Prize
list B: Prizes offered for special achievements (volumes I to V)
Prize list C: Prizes offered around the strand
model (volume
VI)
The text contains over 1700 challenges. For some challenge solutions of particular didactic or research value I offer special prizes. This list is now considerably expanded. The first good solution I receive will be added to the free physics textbook, together with the sender's name. Partial prizes may also be awarded. To apply for a prize, mail a solution to christoph@motionmountain.net. Prize list B is for special achievements. Some challenges from prize list C could lead to publications or form chapters in a PhD thesis.
Der Rechtsweg ist ausgeschlossen.
MY FAVORITE:
Challenge F: Determine the ropelength of the Higgs
tangle. Prize: secret.
PRIZE LIST A: Prizes offered for solving teaching challenges (volumes I
to V)
Challenge A 19: Propose solutions to
challenges marked as "ny".
Prize: 10 euro each.
Challenge A 18: Take and send in
pictures about striking examples of motion in biology or in any other
field.
Prize: 50 euro.
Challenge A 17: Find a research
literature reference for the difficulties encountered when trying to
observe classical tachyons, i.e. the difficulties encountered when
a classical tachyon (assuming it exists) flies across your field
of view. (There is such a reference somewhere, I know it from hearsay.)
Prize: 50 euro. One attempt so far.
Challenge A 16: Write an article about
the site and book in a newspaper or journal.
Prize: 50 euro.
Challenge A 15: Supply photos and
graphics for wave interference, polarization, diffraction, refraction, wave
damping, and wave dispersion. Prize: 20 euro each.
Challenge A 14: Take and send in a
photograph of how a candle flame reacts to a rubbed comb or, better, of how
it splits in a high electric field. Prize: 50 euro.
Challenge A 13: Send in a quality CAD
drawing of a Foucault gyroscope. (One attempt so far.) Prize: 50
euro.
Challenge A 12: Provide figures of the
most important topological defects: twirls, hedgehogs, etc.
Prize: 10 euro.
Challenge A 10: Supply details on the
mathematics of tree growth: the laws about their proportions, the height of
their trunks, the significance of the principle of minimum effort, etc.
Prize: 50 euro.
Challenge A 9: Convince Adobe to
eliminate an ugly and old bug: in Adobe Reader, horizontal line thicknesses
are shown on screen irregularly in wrong, usually exaggerated thicknesses.
That makes tables look horrible. The bug has been noted and communicated
to Adobe by many since version 1 of the program; it is still present in
version 9. This one will receive a special reward, because even several
Adobe engineers gave up on the topic in the past. The reward is 50 euro
plus a paper copy of the 6 volumes signed by the author, with a special
thank you letter in the name of all graphics artists worldwide. Two
attempts so far.
Challenge A 8: Explain the problems
in performing a Bohm-type experiment with two nuclei that are first near
each other and then separated. Prize: 50 euro.
Challenge A 7:
Taking a combined photograph of a rainbow,
similar to the one
by Stefan Zeiger, but
including a third segment with the ultraviolet picture. Prize: 50 euro.
Challenge A 6:
Extending the belt trick to spin 3/2.
The Dirac belt trick simulates the behaviour of a spin
1/2 particle.
What is the construction for a composed spin 3/2 particle? For an elementary spin
3/2 particle? Prize: 50 euro. One attempt so far.
Challenge A 5: The simplest unsolved knot
problem. Imagine an ideally wobbly rope, that is, a rope that has
the same radius everywhere, but whose curvature can be changed as one
prefers. Tie a trefoil knot into the rope. By how much do the ends of the
rope get nearer? In 2011, there are only numerical estimates for the
answer: about 10.1 diameters. There is no formula giving the number 10.1
yet - can you find one? Alternatively, solve the following problem: what
is the rope length of a closed trefoil knot? Also in this case, only
numerical values are known -- about 16.33 rope diameters -- but no exact
formula. Prize: 500 euro – and publish the
solution! One attempt so far.
Challenge A 4:
Rotation in special relativity. Make a movie
of a sphere/football with relativistic speed and relativistic rotation speed. Show the
strange effects that appear. Prize: 100 euro – and publish the
solution! Half an attempt so far.
Challenge A 3: Classical Lagrangian for
waves. Use the relation for the errors in angular frequency and
time for wave packets, dw dt > 1/2, to show that the classical action for a
wave is bounded below. Find the precise bound by assuming that the initial
and final points for which the action is determined must themselves obey
the wave packet relation. Prize: 100 euro – and publish the
solution!
Challenge A 2: The 'tangles inside a sphere'
problem. This problem combines topology, statistics and geometry.
