Download Philosophy, Epistemology and History of Science I+II

SHS Course
Philosophy, Epistemology and History
of Science I+II
Prof. Michael Esfeld
∗
Academic Year 2016–17
Manual Version: September 12, 2016
The goal of this one-year master level course is to work on philosophical issues
in the exact sciences.
– What is a law of nature?
– What does physics say about space and time?
– What is matter according to quantum mechanics?
– Do numbers really exist?
– Why can mathematics be used in so many areas?
This is only a sample of questions we’re going to address in this course. After
the introductory lectures, you work in small groups on a particular project and
present your intermediate results to the whole group by the end of the first term.
You then write an essay by the end of the second term. You’re free to choose
the project that you like, and we encourage you to work on philosophical issues
in the area you study at EPFL. We propose several interdisciplinary projects in
the philosophy of physics in cooperation with the physics department.
∗. B [email protected].
Contents
I. Organization
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1. Supervisors
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2. The Program
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3. What You Are Expected to Do
3.1. The Essay Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. The Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3. The Essay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4. Schedule
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5. How to Write an Essay?
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6. Online Resources
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II. The Projects
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7. Metaphysics of Physics
7.1. What Is a Law of Nature? . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2. What Is Matter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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8. Philosophy and History of Classical Physics
8.1. Aristotle on Space, Time, and Motion . . . . . . . . . . .
8.2. Newton and Leibniz on Space, Time, and Motion . . . . .
8.3. Shape Space: The Physics of Relational Space . . . . . .
8.4. Does the Electromagnetic Field Exist? . . . . . . . . . .
8.5. The Self-Interaction Problem in Classical Electrodynamics
8.6. Entropy and the Arrow of Time . . . . . . . . . . . . . .
8.7. Probabilities in Deterministic Theories . . . . . . . . . . .
9. Philosophy of Relativistic Physics
9.1. The Twin Paradox . . . . . . . . . .
9.2. Mass and Energy in Special Relativity
9.3. Space-Time in General Relativity . .
9.4. Is Time Travel Possible? . . . . . . .
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10.Philosophy of Quantum Mechanics
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10.1. Problems in Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . 16
10.1.1. Is Quantum Mechanics Incomplete? . . . . . . . . . . . . . . . . . . 16
10.1.2. Bell’s Theorem and Quantum Non-Locality
10.1.3. Einstein’s Boxes . . . . . . . . . . . . . .
10.1.4. The Measurement Problem . . . . . . . .
10.1.5. Contextuality . . . . . . . . . . . . . . . .
10.2. Interpretations of Quantum Mechanics . . . . . .
10.2.1. Collapse Theories . . . . . . . . . . . . .
10.2.2. The de Broglie–Bohm Quantum Theory . .
10.2.3. Many–Worlds . . . . . . . . . . . . . . .
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11.Philosophy of Mathematics
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11.1. Do Mathematical Objects Exist? . . . . . . . . . . . . . . . . . . . . . . . 21
11.2. Why Is Mathematics so Successful in Application? . . . . . . . . . . . . . . 21
Part I.
Organization
1. Supervisors
Either Mario Hubert1 or Dr. Dustin Lazarovici2 supervise your project. For all organisational
question please contact Mario Hubert.
2. The Program
The goal of this master program is to work on philosophical issues related to physics or
mathematics. You choose a project and work in groups of 1–3 students. By the end of the
autumn term, you prepare an essay plan and give a presentation. During the spring term, you
write an essay based on your previous work. You can freely choose among the projects that
you find in Part II of this manual. And you are welcome to choose a project that discusses
philosophical issues in the area you study at EPFL. We propose projects in the following five
fields:
– Metaphysics of Physics,
– Philosophy and History of Classical Physics,
– Philosophy of Relativistic Physics,
– Philosophy of Quantum Mechanics,
– Philosophy of Mathematics.
If you wish to work on a topic that is not listed in this manual, please contact Mario Hubert.
3. What You Are Expected to Do
1. Follow the introductory lectures starting on 21 September 2016.
2. Find a group and a project by 19 October 2016.
3. Submit an essay plan at least 7 days before your presentation.
4. Present your plan at the end of the autumn term.
5. Finish the essay by 1 May 2017.
1. B [email protected]
2. B [email protected]
1
3.1. The Essay Plan
The essay plan is intended to help you prepare your final essay. It should comprise 2–3 pages
written in whole sentences. And it should include
1. the working title of your final essay,
2. your names,
3. the last date when you revised your essay plan,
4. an introduction,
5. your research question,
6. how you’re going to address that question, and
7. a list of references.
Send your essay plan to your supervisor at least 7 days before your presentation. We only
accept PDF. You can write the essay plan in English, French, or German.
3.2. The Presentation
On the basis of your essay plan, you prepare a presentation. You should present your essay
plan in 15 minutes, followed by a 15 minutes discussion. The whole session is in English.
The presentation, in conjunction with your essay plan, will be graded.
