awesome.

http://www.foxnews.com/scitech/2011/12/14/slow-mo-video-catches-light-at-1-trillion-frames-second/

last minute questions

Folks,

Quite a few of you have emailed last minute questions. I'm teaching all day, including giving a lecture at lunchtime.

Please don't take offense if I do not get back to you before exam time. I think I answered all the questions up to around 5 pm yesterday. There has been an onslaught in the past few hours.

That said, I"ll endeavor to be in the lecture hall by 4:45 latest.

And now back to my lunchtime lecture......

SL

Text references

Ch 10, all but section 10

Ch 11, up to section 8

Cn 13, sections 5&6

Ch 14, mainly lenses

Read for clarification and further info

More ponderable questions

1. What exactly is the focal length of a lens or mirror? Is it where an image always forms? Under what circumstances do images form there?

2. What types of lenses or mirrors form real images? What types of lenses or mirrors form virtual images?

3. What is an interference pattern?

4. Given two circuits, one with 3 identical resistors in series and one with 3 identical resistors in parallel:

a. which one has the greatest resistance?
b. which one draw the most current from the battery?
c. which one will have brightest light bulbs (if the resistors in question were light bulbs)?
d. which one will kill the battery most quickly

5. What represents some of the best current "proof" that relativity is a real thing?

6. Why does a charged balloon stick to a wall?

7. When you "charge" something positively, what have you done? If you had charged something negatively, what have you done?

8. What are the primary components of motors?

Final exam topics

Relativity and Einstein
Electromagnetic induction (generators)
Electromagnetism (motors, too)
Magnetism
Series circuit
parallel circuit
Ohm's Law (V = IR)
Current (in amperes)
Resistance (in ohms)
Voltage (in volts)
Electrostatics - Coulomb's law
Charge (proton, electron)
Diffraction
Holography
Optics - images formed by lenses and mirrors
Real vs. Virtual images

Know these things:

the difference between real and virtual images
the basics of interference patterns
the basics of holography
what charge is
the difference between proton and electron and neutron
the difference between voltage, current and resistance
the inverse square law idea of Coulomb's laws
relevant units
how to use Ohm's law to calculate current
the difference between series and parallel circuits
magnets and electromagnets - differences, similarities
what electromagnetism is
what electromagnetic induction is
the gist of special relativity (time dilation, length contraction)

Some practice questions:

1. Consider 2 twins: Stacey and Spacey. Stacey stays put and Spacey travels in a spaceship at 1/2 the speed of light. Upon her return, how would Stacey and Spacey compare their ages?

2. In the above example, how would Spacey compare the distance traveled (on her spaceship odometer) to the distance measured before the trip began?

3. What's the big deal about Einstein's "Miracle Year"?

4. What is required for electromagnetic induction to occur? (Basically, how do generators work?)

5. What is required for electromagnets to work? (What is a telegraph?)

6. What do magnets and electromagnets have in common?

7. What is the difference between AA, AAA, C and D batteries?

8*. What is the typical household voltage in the USA?

9*. Speaking of household voltage in the USA - does it provide direct (constant) or alternating current?

10. What current results from a 9-V battery in series with a 100-ohm resistor?

11. What current would result from a 9-V battery in series with TWO 100-ohm resistors?

12. In problems 10 and 11 above, if the resistors were light bulbs, which would be brighter?

13. If you had 2 100-ohm light bulbs in parallel with a 9-V bulb, what would be the current through EACH one? Would they be brighter, dimmer or the same as one bulb? How about compared to TWO identical bulbs in series?

14. What is the difference between electrons and protons, considering their:
a. charge
b. mass
c. location in an atom

15. Two identical charges are some distance apart. What can you say about the force between them (attractive, repulsive?)

16. In the previous problem, if the distance were doubled, what would happen to the force?

17. A convex lens ALWAYS gives a real image? True or false? Discuss.

18. What is the difference between a real and virtual image?

19. What exactly are holograms?

20. What can interference patterns show you?

* Not discussed in class.

Worth a read.

How Einstein Changed the Way We Think About Science

John D. Norton
Department of History and Philosophy of Science, University of Pittsburgh
Pittsburgh PA 15260. Homepage: www.pitt.edu/~jdnorton
This page is available at www.pitt.edu/~jdnorton/goodies

This is an expanded version of my "What Is Einstein's Legacy to Me? Philosophy of Science" appearing in Imagine (Johns Hopkins Center for Talented Youth) Vol. 13, Issue 1, September/October, 2005.



