easily understandable by the scientists of their intended domain. 

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Early Work

These models rely on simple and abstract theoretical principles of symmetry and the methods of calculation, actually used by the domain scientists.

	In contrast, the systems developed for knowledge discovery and data mining are not bound by any theory of science. Their discoveries are not explainable in theoretical terms that interlink the phenomena with the underlying formal structure of a scientific theory (Example: knowledge discovery from medical databases). 
However, if such knowledge discoveries lead to further research so that they can be explainable within the related scientific theory, they will have the chance of being reliable and useful, and of being accepted by the scientists of the domain.

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	Early Work

	One might think that the discoveries in early modern science by scientist such as Galieo and Kepler, look like knowledge discovery. Yet, this would not be true for two reasons: First, both scientists made use of an available theoretical framework descending from Aristotle, Ptolemy and the Medieval astronomers. 

Second, the simple methods of calculation that they used aimed at reaching a definite theoretical end, the abstract notion of the invariant. Such discoveries later led to the development of the modern theories in phycics and astronomy.

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	Consistency, Completeness and Symmetry

	Current theory development in physical sciences relies on the principles of consistency, completeness and symmetry.

To be useful, scientific theories are required to be consistent and complete as best as possible.

	Let us now see how each of these constraints are used in theory development, starting with consistency.

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	Inconsistency

	There are two main types of inconsistency concerning a theory in physical sciences: Formal inconsistency, and factual inconsistency. 

Formal inconsistency arises when the theory has two or more hypotheses that  contradict one another. Formal inconsistencies can be divided in two categories: Logico-mathematical, and conceptual.

	Logical inconsistencies are easier to detect and are usually eliminated in the early development of a theory by logical operations (e.g. by deleting one of the contradicting hypotheses). 

Conceptual contradictions are more difficult to identify and eliminate. They come into notice in the later stages of theory development. 

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Inconsistency

Contradictions can be eliminated by restricting the extensions of some  of the  theoretical concepts in them (Example: The concepts of particle and wave). In other cases, the most fundamental assumptions or concepts are changed (Example: Transition from the phlogiston to the oxygen theory). 

	Factual inconsistencies arise when the description of an observable fact is deducible from the theory, and yet the opposite of this description is observed in related experiments. 

Factual contradictions are eliminated by changing the assumed properties of the theoretical entities until a consistent set of properties are obtained. We shall see the examples of this type of operation in relation with theory revision in particle physics. 
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	Incompleteness 
 
	A theory is said to be incomplete, when we cannot explain with it a certain well defined observation result in its scope, despite that the observations have been carried out in accordance with the theory. 

When a theory is decided to be incomplete, the problem is in general solved by adding a new hypothesis to the theory (Example: Einstein’s addition of a term involving the cosmological constant).

	In theory development, addition of  a new hypothesis can have one of the two effects.
 i) The new hypothesis expands the scope of the theory,
	ii) The new hypothesis restricts extension of the theory.

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	Symmetry  

	We are all familiar with symmetry in many forms in geometry. Symmetry is an abstract and general property of physical interactions. 

In kinetics, two colliding elastic balls on a planar surface contine their paths obeying  a more abstract form of symmetry, which is expressed as the conservation of energy and momentum.

	In particle physics, still more abstract forms of symmetry is assumed to be in effect. Some of these are: The conservation of energy, spin, and the quantum values such as the baryon, lepton, electron and muon numbers. 
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	Symmetry

Most of the symmetries in particle interactions are expressed in simple arithmetical equations. The symmetry rules used in particle physics can be stated as follows:

i)  All valid particle interactions must conserve all (known) quantum properties.
valid(R) -->  conserves(R,qi). (R: interaction, qi: q-property)

ii)  Unobserved reactions are not valid.5
         	not observed(R) --> not valid(R).

iii)  All observed reactions conserve all known quantum properties.
         observed(R)   -->  conserves(R, qi).

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	Completeness and Theory Development 
 
Here, we analyze a series of discoveries in particle physics between the years 1930 and 1960, using the results of our system BR-4. There are two types of incompleteness concerning particle interactions:

	a) A reaction is not valid by the theory’s symmetry constraints, despite that it has been observed. 

	b)  A reaction is theoretically valid, but not observed.

	The incompleteness of type (a) led to the discovery of the neutrino in particle physics, and type (b) led to the discovery of quantum properties (baryon and lepton) as will be explained.

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Discovery Operators of BR-4

	The system has the following discovery operators:

	OP1 : Classifies reactions as observed/unobserved.
 
	OP2 : Checks for completeness type (a).

	OP3 : Formulates decay and collision reactions.

