The Birth of Quantum Mechanics

Louis De Broglie

Max Planck started Quantum Mechanics in 1900. One of the great ironies in Science History is that he never liked the field, indeed, fought against it for the majority of his life, like a Father whose standards for his son are so high that the child always disappoints him, although outside observers know the father is being too tough and stubborn.

Which is not to say Planck wasn't a nice man, because he was. His life had a great sadness though: He had four children, and all died before him, one each of his two sons in the two World Wars, and his two daughters in childbirth. They say the 3rd greatest sadness that can befall a person is Divorce, the second the death of a lifelong spouse, but the saddest of all is the loss of your child, and that happened to Max 4 times. :-(

But he also fathered QM, clearly the most unexpected and outstanding scientific discovery of his age, or any other.

Within 5 years a patent clerk in Switzerland added to the theory, and gave Planck his due. Planck wasn't completely in agreement with young Albert Einstein's interpretations, but he was grateful for the acknowledgment, and promoted Einstein within the Physics community. The rest is History.

Niels Bohr added still more to the theory in 1913, and the 3 first Greats in QM were established.

And there the theory stood, with more questions than answers, as new theories often do, and for a good long time.

Finally, a young Physics student named Louis De Broglie tackled a thorny problem in QM with his Doctoral Dissertation in 1924. Is his own words:

"The fundamental idea of [my 1924 thesis] was the following: The fact that, following Einstein's introduction of photons in light waves, one knew that light contains particles which are concentrations of energy incorporated into the wave, suggests that all particles, like the electron, must be transported by a wave into which it is incorporated... My essential idea was to extend to all particles the coexistence of waves and particles discovered by Einstein in 1905 in the case of light and photons."

... Louis-Victor-Pierre-Raymond, 7th duc de Broglie

In other words: If waves of light can act as particles, can particles then act as waves? Because they can, and in certain circumstances as we shall see: they do.

The significance of De Broglie's thesis is that it started the second revolution in Quantum Mechanics, indeed it opened the floodgates of discovery in the field, and within 5 years the other Greats in Quantum Mechanics would complete the theory, men such as Max Born, Pascual Jordan, Werner Heisenberg, Erwin Schrodinger, Wolfgang "The New Einstein" Pauli, and Paul Dirac, with a tremendous assist by mathematician Hermann Weyl and Group Representation Theory.

De Broglie's work is beautifully simple, easy enough to be understood by a bright 8th-grader science student, let alone a high-school-er. Which begs the question: WHY are we waiting until college to teach our children Quantum Mechanics? Well I don't know why. Because the teachers don't understand it, perhaps? Well, that's an issue and question for another time.

In any event, here's the theory, below. From Andrew Thomas' wonderful webpage: What is Reality?, from the first chapter: Quantum Mechanics: An Introduction:


Quantum mechanics could be said to have started in 1900 when Max Planck made the discovery that light, which was considered to be purely wave-like, was in fact composed of energy which came in discrete packets (called "quanta").


In the Planck formula, the energy of the packets, e, is proportional to the light frequency, f, the constant of proportionality being Planck's constant, h:



This result suggested that waves (light) were in fact composed of particles. The converse of this result came in 1923 when Louis de Broglie (pronounced to rhyme with "destroy") suggested that matter (particles) behaves as a wave (as is evident in the double-slit experiment), the wavelength, , being inversely proportional to the particle's momentum, p.


Here's the derivation:



We now know that absolutely everything in the known universe is made out of these strange particle/wave entities which obey these two formulae for quantum behaviour, given above.

Max Planck

PROVE It !!!

May people are afraid to major in Mathematics, because they are afraid they will have to "prove" things, and that seems hard. Well OK fine, it's not that easy, but it's not THAT hard either. FEAR is the enemy, and each of us have to overcome it. For an example of how easy it CAN be, I offer up this rerun of a post I made this past February, and hopefully the proof itself will show how beautiful mathematics truly is:

There can be only five regular polyhedra. Somebody had to prove that once, and the proof is beautiful. 

The man who proved it was the little known (except to mathematicians) Theaetetus, instructor/professor at Plato's Academy. Along with Plato, Aristotle and Euclid, he stands out as the greatest of the great from that important time and place.


To read more about him (I'll close with his Wikipedia entry) I strongly recommend reading Chapter 4 of this book:

 Euler's Gem by Dave Richeson

In fact, buy the book and read all the chapters. The proof below comes from Chapter 5 soon thereafter.


The Proof:


Consider a regular polyhedron. Each face is a regular polygon having n sides, and m edges of the polyhedron meet at each vertex (corner).


Because every face must have at least three sides, n is greater than or equal to 3, and because at least three edges meet at each vertex, m is greater than or equal to 3.


Every angle of every face has the same measure, call this angle: theta. 

At each vertex there are m faces, each contributing a plane angle with measure theta.


From Euclid's theorem, it follows that m times theta must be  less than 360 degrees.


For which m and which n is this possible?


When n = 3, the faces are equilateral triangles, so theta = 60 degrees. (The measure of an interior angle of a regular n-sided polygon is 180 degrees times (n-2)/n.)