We all know of Einstein's contribution to modern physics. Through his theories of relativity he showed us that there is a fastest possible speed and that light moves at it. He showed us that gravity is a curvature of spacetime. And he laid the foundations of modern quantum mechanics when he proposed that light really comes in little bundles of energy he called quanta. Any philosopher of science interested in the nature of space, time and matter has to take notice, for our accounts of all three were changed fundamentally by Einstein's hand.

What is less well recognized is how Einstein's work altered our understanding of the nature of science itself. To begin, he changed our ideas of how to do theoretical science. In 1905, he showed us how to make sense of the odd fact that light always propagates at exactly the same speed c, no matter how fast we go. The trick was to see that when we change our state of motion, we change our judgments of which events are simultaneous. His lucid analysis, laid out in the opening pages of his famous 1905 special relativity paper, was especially vivid. He used a thought experiment, in which asked us to imagine two clocks exchanging light signals and observers in different states of motion. The signals bounce, the clocks tick and altogether too quickly the final, astonishing result emerges.

The apparent ease with which ordinary thought experiments could yield extraordinary results was inspiring. It led many to try to copy his method They sought new theories, not in novel experiments, but in astonishing revisions of familiar notions like space and time, through carefully crafted thought experiments. These efforts rarely succeeded for those who are not Einsteins.

Another notion was read from Einstein's analysis of 1905. It was a view of which concepts may be used in science. They must be defined by the operations needed to measure the concept. So we can only use the concept of the simultaneity of two events if we can specify just how we may determine their simultaneity, by, for example, operations with light signals. This stringent demand is very effective if our goal is to force critical re-evaluation of some dubious concept. However it is as likely to cause problems where there should be none, for few of our concepts really conform to its standards.

Einstein invented neither the notion of the thought experiment nor the operational definition of a concept. He merely used them more perfectly than any who had gone before him.

The most enduring change brought by Einstein's work was to shake our sense of certainty. When Einstein entered science at the start of the 20th century, there was a strong sense of its stability. In antiquity, Euclid had described perfectly how space really is. In the 17th century, Newton had discovered the dynamics that govern time and matter. It is only from the perspective of this certainty that we can now understand the project of the influential eighteenth century philosopher Immanuel Kant. He felt compelled to devise an explanation of why all our experience must conform to the geometry of Euclid and the mechanics of Newton. The project now seems misplaced. Einstein showed us that both theories can fail when we enter the realms of the cosmically large, the very heavy, the atomically small and the very fast.

Einstein was not the only one to show us the fragility of our knowledge. But he was the first, the most effective, and the best remembered. He showed us that the old certainties had failed. So, we concluded, surely anything that replaces them could fail again.

The old confidence in our knowledge was based on the notion that experiment and experience could bear quite directly on our science. Some, like Ernst Mach, thought that all of science was or should be nothing more than compact summaries of experience. While this idea was always somewhat dubious, it could survive because even the most complicated theory of the era, Maxwell's electrodynamics, appeared to remain close to experience. For each of Maxwell's equations, one could point to experiments that seemed to be expressed just by that equation.

This sense of the closeness of theory to experience was shattered by Einstein's general theory of relativity. It required a new and complicated mathematics then unfamiliar to most physicists. Yet most of its predictions were no different than those of Newton's much simpler theory. If theories were merely summaries of experience and did not add to them, how could two theories, so much in agreement on experience, differ so much in structure?

Einstein's physics and the new physics developed by others in the twentieth century led to a sense of the fragility of theories and the powerlessness of evidence to pick out the unique truths of nature. Philosophers of science struggled to accommodate this new sense within their systems, all the while seeking to fit their ideas with Einstein's theories.

Einstein's own diagnosis of this gap between experience and theory was extreme. He proclaimed that concepts and theories are "free inventions of the human spirit" and that no method could assuredly take us from experience to the true theory. Here he contradicted the optimism of the nineteenth century during which many felt that scientific discovery could be reduced to simple recipes. John Stuart Mill continued a tradition extending back to the seventeenth century Francis Bacon. To identify the cause of some effect, he believed, one merely needed to collect cases in which the effect was present and those in which it was not. The cause could then be read directly from the systematic differences between the cases.

Later in life, Einstein came to a radical solution of the problem of responsibly practicing science while still believing that its core concepts are free inventions. Drawing on his discovery of general relativity, he concluded that the right concepts and theories could be found merely by seeking the mathematically simplest theories.

In my view, Einstein's response was too optimistic in his confidence that mathematical simplicity could be the guide to the truths of nature. Einstein was able to make no major discovery using this principle during the decades of his legendary and ultimately barren search for a unified field theory.

