A Geometric Theory of Everything: Scientific American

A Geometric Theory of Everything

Deep down, the particles and forces of the universe are a manifestation of exquisite geometry

By A. Garrett Lisi and James Owen Weatherall | November 29, 2010 | 67

Also, read about the statistical bump at FERMI lab:

Big noises about a little bump at Fermilab

By Hamish Johnston

Particle physics blogs are buzzing about an innocuous-looking bump in data taken by the CDFexperiment at Fermilab in Chicago – and the possibility that it could be evidence for a new particle.

The unexplained signal was spotted in a study of W and Z boson pairs that are created when protons and antiprotons collide in Fermilab’s Tevatron collider. It appears at about 120–160 GeV /C²in the distribution of jets that are produced in the collisions. The bump has a statistical significance of “three-sigma”, which means that there is a one in 370 chance that the bump is not real.

While that might sound convincing to you and me, particle physicists don’t accept a new result until it has been established at five-sigma – about one in two million chance of not being real. Another problem is that CDF’s sister experiment D0 doesn’t see the bump. Rumours are also circulating thatATLAS at CERN has not seen it.

But if the bump is real, what could it be?

Theoretical physicists are now hard at work trying to explain the bump, and at least one paper – with the intriguing title Technicolor at the Tevatron – has already been posted on the arXiv preprint server. No doubt many more will follow.

What are other physicists saying?

In his blog, Tommaso Dorigo sketches out three possible ways that the bump could be an artefact of how the experiment was done or the data were analyzed. But if the bump is real, he thinks that it could be evidence for a new particle – but not a Higgs boson.

Adam Falkowski seems to agree. “It is not a Higgs; anything Higgsish with 150 GeV mass would prefer decaying to a pair of W bosons rather than to two light jets,” he writes in his blog.

But what about a “non-standard Higgs”? Flip Tanedo explores that possibility in this blog entry.

The story has also captured the imagination of veteran science writer Dennis Overbye in an article in the New York Times. However, most of the leading physicists interviewed by Overbye seem sceptical, yet excited.

Giovanni Punzi from CDF is “strongly thrilled…and cautious at the same time”, New York University’s Neal Weiner says “If it holds up, it’s very big”, and Lisa Randall at Harvard comments “It is definitely interesting, if real”.

We’ll have to wait and see. In the meantime you can read a preprint describing the bump here.

Posted by Hamish Johnston on Apr 7, 2011 5:34 PM | Permalink

Do Thought Experiments Manifest as Paradigm Change

within the Context of Kuhn’s Revolutionary Science?

Joaquin

I. Introduction

Science is divided into two different types (according to Kuhn), normal science and revolutionary science. Normal science works within: established paradigm, defined terms, and real experiments. Normal science is confined to sensationism in the practice of performing experiments and recording the results, the method. Normal science denies thought experiment a role within the method. Normal science builds off prior scientific theory and accumulates progress through time. Normal science often struggles to explain anomalous evidence.

Anomaly is an essential component within revolutionary science. Anomalies that are a result of real experimentation are often discarded because of the (theory-laden) nature of normal science practiced within an existing paradigm. Thought experiments often create anomalies that can not be solved within a paradigm. Anomalies can indicate the point where a paradigm begins to enter into a crisis. A crisis often gives rise to revolutionary science that can explain the anomalous evidence and predict future results. Revolutionary science works to create a new paradigm that rejects theories, re-conceptualizes experiments, and redefines terms.

A thought experiment has many definitions, according Sorenson, a thought experiment is:

an experiment that purports to achieve its aim without the benefit of execution. The aim of any experiment is to answer or raise its question rationally. [italics in original]

This definition does not imply that the experiment posed by a thought experiment could not be performed, it is just not necessary to achieve its aim. There are a few different types of thought experiments as well, each with a different aim. According to Brown (Horowitz, p124-5) there are three, destructive, constructive, and platonic (which are simultaneously destructive and constructive). All three types of thought experiment are addressed within this paper. Two different thought experiments will be examined in detail, one by Galileo, one by Einstein. Two other uses of thought experiment are looked at, though not in detail, by Darwin and Schrodinger. All of these thought experiments are within revolutionary science.