	OP4 : Checks for completeness type (b).

	OP5 : Checks for consistency.

	Discovery of the Neutrino

	In the early 1930s, physicists were puzzled by the fact that the observed reaction, in which a neutron decays into a proton and an electron

         n  -->  p + e 

does not conserve energy and spin.

	The situation and the task that the physicists were faced can be represented as: 

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	Discovery of the Neutrino

Situation: An observed reaction is not valid by some quantum constraint despite that the assigned q-values are correct.
Decision: The current theory is incomplete. An observed phenomenon cannot be explained. Therefore,

	i) The assigned q-values are incorrect and need to be revised, (in this case, the assigned q-values are known to be correct), or 

	ii) An undetected particle is missing in the reaction formula.

Action: Introduce a new hypothesis. A new particle exists with certain properties.

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BR-4’s rediscovery of the Neutrino 
 	
Inputs :   The list of known particles: (p, n, e, /e, gamma)

		        Quantum properties of known particles:		
	   
		particle		charge	spin		
				---------------------------------------
  					p		 1		0.5
					n	  	 0		0.5
					e		-1		0.5
					/e		  1		0.5
					gamma	  0		0
				----------------------------------------	

		Known reactions:	n --> p + e  
e + /e  --> gamma
p+p --> p+p
						gamma --> e + /e

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Outputs: Posited particle:	neutrino  (nu)
	
	       q-properties of nu:    	charge: 0
					  		spin:     0.5
	
	        Formulated reactions of nu: 		

n --> p + e + nu
							nu + n  --> p + e

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Discovery of Baryon Number

	In the 1930s, the physicists were puzzled by the fact that unlike the neutron which decays into a proton, electron and neutrino, the proton decay has never been observed, e.g.: 

                             p -\->  e  +  /e  +  /e 
or,                         p -\->  /e  + gamma

despite that these reactions conserve the then known quantum properties; e-charge and spin.

	BR-4 formulates the two reactions above as valid reactions for proton decay. The situation-task schema for the system is as below:

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Discovery of Baryon Number

               Situation: A theoretically valid reaction (p -> /e + gamma) has never been observed.

               Decision: The theory is incomplete. An observation statement cannot be explained.

               Action:  Introduce a new quantum property, such that the unobserved reaction violates its conservation. (Violation of a new symmetry would explain the observation statement.)

	The inputs and outputs of the program are given next.

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	BR-4’s rediscovery of Baryon Number

	Inputs : 	The list of known particles (n, p, e, /e, nu, /nu, gamma).
		The q-properties of known particles:
particle		charge	spin		rest-mass
		---------------------------------------------------------------
  			p		  1		0.5	       938.28 (MeV)
			n	  	  0		0.5	       939.57 	
			e		 -1		0.5	           0.511	
			/e		  1		0.5		  0.511
			gamma	  0		0		  0
			nu		  0		0.5		  0
		---------------------------------------------------------------

New reactions formulated by BR-4 
	p --> e + /e + /e  
p -> /e + gamma

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	Outputs :	Posited new quantum property: (q1).
Determined q1 values for particles (corresponding to the baryon numbers):

particle		q1
			---------------------------
  			p			1		
		n			1
			e		 	0		
			/e		  	0	
			gamma	  	0	
			nu		  	0	
			----------------------------
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	Theory revision 

When a new quantum property is introduced, for each known particle a quantum value of the new property must be assigned. 

The assignment must be such that it obeys the related symmetry in all the interactions of the particle. Initially, there are several sets of alternative value assignments for the particles in a reaction. One set of quantum values is selected, and tested for all observed reactions. 

Any observed reaction that does not appear to obey the symmetry of the new property means a contradiction, and such contradictions require the assignments of an alternative value set. The situation-task schema can be given as follows:

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	Theory Revision

              Situation:  There are several alternative sets of quantum values. An arbitrarily selected set of values are not conserved for an observed reaction. (An observed reaction is not valid.)

              Decision:   The current set of values are inconsistent with the observed reactions.

              Action:      Select an alternative set of values. Repeat the process until the consistent set of values are found, or all sets of values have been tried. 

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	Conclusion

	Computational discovery of scientific knowledge differs from knowledge discovery mainly in that the discovered knowledge is meaningful within the framework of the theory of the related field of science. 

	We have described how the completeness constraint of a theory, coupled with symmetry and consistency led to two discoveries in particle physics: Thediscovery of the elementary particle neutrino, and the quantum property baryon number.

	We have used our discovery model BR-4 to simulate the two discoveries, giving the descriptions of the problem states and the system’s inputs and outputs in each case.

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