Grading
You’ll get a grade for the autumn term that depends on your essay plan and your presentation.
You don’t need to understand all the details of your topic as this is probably your first
encounter with this field, but we expect you to confidently present the main ideas. We’ll
grade how well you understood the most important issues and how you respond to questions
in the discussion session. You should focus on your essay plan in finding an interesting
research question and in formulating your future strategy.
3.3. The Essay
Reader
When writing the essay imagine that you address a master student at EPFL. Your aim is to
write a scientific paper that any of your peers can understand.
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Language
You can write your essay in English, French, or German. We, however, recommend you to
write the essay in English because almost all relevant literature is in English. The correct
use of language is very important. So please find someone who will proofread your essay—in
particular, if you write your essay in a foreign language.
Structure
Your essay should include the following elements:
– title,
– names of the authors,
– date of last update,
– abstract (≤ 150 words),
– word count,
– main text (introduction, core sections, conclusion),
– bibliography.
The purpose of the abstract is not only to summarize your essay but also to show that
your project is relevant and the article is worth reading.
The main text will be separated into several sections. The first section is always an
introduction to your topic. You don’t need to name it “Introduction”. If you happen to find
a more suitable title for the introduction, use it.
After the introduction, you present your main arguments to answer your research question.
Papers in philosophy and in the natural sciences strongly differ in this part. Here you need to
discuss different arguments, quote important literature, and evaluate different approaches.
The last section should be a conclusion. Writing a good conclusion isn’t that easy since it’s
supposed to differ from your abstract and from a mere summary. As with the introduction,
you don’t need to name the last section “Conclusion.” In the end, your paper will look like
a standard research paper in philosophy of physics or philosophy of mathematics.
Length
The word limit depends on the number of authors:
– 1 author: 4000–5000 words,
– 2 authors: 5000–6000 words,
– 3 authors: 6000–7000 words.
The word limits comprise everything in the main text, including headings, quotes, and footnotes. The abstract and the bibliography are excluded from the word count.
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Citations
Please use an author-year citation format as we use it in this manual below. When you refer
to the literature, make sure that you always cite the source as precisely as possible. We’ll
give you more guidelines on how to cite properly in the last lecture. Citations that are not
indicated as such (e.g. copying from the internet) is plagiarism.
Grading
We’ll grade your essay with respect to the following criteria (in order of importance):
– How good are your arguments?
– How well have you discussed your research question?
– How well have you understood the details?
– Does your essay contain superfluous arguments?
– Does the essay fulfill the formal requirements?
– Do you make linguistic errors?
Drafts vs. Final Version
We recommend that you write your draft using double spaced lines. This makes it easier to
insert comments in your draft. The final version is to be submitted in a single spaced layout.
Submission
Please send the final version of your essay to your supervisor by 1 May 2017. We only
accept PDF. Please use the official cover page that you can download from the website.
4. Schedule
Autumn Term ’16
The autumn term is divided into three parts:
1. Lectures
Location: Room INR 219.
21 September
16h15-17h30: Introduction to the Program. (Prof. Esfeld)
17h45-18h45: Natural Philosophy: Newton on Physics and Philosophy. (Prof. Esfeld)
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28 September
16h15-17h30: Philosophy of Space and Time: Leibniz vs. Newton (Prof. Esfeld)
17h45-18h45: What Is a Law of Nature? (Prof. Esfeld)
5 October
16h15-17h30: Theory and Ontology. (Dr. Lazarovici)
17h45-18h45: Philosophy of Space and Time after General Relativity Theory. (Dr. Lazarovici)
12 October
16h15-17h30: Quantum Physics: Non-Locality and the Measurement Problem. (Prof. Esfeld)
17h45-18h45: The Ontology of Quantum Physics. (Prof. Esfeld)
19 October
16h15-17h30: Philosophy of Mathematics. (M. Hubert)
17h45-18h45: How to Write an Essay. (M. Hubert)
2. Preparation of the Essay Plan
– No lectures until the presentations.
– Definite fixing of the groups and essay subjects by 19 October.
– One required meeting with your supervisor.
– Submit the essay plan to your supervisor at least 7 days before your presentation.
3. Presentations
Location: Room INR 219.
Four sessions from 16:15 to 19:30:
– 30 Nov.,
– 7 Dec.,
– 14 Dec.,
– 21 Dec.
Spring Term ’17
During the spring term you write your essay. There are no lectures. But you need to meet
your supervisor three times throughout the semester:
1. Intermediate session I in February and March.
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2. Intermediate session II in April.
3. Final feedback in May.
We’ll prepare a schedule for the meetings at the beginning of spring term. Further meetings
on request. Submit your completed essay by 1 May 2017. After that you meet your
supervisor to receive final feedback. If your essay needs improvement, you can submit a
revised version by 2 June, 2017.
