What are the take away lessons about natural philosophy that an educated lay person should glean from reading about modern physics?
1. The universe and everything in it can (in principle) be described in every way that we are able to observe by Einstein's Theory of General Relativity and the Standard Model of Particle Physics (generally abbreviated to the "Standard Model" or "SM"). Einstein's Theory of Special Relativity, set forth a few years before General Relativity, is embedded in both General Relativity and the Standard Model
General Relativity theory is essentially unchanged from its form a century ago, although the measured values of its three key constants (the gravitational constant, the speed of light, and the cosmological constant) have been refined over the last century.
The Standard Model was formulated about 50 years ago, although the process of measuring it couple dozen physical constants is ongoing (no meaningful measurement has yet been made at all of one of them, the CP violation parameter for neutrinos), the last of the particles it predicts called the Higgs boson, was only formally discovered this year, and the Standard Model was revised once in the last fifteen years or so to reflect the discovery that neutrinos have a low, but non-zero rest mass.
2. Special relativity provides that the speed of light in a vacuum is an absolute speed limit on everything in nature. Massless particles such as photons move at the speed of light in a vacuum and do not experience time in their frame of reference. As massive particles move close to the speed of light it takes increasingly more energy to achieve the same increase in speed, time slows down for the particles, and space is warped on the particle in motion. Thus, the rate at which time passes is not uniform but instead depends upon the speed of the person measuring it, although there are formulas to precisely determine the relative rate at which time passes for one observer relative to another one.
3. General relativity describes gravity more accurately than Newton's law which provides that the attractive force of gravity between two objects is equal to the product of the masses of two objects divided by the square of their distance from each other times the gravitational constant G.
General relativity states that all mass and energy are equivalent to each other via the equation E=mc^2 where m is mass and c is the speed of light in a vacuum. In general relativity, gravity influences massless particles like photons rather than only influencing matter. Even empty space has a low uniform level of mass-energy described completely by the cosmological constant and called "dark energy." Gravity, in general relativity, is a function not just of the aggregate distribution of mass-energy in the universe, but also of the motion of those mass-energy particles. For example, a planet in motion relative to something else (e.g. the Sun) has a different gravitational field than a planet at rest. Time slows down in strong gravitational fields relative to weak gravitational fields. Gravitational effects propogate in waves moving at the speed of light in a vacuum. Gravity has an effect in General Relativity by altering the shape of space-time which is perfectly smooth and continuous (apart from singularties) in the theory.
General relativity does not have a preferred reference frame, but there are formulas by which the location and direction of movement of everything in the universe relative to one observer with one rate of time progression can be converted consistently into the location and direction of movement of everything in the universe relative to another observer with another rate off time progression.
General relativity's formulas, when applied to the distribution of stars and other matter and radiation observed by astronomers, imply two important phenomena which are called singularities. One is that we live in an expanding universe that is about 13.7 billion years old (and has a radius of about 13.7 billion light years) whose stages of expansion can be described consistently back to the first few seconds after the "Big Bang".
The other singularities in General Relativity arise when mass-energy is concentrated in a sufficiently small space and are called "Black Holes" because particles that cross the "event horizon" of a black hole cannot return from it (there is such a thing as black hole radiation caused by the behavior of particles right on the event horizon).
General relativity is a deterministic, field based theory, rather than a probabilistic particle based theory like thte Standard Model.
4. The Standard Model describes all of the stuff in the universe as being made up of quarks, leptons and bosons, all of which are assumed to be point-like with zero volume.
There are six kinds of quarks that are the core constituents of protons, neutrons and a variety of unstable quark composite particles called hadrons that are bound together by the strong nuclear force via the exchange of eight kinds of massless paticles called gluons (which can also form unstable gluon only composite particles called glueballs). The nuclear strong force holds atomic nuclei together (albeit somewhat indirectly). The quarks that make up a proton or neutron or other exotic hadron make up only a small percentage of the composite particle's rest mass; most of it can be attributed to the gluons which add mass to the composite particle via the strong nuclear force energy that they exchange even though the gluons themselves are massless. Quarks cannot exist in isolation; they are always "confined" by gluons in composite particles (except for top quarks which decay so fast via the weak force discussed below that they have no time to form composite particles). Quarks, in addition to having electromagnetic charges, have one of three kinds of "color charge" and all composite particles must be color neutral. Gluons each have two color charges.
There are six kinds of leptons as well - the electron and two identical but heavier and unstable version of the electron, and three kinds of neutrinos which are very light, lack electrical charge and don't interact with other matter very strongly.
In addition to gluons, there are three other kinds of bosons, which are the means by which forces are carried between particles in the Standard Model.
The first is the massless, electrically neutral photon carries the electromagnetic force between particles with electric charges (all quarks, electrons and their two heavy cousins, and a couple kinds of bosons we haven't discussed yet). We understand the interactions of photons and charged particles essentially perfectly via a subpart of the Standard Model known as QED. Mostly, QED reduces in complex, many particle situations to the pre-20th century theory of electricity and magnetism called "Maxwell's Equations" but QED have a very different mechanism than Maxwell's Equations that permits some kinds of electromagnetic interactions such as the "tunnelling" phenomena exploited in every transistor, that are not permitted by Maxwell's equations.
