Five Reasons That We Know The Standard Model And General Relativity Aren't Complete
1. The Standard Model of particle physics is consistent with special relativity (i.e. the adjustments to the rate at which time flows and to momentum relative to Newtonian mechanics associated with particles that move at speeds near the speed of light). But, the Standard Model is not theoretically consistent with gravity and does not provide a quantum mechanical theory of gravity.
These issues are particularly acute at very small distances, at very high energy scales, and in very strong gravitational fields. (Fortunately, in most practical circumstances, the Standard Model alone, or general relativity alone, can be deployed to analyze a question in circumstances where we can be comfortable that quantum effects or relativistic effects, respectively play an insignificant role.)
2. Phenomena attributed to dark matter are observed. No Standard Model particles, fundamental or composite, appears to be capable of providing a good fit to the inferred behavior of dark matter, and no Standard Model fermion or term in the equations of general relativity can explain this phenomena. Needless to say, to the extent that dark matter particles do exist, we don't know how they are created.
3. Neither the Standard Model, nor general relativity, provide an explanation for cosmological inflation in the wake of the Big Bang, despite mounting evidence that inflation or some other similarly remarkable thing happened, for example from BICEP-2.
4. There are approximately 4*1079 baryons in the universe. The ratio of anti-baryons to baryons in the universe is on the order of 10-11 or less (approximately 1/8th are neutrons and approximately 7/8th are protons).
We have no Standard Model explanation for the baryon asymmetry of the universe, in other words, why there are many more quarks than anti-quarks in the universe, which in the language of quantum physics is described technically as the question of how the universe acquired a substantial non-zero baryon number (baryon number is defined as sum of quarks minus the sum of anti-quarks divided by three). This means that we need a beyond the Standard Model baryogenesis mechanism (assuming that the baryon number and lepton number generated in the Big Bang was zero).
There is a Standard Model process that can give rise to baryogenesis called a sphaleron process, but the consensus of theorists who have studied this process is that this process could not give rise to a 10-11 anti-baryon to baryon ratio within the parameters of mainstream cosmology theories that we are aware of at this time.
Note that baryon asymmetry itself (and likewise charged lepton asymmetry) really isn't all that remarkable in a universe that is not a vacuum. We would expect matter-antimatter annihilation to convert to energy all of quarks in the universe that have corresponding anti-quarks, over time. Assuming that we can estimate the total mass-energy of the universe that is not captured in pure matter, and that mass-energy conservation holds, we can even estimate what percentage of the mass-energy from the Big Bang either never entered a matter state, or generated particles and anti-particles that subsequently annihilated each other. But, finding a way for such an extreme asymmetry to arise isn't obvious when one assumes that the Big Bang starts in pure energy state that is neutral between matter and antimatter and has no net fermion numbers.
5. We don't know if the universe has a non-zero lepton number (i.e. if the sum of charged leptons and neutrinos in the universe is greatly in excess of the number of charged anti-leptons and anti-neutrinos in the universe), but this is very likely.
There are about 3.5*1079 charged leptons in the universe. The ratio of charged anti-leptons to leptons is almost exactly the same as the ratio of anti-baryons to baryons in the universe. There are also about 1.2*1089 neutrinos in the universe and we don't have reliable measurements of the ratio of anti-neutrinos to neutrinos in the universe, although the early indications are that the number of anti-neutrinos exceeds the number of neutrinos in the universe by many orders of magnitude more than the baryon asymmetry in the universe. If the ratio of anti-neutrinos to neutrinos in the universe differs from 1 by even 10-9, then we need a beyond the Standard Model explanation for leptogenesis (assuming that the baryon number and lepton number generated in the Big Bang was zero). And, if this asymmetry was sufficiently great, it could not be generated by a sphaleron process.
