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Philosophy of Science

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Chasing the Light:
Einstein's Most Famous Thought Experiment

Here's how to make sense of Einstein's famous thought experiment in which he chases after a beam of light and is troubled to conclude that he arrives at a frozen waveform.

How did Einstein Discover the Relativity of Simultaneity?

The celebrated discovery may not have happened through Einstein's reflections on clocks and how to synchronize them with light signals. With the help of Lorentz's work of 1895, Einstein may have recognized that the relativity of simultaneity could be read from two well known experimental results, Fizeau's measurement of the velocity of light in moving water and stellar aberration.

moving coil From the Magnet and Conductor to the Relativity of Simultaneity A simple thought experiment shows that the relative existence of the induced electric field in Einstein's celebrated magnet and conductor thought experiment already forces the relativity of simultaneity.

Atoms Entropy Quanta
Einstein's Statistical Physics of 1905
Einstein's work in statistical physics of 1905--from his dissertation to his light quantum paper--is unified by a single insight: Physical systems that consist of many spatially localized, independent micro-components have distinctive macro-properties.

The Fastest, Simplest, Quickest Derivation Ever of the Ideal Gas Law The ideal gas law pops up in so many places where there aren't gases because its derivation does not require the system at issue to be a gas. It can be a solute in solution, suspended particles or even independent light quanta.

Which is the Most Cited of Einstein's Papers of 1905? So you think you can guess...?

How big is an atom? Even if you think you know, this little exercise is enlightening.

How Einstein Changed the Way We Think About Science

At the same time as he brought us the greatest advances in scientific knowledge in centuries, he made us more skeptical of scientific knowledge.

De Sitter hyperboloid How Did Einstein Think? Here's an informal tour that goes from the importance and origins of Einstein's flashes of inspiration to the sorts of mathematical thinking he favored.

Prepared for cityLIVE! "everything einstein," November 15, 2007.
Zurich Notebook A Peek into Einstein's Zurich Notebook Here's a chance to look over Einstein's shoulder and watch him in line by line detailed calculations as he is making the greatest discovery of his scientific career, the general theory of relativity.

tree logo Einstein for Everyone: a web*bookTM This web*bookTM has nearly 40 chapters and surveys Einstein's physics, its history and philosophical significance. The text is written at an introductory level and is drawn from my course "Einstein for Everyone" at the University of Pittsburgh.

The Three Principal Problems of Philosophy of Modern Physics

Philosophy of physics addresses many problems of many different types. It turns out that many of them can be seen as arising when we try to reconcile the three main elements of modern physics: mathematical structures, physical ontology and appearances.

small clock Time Really Passes A common belief among philosophers of physics is that the passage of time of ordinary experience is merely an illusion. The idea is seductive since it explains away the awkward fact that our best physical theories of space and time have yet to capture this passage. I urge that we should resist the idea. We know what illusions are like and how to detect them. Passage exhibits no sign of being an illusion.
gas expansion When a Good Theory meets a Bad Idealization: The Failure of the Thermodynamics of Computation

(very short version for experts)
No Go Result for the Thermodynamics of Computation
The "thermodynamics of computation" is a striking example of a theory created by bad idealizations. It considers computational processes on molecular scales and, by selectively idealizing away fluctuations, concludes that erasure is the only computational process that necessarily creates entropy. A no go result shows that these fluctuations cannot be idealized away selectively.
Maxwell's demon The Simplest Exorcism of Maxwell's Demon
No Information Needed
Efforts to exorcise Maxwell's demon have focused on the information processing a demon supposedly must do. There is a much simpler exorcism. If the demon and thermal system combined are a Hamiltonian system, then the intended operation of the demon must compress the overall phase space, in violation of Liouville's theorem.
clock escapement What is Time?
Or, Just What do Philosophers of Science Do?
This question, we are told, is "...a deep question, and it has no simple answer." That is wrong. It is a trite question that gains the mere appearance of depth cheaply by hidden presumptions.
small fuse The Burning Fuse Model of Unbecoming in Time In the burning fuse model of unbecoming in time, the future is real and the past is unreal. It is used to motivate the idea that there is something unbecoming in the present literature on the metaphysics of time: its focus is merely the assigning of a label “real.”
RNG flow thumb Confusions over Reduction and Emergence in the Physics of Phase Transitions Are phase transitions a banner instance of emergence or treated reductively by renormalization group methods? The answer depends on how you define levels between which the relations of reduction and emergence obtain.
Boltzmann brain You are not a Boltzmann Brain A Boltzmann brain, complete with false memories of a non-existent past, pops into existence momentarily as an extremely improbably fluctuation from a universe in thermal equilibrium. I argue that it is not a scientifically well-grounded version of Descartes' deceiving demon.
"Turtles all the way down." Imagine that the world is supported by an infinite tower of turtles. Does the infinity of the tower of turtles protect it from the pull of gravity? Will the tower stand or fall?
Castles in the air Is it possible to design a foundation for a castle that can float in the air? Here is a design in which the castle rests on an infinite sequence of courses of stones that fill only a finite height.

What is the Lift of an Infinite Helicopter Rotor at Rest? Think you know? A very simple thought experiment yields a surprising result. From it we learn an interesting moral about thought experiments.
The Dome: A Simple Violation of Determinism in Newtonian Mechanics Here is an unexpectedly simple violation of determinism in Newtonian mechanics. The mass on the dome may spontaneously be set in motion with no cause for the time or direction of the motion.
Induction without Probabilities Must our degrees of belief be probabilities? I urge that if we are inferring inductively over indeterministic systems like the dome, then they cannot responsibly be probabilities.
three atom algebra What Logics of Induction are There? Here is a large class of inductive logics based on the idea that the inductive strength of support can be defined in terms of the deductive relations among propositions.
blacksmiths The Point of Intractability What does it take to do good, novel work in philosophy of science? If it easy to write, you can be assured it's already been done. That's why it's easy. The beginning of good, novel work is the identification of the point of intractability, where everything seems too hard and nothing works.
How Not To Do Philosophy of Science On the way to good work in philosophy of science are many, tempting traps. Here is a short compendium to help you avoid them and help you see them when others are tempted.

Last Donut "Who Took the Last Donut?" (offsite)

(some) Faces at the Center
Since 2006 I've been directing the University of Pittsburgh's Center for Philosophy of Science. In my "donuts" reporting on the Center's website, I recount the academic and human sides of just what is going on behind the scenes.
Secrets of Einstein Research Revealed Not all techniques used by historians of science are as straightforward as you think.
Newton's stone Ethics of Imaginary Research It is standard in public policy to implement regimes of regulation that control unrealized harms that are only plausibly imagined. We urge that this policy should be applied consistently in all areas of research.

See a yellow bouncing ball.