5. How to Write an Essay?
Style
Writing is a skill that you can only achieve through regular practice and proper teaching. Before preparing your essay, please read the guidelines on writing a paper by the the philosopher
Jim Pryor at NYU. If you’re interested in improving your writing skills in general, Strunk Jr.
and White (1999) is a brief and concise classic.
Punctuation
The English language has its own rules of punctuation. Good punctuation gives a clear
structure to your text and helps the reader to grasp the correct meaning of a sentence. Trask
(1997) is a primer on English punctuation (link to the online version). Some important rules
are also included in Strunk Jr. and White (1999, Sec. 1.2–1.8)
Dictionaries and Thesaurus
There are certain tools that every writer is supposed to use. First, a proper dictionary is
indispensable. We recommend the following two dictionaries:
– the Oxford Dictionary of English (ODE),
– the Oxford Advanced Learner’s Dictionary (OALD).
The OALD uses easier explanations and contains simpler examples. Second, in order to
enlarge your vocabulary, a thesaurus is extremely helpful. The ODE contains a huge database
of synonyms.
References
Strunk Jr., William, and E. B. White. 1999. The Elements of Syle. 4th ed. Boston: Allyn and
Bacon.
Trask, Robert Lawrence. 1997. The Penguin Guide to Punctuation. London: Penguin. http:
//www.sussex.ac.uk/informatics/punctuation.
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6. Online Resources
Open peer-reviewed sources on the internet are:
– The Stanford Encyclopedia of Philosophy (SEP).
– The Internet Encyclopedia of Philosophy (IEP).
– Scholarpedia.
The SEP is a comprehensive and widely-used encyclopedia. There you can find articles on
all topics in philosophy. The IEP is a very helpful and probably easier resource, too, but it
contains fewer entries than the SEP. On Scholarpedia, you can find many articles on physical
topics. Use these encyclopedias to get supplementary information for your project.
Don’t use any other source on the internet unless you find it in this manual or get recommendations by your supervisor! Most sites contain imprecise or even wrong information.
In Wikipedia, for example, you rather find what people think than what is true. Though it
may be useful for getting a first overview on a topic, it’s not meant to be a scientific source.
Therefore, never cite articles from Wikipedia in your essay.
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Part II.
The Projects
You can choose as your project any of the “propositions de travail” included in the textbook
Physique et Metaphysique: Une Introduction à la Philosophie de la Nature by Michael Esfeld.
This book is a primer on many topics that you can find below. Apart from the suggestions
in the book, we list the following projects below.
7. Metaphysics of Physics
7.1. What Is a Law of Nature?
There are two major doctrines discussed in current philosophy of science on the meaning
of laws of nature: Humeanism and dispositionalism. Humeanism postulates that the world
develops in a contingent way, and the laws of nature are an efficient summary of the history
of the universe so far. An introduction to this metaphysical framework can be found in Esfeld
(2012, Chap. 2).
Dispositionalism challenges the Humean point of view in that it argues that the world
doesn’t evolve in a contingent way. Instead, there are properties on the fundamental level of
the world that govern the behavior of all the objects. A law of nature is then the representation
of what these properties do to the objects. Esfeld (2012, Chap. 3) and Lange (2002, Chap.
3) give a brief introduction to dispositionalism.
7.2. What Is Matter?
In quantum mechanics, it’s mysterious what is meant by a particle, because physicists often
say that before a measurement a particle neither has a position nor a velocity. The notion of
primitive ontology emphasizes that if particles exist they always possess a definite position
and velocity—similar to classical mechanics. Allori (2013, 2015) are good introductions
to the meaning of a primitive ontology. And as she shows, this notion isn’t restricted to
quantum mechanics at all; it constrains the formulation of all physical theories. Maudlin
(2013, pp. 142–9) argues that only with the help of a primitive ontology can physics make
the connection between theory and experimental data.
Online Lectures
– How Theory Meets Data by Tim Maudlin.
– What Theories Qualify as Quantum Theories without Observers? by Tim Maudlin.
– A Physicist Looks at Idealism and Relativism by Jean Bricmont.
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References
Allori, Valia. 2013. “Primitive Ontology and the Structure of Fundamental Physical Theories.”
In The Wave Function: Essays on the Metaphysics of Quantum Mechanics, edited by
Alyssa Ney and David Z. Albert, 58–75. New York: Oxford University Press.
. 2015. “Primitive Ontology in a Nutshell.” International Journal of Quantum Foundations 1 (3): 107–122.
Esfeld, Michael. 2012. Physique et Metaphysique: Une Introduction à la Philosophie de la
Nature. Lausanne: Presses polytechniques et universitaire romandes.
Lange, Marc. 2002. An Introduction to the Philosophy of Physics: Locality, Fields, Energy,
and Mass. Oxford: Blackwell.
Maudlin, Tim. 2013. “The Nature of the Quantum State.” Chap. 6 in The Wave Function:
Essays on the Metaphysics of Quantum Mechanics, edited by Alyssa Ney and David Z.
