Recently, the European Journal of Physics had a special issue (Volume 20, Number 6, November 1999) titled the "Unsolved Problems in Physics". So, as the 20th Century finally nears it's end, it seems appropriate to provide a list much in the spirit of Hilbert. Therefore, I've decided to try my hand at providing a formulation. However, if this were merely an exercise in regurgitating what "everyone knows are the 'unsolved problems'" (e.g. the widely expected future discovery of the (perpetually) soon-to-be-found Theory of Quantum Gravity), it would not be worthwhile. Instead, the issues listed below have been chosen with foresight with the expectation that they will, indeed, become serious turning-point issues over the next 100 years. Some of them aren't even recognized currently as problems, and some are not appreciated as being problems as such, or otherwise as problems which Physics can address. A few, however, are in fact regurgitations ... but just a few. But, in general, you will agree that I've taken a much more ambitious track here. Outline: (1) COSMIC RAYS THAT PACK A *HUGE* WALLOP! (2) THE FIRST IMAGE (3) DARK MATTER and DARK ENERGY (4) THE MISSING NEUTRINO PROBLEM (5) THE ORIGIN OF MASS & INERTIA (aka THE HIGGS PROBLEM) (6) THE HIGGS-GRAVITY CONNECTION (7) THE DEFINITION OF A MASS UNIT (8) THE ORIGIN OF SCALE, UNITS & FUNDAMENTAL 'CONSTANTS' (9) THE RELATION OF THE WEINBERG ANGLE TO THE 8-15-17 RIGHT TRIANGLE (10) WHY DOES THE SECOND LAW FAIL? (11) THE MEANING OF PROBABILITY (12) THE *REVERSE* SCHROEDINGER CAT PARADOX (13) WHAT IS CAUSALITY? (add in TIME TRAVEL and FREE WILL) (14) CAN THE FUTURE BE REMEMBERED? (15) DUAL UNIVERSES (16) VACUUM ENERGY (17) MACROSCOPIC EPR (18) THE GEOMETRY MEASUREMENT PROBLEM (19) WHAT (IF ANYTHING) SURVIVES DEATH? (20) ANTIGRAVITY (1) COSMIC RAYS THAT PACK A *HUGE* WALLOP! [This was described in quite a bit of detail in the European Journal of Physics too and has attracted quite a bit of attention elsewhere] This relates to the fact that there are occasionally cosmic rays which strike the Earth's atmosphere with a punch actually equal in force to somebody's fist punching you. There are no known processes (not even supernovas) which can spawn particles with that kind of energy. So, where did they come from? An interesting application of the phenomenon of cosmic rays in general is that it may be possible to set up natural laboratories in outer space which use cosmic rays to perform extremely high energy scattering/collision experiments. (2) THE FIRST IMAGE This is not entirely unrelated to (A). As refinements are made to currently technology, it will be possible to view the cosmic microwave background with greater and greater degrees of resolution. It's not widely appreciated that this radiation is in encrypted form nothing less than the first viable image of the Universe! The gradual coming into focus of this background is almost like the situation where you gradually bring your TV set into focus only to be dumbstruck by what suddenly appears on the screen. It's daunting and almost scary to think of what will be seen, when the First Image comes into focus. (3) DARK MATTER and DARK ENERGY This point will not be belabored too much here. About 2/3 of the Universe's mass content seems to come from a dark energy source. This source seems to have many of the characteristics (as determined by carrying out simulations) to a scalar field. About 1/3 seems to come from a dark matter source, and only a small part of it is accounted for by Baryons. (4) THE MISSING NEUTRINO PROBLEM (A continuation of (3), in fact) Recent evidence indicates that the various neutrino flavors oscillate. What this means, in effect, is that the neutrino states that naturally correspond to the Weak Force are actually skew with respect to the mass eigenstates (which means, among other things, that at least 2 of the 3 neutrinos have mass). However -- and this is the issue (4) refers to -- it seems that when neutrinos oscillate, some do NOT change into neutrinos of the other flavors, but inexplicably drop off the face of the universe. Where did they go? Neutrinos (of the left-handed variety) are thought to make a small contribution to the Dark Matter. But what about the right-handed variety? Their only link to the rest of the particle world is through the scalar Higgs field (and through gravity). Other than this, they are completely unobservable. If a neutrino is represented by an ordinary Dirac 4-component spinor, then its handedness will be relative to the state of motion of the observer. Did the lost left-neutrinos become right-handed? This raises the rather disturbing