How Deterministic Is Determinism?

[dlorde]

With a small addendum that we can get a sort of determinism back with the Many Worlds Interpretation.

The physicist Sean Carroll has a pretty interesting blog post on this subject: http://www.preposterousuniverse.com/blog/2011/12/05/on-determinism/

I wasn't really sure what the best quote to take from the post is, and it's probably best to read the whole thing, but here's a short sample:

If I understand it correctly, MW is generally considered to be deterministic but giving the appearance of randomness by the observer selection effect - each possible outcome is seen by a 'version' of the observer, but for each observer version, the outcome necessarily appears random.

 

[Roboramma]

If I understand it correctly, MW is generally considered to be deterministic but giving the appearance of randomness by the observer selection effect - each possible outcome is seen by a 'version' of the observer, but for each observer version, the outcome necessarily appears random.

Yep.

 

[jimbob]

It certainly seems likely that it is impossible to completely remove randomness from a system due to quantum mechanical issues at least.

But that doesn't rule out the possibility that things are completely deterministic, we just don't know how to figure out the result before hand because it is impossible to get that information.

Suppose nothing is random. The entire universe is set on a deterministic path and there is nothing that can be done to change it in the least. We think we are in charge. We work to optimize results for ourselves by figuring out which is the most likely path to provide the best results for ourselves, but it doesn't matter. The universe is set up in a particular way and what will happen, will happen including the thoughts we might have about the decision facing us.

I think the theorizing above is worthless because the theory postulated seems to preclude ever being able to test it. But maybe somebody has some thoughts about it?

I would say that
https://en.wikipedia.org/wiki/Bell_test_experiments are aimed at looking at that question, and I would say that the best explanation is that the universe hasn't predetermined the result of a lot of the experiments - i.e. they are random.


Or at least one has to posit quite convoluted and ubiquitous mechanisms if there is a deterministic explanation.

I can see how the Many Worlds explanation sort of gets it out of it, but I'm not sure how it has any practical difference.


------------------------------------------------------

Looking at it from a more philosophical point of view, I think that true randomness makes a lot of ultimate explanations less problematic than a fully deterministic universe in the manner of Blaise Pascal.

For example, my understanding is that immediately after the big bang, conditions would have been uniform, throughout the entire young universe. If you don't allow random fluctuations - I can't see how you create the conditions for structure. (I am aware that this might be due to my lack of understanding - my background is more in applied physics, and I'm an engineer, so this is outside my knowledge). With random fluctuations, however, the mechanism is fairly straightforward.

 

[caveman1917]

Just because something has a non-zero probability doesn't mean that it can happen in the real world. There is a positive probability that you can scramble and egg, drop it to the floor, and it form a whole egg, but it will never happen.

In an infinite universe it not only has happened, but continuously happens an infinite number of times.

 

[caveman1917]

Yeah. I think the translational energy will be smaller, around 10^-3 J. So that makes the drag closer to the right order to interfere, depending on how the turbulence works out.

The absolute magnitude of the initial energy isn't the relevant aspect, but how small changes in that magnitude relate to how predictable the outcome is. If we assume air resistance is an increasing function of (rotational) velocity, then during the 1-second toss more energy would be sapped from a 10 J coin than a 1 J coin. And lastly there's turbulence, or more generally any unpredictability in the air resistance function, at high rotation rates.

 

[jt512]

In an infinite universe it not only has happened, but continuously happens an infinite number of times.

Luckily, that doesn't matter to us in our instantiation of the universe.

 

[TubbaBlubba]

The absolute magnitude of the initial energy isn't the relevant aspect, but how small changes in that magnitude relate to how predictable the outcome is. If we assume air resistance is an increasing function of (rotational) velocity, then during the 1-second toss more energy would be sapped from a 10 J coin than a 1 J coin. And lastly there's turbulence, or more generally any unpredictability in the air resistance function, at high rotation rates.

It's not totally irrelevant since we can make a first-order guesstimate of the change in energy that would correspond to "flipping" the outcome. Of course one woud actually need to set up Hamilton's equations and perturb it to do that properly.

 

[caveman1917]

It's not totally irrelevant since we can make a first-order guesstimate of the change in energy that would correspond to "flipping" the outcome.

Let's ignore translational velocity, assume a coin of unit mass is fixed to a horizontal frictionless axis. It starts heads up, then we give it an initial angular velocity w_0 and the outcome is defined by which side points up after 1 second.

Define a function f: R^+ -> {H,T}: w_0 -> outcome(w_0)

Let p_i be the sequence of "flipping points" in f, so the sequence of points where f goes from H to T or vice versa.

Define a function err: R^+ -> R^+: x -> |p_above(x) - p_below(x)|, giving for each w_0 the length of the interval with the same outcome as w_0, effectively proportional to our available error range before we mispredict.

