Boundary between deterministic reality and probabilistic reality

Galteeth

Is there a firm boundary?

For example, if a scientist makes an observation which is probabilistically determined, his actions (for example recording data) are altered, although we would generally think of a scientist as a deterministic system. How do physicists deal with this conceptualy?

DrChinese

It is not generally agreed that there is a deterministic reality in the first place. So can you be more specific in your question?

granpa

if I create a computer game that uses a random number generator (say a mersenne twister seeded with the game start time) to vary the action then is the game deterministic or probabilistic?

vanesch

You can say about a theory whether it is deterministic or probabilistic, but you can't really say of nature whether it is one or the other, unless it is deterministic

Let me explain. A *theory* can be deterministic or probabilistic, whether the end results of the theory are probability distributions, or "fixed outcomes". Newton's mechanics is deterministic in its dynamics, but doesn't say anything about its initial conditions: if the initial conditions are fixed "precisely" (which is hard to do with real numbers...), then the dynamics is "precise". If the initial conditions are specified in a probabilistic way, then the outcomes are also probabilistic (classical statistical mechanics).

Quantum theory as it is usually formulated is probabilistic of course: the results of it are probability distributions.

Now, what is "deterministic" ? We could postulate that "deterministic" means: *if* we know the "state" of nature at a certain point in "time", *then* we can calculate, with certainty, the future "state" of nature.

But that doesn't need to be the only form of determinism. *If* my theory is a "magic book" in which all successive states of nature as a function of time are *listed*, then that theory "the magic book" theory, would be also deterministic, although no "evolution" rules are given to go from one state at a given time to another state at a later time. In other words, the "state" of nature at a given time is in no way an indication of the "next" state, but nevertheless, with my magic book, I would know everything that happens, at all times, precisely.

Now, given that it is always in principle *possible* to consider that magic book theory (call it "fatalism") as the "correct" theory of nature, it is impossible to say that nature is not deterministic in this sense.

DrChinese

Generally that would be called determinisitic because the same seed gives rise to the same game every time.

vanesch

You could even say that to the programmer, it is deterministic, and to the user, it is probabilistic

VikingF

So, what you are saying is, if I have a "magic book", where each page has a number written on it, it could be no "correlation" between e.g. the number on page 55 and the number on page 56, but when reading the number on page 55, the number on page 56 are already determined (since it is already written there), even though we haven't read it yet, and even though it cannot be calculated based on the numbers on page 1 to 55? Did I understand your analogy correct?

Isn't this idea called Eternalism or B-theory of time?

vanesch

Yes. What I mean is, it could be conceivable that there is no "general formula" that links the number on page 55 with the one on page 56 ; general formula that is "simpler" than the book itself, but you could *imagine* that such a book could "exist" (say, a gift from a deity or something of the kind). Now, such a book would then be a "theory" which is entirely deterministic, as indeed, the numbers ARE already written in it, and you can look into that book at any page, and read it.

A simple analogy would be a movie. In as much as you would take the movie "for real", anything can happen in the movie, and maybe there's no sensible "formula" at all that allows you, after having watched the first half hour or so, to predict what will happen in the last half hour, even after taking the movie data from the first half hour (which is ALL the "movie universe" contains in that time - there are no possible hidden variables in the "movie universe" apart from the data on the DVD). But nevertheless the movie is deterministic because the last half hour is also "already fixed" on the DVD, even though you cannot derive it from the first half hour. So in as much as you give some reality to the movie universe, and for the characters IN the movie, it seems that their universe seems pretty random in the middle of the movie, nevertheless there "exists" a DVD where everything of what will happen to their universe is already fixed. At no point, it has been said that the content of the DVD is in one way or another available to the characters of the movie. At no point it has been said that there is a way for the characters to FIND OUT what's the content of the DVD before they "live" it. But the DVD "exists".

Again, this is just an analogy, to illustrate the difficulty of saying that the universe IS stochastic. Only about a theory, you can say whether it is deterministic or stochastic, and that's pretty simple to find out: does the theory crunch out probabilities or does it crunch out "for sure" states ? Our movie characters can only have stochastic theories about the rest of the movie, but nevertheless the movie is deterministic, because fixed on a DVD support.