possibility that this field could actually be serving as a vast, almost one-way, cosmic dumping ground for matter. (5) THE ORIGIN OF MASS & INERTIA (aka THE HIGGS PROBLEM) This is, in fact, not entirely unrelated to issue (3) too. It is a not-so-well-known fact that in Quantum Field Theory particles have to be massless in order to retain consistency. In order to recover the semblance of mass, the existence of a scalar field is required. The lowest common denominator of what such a field comprises is what appears in the Standard Model (as the Higgs mechanism). However, it is widely believed that this mechanism is merely a temporary stop-gap, or place-holder, until the Real Theory comes along. Its set of features are supported by solid arguments as being the least common denominator of what ANY mass-producing mechamism would look like at low-energy scales. What, exactly is the underlying theory? (6) THE HIGGS - GRAVITY CONNECTION (Really, a continuation of (5)) A little thought reveals the true nature and true extent of this problem: the underlying problem addressed by the Higgs mechanism is nothing less than the leading vanguard of the sudden and unexpected intrusion of gravity, itself, into Quantum Field Theory! According to the equivalence principle (EP), inertia and gravitational mass are two forms of the same thing. To state it another way: an object moving under influence of gravity, by EP, is simply moving under its own inertia. Therefore, mass is a property of matter that directly relates to gravity. Therefore, it is not suprising that QFT cannot allow the direct inclusion of mass (in a gauge invariant way) for any of its fields. QFT simply does not have any concept of gravity in it. But, at the same time, it also means that any attempt to arrive at a mass-generating mechanism for quantum fields must, ipso facto, amount to nothing less than an attempt (or the beginnings of an attempt) to account for gravity, itself? So, to somewhat reiterate the final question of (5): what exactly is the connection between the (yet-to-be-discovered) theory underlying the Higgs mechanism and the phenomenon of gravity? >From the point of view of General Relativity, the selection of a mass unit corresponds to the selection of a length scale. Therefore, somehow, the symmetry breaking mechanism of Higgs must somehow be intimately tied to a conformal symmetry breaking mechanism. What connection does the apparent spontaneous breaking of conformal scale have with the failure of Weyl to provide a viable conformally-invariant alternative to Einstein's General Relativity? (7) THE DEFINITION OF A MASS UNIT Suprisingly, it is still the case that the formal legally binding definition of the mass unit is that chunk of matter sitting somewhere in Paris. There is, as of yet, no legally binding definition of a mass scale which relies on purely physical processes. (8) THE ORIGIN OF SCALE, UNITS & FUNDAMENTAL 'CONSTANTS' A common convention in Physics literature is to identify key 'constants' are renderings of the pure dimensionless number 1 (e.g., the almost cliche, "let us choose units such that c = 1"). Recently, the ISO enacted a definition for the meter in terms of the light-second. Currently, a meter is legally 1/299792458 of a light-second. A controversy that surrounds this decision is "how do we know if light speed is actually constant?" But, in reality, the problem that's actually raised is: how do we know ANY units are 'constant'? Or more to the point: what does it mean for units to be 'constant'? Since all measurements are taken as dimensionless ratios with respect to units, how does one even define or directly observe or assign physical meaning to the notion of 'variableness' to a unit? The problem underlying all of this is the following: Why do things in the physical world seem to require 'units' to measure them with? What are 'dimensions' (e.g., length, time, mass, etc.) and where do they come from? Where does scale, itself, come from? And what are the invariant structures underlying it? Note that this is NOT the same issue as Conformal Symmetry, which Weyl attempted to address in the early part of the 20th century. The reason is that even before you define, operationally, a set of coordinates for space-time (thereby effecting the hypothesis that space-time is locally Euclidean), you need to first define the units with respect to which you're making these definitions. The appearance of units is logically prior to the assignment of any kind of manifold structure to space-time, and thus lies at an entirely different and much deeper level than the issue of the conformal invariance of the manifold's