Albert, 126–53. New York: Oxford University Press.
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8. Philosophy and History of Classical Physics
8.1. Aristotle on Space, Time, and Motion
Aristotle (384–322 BC) was one of the big three of ancient Greek philosophy apart from
Socrates and Plato. He described in detail the nature of space and time, which is totally
different from what we usually think them to be. Maudlin (2012, pp. 1–4) and Huggett
(1999, Chap. 4) introduce his ideas in a very comprehensible way.
8.2. Newton and Leibniz on Space, Time, and Motion
Isaac Newton (1643–1727) wasn’t only an outstanding physicists; he was a good philosopher,
too. His conception of absolute space and time has shaped the discussion until now. Maudlin
(2012, Chaps. 1–2) gives a very comprehensible introduction to Newton’s ideas. Huggett
(1999, Chap. 7) presents the original passages written by Newton and supplements them
with helpful commentaries.
G. W. Leibniz (1646–1717) was the main competitor of Newton. His conception of relational space and time are found in his discussion with his contemporary Samuel Clarke in
an exchange of letters, famously named the Leibniz-Clarke correspondence. Maudlin (2012,
Chap. 2) discusses excerpts of this correspondence in a clear way. Huggett (1999, Chap. 8)
is another good source for understanding this debate.
8.3. Shape Space: The Physics of Relational Space
Who won the Newton-Leibniz debate? While there are strong philosophical arguments in
favor of relationalism, our best physical theories – starting with Newtonian gravity – are
not purely relational theories but presuppose an absolute background space. Attempts to
formulate classical mechanics as a relational theory, in accordance with the philosophy of
Leibniz and Mach (1919), leads to a formulation on the so-called shape space, where a
particle configuration is described only in terms of its shape, independent of absolute location,
orientation or scale. This research program was championed, in particular, by Barbour and
Bertotti (1982) and leads to very interesting mathematics as well as to a radically new
conception of physical interactions (see also Barbour 2003; Montgomery 2015). Whether
the framework is physically and philosophically satisfying is, however, subject to ongoing
debate (Pooley and Brown 2002).
8.4. Does the Electromagnetic Field Exist?
The existence of the electromagnetic field isn’t disputed in general. There are, however,
various arguments against its reality. A thorough but accessible discussion can be found
in Lange (2002, Chaps. 1–2 and 4–6). Mundy (1989) presents a shorter and more historic
approach.
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8.5. The Self-Interaction Problem in Classical Electrodynamics
This is a serious problem in Maxwell-Lorentz electrodynamics, which is mostly ignored in
physics courses. The theory breaks down for the simplest case of a universe consisting only
of one charged particle, because the interaction of the electromagnetic field on the particle
itself leads to infinities. This problem is described in Barut (1980, Chap. V), as well as some
workarounds on how to cope with the self-field within the Maxwell-Lorentz theory. Some
people argue that you have to replace the theory. There are now three proposals:
– Keep the field and add non-linear equations. Born and Infeld (1934) pioneered this
idea. Kiessling (2012) summarizes the current situation of the Born-Infeld theory.
– Keep the field and change the Maxwell equations to higher-order (linear) equations.
This is the Bopp–Podolsky theory (see Perlick 2015).
– Another strategy was followed by Wheeler and Feynman (1945, 1949). Their idea was
to get rid of the field and develop a pure action-at-a-distance theory.
8.6. Entropy and the Arrow of Time
Ludwig Boltzmann is the founder of statistical mechanics. His main concern was that Newton’s law of motion is time reversal invariant, while our world prohibits certain time-reversed
processes. Some time-reversed processes cannot take place because they would violate the
second law of thermodynamics, which says that entropy has to increase. Very good introductions to Boltzmann’s ideas can be found in Bricmont (2001), Goldstein (2001), and Lebowitz
(1993, 2008). Lazarovici and Reichert (2015) respond to critiques and misunderstandings of
Boltzmann.
Online Lectures
– Time’s Arrow and Entropy: Classical and Quantum by Joel Lebowitz.
– Introduction to Thermodynamics and Statistical Mechanics by David Albert.
– The Reversibility Objections and the Past Hypothesis by David Albert.
– The Epistemic and Causal Arrows of Time by David Albert.
8.7. Probabilities in Deterministic Theories
In a deterministic theory, there are no probabilities in the dynamical laws. But still one can and
need to introduce probabilities in order to make empirical predictions. The success of classical
mechanics rests on the use of probabilities although the basic laws are Newtonian. Good
introductions to this topic are Bricmont (2016, Sec. 3.4), Maudlin (2011), and Oldofredi
et al. (2016).
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References
Barbour, J., and B. Bertotti. 1982. “Mach’s principle and the structure of dynamical theories.”
Proceedings of the Royal Society A 382:295–306.
Barbour, Julian. 2003. “Scale-invariant gravity: particle dynamics.” Classical and Quantum
Gravity 20 (8): 1543.