The second set of bosons are the W+, W- and Z boson which collectively make up the "weak force" that is most comonly observed as the source of nuclear radiation. These bosons are massive, travel at less than the speed of light, are unstable, and operate only at short ranges. The W+ and W- bosons are emitted from time to time by quarks and leptons and when this happens, these particles change into different kinds of particles - up type quarks turn into some kind of down type quark; down type quarks turn into some kind of up type quark, electron-like leptons turn into neutrinos, and neutrinos turn into electron-like leptons. Z bosons act sort of like short range heavy photons and do not change an emitting or receiving particles type. Usually, heavier versions of quarks and leptons very swiftly emit W bosons and decay into lighter quarks or leptons. These decays closely follow a very precisely understood theoretical formula.
Every particle in the Standard Model has an antiparticle which is identical to the ordinary particle except that it is reserved in charge and parity (think of this as direction of rotation about an axis of motion, although this is merely a heuristic way of understanding it) while having an identical mass. Antimatter has been observed and is routinely generated in certain weak force decays.
The Standard Model formulas are completely symmetric going forward and backward in time, except for certain W boson interactions which exhibit "CP violation" which is to say that these processes and the antiparticle version of these processes progress at different rates.
The last kind of boson is the Higgs boson, which is part of the unified Standard Model understanding of the weak force and the electromagnetic force, both of which are nearly perfectly understood. The Higgs boson is also very heavy and its interactions with massive particles is the source of fundamental particle mass (although as noted above, most of the mass in the universe comes from gluons exchanged in protons and neutrons).
The movement of particles in the Standard Model, particle decays, and force particle emissions are fundamentally probabilistic. The Standard Model's formulas tells us precisely the probability of certain outcomes being observed in particular experiments but the outcome is fundamentally unknowable until it is observed, and there is only a specific well defined level of precision with which it is theoretically possible to observe particles. Prior to being observed called "collapsing the wave function" quantum mechanical behavior is essentially in limbo made up of a probability field of all possible outcomes in the proper proportions at the same time.
5. The Standard Model has a great many measured constants that most people believe have some deeper relationship to each other that could be revealed with a more fundamental theory. There are many Standard Model constants that have been measured only fairly inaccurately, particularly in the area of neutrino physics. The math involved in understanding quark-gluon interactions (described by a part of the Standard Model called quantum chromodynamics or QCD for short) is much harder than the math involved in electromagnetic and weak force interactions and while experimental results and theoretical predictions from QCD consistent, the theoretical predictions are numerical approximations of the actual equation results that are precise only to about +/- 1%.
6. Conservation laws are important in both General Relativity and the Standard Model. For example, the total amount of mass-energy is conserved, and mass and energy are separately conserved except in nuclear interactions. The amount of net electromagnetic charge in the universe is neutral and conserved in all interactions. The net QCD color charge in the universe is conserved. Every interaction perserves CPT, which is to say a combined combination of electromagnetic charge sign, parity, and time direction (thus a CP violation is equivalent to a time reversal). The number of quarks and leptons net of anti-quarks and anti-leptons in an interaction is conserved subject to very specific and narrow exceptions. Net momentum, both angular and linear are conserved.
7. While we are close to understanding all of the laws of nature, we aren't there yet.
There are deep theoretical inconsistencies between General Relativity and the Standard Model that have not been resolved. General relativity does not have a quantum mechanical description and the Standard Model does not have a background independent description. For example, if Standard Model particles were truly point-like, then General Relativity would declare that each of them was a "black hole."
The very early instants of physics after the Big Bang (called "inflation") and a phenomena seen in astronomy called "dark matter" do not have explanations that fit neatly into General Relativity and the Standard Model.
Fortunately, the circumstances where both theories are needed at once to understand nature are few and involve extreme situations. You simply know which theory to use when.
There are hints from the relationships of various theoretical constants in physics that distances less than a certain exceedingly tiny length (much, much smaller, for example, than the theoretical "electron radius" of non-quantum physics) called the Planck length, may be ill defined or not exist as the fundamental make up of space-time may be made up of tiny grains rather than being truly smooth and continuous.
In general, there are strong suspicions that General Relativity and the Standard Model may not be completely accurate in extreme situations such as in describing the physics of the events shortly after the Big Bang, and the interaction of particles at extremely high energies and in the immediate vicinity of black holes.
A variety of beyond the Standard Model theories and variations on General Relativity have been proposed and all of the serious ones would be consistent with all measured experimental data but differ in some other way, or to explain dark matter. There are perhaps dozens classes of credible beyond the Standard Model or General Relativity variants with some serious basis that aren't ruled out by experiment. Theoretical physicists publish endlessly on these and huge physics experiments try to determine if any of them might be right. Many theories propose that seemingly absolute laws of nature are actually broken in some sort of rare or hard to measure circumstance.
Some of leading variants under consideration are "Cold Dark Matter", "Warm Dark Matter", "Inflation", various versions of "Loop Quantum Gravity", various versions of Supersymmetry, Supergravity, various versions of String Theory, various version of "Modified Gravity", some very subtle technical tweaks to General Relativity, enthropic gravity, holographic gravity, Kaluza-Klein theories, various grand unified theories based on Lie algebras and Lie groups, Majorana mass neutrino variants on the Standard Model, sterile neutrino theories, "Technicolor", Linear Sigma models, and more. Each of these predicts paticles and/or forces not found in the Standard Model or General Relativity to explain some not well understood part of it or just to explore what other theories could work to explain nature. But, the bounds of current experiment mean that all of them must be very subtle tweaks to the existing core theories.