metric. Applying the reasoning similar to that used in Gauge Field Theory, it would in fact seem to be the case that each dimension is in fact a dimension of a deep-lying conformal symmetry and that, as such, would require some kind of 'gauge field'. What is the connection between dimensional-gauge (to coin a term) and the fundamental "constants", h, c and G? Are these the dimensional gauge fields, in fact? An example will help clarify the issue further and show how the problem may actually resolve itself. Consider the space-time underlying the classical Newtonian world. Basically, it consists of a "time-line" (i.e., a 1-dimensional manifold), which has pasted at each of its points a copy of a 3-dimensional space. Technically, this is known as a fibre bundle. Now consider the problem of how time is to be measured in this world. We know that we can select any time on this line and call it 0. In fact, we have a large number of calendars and dating conventions which put this principle in effect. Call this point O. The selection of O, in Newtonian Physics, is supposed to have absolutely no bearing on anything relating to physics, per se. Second, we know that any unit may be used to measure time with. In fact, we have a large number of different units in common use (the second, the year, etc.) as well as quite a few which were used historically by different civilizations. Basically, this amounts to selecting a second point I and calling the interval OI a "unit". Likewise, the selection of I will have no physical bearing on anything, according to Newton. But, once these two points are chosen, then according to Newton, all other points on the time line will be uniquely assignable. This is not a trivial observation! What's being described here is nothing less than the invariant structure which underlies the use of time-units: namely, the 3-point function: t: T x T x T -> R (A, B, C) |-> [ABC] [ABC] = "the time of C, measured in units with A=0, B=1" where T denotes the Newtonian "time-line". The problem is then: how is this invariant structure to be characterized? As the reader may verify, this structure can actually be characterized by 3 axioms, as follows: [ABA] = 0 [ABC] + [BAC] = 1, if A, B are distinct [ABC][ACD] = [ABD], if A and B are distinct Thus, the problem of Scale is resolved with respect to the time dimension in the Newtonian world. Now, what about the 3-D fibre in the Newtonian spacetime? If the fibre is an exact copy of Euclidean space, it is in fact possible to (almost) characterize it in scale-invariant terms in a similar fashion! Consider the inverse of the 3-point function above: [,,]: T x R x T -> T (A,r,B) |-> [A,r,B] which is defined such that [AB [A,r,B]] = r (for A & B distinct) [A, [ABC], B] = C (which holds even if A = B). Suprisingly, this operation can actually define a vector space structure (up to the selection of a point O as the origin), by the following 3 axioms: [A, 0, B] = A [A, 1, B] = B [A, rt(1-t), [B, s, C]] = [[A, rt(1-s), B], t, [A, rs(1-t), C]] But to define a scale, one also needs a construction which allows an inner product to be defined. Basically, this amounts to selecting instead of just one point I an entire sphere of points surrounding O and identifying each interval OX for points X on the sphere as a unit "in that direction". The invariant structures that are revealed by a careful analysis of the use of units are neither well-known nor well-understood. This problem gets to be particularly complicated when one considers the space-time world modelled by Riemannian geometry, as it basically amounts to formulating a purely synthetic axiomatic characterization of the geometry in the spirit of Euclid and then using the formulation to address the use of units, in a similar fashion as we did above with the time-line example. (9) THE RELATION OF THE WEINBERG ANGLE TO THE 8-15-17 RIGHT TRIANGLE Why does the Weinberg angle seem to describe a 8-15-17 right triangle? Related to this is the fact that the ratio of the W and Z masses appears to be 15:17. (10) WHY DOES THE SECOND LAW FAIL? It is a well-known fact that the 2nd Law of Thermodynamics fails catastrophically when applied to the backwards-running Universe. Things actually DO spontaneously jump off the ground, people emerge from dust to come alive and jump into their mothers wombs after shrinking down to a certain size. Shards of vases spontaneously assemble themselves into vases. Despite the dramatic nature of this discrepancy, the problem does not seem to be widely appreciated as such. What goes wrong, precisely? The reasoning underlying the development of the 2nd Law can be applied to either