Barut, A. O. 1980. Electrodynamics and Classical Theory of Fields and Particles. New York:
Dover Publications.
Born, M., and L. Infeld. 1934. “Foundations of the New Field Theory.” Proceedings of the
Royal Society of London A: Mathematical, Physical and Engineering Sciences 144 (852):
425–51.
Bricmont, Jean. 2001. “Bayes, Boltzmann and Bohm: Probabilities in Physics.” In Chance
in Physics: Foundations and Perspectives, edited by Jean Bricmont, Giancarlo Ghirardi,
Detlef Dürr, Francesco Petruccione, Maria Carla Galavotti, and Nino Zanghi, 3–21.
Berlin: Springer.
. 2016. Making Sense of Quantum Mechanics. Switzerland: Springer International
Publishing.
Goldstein, Sheldon. 2001. “Boltzmann’s Approach to Statistical Mechanics.” In Chance in
Physics: Foundations and Perspectives, edited by J. Bricmont, D. Dürr, M.C. Galavotti,
G. Ghirardi, F. Petruccione, and N. Zanghì, 39–54. Heidelberg: Springer.
Huggett, Nick, ed. 1999. Space from Zeno to Einstein. Cambridge, MA: MIT Press.
Kiessling, Michael K.-H. 2012. “On the Motion of Point Defects in Relativistic Fields.” In
Quantum Field Theory and Gravity: Conceptual and Mathematical Advances in the
Search for a Unified Framework, edited by Felix Finster, Olaf Müller, Marc Nardmann,
Jürgen Tolksdorf, and Eberhard Zeidler, 299–335. Basel: Springer.
Lange, Marc. 2002. An Introduction to the Philosophy of Physics: Locality, Fields, Energy,
and Mass. Oxford: Blackwell.
Lazarovici, Dustin, and Paula Reichert. 2015. “Typicality, Irreversibility and the Status of
Macroscopic Laws.” Erkenntnis 80 (4): 689–716.
Lebowitz, Joel L. 1993. “Boltzmann’s Entropy and Time’s Arrow.” Physics Today 46:32–38.
. 2008. “Time’s arrow and Boltzmann’s entropy.” Scholarpedia 3 (4): 3348. doi:10.
4249/scholarpedia.3448.
Mach, Ernst. 1919. The Science of Mechanics: A Critical and Historical Account of Its
Development. 4th . Chicago: The Open Court Publishing Co.
Maudlin, Tim. 2011. “Three Roads to Objective Probability.” Chap. 11 in Probabilities in
Physics, edited by Claus Beisbart and Stephan Hartmann, 293–319. New York: Oxford
University Press.
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Maudlin, Tim. 2012. Philosophy of Physics: Space and Time. Princeton, NJ: Princeton University Press.
Montgomery, Richard. 2015. “The Three-Body Problem and the Shape Sphere.” The American Mathematical Monthly 122 (4): 299–321.
Mundy, Brent. 1989. “Distant Action in Classical Electromagnetic Theory.” The British Journal for the Philosophy of Science 40 (1): 39–68.
Oldofredi, Andrea, Dustin Lazarovici, Dirk-André Deckert, and Michael Esfeld. 2016. “From
the Universe to Subsystems: Why Quantum Mechanics Appears more Stochastic than
Classical Mechanics.” Forthcoming in Fluctuations and Noise Letters.
Perlick, Volker. 2015. “On the self-force in electrodynamics and implications for gravity.” In
Equations of motion in relativistic gravity, edited by Dirk Puetzfeld, Claus Lämmerzahl,
and Bernard Schutz, 523–42. Heidelberg: Springer.
Pooley, Oliver, and Harvey R. Brown. 2002. “Relationalism Rehabilitated? I: Classical Mechanics.” The British Journal for the Philosophy of Science 53 (2): 183–204.
Wheeler, John Archibald, and Richard Phillips Feynman. 1945. “Interaction with the Absorber
as the Mechanism of Radiation.” Reviews of Modern Physics 17 (2–3): 157–81.
. 1949. “Classical Electrodynamics in Terms of Direct Interparticle Action.” Reviews
of Modern Physics 21 (3): 425–33.
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9. Philosophy of Relativistic Physics
9.1. The Twin Paradox
Special relativity is a theory with a fixed space-time structure. Everything is not relative in
this theory. Maudlin (2012, Chap. 4) is the best and shortest introduction to the space-time
formulation of special relativity. Another wonderful book is Geroch (1978, Chaps. 1, 5, and
6). With the help of these expositions, you can properly understand the twin paradox, whose
solution is falsely presented in most physics textbooks.
9.2. Mass and Energy in Special Relativity
Einstein’s relation E = mc2 is the most famous physical equation. A brief discussion of
the meaning of mass is presented in Adler (1987) and Okun (1989, 2009). You can find a
detailed treatment of mass, as well as of energy, in Lange (2002, Chap. 8).
