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Assuming they exist (which seems likely according to our current best theories) black holes are very strange things indeed. In particular, the fate of something heading over the black hole horizon depends seems to be different depending on whether you cross the horizon or not.

In the frame of reference of somebody passing through the horizon, the horizon doesn't seem very special at all - you could cross the horizon of a sufficiently large black hole without even noticing. After passing the horizon, however, escape is impossible and you would inevitably end up spaghettified by the massive tidal forces near the central singularity.

In a frame of reference of somebody outside the black hole, the picture is very different. From that perspective, the gravitational time dilation at the horizon means that the progress of the falling object becomes slower and slower, grinding to a complete stop at the horizon itself. The red-shifting of any photons emitted from close to the horizon also means that the object looks redder and redder, going through infra-red, terahertz radiation, microwaves, and radio waves of increasing wavelength until they are too low energy to detect but they never quite stop altogether.

In the meantime, the black hole evaporates by the process of Hawking Radiation. This takes an unimaginably long time - as long as 10¹⁰⁰ years for the largest black holes but if you wait there long enough it will happen. Supposing that you could somehow detect the infalling observer during the entire period of the evaporation, you'd see the infalling observer crossing the horizon at the exact moment that the black hole disappeared altogether in a bright flash of energy (the smaller the black hole, the more it radiates). But of course, at that moment the infalling observer has zero mass-energy (as does the black hole as a whole) so how can it be the same observer in its own frame of reference (when its mass is the same as it was before the experiment began)?

Clearly our current theories of physics are insufficient here - we don't yet have a consistent theory of quantum gravity so we just don't know what happens near a tiny black hole when the spacetime curvature is high enough to be in the quantum regime.

One way out of the apparent paradox is simply that the two observers can never compare notes because whatever information the infalling observer collects is inevitably destroyed at the singularity, and no information from inside the black hole can ever be transmitted to the outside universe. The interior of the black hole is causally disconnected from the outside - it can be considered to exist infinitely far in the future (long after the black hole evaporates) or can even be considered to be an entirely different universe in its own right. If the two observers can never get back together to compare notes (and find that they disagree) there isn't really any disagreement. It's a bit like the Many Worlds Interpration of quantum mechanics - observers in different parallel universes can't subsequently interact so they can't disagree about the observable outcome of some experiment.

But in both of these cases there is a philosophical problem - if the universe is qualitatively different for different observers then it seems to make a mockery of the very idea of an objective reality. Just as the IO Monad theory of subjective experience has no problems with observers disagreeing on matters that make no difference in an objective sense, it seems like general relativity may require that we have no problems with disagreements between causally disconnected objective realities.

I love the idea of futuristic or alien civilizations using advanced technology to create planetary scale art.

I wonder if such an advanced civilization would be able to create a toroidal planet. It would have to be spinning pretty fast for it not to fall into the central hole - fast enough that the effective gravitational field at the outermost ring of the surface would be quite weak and the gravitational field at the innermost ring would be quite strong. The gravitational "down" direction would vary across the surface of the planet and wouldn't be normal to the average surface except on those two rings. I think if you slipped you probably wouldn't fall off (unless the effective gravity was very low) but you would generally fall towards the outermost ring. Any oceans and atmosphere would also be concentrated at the outermost ring. It would be as if there was a planet-sized mountain with its top at the innermost ring and its bottom at the outermost. It would therefore have to be made of something very strong if the minor radius was reasonably large - rock (and probably even diamond) tends to act as a liquid at distance scales much larger than mountains.

I need to try to remember to google my ideas before writing about them. Having written this, I've just discovered that lots of people have thought about this before.

I didn't pay too much attention to "surfer dude" Garrett Lisi's Exceptionally Simple Theory of Everything when the paper first appeared, but since his TED talk about it was posted last month I have found myself fascinated.

Please excuse any errors in the following - I haven't studied physics at or beyond graduate level, so my understanding may be flawed in some respects.