universe. However, at a key juncture a critical assumption is made: namely that a phase space distribution will evolve in such a way that it becomes scrambled over phase space (even though its total volume remains unchanged). It is then postulated that the correlations encoded by the scrambled state then cease to be "meaningful" The key is the concept of "meaningful correlation"! In the backwards-running universe, the scrambled correlations eventually manifest their meaning in the form of macroscopic order. Apparently, they don't do so in the forwards-running universe. Or do they, on occasion? The key difficulty in addressing the issue is that the empirical method, itself, serves as an effective filter against such phenomena in virtue of the "repeatibility" criterion. So, in reality, the question of whether there are "meaningful" correlations in the forwards-running universe (i.e., a "hidden order" to the scrambled phase space state) is not fully resolved. (11) THE MEANING OF PROBABILITY Directly related to this is the question: What does the statement P(E) = 1/2 mean, empirically? To assign an empirical meaning to a statement, one must state criteria under which the statement is considered to have been refuted. The problem is that the statement P(E) = 1/2 allows for ANY outcome for a series or repeated trials of event E. A statement cannot be falsified by what it says is possible. (Especially, if it says that this possibility almost certainly MUST eventually arise!) Underlying this is the fact that according to some physical theories, there may exist situations when a given event will have different outcomes even in the absence of any conditions that distinguish one instance of the event from another! On the surface, this statement is actually false, since no instance of anything occurs under entirely identical conditions (e.g., the moon and stars are in different positions). The use of probabilities in physical theories compensates for the existence of events whose outcomes seem to have no MEANINGFUL correlation to any condition. The issue is to explain exactly what this underlying phenomenon is which probability is used to compensate for. (12) THE *REVERSE* SCHROEDINGER CAT PARADOX. Consider a situation in which a cat is placed in a box along with a very slowly radiating substance and a Geiger counter which trips a vial of poison. A naive argument would state that the Geiger counter is in a superposition of two states: one where it is tripped, one where it is not; and thus the cat too. This situation pertains until someone opens the box to observe the cat's state. The true paradox relates to the fact that the inside of the box is ALWAYS under continuous observation: theoretically you can see the cat inside by its effect on gravity. Since gravity cannot be shielded, then neither can the observation. So, how it is possible for this or any other superposition of quantum states to ever exist? A good example is the Quantum Eraser. The internal state of the QE should be under continuous observation in virtue of its gravity, but somehow, the QE mechanism can be and has been successfully implemented. Did Gravity simply shut off which the mechanism was active? (13) WHAT IS CAUSALITY? (add in TIME TRAVEL and FREE WILL) The principle of "Causality" is frequently invoked to effect physical arguments that are technically outside the formal structure of the physical theory in question. For instance, the exclusion of advanced fields in Classical Electrodynamics is based on this principle (even though where it is inconsistent with physical reality, e.g., the collapse of the atom, which advanced fields might actually provide a resolution to). The problem is that there is no such principle; and no occurrence of "Causality" exists at the foundation of any physical theory. The closest approximiation of the principle is the "microcausality" postulate of Quantum Field Theory. Are arguments which invoke the principle out of line? If not, then what exactly is the principle being used? There seems to be, in fact, a lot of anthropomorphic baggage tied up with the concept (e.g. even the mere concept of phenomena 'influencing' other phenomena), when the physical world at its most fundamental level may actually not have any notion of cause and effect whatsoever. Directly related to this is the problem of providing a physical rigorous defintion of "cause" and "effect", itself! There are obvious connections of this problem to the issues of time travel and free will, which won't be belabored here, but merely pointed out. (14) CAN THE FUTURE BE REMEMBERED? We remember the past, but do not seem to remember