Insisting that m times theta is less than 360 degrees, we have m times 60 degrees is less than 360 degrees, or m is less than 6. 


So m = 3, 4 or 5 are the only possibilities.


These values of m yield the tetrahedron, the octahedron, and the icosahedron, respectively.


When n = 4, the faces are square, so theta = 90 degrees.


This implies that m times 90 degrees is less than 360 degrees, or m is less than 4. 


So we can only have m=3, and we obtain the cube.


When n = 5, the faces are regular pentagons and theta = 108 degrees. Thus m times 108 degrees is less than 360 degrees, or m is less than 10/3.


So we can have only m = 3, and we obtain the dodecahedron.


When n = 6, the faces are regular hexagons and theta = 120 degrees. But m times 120 degrees being less than 360 degrees implies than m is less than 3, which is impossible.


So there is no regular polygon with hexagonal faces.


We encounter the same problem when n is greater than 6. 


Thus there are no other Platonic solids.


Finis.


So-o beautiful.


This is from Book XIII of Euclid's Elements, the final book, which it is believed Euclid wrote directly from Theaetetus' notes. The most important part of Book XIII is considered to be the proof that there are 5 and only 5 regular (Platonic) solids. 


"Many historians contend that all of the mathematics in Book X and XIII of the Elements is due to Theaetetus." ... Dave Richeson




Theaetetus, Theaitētos, (ca. 417 BC – 369 BC) of Athens, possibly son of Euphronius, of the Athenian deme Sunium, was a classical Greek mathematician. His principal contributions were on irrational lengths, which was included in Book X of Euclid's Elements, and proving that there are precisely five regular convex polyhedra.

Theaetetus, like Plato, was a student of the Greek mathematician Theodorus of Cyrene. Cyrene was a prosperous Greek colony on the coast of North Africa, in what is now Libya, on the eastern end of the gulf of Sidra. Theodorus had explored the theory of incommensurable quantities, and Theaetetus continued those studies with great enthusiasm; specifically, he classified various forms of irrational numbers according to the way they are expressed as square roots. This theory is presented in great detail in Book X of Euclid's Elements.

Theaetetus was one of the few Greek mathematicians who were actually natives of Athens. Most Greek mathematicians of antiquity came from the numerous Greek cities scattered around the Ionian coast, the Black Sea and the whole Mediterranean basin. Likewise, most Greek scientists came from the scattered Greek cities and not from Athens. Athens, and later Alexandria were centers of attraction because of the philosophical schools of Plato (the Academy) and Aristotle (the Lyceum), and the renowned Museum and Great Library. The Academy of Plato operated in Athens for almost 600 years, and served as educational center even for some of the early fathers of the Christian church.

He evidently resembled Socrates in the snubness of his nose and bulging of his eyes. This and most of what we know of him comes from Plato, who named a dialogue after him, the Theaetetus. He apparently died from wounds and dysentery on his way home after fighting in an Athenian battle at Corinth, now widely presumed to have occurred in 369 BC.

The crater Theaetetus on the Moon is named after him.

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External links

• A Discussion of Theaetetus' Contributions to Euclid's Elements

STEVEN JOBS (1955-2011)

‎"Don’t be trapped by dogma — which is living with the results of other people’s thinking. Don’t let the noise of others’ opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary.” 


- Steve Jobs


Rest In Peace

List of Unsolved Problems in Mathematics

This article lists some unsolved problems in mathematics. See individual articles for details and sources.

Contents 1 Millennium Prize Problems 2 Other still-unsolved problems 2.1 Additive number theory 2.2 Number theory: prime numbers 2.3 General number theory 2.4 Algebraic number theory 2.5 Discrete geometry 2.6 Ramsey theory 2.7 General algebra 2.8 Combinatorics 2.9 Graph theory 2.10 Analysis 2.11 Dynamics 2.12 Partial differential equations 2.13 Group theory 2.14 Set theory 2.15 Other 3 Problems solved recently 4 See also 5 References 5.1 Books discussing unsolved problems 5.2 Books discussing recently solved problems

[edit] Millennium Prize Problems

Of the seven Millennium Prize Problems set by the Clay Mathematics Institute, six have yet to be solved:

• P versus NP
• Hodge conjecture
• Riemann hypothesis
• Yang–Mills existence and mass gap
• Navier–Stokes existence and smoothness
• Birch and Swinnerton-Dyer conjecture.

The seventh problem, the Poincaré conjecture, has been solved. The smooth four-dimensional Poincaré conjecture is still unsolved. That is, can a four-dimensional topological sphere have two or more inequivalent smooth structures?