The mass of all of the dark matter in the universe is about 2*1086 keV. In the case of warm dark matter scenarios with 2 keV dark matter particles, there are about 1,200 neutrinos in the universe for every dark matter particle. In the case of cold dark matter scenarios with dark matter particles with a mass on the order of 20 GeV, there are about 12,000,000,000 neutrinos for every dark matter particle. If dark matter particles are "thermal relics" and have a mass on the order of 1 eV - 10 eV, which they would need to in order to balance out any significant imbalance between neutrinos and anti-neutrinos in the universe, they would be "hot dark matter" particles which could not reproduce observed dark matter phenomena in the universe (in principle, such light dark matter particles are possible if they are generated non-thermally and have much lower mean velocities than thermal relic dark matter would). Thus, even if dark matter particles carried a positive lepton number, this is almost certainly not sufficient to make the lepton number in the universe.
Also, the Standard Model sphaleron process which is the only means of baryongenesis and lepton genesis in the Standard Model, conserves the quantity B-L (baryon number minus lepton number in the universe).
If there is even a 1% excess of anti-neutrinos over neutrinos in the universe (and the reality is that the excess is probably profoundly greater than that), then B is much greater than zero, L is much less than zero, and B-L is much less than zero.
Ten More Reasons To Explore Beyond The Standard Model Physics Or Within The Standard Model Physics
1. There are very strong hints that the experimentally measured parameters of the Standard Model have deeper connections to each other than we understand and understanding these relationships would both deepen our understanding of the laws of nature, and allow us to use more precisely measured experimental constants to obtain more precise values for less precisely measured experimental constants of the Standard Model.
2. The discovery of additional relationships and symmetries in the laws of physics might make it possible to greatly simplify the calculations involved in applying the Standard Model.
3. There are processes such as the mechanism by which neutrinos acquire mass, neutrino oscillation, the hadronic physics of large classes of mesons and possibly some exotic baryons as well, that the Standard Model does not understand well, either theoretically, or in an operational manner that we can use to make practical calculations. This suggests that either there are some missing or not quite correct pieces in our current understanding of neutrino physics and QCD, or that there are some subtle corollaries of existing equations of Standard Model physics that we have not yet recognized.
4. We have not been able to experimentally validate the Standard Model and general relativity in circumstances of extremely high energies (especially those approaching the "GUT" scale of 1016 GeV and the Planck scale of 1018 GeV, extremely strong gravitational fields, and extreme short distances (especially at the Planck scale), where it is plausible to think, for a variety of theoretical reasons, that new physics may be lurking.
High energy scales present in the very early universe are a natural place to expect beyond the Standard Model and beyond general relativity physics that could help explain inflation, baryogenesis, leptogenesis, the creation of dark matter, dark energy, and the topology of the universe. Many of the apparent discrepancies between general relativity and the Standard Model also manifest themselves in this regime in ill understood ways.
5. Multiple decades of theoretical research into supersymmetric theories, supergravity, and string theories suggest that that are certain properties of any kinds of laws of physics that could explain the Standard Model and general relativity at once in a mathematically consistent way. In general, these theories point to the strong possibility that there is a deeper reality with more than the familiar three dimensions of space and one dimension of time, and to the likelihood of additional possible particle states at high energies.
6. We have not ruled out the possibility that the space-time does not actually have a smooth, continuous, local, real and causal structure. Indeed, entanglement phenomena in quantum mechanics appears to strongly imply that the laws of the universe cannot simultaneously be local, real and causal. Quantum mechanics equations can give us results but doesn't tell us which of these things is not true to give rise to them, or in the alternative, why these concepts are conceptually flawed. There is effectively a "black box" between the start point and the observed end point in quantum mechanical equations.
7. It is very plausible that our understanding of the distinction between particles and the vacuum may be inadequate or flawed. Particles may actually be localized excited states of space-time, rather than separate objects existing within a separate background of space-time. A better understanding of this might explain, for example, why the Higgs field's vacuum expectation value does not give rise to a cosmological constant much larger than is observed, or why multiple different conservation laws (like conservation of lepton number and baryon number) flow from some deeper principle derived from particles that are excited states of the vacuum rather than objects within it.
8. We don't understand the meaning of the "arrows of time" in the laws of physics very well. At the fundamental physics equation level, only CP violation is not time symmetric, and it observes CPT conservation, so violations of time symmetry take place only in very narrow circumstances.