9.3. Space-Time in General Relativity
Geroch (1978, Chap. 7 and 8) and Maudlin (2012, Chap. 6) are conceptual introductions
to general relativity that use the least amount of mathematical formalism. From there you
can go in two directions. One problem is to analyze whether general relativity is committed
to space-time as a substance (similar to Newton’s absolute space) or to a relational spacetime (following the tradition of Leibniz). Another problem is whether general relativity is a
deterministic or indeterministic theory. The hole argument plays a major role for both kinds
of issues. The argument can be found in Earman and Norton (1987), and is thoroughly
discussed by Earman (1989, Chap. 9). Maudlin (1988, 1990) critically replied to them.
Hoefer (1996) gives a good account on the metaphysics of space-time substantivalism.
Online Lectures
Einstein’s Discovery of the General Theory of Relativity by John Norton.
9.4. Is Time Travel Possible?
General Relativity allows for time travel. But is this really possible in our actual world?
Arntzenius and Maudlin (2002) discuss this issue. Their article is also an entry in the
Stanford Encyclopedia of Philosophy.
References
Adler, Carl G. 1987. “Does mass really depend on velocity, dad?” American Journal of Physics
55 (8): 739–43.
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Arntzenius, Frank, and Tim Maudlin. 2002. “Time Travel and Modern Physics.” In Time,
Reality & Experience, edited by Craig Callender, 169–200. Cambridge, UK: Cambridge
University Press.
Earman, John. 1989. World Enough and Space-Time. Cambridge, MA: MIT Press.
Earman, John, and John Norton. 1987. “What Price Spacetime Substantivalism? The Hole
Story.” The British Journal for the Philosophy of Science 38 (4): 515–25.
Geroch, Robert. 1978. General Relativity from A to B. Chicago: The University of Chicago
Press.
Hoefer, Carl. 1996. “The Metaphysics of Space-Time Substantivalism.” The Journal of Philosophy 93 (1): 5–27.
Lange, Marc. 2002. An Introduction to the Philosophy of Physics: Locality, Fields, Energy,
and Mass. Oxford: Blackwell.
Maudlin, Tim. 1988. “The Essence of Space-Time.” In Proceedings of the Biennial Meeting
of the Philosophy of Science Association, 2:82–91.
. 1990. “Substances and space-time: What Aristotle would have said to Einstein.”
Studies in History and Philosophy of Science Part A 21 (4): 531–61.
. 2012. Philosophy of Physics: Space and Time. Princeton, NJ: Princeton University
Press.
Okun, Lev Borisovich. 1989. “The Concept of Mass.” Physics Today 42 (6): 31–6.
. 2009. “Mass versus Relativistic and Rest Masses.” American Journal of Physics 77
(5): 430–1.
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10. Philosophy of Quantum Mechanics
10.1. Problems in Quantum Mechanics
10.1.1. Is Quantum Mechanics Incomplete?
The EPR paper (Einstein, Podolsky, and Rosen 1935) has ignited a huge discussion on the
foundations of quantum mechanics that is still going on today. You must read the original
paper for this project; it’s still accessible to modern physicists, and it lets you evaluate the
reactions to it. Unfortunately, the EPR argument has been misunderstood or just ignored by
most physicists.
Einstein’s aim was to show that quantum mechanics is incomplete. Since EPR use for their
argument position and momentum observables, their paper was generally misunderstood to
show how to violate Heisenberg’s inequality. So Bohm (1989, pp. 614–22) presented the
argument using spin observables; here it’s obvious that EPR is about incompleteness. In
fact, Einstein used spin in an unpublished manuscript (Sauer 2007). Norsen (2006, Sec. I
and II) gives a particularly clear exposition of the EPR argument.
Online Lectures
What Bell Did by Tim Maudlin.
10.1.2. Bell’s Theorem and Quantum Non-Locality
Bell’s theorem shows that non-locality is a physical feature of our world, and it’s regarded
as one of the most important discoveries in the history of physics. It’s a historical fact
that Bell’s theory has been misunderstood by most physicists. Bell’s proof presupposed
the EPR argument (Bell 2004a, 2004c). Without appreciating EPR, Bell’s theorem can be
misinterpreted as a no-hidden-variables theorem or a theorem refuting local realism; in fact,
it’s a non-locality theorem. His argument is analyzed by Norsen (2006) and Goldstein et al.
(2011). In particular, Bell’s theorem does not refute realism, whatever that may be.Norsen
(2011) thoroughly discusses of Bell’s theorem and common misunderstandings, and he shows
a version that is not based on EPR.
Mermin (1985) introduces Bell’s theorem without physics by concentrating just on the
statistical pattern of non-local correlations. This is the best introductory article to understand
non-locality and the meaning of Bell’s theorem.
Online Lectures
– Spooky Actions At A Distance? by David Mermin.
– What Did Bell Really Say? by Jean Bricmont.