The question is how err grows. Assuming no air resistance and hence constant rotation, err is constant, all the p_i are at 0.5k with k \in N. So err would be independent of w_0 (which is proportional to the initial energy, so independent of the initial energy).

Assuming air resistance is linear in angular velocity, angular velocity would decay exponentially, and err would decay as w_0^-1[*]. Which does depend on the initial energy, but not in the way you seemed to argue, a bigger initial energy is better than a smaller one. Because what you really want to do is to change the coin's angular velocity as much as you can in the space of 1 second which, with any air resistance which is strictly increasing in angular velocity, is to be had at higher initial energy rather than smaller.

The real question is, since the behaviour of err depends on the air resistance function, what happens to err when air resistance becomes super-linear in angular velocity or even goes turbulent and chaotic? For example if we can get err to decay exponentially then we should be good for claiming that a coin toss is inherently unpredictable even under a deterministic Newtonian model. Well, assuming that this happens at "reasonable" angular velocities for an actual coin toss.

* ETA: actually it's still constant but at a higher frequency, the distance between all p_i is still the same, it's just a lower constant than in the "no air resistance" case. It stops being constant if air resistance is super-linear in angular velocity.

 

[kellyb]

Let's ignore translational velocity, assume a coin of unit mass is fixed to a horizontal frictionless axis. It starts heads up, then we give it an initial angular velocity w_0 and the outcome is defined by which side points up after 1 second.

Define a function f: R^+ -> {H,T}: w_0 -> outcome(w_0)

Let p_i be the sequence of "flipping points" in f, so the sequence of points where f goes from H to T or vice versa.

Define a function err: R^+ -> R^+: x -> |p_above(x) - p_below(x)|, giving for each w_0 the length of the interval with the same outcome as w_0, effectively proportional to our available error range before we mispredict.

The question is how err grows. Assuming no air resistance and hence constant rotation, err is constant, all the p_i are at 0.5k with k \in N. So err would be independent of w_0 (which is proportional to the initial energy, so independent of the initial energy).

Assuming air resistance is linear in angular velocity, angular velocity would decay exponentially, and err would decay as w_0^-1[*]. Which does depend on the initial energy, but not in the way you seemed to argue, a bigger initial energy is better than a smaller one. Because what you really want to do is to change the coin's angular velocity as much as you can in the space of 1 second which, with any air resistance which is strictly increasing in angular velocity, is to be had at higher initial energy rather than smaller.

The real question is, since the behaviour of err depends on the air resistance function, what happens to err when air resistance becomes super-linear in angular velocity or even goes turbulent and chaotic? For example if we can get err to decay exponentially then we should be good for claiming that a coin toss is inherently unpredictable even under a deterministic Newtonian model. Well, assuming that this happens at "reasonable" angular velocities for an actual coin toss.

* ETA: actually it's still constant but at a higher frequency, the distance between all p_i is still the same, it's just a lower constant than in the "no air resistance" case. It stops being constant if air resistance is super-linear in angular velocity.

Ok, but since the coin exists within nature, which is beyond dimensionless boundaries, and quantum physics is understood as symbolic representations within neural networks, the act of observations corresponds to an expression of observations.

So, like:

 

[TubbaBlubba]

Let's ignore translational velocity, assume a coin of unit mass is fixed to a horizontal frictionless axis. It starts heads up, then we give it an initial angular velocity w_0 and the outcome is defined by which side points up after 1 second.

Define a function f: R^+ -> {H,T}: w_0 -> outcome(w_0)

Let p_i be the sequence of "flipping points" in f, so the sequence of points where f goes from H to T or vice versa.

Define a function err: R^+ -> R^+: x -> |p_above(x) - p_below(x)|, giving for each w_0 the length of the interval with the same outcome as w_0, effectively proportional to our available error range before we mispredict.

The question is how err grows. Assuming no air resistance and hence constant rotation, err is constant, all the p_i are at 0.5k with k \in N. So err would be independent of w_0 (which is proportional to the initial energy, so independent of the initial energy).

Assuming air resistance is linear in angular velocity, angular velocity would decay exponentially, and err would decay as w_0^-1[*]. Which does depend on the initial energy, but not in the way you seemed to argue, a bigger initial energy is better than a smaller one. Because what you really want to do is to change the coin's angular velocity as much as you can in the space of 1 second which, with any air resistance which is strictly increasing in angular velocity, is to be had at higher initial energy rather than smaller.

The real question is, since the behaviour of err depends on the air resistance function, what happens to err when air resistance becomes super-linear in angular velocity or even goes turbulent and chaotic? For example if we can get err to decay exponentially then we should be good for claiming that a coin toss is inherently unpredictable even under a deterministic Newtonian model. Well, assuming that this happens at "reasonable" angular velocities for an actual coin toss.

* ETA: actually it's still constant but at a higher frequency, the distance between all p_i is still the same, it's just a lower constant than in the "no air resistance" case. It stops being constant if air resistance is super-linear in angular velocity.