[edit] Other still-unsolved problems

[edit] Additive number theory

• Goldbach's conjecture and its weak version
• The values of g(k) and G(k) in Waring's problem
• Collatz conjecture (3n + 1 conjecture)
• Gilbreath's conjecture
• Erdős conjecture on arithmetic progressions
• Erdős–Turán conjecture on additive bases
• Pollock octahedral numbers conjecture

[edit] Number theory: prime numbers

• Catalan's Mersenne conjecture
• Twin prime conjecture
• Are there infinitely many prime quadruplets?
• Are there infinitely many Mersenne primes (Lenstra–Pomerance–Wagstaff conjecture); equivalently, infinitely many even perfect numbers?
• Are there infinitely many Sophie Germain primes?
• Are there infinitely many regular primes, and if so is their relative density e ^{− 1 / 2}?
• Are there infinitely many Cullen primes?
• Are there infinitely many palindromic primes in base 10?
• Are there infinitely many Fibonacci primes?
• Are there infinitely many Wilson primes?
• Are there any Wall–Sun–Sun primes?
• Is every Fermat number 2²ⁿ + 1 composite for n > 4?
• Is 78,557 the lowest Sierpinski number?
• Is 509,203 the lowest Riesel number?
• Fortune's conjecture (that no Fortunate number is composite)
• Polignac's conjecture
• Landau's problems
• Does every prime number appear in the Euclid–Mullin sequence?

[edit] General number theory

• abc conjecture
• Do any odd perfect numbers exist?
• Do quasiperfect numbers exist?
• Do any odd weird numbers exist?
• Do any Lychrel numbers exist?
• Is 10 a solitary number?
• Do any Taxicab(5, 2, n) exist for n>1?
• Brocard's problem: existence of integers, n,m, such that n!+1=m² other than n=4,5,7
• Distribution and upper bound of mimic numbers
• Littlewood conjecture

[edit] Algebraic number theory

• Are there infinitely many real quadratic number fields with unique factorization?

[edit] Discrete geometry

• Solving the Happy Ending problem for arbitrary n
• Finding matching upper and lower bounds for K-sets and halving lines
• The Hadwiger conjecture on covering n-dimensional convex bodies with at most 2ⁿ smaller copies

[edit] Ramsey theory

• The values of the Ramsey numbers, particularly R(5,5)
• The values of the Van der Waerden numbers

[edit] General algebra

• Hilbert's sixteenth problem
• Hadamard conjecture
• Existence of perfect cuboids

[edit] Combinatorics

• Number of Magic squares (sequence  A006052)
• Finding a formula for the probability that two elements chosen at random generate the symmetric group S_n
• Frankl's union-closed sets conjecture: for any family of sets closed under sums there exists an element (of the underlying space) belonging to half or more of the sets
• The Lonely runner conjecture: if k + 1 runners with pairwise distinct speeds run round a track of unit length, will every runner be "lonely" (that is, be more than a distance 1 / (k + 1) from each other runner) at some time?
• Singmaster's conjecture: is there a finite upper bound on the multiplicities of the entries greater than 1 in Pascal's triangle?
• The 1/3–2/3 conjecture: does every finite partially ordered set contain two elements x and y such that the probability that x appears before y in a random linear extension is between 1/3 and 2/3?
• Conway's thrackle conjecture

[edit] Graph theory

• Barnette's conjecture that every cubic bipartite three-connected planar graph has a Hamiltonian cycle
• The Erdős–Gyárfás conjecture on cycles with power-of-two lengths in cubic graphs
• The Hadwiger conjecture relating coloring to clique minors
• The Erdős–Faber–Lovász conjecture on coloring unions of cliques
• The total coloring conjecture
• The list coloring conjecture
• The Ringel–Kotzig conjecture on graceful labeling of trees
• The Hadwiger–Nelson problem on the chromatic number of unit distance graphs
• Deriving a closed-form expression for the percolation threshold values, especially p_c (square site)
• Tutte's conjectures that every bridgeless graph has a nowhere-zero 5-flow and every bridgeless graph without the Petersen graph as a minor has a nowhere-zero 4-flow
• The Reconstruction conjecture and New digraph reconstruction conjecture concerning whether or not a graph is recognizable by the vertex deleted subgraphs.
• The cycle double cover conjecture that every bridgeless graph has a family of cycles that includes each edge twice.
• Does a Moore graph with girth 5 and degree 57 exist?

[edit] Analysis

• the Jacobian conjecture
• Schanuel's conjecture
• Lehmer's conjecture
• Pompeiu problem
• Is γ (the Euler–Mascheroni constant) irrational?
• the Khabibullin’s conjecture on integral inequalities

[edit] Dynamics

• Fürstenberg conjecture – Is every invariant and ergodic measure for the  action on the circle either Lebesgue or atomic?
• Margulis conjecture — Measure classification for diagonalizable actions in higher-rank groups

[edit] Partial differential equations

• Regularity of solutions of Vlasov–Maxwell equations
• Regularity of solutions of Euler equations

[edit] Group theory

• Is every finitely presented periodic group finite?
• The inverse Galois problem
• For which positive integers m, n is the free Burnside group B(m,n) finite? In particular, is B(2, 5) finite?

[edit] Set theory

• The problem of finding the ultimate core model, one that contains all large cardinals.
• If ℵ_ω is a strong limit cardinal, then 2^ℵ_ω < ℵ_ω1 (see Singular cardinals hypothesis). The best bound, ℵ_ω4, was obtained by Shelah using his pcf theory.
• Woodin's Ω-hypothesis.
• Does the consistency of the existence of a strongly compact cardinal imply the consistent existence of a supercompact cardinal?
• (Woodin) Does the Generalized Continuum Hypothesis below a strongly compact cardinal imply the Generalized Continuum Hypothesis everywhere?
• Does there exist a Jonsson algebra on ℵ_ω?
• Without assuming the axiom of choice, can a nontrivial elementary embedding V→V exist?
• Is it consistent that ?
• Does the Generalized Continuum Hypothesis entail  for every singular cardinal λ?

