Philosophy

Mathematical Universe v. Boltzmann Brains

I’m a fan of the Mathematical Universe idea. Or rather, I was. I think I came up with the idea independently of (and before) Max Tegmark, based on one of my old LiveJournal blog-post dated “2007-01-12” (from context, I think that’s YYYY-MM-DD, not YYYY-DD-MM).

Here’s what I wrote then, including typos and poor rhetorical choices:

Ouch, my mind hurts. I've been thinking about The Nature of Reality again. This time, what I have is the idea that from the point of view of current science, the universe can be described as a giant equation: each particle obeys the laws of physics, which are just mathematical formula. Add to this that an mathematical system can exist before anyone defines it (9*10 was still equal to 90 before anybody could count that high), and you get reality existing because its underlying definitions do not contradict each-other.

This would mean that there are a lot of very simple, for lack of a better word, "universes" along the lines of the one containing only Bob and Sarah, where Sarah is three times the age of Bob now, and will be twice his age in 5 years' time. But it would also mean that there are an infinite number of universes which are, from the point of view of an external observer looking at the behaviour of those within them, completely indistinguishable from this one; this would be caused by, amongst other things, the gravitational constant being represented by an irrational number, and the difference between the different universes' gravitational constants varies by all possible fractions (in the everyday sense) of one divided by Graham's number.

Our universe contains representations of many more simple ones (I've described a simple one just now, and you get hundreds of others "universes" of this type in the mathematics books you had at school); you cannot, as an outside observer, interfere with such universes, because all you end up with is another universe. The original still exists, and the example Sarah is still 15. In this sense of existence, the Stargate universe is real because it follows fundamental rules which do not contradict themselves. These rules are of course not the rules the characters within it talk about, but the rules of the Canadian TV industry. There may be another universe where the rules the characters talk about do apply, but I'm not enough of a Stargate nerd to know if they are consistent in that way.

The point of this last little diversion, is that there could be (and almost certainly is) a universe much more complex than this one, which contains us as a component. The question, which I am grossly unqualified to contemplate but tried anyway (hence my mind hurting), is what is the most complex equation possible? (Apart from "God" in certain senses of that word). All I feel certain of at the moment, is that it would "simultaneously" (if you can use that word for something outside of time but containing it) contain every possible afterlife for every possible subset of people.

Tomorrow I will be in Cambridge.

Since writing that, I found out about Boltzmann brains. Boltzmann brains are a problem, because if they exist at all then it is (probably) overwhelmingly likely that you are one, and if you are one then it’s overwhelmingly likely that the you’re wrong about everything leading up to the belief that they exist, so any belief in them has to be irrational even if it’s also correct.

Boltzmann brains appear spontaneously in systems which are in thermal equilibrium for long enough (“long enough” being 101050 years from quantum fluctuations), but if you have all possible universes then you have a universe, an infinite number of universes, where Boltzmann brains are the most common form of brain — Therefore, all the problems that apply to Boltzmann brains must also apply to the Mathematical Universe.

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Science, SciFi, Technology

Kessler-resistant real-life force-fields?

Idle thought at this stage.

The Kessler syndrome (also called the Kessler effect, collisional cascading or ablation cascade), proposed by the NASA scientist Donald J. Kessler in 1978, is a scenario in which the density of objects in low earth orbit (LEO) is high enough that collisions between objects could cause a cascade where each collision generates space debris that increases the likelihood of further collisions.

Kessler syndrome, Wikipedia

If all objects in Earth orbit were required to have an electrical charge (all negative, let’s say), how strong would that charge have to be to prevent collisions?

Also, how long would they remain charged, given the ionosphere, solar wind, Van Allen belts, etc?

Also, how do you apply charge to space junk already present? Rely on it picking up charge when it collides with new objects? Or is it possible to use an electron gun to charge them from a distance? And if so, what’s the trade-off between beam voltage, distance, and maximum charge (presumably shape dependent)?

And if you can apply charge remotely, is this even the best way to deal with them, rather than collecting them all in a large net and de-orbiting them?

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Science

I am not a quantum physicist

I am not a quantum physicist. I do not write this prediction thinking that it is true or a novel deduction on the nature of reality. I write this prediction in order to test my own understanding of quantum physics.

Given all particles are fields:

  1. Fermions are those fields where probability is in the range 0-1 (or possibly -1 to +1, depending on antimatter).
  2. Bosons are those fields where probability can take on any positive or zero value (possibly also any negative value, depending on antimatter).

This “explains” why two fermions cannot occupy the same quantum state, yet bosons can. Inverted quote marks, because this might turn out to not have any explanatory power.

I’m fine with that, just as I’m fine with being wrong. I am not a quantum physicist. I don’t expect to be right. It would be nicer to find I’m wrong rather than not even wrong, but even that’s OK — that’s why I’m writing this down before I see if someone else has already written about this.