Estimate the number of topologically different tangles that can fit into a
sphere of given volume, with the assumption that every strand, though
flexible, has constant diameter. A glass sphere of radius R contains n
strands of diameter d (d<R), all starting and ending on the surface (at
2n given and fixed points distributed over the surface). How many
topologically different tangles can be formed, under the condition that the
diameter d has the largest possible value for a given n? [Note: in
mathematics, one distinguishes trivial, composed, rational, locally knotted
and prime tangles. The problem asks for the number of possible tangles
that are composed or prime. Locally knotted tangles may be left out of the
counting; rational tangles do not count as topologically different in this
problem.] Prize: 1000 euro – and publish the
solution! One attempt so far.
Solved challenge A 1: The parking
problem. Find the minimum number of times one has to drive
backwards and forwards to leave from a parking space, when the available
space and the geometry of the car are given. Look up the details by
searching for 'car parking' in the book index. After several attempts by
others,
the prize has been awarded to Daniel Hawkins.
Solved challenge A 11: Provide a research
literature reference for the diffusive speed of light in the solar
interior. Prize awarded to Zach Espiritu.
Solved challenge A 20: Produce an
animation that is unique throughout the world, one that shows clearly how
two belts behave as fermions under exchange, complementing the now
standard visualisation that a belt behaves like a fermion under
rotations. Together with the usual belt trick, the animation would
thus visualize the spin-statistics theorem for spin 1/2. The ideas and the
original physical behaviour to be shown are straightforward, but the
graphic work will take a bit of patience. The resulting animation would
extend the applet shown at http://www.gregegan.net/APPLETS/21/21.html
to a situation with two belt buckles and four belts. If you
are interested, get in touch with me. One option could be to start with
the software at http://www.cs.indiana.edu/~hansona/quatvis/Belt-Trick/index.html
and then expaning it. The resulting animation would be unique world-wide,
and I would build it into the text. The prize
goes to Antonio Martos for his wonderful animation shown
here.
PRIZE LIST B: Prizes offered for special achievements (volumes I to V)
Challenge B 3: Translate parts of the
text into Spanish, Italian, German, French or any other language. Click here
for details on how to do it and then let me know. I will find a way to
reward your efforts appropriately.
Challenge B 2: Convert the latex files
into html, and then into daisy or epub format. I will find a way to
reward your efforts appropriately.
Challenge B 1: Propose substantial
improvements to the text. I will reward your input in a way that is
comparable to the other rewards listed here.
PRIZE LIST C: Prizes offered for challenges about the strand
model (volume VI)
Challenge C 1: Determine
how the probability of belt-trick-like rotation for a polymer-tethered ball
depends on the radius of the ball and the number of polymer chains. The
length of the polymers is assumed very large compared to all other
dimensions. Prize: 500 euro – and publish the
solution!
Challenge C 2: Determine the
probability of twists (Reidemeister Type I) moves for a tangle made of two
or three strands. Show that the square of the probability is 1/137.036.
Prize: 1000 euro – and publish the solution!
Challenge C 3: Determine, from
the strand model, how the mass of the W and Z bosons run with energy Prize:
500 euro – and publish the solution!
Challenge C 4: Extrapolate the
measured up and down quark masses to Planck energy, using the standard
model. Prize: 100 euro – and publish the solution!
Challenge C 5: Determine, using
the strand model and ropelength calculations, the mass ratio between the
muon neutrino and the electron. Prize: 500 euro – and publish the
solution!
Challenge C 6: Deduce, using the
strand model, an analytical approximation for particle mass ratios
or particle masses, e.g., based on ropelength or on the W/Z mass ratio
calculation Prize: 1000 euro – and publish the
solution!
Challenge C 7: Find, using the
strand model, an analytical approximation for probabilities of core
shape changes Prize: 1000 euro – and publish the
solution!
Challenge C 8: Formulate, for the
strand model, a simple relation between strand diameter and the Planck time
Prize: 50 euro.
Challenge C 9: Describe, for the
strand model, the relation between strand distance and the modulus of the
wave function
Prize: 50 euro.
Challenge C 10: Deduce in a simple
way, for the strand model or for textbook quantum mechanics,
Schwinger's quantum action principle from the quantum of action.
Prize: 100 euro.
Challenge C 11: Find, for the
strand model, a simple visualization of the weak mixing angle, also called
the 'Weinberg angle'. Prize: 100 euro.
Challenge C 12: Find, for the
strand model, a compelling deduction of the gluon tangles. Prize:
200 euro.
Challenge C 13: Find, for the
strand model, the precise phase choices for a crossing that lead to SU(3)
invariance. Prize: 200 euro.
Challenge C 14: Visualize, for the
strand model, the relation between SU(3) in the harmonic oscillator and
SU(3) due to the third Reidemeister move. Prize: 200 euro.
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