Here's the game. You have 8 numbers (quantum numbers) - let's call them s, t, u, v, w, x, y and z for the sake of argument. Each of these numbers can be either -1, -1/2, 0, 1/2 or 1. So there are 5⁸ = 390625 possible sets of numbers. However, there are certain rules eliminating some combinations:

1. They must be all half-integers (-1/2, 1/2) or all integers (-1, 0, 1).
2. They must add up to an even number.
3. If they are integers, exactly six of them must be 0.

With these rules, there are only 240 possible sets (128 with half-integers and 112 with integers).

If you take these sets as the corners of an 8-dimensional shape, you get the pretty pictures that you might have seen associated with E8 theory.

Each of the 240 possible sets corresponds to a fundamental particle in a model that includes all the standard model particles and gravity.

• 144 of the particles are quarks (up, down, strange, charm, top, bottom)×(spin up, spin down)×(red, green, blue)×(left-handed, right-handed)×(particle, antiparticle). These are the particles that make up the bulk of the mass of atoms (plus some variants).
• 24 of the particles are charged leptons (electron, muon, tau)×(spin up, spin down)×(left-handed, right-handed)×(particle, antiparticle). These are the particles that determine the shapes, textures, colours and chemistry of things (plus some variants).
• 24 of the particles are neutrinos (electron, muon, tau)×(spin up, spin down)×(left-handed, right-handed)×(particle, antiparticle). These don't have much of an effect - trillions of them pass right through your body each second.
• 6 of the particles are gluons (orange, chartreuse, azure, aquamarine, indigo, violet ^[1]), responsible for the "strong force" that holds atomic nuclei together.
• 2 of the particles are W bosons (particle, anti-particle). These cause the "weak force" which is the only way that neutrinos can interact with the other particles. They are quite heavy so never go very far.
• 16 of the particles are frame Higgs bosons (2 types)×(spin up, spin down)×(left-handed, right-handed)×(particle, anti-particle). Interactions with these are what gives particles their mass.
• 4 of the particles are spin connection bosons (spin up, spin down)×(left-handed, right-handed). These are responsible for gravity.

[1] These aren't the names that physicists usually use, but I prefer them.

That adds up to 220 - what about the other 20? Lisi's theory predicts some new particles which we haven't seen (because they're too heavy) but which might turn up in the Large Hadron Collider. These particles fall into two classes:

• 2 of the particles are Pati-Salam W' bosons (particle, anti-particle). These cause a force similar to the weak force but even weaker.
• 18 of the particles are coloured Higgs bosons (3 generations)×(red, green, blue)×(particle, anti-particle). These are like the other Higgs bosons except that they can also interact via the strong force.

Lisi's paper contains several tables which show the values of s, t, u, v, w, x, y and z for each of these particles.

Different combinations of the quantum numbers correspond to the conserved charges that physicists are more familiar with:

• electric charge is (3v+x+y+z)/3.
• colour charges are combinations of x, y and z.
• weak and weaker isospins are (u+v)/2 and (v-u)/2.
• weak hypercharge is (3(v-u)+2(x+y+z))/6.
• two gravitational/spin charges are (s+t)/2 and (t-s)/2.
• a charge corresponding to fermion generations (i.e. electron/muon/tau leptons, up/charm/top quarks and down/strange/bottom quarks) is w.

(Two of these are new charges predicted by E8 theory).

As well as these 240 particles, there are 8 particles with all-zero quantum numbers. The 8 neutral bosons are (I think):

1. The photon (electromagnetic radiation: light, radio waves etc.)
2. The Z boson (weak force)
3. A seventh gluon (strong force)
4. An eighth gluon (strong force)
5. A fifth spin connection boson (gravity)
6. A sixth spin connection boson (gravity)
7. The Z' boson (weaker force)
8. The w particle (generations)

As well as describing all the particles, this theory also describes their interactions. Two particles can combine to form a third (or appear as a result of the third decaying) if and only if you can add up their corresponding quantum numbers and obtain the quantum numbers of the third particle. If one of the three is a neutral boson it must be a neutral boson corresponding to a charge which is non-zero for other two particles.

If you know the quantum numbers for a particle, you can obtain the quantum numbers for the corresponding anti-particle by multiplying them all by -1. So, neutral bosons are their own anti-particles and a non-neutral particle can always interact with its own anti-particle to produce a neutral boson.