In this paper I will address thought experiments used in revolutionary science: Galileo's falling bodies and Einstein's Elevator. Two other thought experimenters that are addressed are Darwin and Schrodinger, although the focus will be on their technique and the implications. Galileo’s thought experiment worked to simultaneously destroy an accepted theory and create a new theory, the platonic type. Einstein's is a constructive thought experiment. Schrodinger's is a destructive thought experiment. All of them create a new paradigm in science, this is Khunian revolutionary science.

Discovery within revolutionary science is often done through thought experiments. Thought experiments are only performed in the mind, their role in the method goes against the foundations of sensationism. Thought experiments create a scenario and the conclusions of that particular situation are representative of the world in general. This way of working from the particular to the general also goes against sensationism.

A destructive thought experiment is most often open ended, that is it asks a question, but does not propose an answer. The lack of an answer to the question, raised by a destructive thought experiment, creates a need for a new theory that can . Theory creation involves creativity and imagination.

II. Thought Experiments Advantages

Thought experiments enable the experimenter to isolate a hypothesis and premise from its auxiliaries. Thought experiments can be modified, nearly instantaneously, as new hypotheses, premises, and theories arise. Thought experiments allow the audience, or the student, to become an active participant within the creation of theories (especially in respect to a destructive thought experiment). The involvement of the audience within the thought experiment is a powerful epistemological (and persuasive) tool that can construct experiments that would not be possible in real experimentation. The author can introduce new theories and concepts to the audience, while forging new connections within existing evidence.

The thought experiment often includes a reconceptualization of evidence. “Concepts never come free from physical implications, and as such their use always provides information about what the world is like. This of course implies that they can err in a non-logical sense, i.e., that the world is not exactly as presupposed by the concept, and exposing these kind of errors is the function Kuhn ascribes to thought experiments.”(Van Dyck, 9) This indicates a path to discovery, which is often non-logical because when a new paradigm is introduced, the choice between paradigms is not always logically clear and distinct. For example, Ladyman refers to the beginning of the Copernican revolution (p. 106). Ladyman credits the revolution coming about as a result of the work of many others (Galileo, Descartes, and Kepler) in completing the theory. Although Ladyman writes, “none of them could be sure that it would ultimately provide a more adequate account of what we observe in the night sky” (p107). Galileo's thought experiment analyzed in this paper was a step toward rejecting the Aristotelian paradigm. Galileo's platonic thought experiment could be used as an argument against the Aristotelian paradigm.

III. Thought Experiments as Arguments

Thought experiment has been compared to forms of argument, known by different names, in various fields of study. For example within the discipline of rhetoric it (thought experiment) bears a striking similarity to enthymeme. “Enthymemes are similar to thought experiments because they both lack the necessary premises to create formal syllogisms.”(Crick, 23) A thought experiment used as an argument by Darwin: “the audience is led from thought experiment to thought experiment, and after the audience is fully committed, it can read the passage on natural selection and consider it true, even though, taken on its own, Darwin's guiding metaphor rests on only the most intangible of foundations.” (Crick, 39) This technique of 'leading' the audience to the conclusion is an important component of thought experiments in general. Darwin uses thought experiments to question an accepted truth about the world. This is a powerful tactic that did not begin, or end, with Darwin. That tactic is the use of thought experiment as a persuasive (rhetorical) tool to communicate an idea that will most certainly have a negative reception.

The rhetorical use of thought experiment to communicate an idea (or theory) to an audience (that is certain to have a negative reaction to the said idea) can not be separated without losing an essential component of thought experiment. Norton (in his chapter about thought experiments within Einstein's work) goes about re-constructing a thought experiment into statements of logic within an argument, in an attempt to understand the thought experiment. Crick criticized Norton for trying to take the “rhetorical power” (or the persuasiveness) away from thought experiments when he tried to reduce them to arguments. Crick maintains, “If thought experiments can be fully reconstructed with only the tools of logic, then they can also be controlled.” This attempt at controlling thought experiments eliminates a key function which they, alone, hold within discovery (theory creation). This attempt to control thought experiments their epistemological value is taken away.