Speaking on an entirely abstract level you're right, but I was trying to get a feel for the orders of magnitude involved with an estimate of the dimensions of the system. With my parameters (200 rotations per second), if we consider the air resistance as a single impulse right at the start, we would need to change the angular velocity by about 0.5% (201 or 199 rotations/second) to flip the outcome. Rotational energy is squared in angular velocity, so this would mean a first order change in rotational energy of 1%. When the total work done by the air in my first-order estimate is a ten-thousandth of a percent it's very hard to see a flip only due to air resistance happening.

Of course if we change the parameters this is not the case. If we make the coin very light, for example. Less self-evidently, if we increase the angular velocity ceteris paribus, the percentage change needed decreases linearly while the energy goes up squared, so the absolute energy needed goes up linearly, so any superlinearity in the air resistance (which is a given) means that it will eventually overcome this barrier.

 

[caveman1917]

Speaking on an entirely abstract level you're right, but I was trying to get a feel for the orders of magnitude involved with an estimate of the dimensions of the system. With my parameters (200 rotations per second), if we consider the air resistance as a single impulse right at the start, we would need to change the angular velocity by about 0.5% (201 or 199 rotations/second) to flip the outcome. Rotational energy is squared in angular velocity, so this would mean a first order change in rotational energy of 1%. When the total work done by the air in my first-order estimate is a ten-thousandth of a percent it's very hard to see a flip only due to air resistance happening.

Of course if we change the parameters this is not the case. If we make the coin very light, for example. Less self-evidently, if we increase the angular velocity ceteris paribus, the percentage change needed decreases linearly while the energy goes up squared, so the absolute energy needed goes up linearly, so any superlinearity in the air resistance (which is a given) means that it will eventually overcome this barrier.

Yes I agree that it's unlikely that "normal" coin tosses will be influenced much due to those effects. It's still an interesting question though, in an abstract sense. For example I knew the heuristic of "air resistance is linear at low speeds and quadratic at high speeds" but now having looked into it some more, apparently there's still quite some open questions about it. I didn't know that, I thought that air resistance was well understood in the non-turbulence case rather than it being some heuristics but nobody really knows exactly.

 

[MRC_Hans]

You'd really have to put a lot of spin into it. It's not true that cats always land on their feet, but if you throw them too high they have more time to recover. A study showed cats who "fell" from the first story did worse than cats that "fell" from a second story. For a while I imagined people flinging cats out different-level windows and recording the results, but it turned out the study was actually using data from cats brought in for treatment. However, there could have been a bias because if a cat landed on its feet, all might be well, no vet visit. Likewise if the cat was dead, there'd be no point in going to the vet.

Certainly, a cat would mostly not need medical attention after falling from first story height. So the preponderance of cats brought to the vet after such falls would be the ones that did, after all, get hurt.

Whereas from greater heights, carers might be more likely to bring it in, just in case.

In my experience^*) a cat can turn feet down in only about half a meter.

Hans

*) yes, as a kid, I tried dropping our cat from various (low) heights, onto a soft surface ... but only till it looked annoyed at me and walked away.

 

[TubbaBlubba]

Yes I agree that it's unlikely that "normal" coin tosses will be influenced much due to those effects. It's still an interesting question though, in an abstract sense. For example I knew the heuristic of "air resistance is linear at low speeds and quadratic at high speeds" but now having looked into it some more, apparently there's still quite some open questions about it. I didn't know that, I thought that air resistance was well understood in the non-turbulence case rather than it being some heuristics but nobody really knows exactly.

It's "well understood" if you just model it as a total, instantaneous momentum transfer from each molecule to the body, I think, which gives a squared factor. This is a decent approximation for non-turbulent fluids at high-ish speeds. Not sure how one derives a linear model.

 

[TubbaBlubba]

I had to think a bit. I suppose at low speeds you assume air resistance to behave like friction, transferring heat, whereas at higher speeds you treat it adiabatically. Ignoring turbulence for the moment.

 

[caveman1917]

It's "well understood" if you just model it as a total, instantaneous momentum transfer from each molecule to the body, I think, which gives a squared factor. This is a decent approximation for non-turbulent fluids at high-ish speeds. Not sure how one derives a linear model.

I had to think a bit. I suppose at low speeds you assume air resistance to behave like friction, transferring heat, whereas at higher speeds you treat it adiabatically. Ignoring turbulence for the moment.

I don't know. I remember the heuristic "linear at low speeds, quadratic at high speeds" from a uni course but don't remember what the argument for it was, it was years ago. The paper linked to in the beginning of the thread uses linear, and from looking up some other papers/discussions on the coin tossing thing there seems to be some debate on its exact form, with suggestions going from linear over 3/2 to quadratic and even higher.

Don't we have a resident fluid mechanics expert?