9. The path integrals that govern the propagation of particles in the Standard Model sum up how probability amplitudes evolve for every possible path that a particle could take from point A to point B. Surprisingly, to produce the correct values, these paths must include paths that would seem to be impossible in order to produce the correct answers.
For example, the path integral for the propagation of a photon must consider paths in which a photon travels at greater than, and less than, the speed of light, despite the ordinary assumption of general relativity that massless particles always travel at exactly the speed of light. Similarly, so long as conservation of mass-energy is conserved in the end state of a path, intermediate steps in a path of a propagating particle in the Standard Model can "borrow" mass energy in what is called a "virtual particle" path - these phenomena which include the concept of "tunneling" in transistors, and oscillations between neutral meson states, are absolutely critical to how life works as we observe it on a day to day basis.
This suggest that our concept of many of the laws of nature as "absolute" is merely a classical approximation of how the universe really works. Disparities between classically permitted paths and those that must be considered in quantum physical path integrals suggest what kind of deeper structure the universe might hold that we usually ignore because these effects usually average out.
10. It is not clear that the concept of an "observation" that collapses the wave function of a quantum mechanical particle is rigorously defined in the leading Copenhagen interpretation of quantum physics.
Justifications For Beyond The Standard Model Physics That Don't Impress Me
1. Many theorists consider issues in quantum physics such as "the hierarchy problem", the "strong CP problem", "fine tuning" and "naturalness" to be important motivations for further research into beyond the Standard Model physics, and sometimes seek explanations of the parameters of the Standard Model or general relativity based upon concepts like the anthropic principle (i.e. the laws of nature must be such that we can exist to observe them), and the multiverse (i.e. that our universe is a likely combination of all conceptually possible universes).
Neither these motivations, nor these explanations, impress me.
These motivations, essentially, presume that we have any way of knowing what values of Standard Model parameters (or BSM parameters) to expect.
If Nature decides that the Higgs boson mass should be just so, or that the CP violating parameter of the QCD equations should be zero, or that neutrinos should have masses wildly smaller than the masses of other fermions, that is Her prerogative, and She doesn't need any additional laws of physics to set them at those values. If these choices seem "unnatural" or "fine tuned" then clearly the problem is with the way we are looking at the situation, since what is, is.
If it would be really cool if the gauge couplings of the Standard Model unified, but all available evidence suggests that they do not, then maybe that bit of numerology is just barking up the wrong tree and seeing deep meaning in a mere near coincidence. If the Higgs boson mass seems wildly fine tuned, then maybe our hypothesis about how it is generated is wrong and it can be derived from one or more much simpler mechanisms in which context its value seems far more natural - the unnatural aspect may have much more to do with a highly unnatural and contorted higher order loop approach we use to determine its mass than anything else.
Looking for deeper relationships between parameters we know is one thing, assuming that there must be new pieces to the puzzle based purely on a desire to make Nature fit some arbitrary notion of mathematical beauty is another.
These explanations (the anthropic principle and the multiverse), meanwhile are basically, unscientific ways of generating just so stories.
2. I am similarly unimpressed with those who believe that M-Theory is the only possible path to fundamental physics truth.
In essence, M-Theory and its low energy supergravity approximations, make assumptions about the right way to merge gravity and the rest of quantum physics that have not been very fruitful beyond the not particularly string theory restricted observation that a fundamental massless spin-2 gauge boson has the right properties and right number of degrees of freedom to largely reproduce the gravitational attributes of general relativity.
Specific variations of M-theory that reproduce the particles and interactions that we observe, while not predicting particles and interactions that we do not observe have not been successful after several decades of theoretical work by a large share of the entire theoretical physics community. None of the predictions particular to what is added to the Standard Model by supersymmetry or string theory have been borne out.
Many aspects of M-theory, such as its infamous 11 dimensions, appear to be artifacts of trying to integrate gravity in a unified way into a TOE in a manner that dilutes it relative to other Standard Model forces. Thus, some of the immense complexity of M-theories basically flows from a desire to tweak the magnitude of one coupling constant so that a unified approach can be taken. The price of consistency on this front is high relative to its costs.