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Science, Technology

Railgun notes #2

[Following previous railgun notes, which has been updated with corrections]

Force:
F = B·I·l
B = 1 tesla

I: Current = Voltage / Resistance
l: Length of armature in meters

F = 1 tesla · V/R · l
F = m · a
∴ a = (1 tesla · V/R · l) / m

Using liquid mercury, let cavity be 1cm square, consider section 1cm long:
∴ l = 0.01 m
Resistivity: 961 nΩ·m
∴ Resistance R = ((961 nΩ·m)*0.01m)/(0.01m^2) = 9.6×10^-7 Ω
Volume: 1 millilitre
∴ Mass m = ~13.56 gram = 1.356e-2 kg
∴ a = (1 tesla · V/(9.6×10^-7 Ω) · (0.01 m)) / (1.356e-2 kg)

Let target velocity = Escape velocity = 11200 m/s = 1.12e4 m/s:
Railgun length s = 1/2 · a · t^2
And v = a · t
∴ t = v / a
∴ s = 1/2 · a · (v / a)^2
∴ s = 1/2 · a · v^2 / a^2
∴ s = 1/2 · v^2 / a
∴ s = 1/2 · ((1.12e4 m/s)^2) / ((1 tesla · V/(9.6×10^-7 Ω) · (0.01 m)) / (1.356e-2 kg))

@250V: s = 0.3266 m (matches previous result)

@1V: s = 81.65 m
I = V/R = 1V / 9.6×10^-7 Ω = 1.042e6 A
P = I · V = 1V · 1.042e6 A = 1.042e6 W

Duration between rails:
t = v / a
∴ t = (1.12e4 m/s) / a
∴ t = (1.12e4 m/s) / ( (1 tesla · V/(9.6×10^-7 Ω) · (0.01 m)) / (1.356e-2 kg) )

(Different formula than before, but produces same values)
@1V: t = 0.01458 seconds

Electrical energy usage: E = P · t
@1V: E = 1.042e6 W · 0.01458 seconds = 1.519e4 joules

Kinetic energy: E = 1/2 · m · v^2 = 8.505e5 joules

Kinetic energy out shouldn’t exceed electrical energy used, so something has gone wrong.

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Railgun notes

Force on the projectile of a railgun:
F = B·I·l
B: Magnetic field
I: Current
l: Length of armature

Current = Voltage / Resistance

Resistivity of seawater:
ρ = 2.00×10^−1 (Ω·m) (because = (Ω/m-length)*(cross-sectional area))

Let cavity be 1cm square, consider section 1cm long:

Volume: 1 millilitre
mass (m): ~1 gram = 1e-3 kg
Cross-section: 1e-4 m^2
Armature length (l): 1e-2 m
Resistance: ((2.00×10^−1 Ω·m)*0.01m)/(0.01m^2) = 0.2 Ω (got that wrong first time! Along with all that followed, which is now updated…)
∴ current (I) = Voltage (V) / 0.2 Ω

Rare earth magnets can be 1 tesla without much difficulty. Assume that here.

F = 1 T · (V/0.2 Ω) · (1e-2 m)

Target velocity: 11.2 km/s = Escape velocity = 11200 m/s
v = at = 11200 m/s
∴ a = (11200 m/s) / t
s = 1/2 · a · t^2
∴ s = 1/2 · ( (11200 m/s) / t ) · t^2
= 1/2 · (11200 m/s) · t
or: t = s / (1/2 · (11200 m/s))
F = ma = (1e-3 kg) · a
∴ a = F / (1e-3 kg)
∴ t = (11200 m/s) / (F / (1e-3 kg))
= (11200 m/s) · (1e-3 kg) / F
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / F
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / ( 1 T · (V/0.2 Ω) · (1e-2 m) )

Say V = 250 volts:
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / ( 1 T · (250V/0.2 Ω) · (1e-2 m) ) = 5020m (not ~501760 meters)

Say V = 25,000 volts:
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / ( 1 T · (25000V/0.2 Ω) · (1e-2 m) ) = 50.2m (not ~5017.6 meters)

Liquid mercury instead of seawater:
Resistivity: 961 nΩ·m = 0.961e-6 Ω·m
Resistance: 9.6e-7 Ω (got this one wrong the first time, too!)
Density: 13.56 times water
F = 1 T · (V/9.6e-7 Ω) · (1e-2 m)
s = 1/2 · (11200 m/s) · (11200 m/s) · (13.56e-3 kg) / ( 1 T · (V/9.6e-7 Ω) · (1e-2 m) )
@250 volts: s = 0.3266 meters (not 3.266m as before correction)
@25kV: s = 3.266 millimetres (not 32.66 millimetres as before)

Power (DC): P = IV where I = V/R,
R = 9.6e-7 Ω
@250 volts: I = 250 / R = 250 V / 9.6e-7 Ω = 2.604e8 amperes (x10 more than before correction)
∴ P = 65.1 gigawatts (x10 than before)
@25kV: I = 25000 / R = 25000 V / 9.6e-7 Ω = 2.604e10 amperes (x10 more than before)
∴ P = 651 terawatts (x10 than before)

Duration between rails:
From t = s / (1/2 · (11200 m/s))
@250 volts:
t = 0.3266 meters / (1/2 · (11200 m/s)) = 5.8321×10^-5 seconds (x10 less than before correction)
@25kV:
t = 3.266 millimetres / (1/2 · (11200 m/s)) = 5.8321×10^-7 seconds (x10 less than before)

Electrical energy usage:
E = P · t
@250 volts:
E = 65.1 gigawatts · 5.8321×10^-5 seconds = 3.797×10^6 joules (unchanged by correction)
@25kV:
E = 651 terawatts · 5.8321×10^-7 seconds = 3.797×10^8 joules (unchanged by correction)
(For reference, 1 litre of aviation turbine fuel is around 3.5e7 joules)

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