And Einstein's notion that concepts and theories are free inventions not fixed by experience seems too pessimistic, for science seems time and again to be able to determine the right theory on the basis of evidence. In the face of this commonplace of science, Einstein too seems to have had some difficulty maintaining his notion of free invention. He likened nature to a "well-designed word puzzle." While we may try to solve it with many words, only one "really solves the puzzle in all its parts."

This last view seems to me to capture much better the real power of evidence to point to a definite theory. If the equivalence of energy and matter expressed by E=mc2 is based on free inventions, why is there no alternative that enjoys equally powerful support from our experiences and experiments?



Some Reading

Einstein, Albert. Relativity: The Special and the General Theory. Methuen & Co., 1920.

Einstein, Albert. Ideas and Opinions. New York: Bonanza Books, 1954.

Howard, Don A., "Einstein's Philosophy of Science", The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.) http://plato.stanford.edu/archives/spr2004/entries/einstein-philscience/.


John D. Norton is a licensed and certified dilettante whose hobby is the study of Einstein's work and thought. This hobby has so overtaken his life that he has little time for anything else and is Professor of History and Philosophy of Science and (Sept. 2005-) Director of the Center for Philosophy of Science at the University of Pittsburgh.

Copyright John D. Norton, May 14, 2005.

>

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/index.html

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http://plato.stanford.edu/archives/spr2004/entries/einstein-philscience

Einstein notes

Notes from class:

And then there was Einstein…

Albert Einstein 1879-1955

http://www.aip.org/history/einstein/index.html

What’s happening around the turn of the 20th century? Physics was set to explode with 30 brilliant years of excitement and unprecedented activity

X-rays – Roentgen

Radioactivity – Becquerel, Marie & Pierre Curie

Blackbody radiation (and the quantum discontinuity) – Planck

1905/6 – Einstein publishes 6 major papers:

a) “On the electrodynamics of moving bodies”

b) “Does the inertia of a body depend upon its energy content?”

c) “On a heuristic point of view about the creation and conversion of light”

d) “On the theory of the Brownian movement”

e) “On the movement of small particles suspended in stationary liquid demanded by the molecular-kinetic theory of heat”

f) “A new determination of molecular dimensions”

What are these about anyway?

a. Special relativity (SR)

b. E = m c2 (actually, L = m c2)

c. Photoelectric effect, light quanta, fluorescence

d. Same as title

e. Brownian motion agan

f. Avagadro’s number, etc.

Now, these are interesting (and very different fields of study), but is this why we revere Uncle Al? Not necessarily. Others (Poincare, Lorentz) were working on what would become SR. Planck had introduced the quantum discontinuity (E = h f) and quantum mechanics (QM) would have many contributors. The photoelectric effect had also several investigators (Lenard, et.al.).

Mostly, Einstein’s legend grows because of General Relativity (GR), which appears 1912-1915 and later and on which he worked largely alone with pad and pen. He forced us to re-examine how we see ourselves in the universe; indeed, how we think of gravitation. All of this around the time his marriage was falling apart (he married young after fathering 1 illegitimate child) and he began an affair with his cousin (whom he would later marry). Also, between 1902 and 1909, Einstein held a modest post in Bern, Switzerland as a Patent Clerk. By 1914, he would be director of the Kaiser Wilhelm Institute (later Max Planck Institute).

Special Relativity

Spaceship – Inside an inertial reference frame (constant velocity), you can’t tell whether or not you’re moving (“Principle of Relativity”)

Biographical notes

1879 – born in Ulm, Germany

1884 – receives first compass

1895 – attempts to gain entrance to Swiss Polytechnic (and finish high school early), but is rejected

1896 – begins Federal Polytechnic (ETH) in Zurich, Switzerland

1898 – meets Mileva Maric

1900 – graduates from ETH

1901 – Einstein becomes Swiss citizen and moves to Bern; Mileva becomes pregnant

1902 – Lieserl born (put up for adoption); Hermann dies

1903 – Albert and Mileva marry

1904 – Hans Albert born

1905 – Einstein’s “Annus Mirabilus”, his miracle year; Ph.D. (Zurich)

1919 – divorces Mileva (having lived apart for 5 years); marries Elsa; GR verified

1921 – awarded the Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".

1933 – settles in Princeton, NJ

1936 – Elsa dies

1939 – E. writes FDR

1940 – E. becomes American citizen

1949 – Mileva dies

1955 – E. dies

http://www.aip.org/history/einstein/index.html

http://www.albert-einstein.org/

http://einstein.stanford.edu/

http://en.wikipedia.org/wiki/Einstein

General Relativity

By 1907, E. wanted to advance the SR theory to include non-inertial (accelerated) frames of reference. Around this time, E. has the “happiest thought of my life”. In a uniformly accelerated spaceship, a stationary thing (ball, etc.) would appear to be falling (accelerating) down – it would be indistinguishable from normally accelerated motion. Light, too, follows this idea. Two clocks at different ends of an accelerated spaceship would be out of sync. Gravity is the result of the curvature of space and time?