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10.1.3. Einstein’s Boxes
Einstein’s boxes is a particularly simple thought experiment, which can illustrate the EPR
argument in a much simpler setting. It is that powerful that it can be used to illustrate
non-locality, too. Norsen (2005) introduces this thought experiment and shows how it can
be used to form an EPR-like argument and show non-locality.
10.1.4. The Measurement Problem
The measurement problem is the biggest problem in quantum mechanics, and it’s mostly not
mentioned in physics courses. A classic text on the measurement problem is Maudlin (1995a).
Schrödinger (1983) rephrases the measurement problem with his famous cat thought experiment. Maudlin (1995b) shows how Bohmian mechanics solves the measurement problem.
Brown and Wallace (2005) show how the Many–Worlds interpretation solves the measurement problem.
10.1.5. Contextuality
A physical theory is contextual if it says that the experimental outcomes depend on the way
measurements are done. Before Bell proved is famous theorem, physicists discovered that
supplementing quantum mechanics with hidden variables will make the theory contextual.
There is no hidden variables theory that has pre-determined values for all observables. Of
course, these theorems were misunderstood too; often there are regarded as no-hidden variable theorems that rule out any quantum theory with hidden variables—the de Broglie-Bohm
theory is a counter example. The moral is rather that it’s not trivial to add hidden variables
while being consistent with the quantum predictions.
Bricmont (2016, Sec. 2.5.2 and 2.F) is a very good introduction to contextuality and nohidden-variables theorems. Mermin (1993) also presents these theorems in a clear way, and
he makes the connection to non-locality. Bell (2004b) analyzed famous no-hidden-variable
theorems and unravelled some of their flaws. Bell’s paper is quite difficult, but it’s worth
working through.
10.2. Interpretations of Quantum Mechanics
10.2.1. Collapse Theories
A possible answer to the measurement problem are the so called collapse theories of quantum
mechanics. This kind of quantum theory was developed in the 1980s by the physicists G.
Ghirardi, A. Rimini, and T. Weber; it’s therefore also named “GRW quantum theory”. A
very accessible introduction by one of the founding fathers is Ghirardi (2004, Sec. 16.8 and
Chap. 17). After many years of development and philosophical struggles, the GRW theory
appears now in two versions: there is a matter distribution theory (GRWm ) and a flash theory
(GRWf ). A good introductory article on the different versions of the GRW–theory is Lewis
(2006).
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10.2.2. The de Broglie–Bohm Quantum Theory
Another solution to the measurement problem is provided by the de Broglie–Bohm theory.
Dürr (2001), Goldstein (2010), and Passon (2006) give a concise overview of this theory.
Online Lectures
– A video series on Bohmian mechanics.
– Bohmian Mechanics: Speakable Quantum Physics by Detlef Dürr.
– Bohmian Mechanics by Stefan Teufel.
10.2.3. Many–Worlds
The Many–Worlds Interpretation is also a reaction to the measurement problem. It doesn’t
change the mathematical formalism of textbook quantum mechanics, but it postulates a very
surprising ontology: after every measurement the whole universe multiplies so that in every
branch there is exactly one measurement outcome. This theory was proposed for the first
time by the physicist Hugh Everett III in his doctoral thesis in 1957. Wallace (2012) is now
the most thorough reference. In his review, Maudlin (2014) criticizes Wallace, as well as the
Everett interpretation in general.
Online Lectures
– The Emergent Multiverse I: The Plurality of Worlds by David Wallace.
– The Emergent Multiverse II: The Probability Puzzle by David Wallace.
References
Bell, John Stuart. 2004a. “On the Einstein-Podolsky-Rosen Paradox.” Chap. 2 in Speakable
and Unspeakable in Quantum Mechanics, 14–21. Cambridge, UK: Cambridge University
Press.
. 2004b. “On the Problem of Hidden Variables in Quantum Mechanics.” Chap. 1 in
Speakable and Unspeakable in Quantum Mechanics, 1–13. Cambridge, UK: Cambridge
University Press.
. 2004c. “The Theory of Local Beables.” Chap. 7 in Speakable and Unspeakable in
Quantum Mechanics, 52–62. Cambridge, UK: Cambridge University Press.
Bohm, David. 1989. Quantum Theory. New York: Dover Publications.
Bricmont, Jean. 2016. Making Sense of Quantum Mechanics. Switzerland: Springer International Publishing.
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Brown, Harvey, and David Wallace. 2005. “Solving the Measurement Problem: De BroglieBohm Loses Out to Everett.” Foundations of Physics 35:517–40.
Dürr, Detlef. 2001. “Bohmian Mechanics.” In Chance in Physics: Foundations and Perspectives, edited by J. Bricmont, D. Dürr, M.C. Galavotti, G. Ghirardi, F. Petruccione, and
N. Zhangì, 115–31. Heidelberg: Springer.
Einstein, Albert, Boris Podolsky, and Nathan Rosen. 1935. “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Physical Review 47 (10): 777–
80.