[edit] Other

• Invariant subspace problem
• Problems in Latin squares
• Problems in loop theory and quasigroup theory
• Dixmier conjecture

See also: List of conjectures

[edit] Problems solved recently

• Circular law (Terence Tao and Van H. Vu, 2010)
• Hirsch conjecture (as announced by Francisco Santos Leal, 2010)
• Road coloring conjecture (Avraham Trahtman, 2007)
• The Angel problem (Various independent proofs, 2006)
• The Langlands–Shelstad fundamental lemma (Ngô Bảo Châu and Gérard Laumon, 2004)
• Stanley–Wilf conjecture (Gábor Tardos and Adam Marcus, 2004)
• Green–Tao theorem (Ben J. Green and Terence Tao, 2004)
• Cameron–Erdős conjecture (Ben J. Green, 2003, conjectured by Paul)^[1]
• Poincaré conjecture (Grigori Perelman, 2002)
• Catalan's conjecture (Preda Mihăilescu, 2002)
• Kato's conjecture (Auscher, Hofmann, Lacey, McIntosh, and Tchamitchian, 2001)
• The Langlands correspondence for function fields (Laurent Lafforgue, 1999)
• Taniyama-Shimura conjecture (Wiles, Breuil, Conrad, Diamond, and Taylor, 1999)
• Kepler conjecture (Thomas Hales, 1998)
• Milnor conjecture (Vladimir Voevodsky, 1996)
• Fermat's Last Theorem (Andrew Wiles and Richard Taylor, 1995)
• Bieberbach conjecture (Louis de Branges, 1985)
• Princess and monster game (Shmuel Gal, 1979)
• Four color theorem (Appel and Haken, 1977)

[edit] See also

• Hilbert's 23 problems
• Smale's problems
• Timeline of mathematics
• List of conjectures#Open_problems
• List of statements undecidable in ZFC

[edit] References

1. ^ Green, Ben (2004), "The Cameron-Erdős conjecture", The Bulletin of the London Mathematical Society 36 (6): 769–778, arXiv:math.NT/0304058, doi:10.1112/S0024609304003650, MR2083752.

• Unsolved Problems in Number Theory, Logic and Cryptography
• Clay Institute Millennium Prize
• Weisstein, Eric W., "Unsolved problems" from MathWorld.
• Winkelmann, Jörg, "Some Mathematical Problems". 9 March 2006.
• List of links to unsolved problems in mathematics, prizes and research.
• Michael Waldschmidt (2004). "Open Diophantine Problems". Moscow Mathematical Journal 4 (1): 245–305.
• Open Problem Garden The collection of open problems in mathematics build on the principle of user editable ("wiki") site
• AIM Problem Lists
• Unsolved Problem of the Week Archive. MathPro Press.
• The Open Problems Project (TOPP), discrete and computational geometry problems

[edit] Books discussing unsolved problems

• Fan Chung; Ron Graham (1999). Erdos on Graphs: His Legacy of Unsolved Problems. AK Peters. ISBN 1-56881-111-X.
• Hallard T. Croft; Kenneth J. Falconer; Richard K. Guy (1994). Unsolved Problems in Geometry. Springer. ISBN 0-387-97506-3.
• Richard K. Guy (2004). Unsolved Problems in Number Theory. Springer. ISBN 0-387-20860-7.
• Victor Klee; Stan Wagon (1996). Old and New Unsolved Problems in Plane Geometry and Number Theory. The Mathematical Association of America. ISBN 0-88385-315-9.
• Marcus Du Sautoy (2003). The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics. Harper Collins. ISBN 0060935588.
• John Derbyshire (2003). Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Joseph Henry Press. ISBN 0309085497.
• Keith Devlin (2006). The Millennium Problems - The Seven Greatest Unsolved* Mathematical Puzzles Of Our Time. Barnes & Noble. ISBN 0-7607-8659-8.
• Vincent D. Blondel, Alexandre Megrestski (2004). Unsolved problems in mathematical systems and control theory. Princeton University Press. ISBN 0-691-11748-9.

[edit] Books discussing recently solved problems

• Simon Singh (2002). Fermat's Last Theorem. Fourth Estate. ISBN 1841157910.
• Donal O'Shea (2007). The Poincaré Conjecture. Penguin. ISBN 978-1-846-14012-9.
• George G. Szpiro (2003). Kepler's Conjecture. Wiley. ISBN 0-471-08601-0.
• Mark Ronan (2006). Symmetry and the Monster. Oxford. ISBN 0-19-280722-6.

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List of Unsolved Problems in Physics

This is a list of some of the major unsolved problems in physics. Some of these problems are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.