Why does the Earth follow the Sun? Gravity – the very presence of the Sun causes Earth to veer from its otherwise straight (Newtonian inertial) path. With the Sun, it takes an elliptical path as its natural motion. Getting to this point, and showing that mass alters space and time is the real genius.

There is a breakdown of the observed geometry (Euclidean). E. must use non-Euclidean geometry (Gauss, surfaces, infinitesimal geometry) to consider the behavior of things (rods, etc.) on surfaces. He also considers the shortest distance between 2 points on a sphere (geodesic, great circle). He obtains the mathematical advice of his friend Marcel Grossman and studies (at great length) tensor calculus, differential geometry, Riemann and Minkowski math … it’s all puzzle solving. Soon, the principle of equivalence emerges. Eventually, the gravitational field equations appear (to show how matter “produces” gravity. GR was mostly worked out by 1913

STUDENT IN NEED OF HELP

Folks,

My apologies (to the student) for not announcing this in class. A member of the class is requesting help with class notes. If you attend class regularly and take complete and legible notes, please consider copying your notes for this student's personal study use. You will be given a copy card and paid $100.

See me in class for details. I can put you in touch with the student.

Again, I apologize to the student for not announcing this during the past class.

SL

Images from Series and Parallel notes

Some ideas from the Magnetism sessions

As in the case of charge, magnetic poles are divided into North and South poles.

A North magnetic pole is one that is attracted to the Earth's magnetic north pole. This means that the Earth's magnetic north is ACTUALLY A SOUTH POLE (magnetically speaking).

Like poles repel.
Opposite poles attract.
Each magnet MUST have at least one north and one south pole.
Magnetic fields are real, though the field lines are imaginary. Field lines indicate the direction that a compass needle would take in the vicinity of the magnet.

Magnetic north on the Earth is near Ellesmere Island in Northern Canada, several hundred miles from true (geographic) North - the North Pole.

For gory detail:

http://en.wikipedia.org/wiki/North_Magnetic_Pole

To find true/geographic North, it has historically been done by following Polaris (the pole-star, the lodestar, the North star). Polaris is actually not all that bright (though in the top 50). You need to find the Big Dipper (the rear end of Ursa Major) and follow the two pointer stars at the end of the scoop - these point to Polaris (which is in Ursa Minor). [If you were to follow the "arc" of the handle, it would take you to the bright star Arcturus, as in "follow the arc to Arcturus".]

FYI - "Star Hopping" is a great way to learn your way around the sky. I like the free star chart site:

http://www.skymaps.com/

Magnetic fields are related to electron spins. Electrons act like miniature (extremely miniature) spinning tops. There is a magnetic element associated with their spins. If spins align, more or less, an object can be said to be somewhat magnetic. More spin alignments (domains) means more magnetism. Materials that do this well are said to be ferromagnetic.

As it turns out, metals do this best, as they often have free electrons. In the core of the Earth, molten metal convects (rises and falls) giving the Earth a good magnetic field - measurable from the surface and beyond. Several planets have magnetic fields.

In general, the motion of charges leads to magnetic fields. If you have charge travel through a wire, electrons can be thought of as moving together - this causes a magnetic field. The magnetic field generated by a current passing through a wire is often small, but if you coil the wire upon itself, the magnetic fields add up. Several hundred turns of wire (with current running through them) can produce quite a strong electromagnet. Understanding electromagnets allows us to understand motors.

Current causes magnetism - something shown in the earth 19th century by Hans Oersted. As it happens, the reverse is also true: magnetism can causes current, but it must be a CHANGE in the magnetic field. The magnet (or conductor/coil through which it travels) must move. There must be some relative change between coil and magnet - either the coil must move or the magnet must move.

This is referred to as electromagnetic induction, and it is the secret to understanding generators. If a coil moves in a magnetic field, a current is generated inside it. Imagine turbines at the bottom of Niagara Falls (or any waterfall) - water hits the turbine and makes it spin. Inside the turbines are large coils of wire, free to rotate. These coils spin within a permanent magnetic field inside the turbine - this generate large amounts of current. Similarly, you can burn fossil fuels to heat water and generate steam. The steam is fed into a turbine, also generating large amounts of current.

It's all about moving conductors in magnetic fields!

Magnetism