E8 theory does have some problems:

1. It seems to imply a very large cosmological constant.
2. Some of the higher generations of fermions have the wrong charges.

But these problems may be surmountable with more work and experimental data. Even if E8 theory is not correct in its current form, the pattern is so compelling that there is surely some nugget of truth in there somewhere that will form part of the final theory. It's not the end of physics and probably not even the beginning of the end, but it might just be the beginning of the end of the beginning.

Learning about all this stuff makes me want to create an E8 screensaver that simulates a soup of E8 particles all colliding with each other and interacting as they would at very high energies where the symmetries are unbroken. I wrote something similar many years ago when I learnt about quantum electrodynamics (a soup of electrons and photons) but this one would be much more colourful and interesting.

Most of the properties of materials (including all of chemistry) are modelled by assuming atomic nuclei to be indivisible particles. You can derive almost all chemistry and properties of materials from the laws of quantum mechanics and the masses and charges of electrons and nuclei.

Nuclear physics, on the other hand, is all about the internals of the nuclei and (except under extreme conditions) a nucleus is unaffected by electrons and other nuclei (even in electron capture the particular chemical configuration of an atom doesn't affect its decay rate significantly).

This is useful in some ways - you can replace some nuclei with different isotopes (for example in nuclear medicine) without changing the chemistry. Of course, once it decays (other than gamma decay) the nuclear charge will change and the chemistry will be different.

Suppose that nuclear decay rates did depend significantly on chemical configuration - what would the consequences be? The obvious consequence is that it would be possible to make nuclear weapons that are more difficult to detect, since they could be made non-radioactive until they undergo a chemical reaction.

More subtly, there would be a whole new spectrum of chemical processes made possible by the storage of energy in (and release of energy from) the atomic nuclei. This could lead to new (cleaner, safer) forms of nuclear power, and all sorts of other interesting applications.

This is all wild speculation of course, but this suggests there is still much that we don't understand about atomic decay processes.

Almost every fundamental new discovery in physics so far has yielded great advances in technology. The exception seems to be general relativity - probably because gravity is such a weak force, it's difficult to make consumer items out of it.

I like to wonder what new technologies we could hope (in our wildest dreams) to obtain with a complete theory of physics. It might take a while, because we don't even know of any practical way of even getting experimental evidence for a grand unified theory so far, let alone make technology from those experimental results.

One possibility is new particles. Many promising theories predict various new particles. Unfortunately most particles other than the ones that make us up tend to be very short-lived and therefore don't yield any new materials. But if we do find a new long lived particle (and it doesn't cause a phase transition that swallows us all up) there is a possibility of new materials heavier, lighter, stronger or with better information storage abilities than the ones we have.

Another possibility is gravitational engineering. Particularly if we can find a way to violate the weak energy condition, we might be able to build stable, traversable wormholes, time machines and other such time/space abominations.

Even more far-fetched (but also possible) would be more ways to manipulate matter and energy, as in The Trigger and Ed stories.

When I learned about General Relativity at university I sometimes used to wonder if there was a metric in which this object could exist:

And be what it appears to be, i.e. the straight lines are (lightlike) geodesics and the corners are (locally) right-angles.

Initially, I imagined that such a metric might be possible without any sort of topological defect. In particular, while the triangle would look like the picture above when viewed "face on" it would appear to curve as you moved around it and examined it from different angles. While lightlike geodesics always look straight when you look along them from a point on the geodesic, they can still look curved when viewed externally. The photon sphere around a black hole is an example of a set of such geodesics thought to occur in our universe.

Thinking about it some more, I suspect something strange is going to have to happen in the middle of the triangle - if you try to shrink the triangle to a point, what happens?

Imagine being in this universe and travelling all the way around the triangle. I think that upon doing so, one would find that one had actually only turned through 270 degrees instead of the full 360 (and would also have rotated about the axis of travel). I suspect that this means that such a metric would have to have a topological defect (a cosmic string) passing through the center of the triangle. This would cause a discontinuity when viewing the triangle, so one would not be able to see the entire illusion in all its glory as it is shown above.