Contents 1 Theoretical problems 1.1 Quantum gravity, cosmology, and general relativity 1.2 High energy physics/Particle physics 1.3 Nuclear physics 1.4 Other problems 2 Empirical phenomena lacking clear scientific explanation 2.1 Cosmology 2.2 High energy physics/Particle physics 2.3 Astronomy and astrophysics 2.4 Condensed matter physics 2.5 Biological physics 3 Problems solved in recent decades 4 References 5 External links

Theoretical problems

The following problems are either fundamental theoretical problems, or theoretical ideas which lack experimental evidence and are in search of one, or both, as most of them are. Some of these problems are strongly interrelated. For example, extra dimensions or supersymmetry may solve the hierarchy problem. It is thought that a full theory of quantum gravity should be capable of answering most of these problems (other than the Island of stability problem).

Quantum gravity, cosmology, and general relativity

Vacuum catastrophe

Why does the predicted mass of the quantum vacuum have little effect on the expansion of the universe?

Quantum gravity

Can quantum mechanics and general relativity be realized as a fully consistent theory (perhaps as a quantum field theory)?^[1] Is spacetime fundamentally continuous or discrete? Would a consistent theory involve a force mediated by a hypothetical graviton, or be a product of a discrete structure of spacetime itself (as in loop quantum gravity)? Are there deviations from the predictions of general relativity at very small or very large scales or in other extreme circumstances that flow from a quantum gravity theory?

Black holes, black hole information paradox, and black hole radiation

Do black holes produce thermal radiation, as expected on theoretical grounds? Does this radiation contain information about their inner structure, as suggested by Gauge-gravity duality, or not, as implied by Hawking's original calculation? If not, and black holes can evaporate away, what happens to the information stored in them (quantum mechanics does not provide for the destruction of information)? Or does the radiation stop at some point leaving black hole remnants? Is there another way to probe their internal structure somehow, if such a structure even exists?

Extra dimensions

Does nature have more than four spacetime dimensions? If so, what is their size? Are dimensions a fundamental property of the universe or an emergent result of other physical laws? Can we experimentally "see" evidence of higher spatial dimensions?

Cosmic inflation

Is the theory of cosmic inflation correct, and if so, what are the details of this epoch? What is the hypothetical inflaton field giving rise to inflation? If inflation happened at one point, is it self-sustaining through inflation of quantum-mechanical fluctuations, and thus ongoing in some impossibly distant place?

Multiverses

Are there physical reasons to expect other universes that are fundamentally non-observable? For instance: Are there quantum mechanical "alternative histories" or "many worlds"? Are there "other" universes with physical laws resulting from alternate ways of breaking the apparent symmetries of physical forces at high energies, possibly incredibly far away due to cosmic inflation? Is the use of the anthropic principle to resolve global cosmological dilemmas justified?

The cosmic censorship hypothesis and the chronology protection conjecture

Can singularities not hidden behind an event horizon, known as "naked singularities", arise from realistic initial conditions, or is it possible to prove some version of the "cosmic censorship hypothesis" of Roger Penrose which proposes that this is impossible?^[2] Similarly, will the closed timelike curves which arise in some solutions to the equations of general relativity (and which imply the possibility of backwards time travel) be ruled out by a theory ofquantum gravity which unites general relativity with quantum mechanics, as suggested by the "chronology protection conjecture" of Stephen Hawking?

Arrow of time

What do the phenomena that differ going forward and backwards in time tell us about the nature of time? How does time differ from space? Why are CP violations observed in certain weak force decays, but not elsewhere? Are CP violations somehow a product of the Second Law of Thermodynamics, or are they a separate arrow of time? Are there exceptions to the principle of causality? Is there a single possible past? Is the present moment physically distinct from the past and future or is it merely an emergent property of consciousness? Why do people appear to agree on what the present moment is? (See also Entropy (arrow of time) below)

Locality

Are there non-local phenomena in quantum physics? If they exist, are non-local phenomena limited to transfers of information, or can energy and matter also move in a non-local way? Under what circumstances are non-local phenomena observed? What does the existence or absence of non-local phenomena imply about the fundamental structure of spacetime? How does this relate to quantum entanglement? How does this elucidate the proper interpretation of the fundamental nature of quantum physics?

Future of the universe

Is the universe heading towards a Big Freeze, a Big Rip, a Big Crunch or a Big Bounce? Is our universe part of an infinitely recurring cyclic model?

High energy physics/Particle physics

See also: Beyond the Standard Model

Higgs mechanism

Does the Higgs particle exist? What are the implications if it does not? Is there only one of them?

Hierarchy problem

Why is gravity such a weak force? It becomes strong for particles only at the Planck scale, around 10¹⁹ GeV, much above the electroweak scale (100 GeV, the energy scale dominating physics at low energies). Why are these scales so different from each other? What prevents quantities at the electroweak scale, such as the Higgs boson mass, from getting quantum corrections on the order of the Planck scale? Is the solution supersymmetry, extra dimensions, or just anthropic fine-tuning?

Magnetic monopoles

Did particles that carry "magnetic charge" exist in some past, higher energy epoch? If so, do any remain today? (Paul Dirac showed the existence of some types of magnetic monopoles would explain charge quantization.^[3])

Proton decay and unification

How do we unify the three different quantum mechanical fundamental interactions of quantum field theory? As the lightest baryon, are protons absolutely stable? If not, then what is the proton's half-life?