It's not to say that I think per se that we are characters in a cosmic movie where some deity is playing a cosmic DVD or so, but because this is not totally inconceivable, we can't say anything about the *real* nature of stochasticity of nature, simply because we seem not to be able to do any better than come up with stochastic theories of its workings.

It might be that the workings of our universe are such that it is fundamentally impossible to do any better than that and that we will never have access to the "cosmic DVD", but there's even no way to know that.

So the best we can say, is that for the moment, we only have a stochastic description of nature. Whether nature itself IS stochastic or not is a question to which we don't have any answer.

I don't know these words, so I can't say.

Galteeth

This description reminds me of a debate I would have when playing poker, about probability. Once the cards have been shuffled the outcomes of matchups are determined. Probability is useful to form stochastic theories about what that determined sequence is, but the outcome is no longer dependent on probability (maybe it never was?).

I was always the minority (often of one) in this debate with my friends who played poker.

vanesch

It's also a very good analogy, I'd say !

On the other hand, maybe there are people who would define "deterministic" in a stricter sense, namely, the future is entirely fixed if you know the "state" of the universe at a certain instant. This is what one understands by it, intuitively: can I know/calculate/find out the future if I know the present "well enough" before the future arrives, if only I'm smart/fast/powerful enough. Classical physics is "deterministic" on this account, because there are deterministic evolution equations of the state of nature.

However, what kills this idea IMO is the concept of hidden variables. If we understand by "hidden variables", a part of the "state" of nature which is, in principle, inaccessible to observation, then we have the problem of principle that our "magic book" could be part of those hidden variables. In that case, nature is deterministic, the laws of nature are very simple, namely "do what's on the current page in the book", and we can't access it.

VikingF

"Eternalism" or "B-theory of time" is often referred to as "4D block spacetime". In that view, all points in time exist simpliciter, i.e. there is no "global now". The reason why you experience 20th of October 2009 "now" and not e.g. 20th of October 2011, is because 20th of October 2009 is "here" (according to your current point of view), while 20th of October 2011 is "there" (according to your current point of view). I think your "magic book" or "time DVD" is more commonly known as "4D block spacetime". However, they are great analogies. :-)

Galteeth

It seems to me the difference is that in the magic book scenario, there is no way to predict the future based on the present. I guess causality in that case is an illusion. The block time scenario thing seems more like a philosophical device then a difference in reality.

VikingF

Einstein's "twin paradox" shows that time might be subjective (i.e. one of the twins experiences 100 years as 5 minutes, while the other one experiences 100 years as 100 years, or something like that), and not objective. If it is subjective, then there is no "global now", and the "4D block spacetime" is probably true.

Galteeth

Again, it seems like more of a semantic argument. I understand what you mean but, it's not like they are going backwards in time, they are just locally experiencing the flow of time differently. To put it a different way, it's like all the molecules in the twin's bodies are just moving faster, but he's not seeing the twin back on earth move faster because of the constancy of C.

So it's more like they can't have accurate information about each other untill they're both going at the same speed.

But as I have mentioned, I may be misunderstanding relativity, I'm not a physicist.

EDIT: What I mean is, while there's no universal reference frame, that doesn't translate to the same thing as all time is happening at once.

VikingF

Just to make things clear, I'm no physicist either. :)

My problem is that I cannot see how time can be objective (i.e. the past being fixed, the future being potential/open, and now being the point between) if the experience of it is subjective. If I experience a specific point of time as "now" and you experience another specific point of time as "now", then who is right and who is wrong? And then again, if "my now" is t1 and "your now" is t2, and t1 is before t2, then somehow, I am experiencing "your past" (seen from your p.o.v.), and you are experiencing "my future" (seen from my p.o.v.). How can the future be open if you are "already" there?

Maybe I'm just thinking in the wrong way...

mikeph

The experience of it is not subjective- time is crucially not actually experienced differently, but the observations made will be different. There is no problem here, as causality is never violated, and you will never see someone's future before they see it. You'll just observe them moving slower and with contracted lengths, just as they will see you.

This is all objective and described by a purely deterministic theory.

DrChinese

This is not a generally accepted conclusion, per the usual usage of the terms objective and deterministic. Generally, one of these is considered to be false (per experiment).