Epistemologically, thought experiments are invaluable. Thought experiment allows the audience to perform an experiment and reach the conclusions by themselves that, often, could not be performed in reality. A good (constructive) thought experiment will have the audience thinking of the conclusion before it is even stated. This technique of teaching an audience change within, and among, concepts is an important process found in thought experiment. Another role of thought experiment is that they undermine the accepted 'truth' in persuasive manner (often that is nearly impossible to rationally reject). Presenting the accepted evidence and concepts in a context that leads the audience (or the student) to realize the irrationality (or within Galileo's case, reductio ad absurdum) of the current view. Often a result of a thought experiment is that a new theory is accepted. Existing concepts are re-defined and new connections between concepts are identified. This is referred to as the ability to destroy an accepted theory and create a new theory at once [see Galileo below] Brown considers the Platonic type of thought experiment, “quite remarkable. They are simultaneously destructive and constructive. At one and the same times they can destroy the old theory and create a new one.” (Brown 9)

IV. Galileo's & Einstein's Thought Experiments

First we look at one of Galileo's thought experiments. Galileo was questioning an accepted truth, the Aristotelian view, that objects fall at a rate proportional to their mass. Leading up to the publishing of his book, that contained the following thought experiment, he published a dialogue discussing falling bodies to question the accepted truth. His goal was to demonstrate the self-contradictory nature of the Aristotelian view, exposed by the thought experiment. The Aristotelian theory of falling objects stated that the rate an object falls is directly related to its mass, that is an object with greater mass falls faster than an object with less mass. Galileo proposed: if an object of less mass were tied to an object of greater mass how would the object of less mass affect the rate the object of greater mass fell? Would the object of less mass cause the object of greater mass to fall at a slower rate? The Aristotelian conclusion is that the two objects together fall slower and faster than the heavy object by itself. This anomaly undermined the established teachings of the time. When one performs the thought experiment, it becomes obvious the established 'truth' of the time was false. Not only does Galileo's thought experiment destroy the accepted truth, it also provides space for his theory to be created. Galileo's theory was that the rate objects fall has no relation to their mass. Once one performs the thought experiment Galileo's theory becomes obviously correct and the Aristotelian theory of falling bodies is incomprehensible. Galileo's thought experiment reduces the Aristotelian theory of falling bodies to the absurd. As a result Galileo's theory of falling bodies explained the anomaly created by his thought experiment and predicted the future evidence of further experimentation.

This is a magnificent example of the power of the thought experiment, as it both destroyed the paradigm and created a new one. The tool was used throughout history before Galileo, though not so masterfully. He used it to dismantle the established belief structure of the time, Aristotelianism. Epistemologically, this argument could not be refuted because it explained the anomaly and predicts future experimental evidence. It changed the way people of that time accepted the official teaching.

Next we look at a constructive thought experiment, one of Einstein's, the elevator experiment. Imagine a physicist is drugged and wakes up in an elevator. The elevator is far removed from any gravitational fields, in space. The physicist experiences zero gravity and must attach herself to the floor to keep from floating up to the ceiling. A rope is attached to 'a being' in space that begins to pull the elevator at a uniform rate of acceleration. She is no longer floating. She detaches herself from the floor and she can stand up right as if she were within a gravitational field (such as ours on earth). All the other objects in the elevator 'fall' to the floor just as they would behave within a gravitational field, no longer floating in mid-air. The physicist begins to wonder what has changed, has she suddenly come into contact with a gravitational field? Obviously she was not within the gravitational field a few moments ago. Why, if she is now within a gravitational field, are she and the elevator not falling towards whatever body's gravitational field she has come into contact with? Suddenly she notices a hook in the middle of the roof of the elevator with a steel cable attached to it. Now she figures out what has happened. The cable gradually lowered the elevator down into a gravitational field and the elevator is now at rest. Would she be wrong to assume that she is now stationary, and that before she was in motion? Could she possibly figure out that the opposite was in fact the case? She would not be wrong, but this does make 'a powerful argument for generalized postulate of relativity.' (Einstein quoted in Nersessian, 178) That is, postulate one:”The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion”

Einstein goes about proving the principle of equivalence in this thought experiment. The principle of equivalence states that the laws of physics are the same in an accelerated frame as they are within gravitational field. This allowed Einstein to address motion rather than force when discussing gravity. Later Einstein generalized this special relativity into general relativity. Norton (p137) reconstructs the thought experiment and reconstructs it in the form of an argument. Norton maintains that Einstein takes an “inductive step: (a) the case is typical and will hold for all observable phenomena and (b) the presence of the chest [in our example an elevator] and observer are inessential to the equivalence.” Einstein was correct in generalizing from the particulars in his thought experiment and a new paradigm was created, that of general relativity.