Supersymmetry

Is spacetime supersymmetry realized in nature? If so, what is the mechanism of supersymmetry breaking? Does supersymmetry stabilize the electroweak scale, preventing high quantum corrections? Does the lightest supersymmetric particle comprise dark matter?

Generations of matter

Are there more than three generations of quarks and leptons? Why are there generations at all? Is there a theory that can explain the masses of particular quarks and leptons in particular generations from first principles (a theory ofYukawa couplings)?

Fundamental symmetries and neutrinos

What is the nature of the neutrinos, what are their masses, and how have they shaped the evolution of the universe? Why is there now more detectable matter than antimatter in the universe? What are the unseen forces that were present at the dawn of the universe but disappeared from view as the universe evolved?

Nuclear physics

Quantum chromodynamics

What are the phases of strongly interacting matter, and what roles do they play in the cosmos? What is the internal landscape of the nucleons? What does QCD predict for the properties of strongly interacting matter? What governs the transition of quarks and gluons into pions and nucleons? What is the role of gluons and gluon self-interactions in nucleons and nuclei? What determines the key features of QCD, and what is their relation to the nature of gravityand spacetime?

Nuclei and Nuclear astrophysics

What is the nature of the nuclear force that binds protons and neutrons into stable nuclei and rare isotopes? What is the origin of simple patterns in complex nuclei? What is the nature of neutron stars and dense nuclear matter? What is the origin of the elements in the cosmos? What are the nuclear reactions that drive stars and stellar explosions?

Island of stability

What is the heaviest possible stable or metastable nucleus?

Other problems

Quantum mechanics in the correspondence limit (sometimes called Quantum chaos)

Is there a preferred interpretation of quantum mechanics? How does the quantum description of reality, which includes elements such as the superposition of states and wavefunction collapse or quantum decoherence, give rise to the reality we perceive? Another way of stating this is the Measurement problem - what constitutes a "measurement" which causes the wave function to collapse into a definite state?

Physical information

Are there physical phenomena, such as black holes or wave function collapse, which irrevocably destroy information about their prior states?

Theory of everything ("Grand Unification Theory")

Is there a theory which explains the values of all fundamental physical constants?^[4] Is there a theory which explains why the gauge groups of the standard model are as they are, why observed space-time has 3 + 1 dimensions, and why all laws of physics are as they are? Do "fundamental physical constants" vary over time? Are any of the particles in the standard model of particle physics actually composite particles too tightly bound to observe as such at current experimental energies? Are there fundamental particles that have not yet been observed and if so which ones are they and what are their properties? Are there unobserved fundamental forces implied by a theory that explains other unsolved problems in physics?

Gauge theory

Do non-Abelian gauge theories with a mass gap actually exist?

Empirical phenomena lacking clear scientific explanation

Cosmology

Existence of the Universe

What is the origin of matter, energy, spacetime and the fundamental forces that form the universe / multiverse?

Baryon asymmetry

Why is there far more matter than antimatter in the observable universe?

Cosmological constant problem

Why does the zero-point energy of the vacuum not cause a large cosmological constant? What cancels it out?

Estimated distribution of dark matter and dark energy in the universe

Dark matter

What is dark matter?^[5] Is it related to supersymmetry? Do the phenomena attributed to dark matter point not to some form of matter but actually to an extension of gravity?

The log-log plot of dark energy density ρ _* and material density ρ_m Vs scale factor a . The two straight lines intersect at current epoch.^[6]

Dark energy

What is the cause of the observed accelerated expansion (deSitter phase) of the Universe? Why is the energy density of the dark energy component of the same magnitude as the density of matter at present when the two evolve quite differently over time; could it be simply that we are observing at exactly the right time? Is dark energy a pure cosmological constant, or are models of quintessence such as phantom energy applicable?

Dark flow

What is the cause of a large swath of galaxy clusters all moving towards one part of the universe?^[7]

Entropy (arrow of time)

Why did the universe have such low entropy in the past, resulting in the distinction between past and future and the second law of thermodynamics?^[4]

Horizon problem

Why is the distant universe so homogeneous, when the Big Bang theory seems to predict measurable anisotropies of the night sky larger than those observed? Possible approaches to a solution are inflation and the variable speed of light hypothesis.

Ecliptic alignment of CMB anisotropy

Some large features of the microwave sky, at distances of over 13 billion light years, appear to be aligned with both the motion and orientation of the Solar System. Is this due to systematic errors in processing, contamination of results by local effects, or an unexplained violation of the Copernican principle?

Shape of the Universe

What is the 3-manifold of comoving space, i.e. of a comoving spatial section of the Universe, informally called the "shape" of the Universe? Neither the curvature nor the topology is presently known, though the curvature is known to be "close" to zero on observable scales. The cosmic inflation hypothesis suggests that the shape of the Universe may be unmeasurable, but since 2003, Jean-Pierre Luminet et al. and other groups have suggested that the shape of the Universe may be the Poincaré dodecahedral space. Is the shape unmeasurable, the Poincaré space, or another 3-manifold?

