The text contains over 1700 challenges. For challenge solutions of particular didactic or research value I offer special prizes. 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 firstname.lastname@example.org. Prize list B is for special achievements. Some challenges from prize list C could lead to publications or form chapters in a PhD thesis.
Challenge F: Discover the correct
tangles, in volume VI, for the W and Z boson. The solver will receive a
special prize plus an amount of at least 1000 euro – and the solution
should be published!
Challenge F: Draw as eps a 3d picture
of space-time curvature
like this one and allow me to use it in the text. Your name and copyright
will be mentioned. Prize: 50 euro.
PRIZE LIST A: Prizes offered for solving teaching challenges (volumes I
Challenge A 19: Propose good 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 -
with permission of use. 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 a better reference than Recami, somewhere, I know it
from hearsay. There is also a website somewhere, I saw it and lost it in
2014.) Prize: 50 euro. One attempt so far.
Challenge A 16: Write an article about
the site and book in a newspaper or journal. Prize: a paper
Challenge A 15: Supply beautiful and
clear photos for wave interference, polarization, diffraction, refraction,
wave damping, and wave dispersion.
Prize: 20 euro each.
Challenge A 12: Provide figures of the
most important topological defects: twirls, hedgehogs, etc.
Prize: 10 euro.
Challenge A 10: Supply valuable
details on the mathematics of tree growth: the laws about their
proportions, the height of their trunks, as derived from the principle of
minimum effort, etc. Prize: 50 euro. Two attempts so far
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 XI. 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. Three
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
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 from me, plus eternal fame :-) – thus
publish the solution! Two attempts 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
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
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 13: Send in a quality CAD
drawing of a Foucault gyroscope. Prize awarded to Zach Espiritu.
Solved challenge A 14: Take and send
in a beautiful and clear photograph of how a candle flame reacts to a
rubbed comb or, better, of how it splits in a high electric field.
Prize awarded to Shubham Das and Rakesh Kumar.
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 expanding it. The resulting animation will be unique world-wide,
and I would build it into the text. The prize
goes to Antonio Martos for his wonderful animation shown
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 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 0:
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. First, look at this
video. Then, imagine that the belts are cylindrical polymer chains,
not flat bands, and that there are not only 2, but n of them; also imagine
that the central buckle is a ball - either spherical or ellipsoidal. In
the strand model, the probability for the belt trick is related to the
absolute mass of the elementary particles. So solving this polymer problem
in detail will also advance particle physics. The solver will receive a
special prize plus an amount of at least 500 euro – and the solution
should be published!
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
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 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
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
Challenge C 7: Find, using the
strand model, an analytical approximation for probabilities of core
shape changes. Prize: 1000 euro – and publish the
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 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.
Challenge C 15: Check and
estimate the six basic lepton tangles and their ropelength.
Prize: a surprise.
Challenge C 17: Confirm or invalidate
the new W and Z tangles defined with the help of two strands.
Prize: a surprise.
Solved challenge C 4: Extrapolate the
measured up and down quark masses to Planck energy, using the standard
model. Solved by Shun Zhou.
Solved challenge C 8: Formulate, for the
strand model, a simple relation between strand diameter and the Planck
time. Solved in the new edition of volume VI.
Solved challenge C 12: Find, for the
strand model, a compelling deduction of the gluon tangles. Solved in the
new edition of volume VI.
Solved challenge C 16: Calculate or estimate the ropelength of the (corrected) Higgs tangle (volume VI). Solved by Eric Rawdon and Rob Sharein.
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