I set up an experiment to test quantum anthropics.
Flip four quantum coins. If they all came up heads, stop. If any of them came up tails, flip 5 more coins and (using mnemonics) think really hard about the exact coin flip sequence. If I find myself in a universe where first four coins came up all heads, then with p < 0.0625, quantum weirdness kept me from finding myself in one of the universes the state of my consciousness split me 512-ways.
I got access to a quantum random number generator, resolved to do the experiment, called a friend and told them I was about to do the experiment, and… chickened out and didn’t do the experiment.
If I understand the experiment, your theory is that quantum weirdness makes it more likely to see four heads in a row because you resolved to flip many more coins if you don’t.
Sounds fun. I’ll flip four coins (actually use a string of 0′s and 1′s that’s 4 bits long). If I don’t get four heads, I’ll generate a 10-digit sequence and memorize it. Let’s explore this frontier!
I did it. It didn’t work. My new favorite number is 1 1 0 0 0 0 0 0 0 1.
Reality hack failed.
Let’s try again. If I don’t get 4 heads, I’ll memorize a 20-digit number.
It didn’t work. My other new favorite number is 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1.
I wonder if there’s a better way to test this theory.
I’m not sure if coin flips are quantumly random, or just hard enough to predict. Feels like coins would still work as well in a Newtonian universe. I tried to go with something that something that is clearly caused by quantum effects, like measuring if electron is either polarized up or down or down. Luckily, there’s an app for that.
There are plenty of processes in Newtonian mechanics that amplify small differences. (E.g., in a game of snooker or billiards, it doesn’t take many bounces before quantum fluctuations have a substantial effect on where the ball goes.)
Coin flips in particular aren’t great, though. A skilled coin-flipper can, I think, get any result they want with close to 100% reliability, which suggests that at least some superficially-plausible-looking kinds of coin flip don’t amplify small differences enough.
It wasn’t intended to be obvious, merely true. But (1) I’m merely repeating something I heard from someone I thought credible, so it might turn out to be wrong, and (2) as I recall, “not many” is still rather more than one ever sees in practice in actual games.
So, is it right? I can’t readily find anything on the web where the calculations are done, and I’m too lazy to do them properly myself. What I can find is a good look at a related problem, which gets us at least part of the way.
So, the (excellent) book “The SIAM 100-digit challenge” by Bornemann et al provides solutions to ten problems of the following form. “Here is a mathematical question whose answer is a number. Find the number to at least 10 significant figures”. One of the problems, whose proximity to the billiards question should be clear enough, is as follows. Put a perfect circular mirror of radius 1⁄3 around every (integer,integer) point in the plane. Fire off a photon starting at (1/2,1/10) with velocity (1,0). Where is it after 10 units of time? The answer isn’t particularly important, but it turns out that (1) in that time it bounces 17 times and (2) the growth of any initial error is about a factor of 10^11. That suggests about a factor of 4 per bounce.
So, the next question is what quantum effects do to the initial trajectory of a snooker/billiard ball. The following is surely not the best way to answer that question, and I suspect it yields a considerable underestimate, but let’s see. Consider the first bounce. A change in either the position or the momentum of the ball will alter the angle it bounces at; for balls of mass m and radius r moving at speed v, a change in position by dx will change the angle by something of order dx/r, and a change in momentum by dp will change the angle by something of order dp/(mv). So the angle uncertainty has to be at least something of the order hbar/(mvr), which is probably somewhere around 2x10^-31 radians.
So if a “substantial effect” means, say, 0.1 radians, that means … actually somewhere around 50 bounces, which is distinctly more than the number I thought I remembered. So maybe the bit of folklore I heard was wrong; or maybe I misunderstood or misremembered it; or maybe a better estimate of the effects of quantum phenomena on a billiard ball gives a much larger value.
the three-body problem
… doesn’t have a closed-form solution in classical mechanics, but that’s an entirely separate question from whether it amplifies small quantum effects enough to be useful for generating usable quantum randomness. (I think the answer to that depends on the details, but in any case gravity is weak enough that any 3-body system you make is going to be made up of massive objects moving on rather long timescales; it’ll be much less practical as a quantum randomness amplifier than a system of bouncing billiard balls. Of course both are ridiculous choices anyway.)
You start doing the experiment, you flip four coins, 15⁄16 of you memorize a sequence, 15*32 of you memorized pairwise probably different sequences. In the end, you have a probability of 15⁄16 to find yourself having memorized a sequence. If QI works and half of you who find a tails in a first four coins commit suicide, start-experiment-you only has a 15⁄17 chance to find themselves having found tails and failed to kill themselves.
No, that would do nothing to the anthropic weights of each subtree. I meant ending your life as part of the thought experiment. Why would memorizing numbers do anything special?
I set up an experiment to test quantum anthropics.
Flip four quantum coins. If they all came up heads, stop. If any of them came up tails, flip 5 more coins and (using mnemonics) think really hard about the exact coin flip sequence. If I find myself in a universe where first four coins came up all heads, then with p < 0.0625, quantum weirdness kept me from finding myself in one of the universes the state of my consciousness split me 512-ways.