High energy physics/Particle physics

Electroweak symmetry breaking

What is the mechanism responsible for breaking the electroweak gauge symmetry, giving mass to the W and Z bosons? Is it the simple Higgs mechanism of the Standard Model,^[4] or does nature make use of strong dynamics in breaking electroweak symmetry, as proposed by Technicolor?

Neutrino mass

What is the mechanism responsible for generating neutrino masses? Is the neutrino its own antiparticle? Or could it be an antiparticle that simply cannot join and annihilate with a normal particle because of its irregular state?

Inertial mass/gravitational mass ratio of elementary particles

According to the equivalence principle of general relativity, the ratio of inertial mass to gravitational mass of all elementary particles is unity. However, there is no experimental confirmation for many particles. In particular, we do not know what the weight of a macroscopic lump of antimatter of known mass would be.

Proton spin crisis

As initially measured by the European Muon Collaboration, the three main ("valence") quarks of the proton account for about 12% of its total spin. Can the gluons that bind the quarks together, as well as the "sea" of quark pairs that are continually being created and annihilated, properly account for the rest of it?

Quantum chromodynamics (QCD) in the non-perturbative regime

The equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei, and, among others, mainly numerical approaches seem to begin to give answers at this limit. How does QCD give rise to the physics of nuclei and nuclear constituents?

Confinement

Why has there never been measured a free quark or gluon, but only objects that are built out of them, like mesons and baryons? How does this phenomenon emerge from QCD?^{[citation needed]}

Strong CP problem and axions

Why is the strong nuclear interaction invariant to parity and charge conjugation? Is Peccei-Quinn theory the solution to this problem?

Hypothetical particles

Which of the hypothetical particles predicted by supersymmetric theories and other fairly well known theories actually occur in nature?

[edit] Astronomy and astrophysics

Relativistic jet. The environment around theAGN where the relativistic plasma is collimated into jets which escape along the pole of the supermassive black hole

Accretion disc jets

Why do the accretion discs surrounding certain astronomical objects, such as the nuclei of active galaxies, emit relativistic jets along their polar axes? Why are there quasi-periodic oscillations in many accretion discs? Why does the period of these oscillations scale as the inverse of the mass of the central object? Why are there sometimes overtones, and why do these appear at different frequency ratios in different objects?

Coronal heating problem

Why is the Sun's Corona (atmosphere layer) so much hotter than the Sun's surface? Why is the magnetic reconnection effect many orders of magnitude faster than predicted by standard models?

Gamma ray bursts

How do these short-duration high-intensity bursts originate?^[4]

Supermassive black holes

What is the origin of the M-sigma relation between supermassive black hole mass and galaxy velocity dispersion?^[8]

Observational anomalies

Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). Can the discrepancy between the curves be attributed to dark matter?

Hipparcos anomaly: What is the actual distance to the Pleiades?^{[citation needed]}

Pioneer anomaly^[5]: What causes the small additional sunward acceleration of the Pioneer spacecraft?^[4][5]

Flyby anomaly: Why is the observed energy of satellites flying by earth different by a minute amount from the value predicted by theory?

Galaxy rotation problem: Is dark matter responsible for differences in observed and theoretical speed of stars revolving around the center of galaxies, or is it something else?

Supernovae

What is the exact mechanism by which an implosion of a dying star becomes an explosion?

Ultra-high-energy cosmic ray^[5]

Why is it that some cosmic rays appear to possess energies that are impossibly high (the so called OMG particle), given that there are no sufficiently energetic cosmic ray sources near the Earth? Why is it that (apparently) some cosmic rays emitted by distant sources have energies above the Greisen-Zatsepin-Kuzmin limit?^[4][5]

Rotation rate of Saturn

Why does the magnetosphere of Saturn exhibit a (slowly changing) periodicity close to that at which the planet's clouds rotate? What is the true rotation rate of Saturn's deep interior? ^[9]

[edit] Condensed matter physics

Amorphous solids

What is the nature of the glass transition between a fluid or regular solid and a glassy phase? What are the physical processes giving rise to the general properties of glasses?^[10][11]

Cold fusion

What is the explanation for the controversial reports of excess heat, radiation and transmutations?^[5][12][13]

Cryogenic electron emission

Why does the electron emission in the absence of light increase as the temperature of a photomultiplier is decreased?^[14][15]

High-temperature superconductors

What is the mechanism that causes certain materials to exhibit superconductivity at temperatures much higher than around 50 kelvins?^[4]

Sonoluminescence

What causes the emission of short bursts of light from imploding bubbles in a liquid when excited by sound?^[16]

Turbulence

Is it possible to make a theoretical model to describe the statistics of a turbulent flow (in particular, its internal structures)?^[4] Also, under what conditions do smooth solutions to the Navier-Stokes equations exist? This is probably the last unsolved problem in Classical or Newtonian Physics.

Biological physics

These fields of research normally belong to biology, and traditionally were not included in physics but are included here because increasingly it is physicists who are researching them using methods and tools more popular in physics research than biology.^[17][18]

Synaptic plasticity

It is necessary for computational and physical models of the brain, but what causes it, and what role does it play in higher-order processing outside the hippocampus and visual cortex?