V. Destructive Thought Experiment

A destructive type of thought experiment enables a theorist to create a problem, without knowing a definite answer to it. This offers an opportunity for other individuals to look at the same problem, and attempt to solve it. Each individual can offer insights and background knowledge that will vary greatly. Once a paradigm has been rejected, theorists must question the foundations and assumptions that that paradigm was built upon. This willingness to question the current practices of normal science creates an environment that encourages creativity and new ideas. Rather than the stifling and constricting world that is normal science, revolutionary science looks for new ideas and theories to explain the anomaly and resolve the contradictions raised. The forming of thought experiment into statements of logic eliminates the epistemological value that teaches the audience about the reconceptualization of ideas and concepts.

A destructive thought experiment was used to question the Copenhagen interpretation of quantum physics. Schrodinger's cat-in-a-box thought experiment showed the Copenhagen interpretation “to have a very bizarre and highly counter-intuitive consequence.”(Brown 5) This created a problem that has not been answered. A few theories have been created that question the assumptions made by the Copenhagen interpretation, although none have been proven.

The ability of thought experiment to pose a question without a clear answer encourages others to address the problems (raised by the thought experiment) and to create (discovery) new theories and concepts within a new paradigm. Nersessian elaborates on this point, “often the insights [from] thought experiments... are in the form of problems such as the representations lead to contradictory or physically impossible situations. This warrants thinking that something is wrong with a certain way of representing the world and investigating the problem indicated by the outcome.” (Nersessian 179) Nersessian illustrates how an accepted theory's assumptions can be questioned when pushed to the limit of human representations, through thought experiment. This is when representations within normal science begin to reach the limit and discovery of novel theories within revolutionary science must come into play. Creation of novel theories is often the only way to solve anomalies that arise as a result of destructive thought experiments.

Kuhn puts the idea of discovery within revolutionary science in the form of paradigms. “Discovery, commences with the awareness of anomaly, i.e., with the recognition that nature has somehow violated the paradigm-induced expectations that govern normal science. It then continues with a more or less extended exploration of the area of anomaly.” (Kuhn, p.52-53) Kuhn views the history of science through paradigms. These paradigms influence the experimenter to expect nature to yield evidence that will support the accepted theory. Thought experiment is often involved through the transition of one paradigm, and the beginning of another. Anomalies are important components that destructive thought experiments use to expose false assumptions and limits within a scientific paradigm.

VI. Conclusion

There are many ways of investigating the anomalies and contradictions that arise from thought experiments. Often the only way to solve the puzzles created by thought experiment is to question the very foundations upon which an entire science was built upon. This questioning of normal science practices and assumption can, along with glaring anomalies, create a crisis within a science. The crisis can, and often does, lead many scientists to abandon an entire paradigm of science and choose a different paradigm. Paradigm choice is often influenced by thought experiment. A destructive thought experiment can expose the limits of a representational system's ability to explain novel phenomena. Another constructive thought experiment can introduce a new: theory, conceptual framework, and re-define terms to better explain the evidence. Platonic thought experiments both destroy an old theory and create a new one. Thought experiments manifest themselves as paradigm change within revolutionary science.

Bibliography

Bunge, Mario. Intuition and Science. Englewood Cliffs, NJ.: Prentice-Hall, 1962.

Brown, James Robert. “Thought experiments since the Scientific Revolution”. International Studies in the Philosophy of Science Volume 1 Number 1 September, 1986.

Crick, Nathan. “Conquering Our Imagination: Thought Experiments and Enthymemes in Scientific Argument”. Philosophy and Rhetoric, Vol. 37 No.1, University Park, PA. Pennsylvania State Press. 2004

Horowitz, Tamara and Gerald Massey ed. Thought Experiments in Science and Philosophy. Savage, MD.: Rowman and Littlefield Publishers, 1991.

Giere, Ronald N. Ed. Minnesota Studies in the Philosophy of Science. Minneapolis, MN.: University of Minnesota Press, 1992.

Kuhn, TS. The structure of scientific revolutions. Chicago, IL.: University of Chicago Press, 1970.

Nersessian, Nancy J. Creating Scientific Concepts. Cambridge, MA.: MIT Press, 2008.

Sorensen, Roy A. Thought Experiments. New York, NY. Oxford University Press, 1992.

Van Dyck, Maarten. “The Roles of One Thought Experiment in Interpreting Quantum Mechanics. Werner Heisenerg Meets Thomas Kuhn.”. Center for Logic and Philosophy of Science. University Ghent, Belgium. April 7, 2003.