the future very well or at all. Where, exactly, does this amnesia come from? Or are we perhaps looking at it the wrong way and maybe we actually DO remember the future to some extent? Does the empirical method filter out such phenomena as future knowledge. This question is being posed not merely for biological systems but for all physical systems. (15) DUAL UNIVERSES This eye-catching name refers to the fact that there seems to be an entire spectrum of particles which are not connected to the Standard Model by any interaction, except gravity. To explain this situation further, it helps to see the Standard Model in terms of its connectivity. Consider the diagram below eR <-- gamma, Z --> eR <-- H --> eL <-- W --> nu_L eL <-- gamma, Z --> eL nu_R <-- H --> nu_L <-- Z --> nu_L In highly schematic form, this is a rough depiction of part of the Standard Model Lagrangian in terms of all the ways the different forms of matter interact with one another. Of particle interest is to note that there is only one channel that connects nu_R to the rest of the particle world, thus rendering it virtually invisible! This raises the interesting possibility that this graph (along with the rest of the graph corresponding the Standard Model) is actually only a VERY small subset of an enormous graph, which may actually be disconnected! In such a situation, one could actually have a case (for instance) where multiple Earths could literally occupy the same space, each residing in its own particle-force sector, and each totally and permanently invisible to the other, except in virtue of their gravity. Is the actual particle world composed of sectors which are disconnected from one another? (16) VACUUM ENERGY (This was a problem also listed in the European Journal of Physics volume I cited above). What affect does the zero-point spectrum have on gravity and why is its gravity apparently unseen? If it's being cancelled by an offsetting cosmological constant then what does the offset seem to almost cancel, it but then not quite yet fully cancel it? (17) MACROSCOPIC EPR Are there macroscopic manifestations of EPR type phenomena in the natural world? (18) THE GEOMETRY MEASUREMENT PROBLEM In order to ascertain the geometry of our world, we need to perform measurements. Invariably, these measurements involve the use of Quantum Fields. Therefore, operatonally speaking, Quantum Fields must reside at a much deeper level than geometry. Exactly how can a quantum field be defined without the use of any prior geometric structure? Can a geometry then be defined as a purely secondary derivative of the quantum field? Note that it is actually possible to do this in Minkowski space(!) One can define the operator algebra of a quantum field. The field's [anti]commutators [psi(x), psi(y)] vanish outside the light cone. Thus, one can define the relation (x-y spacelike separated) solely as a relation involving commutators. It is a not-too-widely-known fact that Minkowski space can be completely characterized (up to the selection of a scale and the selection of the past vs. future orientation) by the space-like separation relation; modulo a large number of axioms. Pulling these axioms back through the definition, one has therefore a quantum field, defined as a pure set of operators { psi(x), psi'(x): x ranges over a totally unstructured set }, subject to a set of axioms involving commutators. Ultimately, this means that even derivatives can be defined in terms of the commutators(!) The general problem of defining a general spacetime solely in terms of field operators in like fashion remains unresolved. But it must surely underlie any successful attempt to unify General Relativity and Quantum Field Theory. (19) WHAT (IF ANYTHING) SURVIVES DEATH? The information content of a physical system, seen at the microscopic level, remains constant. This is because the volume occupied in phase space by an ensemble is constant. Since your entire Ego is composed entirely of the information which makes up your memory (of who and what you are; i.e., your self), this means that this entire structure continues to exist in some fashion after the body is gone -- namely as a set of 'scrambled' correlations. This relates directly to issue (10). (20) ANTIGRAVITY Einstein's General Relativity admits solutions which involve antigravity. Does it describe anything which actually exists in the real world? Could the sporadic reports of negative gravity effects (under conditions that seem suspiciously close to those which would lead to Einsteinian anti-gravity; or conditions that seem to involve a manifestation of torsion or the like) be related to this?