Axon guidance

How do axons branching out from neurons find their targets? This process is crucial to nervous system development, allowing the building up of the brain.

Stochasticity and robustness to noise in gene expression

How do genes govern our body, withstanding different external pressures and internal stochasticity? Certain models exist for genetic processes, but we are far from understanding the whole picture, in particular in developmentwhere gene expression must be tightly regulated.

Quantitative study of the immune system

What are the quantitative properties of immune responses? What are the basic building blocks of immune system networks? What roles are played by stochasticity?

Consciousness

What mechanism causes sentience within of arrangements of otherwise non-sentient particles (as with the human brain, for example)? Is this mechanism reproducible?

Problems solved in recent decades

Long-duration gamma ray bursts (2003)

Long-duration bursts are associated with the deaths of massive stars in a specific kind of supernova-like event commonly referred to as a collapsar. However, there are also long-duration GRBs that show evidence against an associated supernova, such as the Swift event GRB 060614.

Solar neutrino problem (2002)

Solved by a new understanding of neutrino physics, requiring a modification of the Standard Model of particle physics—specifically, neutrino oscillation.

Age Crisis (1990s)

The estimated age of the universe was around 3 to 8 billion years younger than estimates of the ages of the oldest stars in our galaxy. Better estimates for the distances to the stars, and the recognition of the accelerating expansion of the universe, reconciled the age estimates.

Quasars (1980s)

The nature of quasars was not understood for decades.^[19] They are now accepted as a type of active galaxy where the enormous energy output results from matter falling into a massive black hole in the center of the galaxy.^[20]

References

1. ^ Alan Sokal (July 22, 1996), "Don't Pull the String Yet on Superstring Theory", New York Times
2. ^ Joshi, Pankaj S. (January 2009), "Do Naked Singularities Break the Rules of Physics?", Scientific American
3. ^ Dirac, Paul, "Quantised Singularities in the Electromagnetic Field".Proceedings of the Royal Society A 133, 60 (1931).
4. ^ ^{a b c d e f g h} Baez, John C. (March 2006). "Open Questions in Physics". Usenet Physics FAQ. University of California, Riverside: Department of Mathematics. Retrieved March 7, 2011.
5. ^ ^{a b c d e f} Brooks, Michael (March 19, 2005). "13 Things That Do Not Make Sense". New Scientist. Issue 2491. Retrieved March 7, 2011.
6. ^ Steinardt, Paul (1997), "Cosmological Challenges For the 21st Century", in Val Fitch et. al., Critical problems in physics: proceedings of a conference celebrating the 250th anniversary of Princeton University, Princeton, New Jersey: Princeton University Press, pp. 138–140,ISBN 9780691057842
7. ^ http://www.dailygalaxy.com/my_weblog/2009/08/dark-flow-discovered-at-edge-of-the-universe-hundreds-of-millions-of-stars-racing-toward-an-cosmic-h.html
8. ^ Ferrarese, Laura; Merritt, David (2000), "A Fundamental Relation between Supermassive Black Holes and their Host Galaxies", The Astrophysical Journal 539: L9–L12, arXiv:astro-ph/0006053, Bibcode2000ApJ...539L...9F, doi:10.1086/312838
9. ^ "Scientists Find That Saturn's Rotation Period is a Puzzle". NASA. June 28, 2004. Retrieved 2007-03-22.
10. ^ Kenneth Chang (July 29, 2008), "The Nature of Glass Remains Anything but Clear", The New York Times
11. ^ "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition." P.W. Anderson (1995), "Through the Glass Lightly", Science267: 1615
12. ^ John R. Vacca (2004), The World's 20 Greatest Unsolved Problems, Prentice Hall, ISBN 9780131426436
13. ^ Feder, T.; John, O. (2004), "Cold Fusion Gets Chilly Encore",Physics Today 58: 27, Bibcode 2005PhT....58a..31F,doi:10.1063/1.1881896
14. ^ http://www.physorg.com/news187421719.html
15. ^ doi:10.1209/0295-5075/89/58001
16. ^ Proceedings: Mathematical, physical, and engineering sciences (Royal Society) 453, 1997, "An unsolved problem in modern physics concerns the phenomenon of sonoluminescence"
17. ^ The Nobel Prizes in Physics 1901-2000
18. ^ The Office of Science - What is Physics?
19. ^ "The MKI and the discovery of Quasars". Jodrell Bank Observatory. Retrieved 2006-11-23.
20. ^ Hubble Surveys the "Homes" of Quasars Hubblesite News Archive, 1996-35

External links

• What don't we know? Science journal special project for its 125th anniversary: top 25 questions and 100 more.
• Physics News Update A weekly physics news bulletin hosted by the American Institute of Physics.
• List of links to unsolved problems in physics, prizes and research.
• Ideas Based On What We’d Like to Achieve
• 2004 SLAC Summer Institute: Nature's Greatest Puzzles
• Dual Personality of Glass Explained at Last
  
  From Wikipedia