Ghirardi, Giancarlo. 2004. Sneeking a Look at God’s Cards: Unraveling the Mysteries of
Quantum Mechanics. Princeton, NJ: Princeton University Press.
Goldstein, Sheldon. 2010. “Bohmian Mechanics and Quantum Information.” Foundations of
Physics 40 (4): 335–55.
Goldstein, Sheldon, Travis Norsen, Daniel Victor Tausk, and Nino Zanghì. 2011. “Bell’s
Theorem.” Scholarpedia 6 (10): 8378. doi:10.4249/scholarpedia.8378.
Lewis, Peter J. 2006. “GRW: A Case Study in Quantum Ontology.” Philosophy Compass 1
(2): 224–44.
Maudlin, Tim. 1995a. “Three measurement problems.” Topoi 14 (1): 7–15.
. 1995b. “Why Bohm’s Theory Solves the Measurement Problem.” Philosophy of
Science 62 (3): 479–83.
. 2014. “Critical Study—David Wallace, The Emergent Multiverse: Quantum Theory
According to the Everett Interpretation.” Noûs 48 (4): 794–808.
Mermin, N. David. 1985. “Is the moon there when nobody looks? Reality and the quantum
theory.” Physics Today 38 (4): 38–47.
. 1993. “Hidden Variables and the Two Theorems of John Bell.” Reviews of Modern
Physics 65, no. 3 (July): 803–15.
Norsen, Travis. 2005. “Einstein’s boxes.” American Journal of Physics 73 (2): 164–76.
. 2006. “EPR and Bell Locality.” AIP Conference Proceedings 844:281–93. doi:10.
1063/1.2219369.
. 2011. “J. S. Bell’s concept of local causality.” American Journal of Physics 79 (12):
1261–75.
Passon, Oliver. 2006. “What you always wanted to know about Bohmian mechanics but
were afraid to ask.” Invited talk at the spring meeting of the Deutsche Physikalische
Gesellschaft, Dortmund, 28-30 March. http://arxiv.org/abs/quant-ph/0611032.
Sauer, Tilman. 2007. “An Einstein manuscript on the EPR paradox for spin observables.”
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy
of Modern Physics 38 (4): 879–87.
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Schrödinger, Erwin. 1983. “The current Situation in Quantum Mechanics.” Chap. I.11 in
Quantum Theory and Measurement, edited by John Archibald Wheeler and Wojciech
Hubert Zurek, 152–67. Princeton, NJ: Princeton University Press.
Wallace, David. 2012. The Emergent Multiverse: Quantum Theory according to the Everett
Interpretation. Oxford: Oxford University Press.
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11. Philosophy of Mathematics
Brown (2008), Colyvan (2012), and Friend (2007) are excellent textbooks on philosophy of
mathematics. You don’t need prior knowledge of logic or calculus. Colyvan (2012) is the
shortest one and provides a good overview on modern topics. Friend (2007) seems to be the
easiest one, as she almost never uses mathematical formulas; she introduces the historical
debates, as well as some recent topics. Brown (2008) introduces many new topics that are
not covered by the other books. All three sources have excellent lists of bibliographies, which
help you in finding supplementary literature.
11.1. Do Mathematical Objects Exist?
The main ontological question is, “Do the mathematical objects exist independently of the
mind, or are they mental constructions?”, while the main epistemic question asks, “How do
we know about mathematical objects?” These questions are as old as mathematics itself
and are already posed by the ancient Greeks. The main branch that grants mathematical
objects its own existence independent of the human mind is Platonism (Friend 2007, Chap.
2; Brown 2008, Chap. 2). Opposing theories are Logicism, Structuralism, and Constructivism
(Friend 2007, Chaps. 3–5). Sometimes the ontological status of mathematical objects can
even constrain or change logic.
11.2. Why Is Mathematics so Successful in Application?
All began with the essay “The unreasonable effectiveness of mathematics in the natural
sciences” by the Nobel laureate Eugene Wigner (1960). He wondered why mathematics
can be successfully applied to all kinds of problems in the natural sciences. Not only is
mathematics a central part of physics, but it plays a pivotal role in biology, engineering,
finance, and economics, too. It seems to be a miracle that mathematics can help us to
extend our knowledge in so diverse and unrelated fields. Colyvan (2012, Chap. 6) and Brown
(2008, Chap. 4) give very good introductions to the questions raised by Wigner.
References
Brown, James R. 2008. Philosophy of Mathematics: A Contemporary Introduction to the
World of Proofs and Pictures. 2nd ed. New York: Routledge.
Colyvan, Mark. 2012. An Introduction to the Philosophy of Mathematics. New York: Cambridge University Press.
Friend, Michèle. 2007. Introducing Philosophy of Mathematics. Stocksfield, UK: Acumen.
Wigner, Eugene P. 1960. “The unreasonable effectiveness of mathematics in the natural
sciences.” Communications on Pure and Applied Mathematics 3 (1): 1–14.
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