I got access to a quantum random number generator, resolved to do the experiment, called a friend and told them I was about to do the experiment, and… chickened out and didn’t do the experiment.
I do not know how to interpret these results :-/
I love this forum.
If I understand the experiment, your theory is that quantum weirdness makes it more likely to see four heads in a row because you resolved to flip many more coins if you don’t.
Sounds fun. I’ll flip four coins (actually use a string of 0′s and 1′s that’s 4 bits long). If I don’t get four heads, I’ll generate a 10-digit sequence and memorize it. Let’s explore this frontier!
I did it. It didn’t work. My new favorite number is 1 1 0 0 0 0 0 0 0 1.
Reality hack failed.
Let’s try again. If I don’t get 4 heads, I’ll memorize a 20-digit number.
It didn’t work. My other new favorite number is 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1.
I wonder if there’s a better way to test this theory.
I’m not sure if coin flips are quantumly random, or just hard enough to predict. Feels like coins would still work as well in a Newtonian universe. I tried to go with something that something that is clearly caused by quantum effects, like measuring if electron is either polarized up or down or down. Luckily, there’s an app for that.
I don’t see any reason for physical coin flips to be provide quantum randomness. This is a better source.
There are plenty of processes in Newtonian mechanics that amplify small differences. (E.g., in a game of snooker or billiards, it doesn’t take many bounces before quantum fluctuations have a substantial effect on where the ball goes.)
Coin flips in particular aren’t great, though. A skilled coin-flipper can, I think, get any result they want with close to 100% reliability, which suggests that at least some superficially-plausible-looking kinds of coin flip don’t amplify small differences enough.
That’s not obvious to me. Evidence..?
E.g. the three-body problem is unsolvable in classical mechanics, without the need to postulate quantum anything.
It wasn’t intended to be obvious, merely true. But (1) I’m merely repeating something I heard from someone I thought credible, so it might turn out to be wrong, and (2) as I recall, “not many” is still rather more than one ever sees in practice in actual games.
So, is it right? I can’t readily find anything on the web where the calculations are done, and I’m too lazy to do them properly myself. What I can find is a good look at a related problem, which gets us at least part of the way.
So, the (excellent) book “The SIAM 100-digit challenge” by Bornemann et al provides solutions to ten problems of the following form. “Here is a mathematical question whose answer is a number. Find the number to at least 10 significant figures”. One of the problems, whose proximity to the billiards question should be clear enough, is as follows. Put a perfect circular mirror of radius 1⁄3 around every (integer,integer) point in the plane. Fire off a photon starting at (1/2,1/10) with velocity (1,0). Where is it after 10 units of time? The answer isn’t particularly important, but it turns out that (1) in that time it bounces 17 times and (2) the growth of any initial error is about a factor of 10^11. That suggests about a factor of 4 per bounce.
So, the next question is what quantum effects do to the initial trajectory of a snooker/billiard ball. The following is surely not the best way to answer that question, and I suspect it yields a considerable underestimate, but let’s see. Consider the first bounce. A change in either the position or the momentum of the ball will alter the angle it bounces at; for balls of mass m and radius r moving at speed v, a change in position by dx will change the angle by something of order dx/r, and a change in momentum by dp will change the angle by something of order dp/(mv). So the angle uncertainty has to be at least something of the order hbar/(mvr), which is probably somewhere around 2x10^-31 radians.
So if a “substantial effect” means, say, 0.1 radians, that means … actually somewhere around 50 bounces, which is distinctly more than the number I thought I remembered. So maybe the bit of folklore I heard was wrong; or maybe I misunderstood or misremembered it; or maybe a better estimate of the effects of quantum phenomena on a billiard ball gives a much larger value.
… doesn’t have a closed-form solution in classical mechanics, but that’s an entirely separate question from whether it amplifies small quantum effects enough to be useful for generating usable quantum randomness. (I think the answer to that depends on the details, but in any case gravity is weak enough that any 3-body system you make is going to be made up of massive objects moving on rather long timescales; it’ll be much less practical as a quantum randomness amplifier than a system of bouncing billiard balls. Of course both are ridiculous choices anyway.)
Here’s how I predict your setup to work, and shame on you for chickening out:
http://sketchtoy.com/66313589
You start doing the experiment, you flip four coins, 15⁄16 of you memorize a sequence, 15*32 of you memorized pairwise probably different sequences. In the end, you have a probability of 15⁄16 to find yourself having memorized a sequence. If QI works and half of you who find a tails in a first four coins commit suicide, start-experiment-you only has a 15⁄17 chance to find themselves having found tails and failed to kill themselves.
What do you mean by “commit suicide” here? Memorize the results of 5 more coins?
No, that would do nothing to the anthropic weights of each subtree. I meant ending your life as part of the thought experiment. Why would memorizing numbers do anything special?