The Physics Quote that changed my life

[trini]

well, if something is all knowing then it must know what's going to happen without calculation

 

[mikeph]

if you CHANGE the initial conditions, you have essentially changed the equation of the problem... if you CHANGE the velocity you will change the equaition used to determine the path of the ball, Hence a new reality.

I think you should place more emphasis on the difference between a governing equation and an initial condition. If you change the velocity, you will NOT change the equation used to determine the path of the ball. That equation is Newton's law for gravity, and is independent of initial conditions. All you do is get a different path, as different constants of integration.

Initial conditions ---> [Governing equations] ---> future state

That is the process, and if the governing equations can be used to find a general solution in terms of the initial conditions then the system is not chaotic. The governing equations are based on reality, and do not change.You cannot know the "EXACT" initial conditions, these are in some sort of real space (for example, real^6 to describe the initial 3-position and 3-velocity of a particle), and since any two distinct numbers in real space has infinitely many numbers between them, you come up with the problem that you can only approximate the initial conditions. For example, if you observe a particle to have x-coordinate of position 3.104, that is always just an approximation to the real value it has, which is going to be an infinitely long string of decimal places - essentially the probability of you picking a random real number and it being an integer is zero, due to the weight of non-integers compared to integers in real space. And the chaotic nature of some systems means that any two arbitrarily close initial conditions will eventually deviate; so even in the absence of probability we get a system which we cannot predict.

 

[vanesch]

However you can have determinism without chaos, eg. a pendulum. Nothing is chaotic in that system, so determinism by itself does not cause chaos. I would guess it arises from there not being an analytic solution to the equations describing a system, which describe it fully.

In fact, the double pendulum IS chaotic Look at the double pendulum here
http://en.wikipedia.org/wiki/Double_pendulum

This is something I am trying to get to grips with: how can a system be totally described by an equation, and its motion cannot be written in closed form?

The set of continuous functions is way way larger than the set of "closed form" solutions when you take a rather small set of "generating" functions (say, all classical functions of Abramowitz and Stegun for instance). Differential equations make up a set of solution functions in the space of continuous (and n times differentiable) functions, but this subset doesn't have anything to do in most cases with that meager subset of "closed form" functions.

Eg. the three body problem (I always talk about this as it is what I did my dissertation on!), the equations are so easy to write down from Newton's law of gravity, but there is no analytic expression for the paths of these objects in terms of their initial conditions (6 vectors of position and momentum). Can any algorithm converge on the correct path for arbitrarily long time? How can it if the motion is chaotic? But nature seems to know one that works for real life. That boggles my mind...

Yes, that's puzzling indeed. But maybe not for the reason you think. You seem to say: how does nature do to "solve this differential equation better than my best computer can". But the real puzzling thing is that there is a differential equation that can be written down in the first place, of which the solution (even though we can't compute it exactly) is what nature is doing!

 

[vanesch]

Think about determining the path of Earth around the sun, I am sure we have a computer somewhere that can determine it with almost 99% correctness(not a word I am guessing) but of course if we knew the very EXACT numbers and correct equations we would then determine it 100%.

Point is, we can't know it. Heck, we can't even *write down* most real numbers. There is only a subset of measure zero of the real numbers that we can write down, and by this I even mean all kinds of "notation" like square root, "solution{}" etc...

The fact that we can't predict it one hundred percent doesn't mean that its chaotic, it just means we have information missing. Like weather, of course what we predict it to do is always changing because we don't have all the correct information. Now let's go back to the ball. Let's say we had the velocity to be 1% off from what it actually was, at first we would see no difference in the paths using the same equations, but eventually they would deviate enough for us to notice, This is partly the basis of the butterfly effect. We can never really predict the future because we are not perfect.

But that was already build in from the moment we postulated that positions were going to be triples of real numbers...

My question still stands though: Could some intelligence, not human, something godly and all-knowing(In other words "perfect"), knowing all the information, not just the ones that we humans understand or know about but EVERYTHING that could possibly be measured, and having all the exact equations, including all of quantum and the rest of the unknown sciences out there. And if this intelligence had sufficient capacity to analyze all the data and equations... THEN can it know both what has happened and what will happen? (past and future)

Well, as I said before, you could simply consider the "law of nature" to be the Book, the entire list of all events in spacetime. A "being" that knew this book, wouldn't even have to "calculate", it would simply "look up" what is happening where at what time slice.

As practical scientific theory it is utterly useless, but it is conceivable as a theory, no ?

As I said before, what is truly amazing is that we can find "simpler" forms of scientific theory that DO give us relationships between events in different time slices. It didn't need to be that way (although probably it did, if there was any form of intelligent life to emerge - so probably no intelligent life form can ever live in a universe where there is not the slightest bit of "causal relation" - that is, simple relations between events in different time slices).

 

[pgardn]

To me events automatically imply time. So we automatically assume events interact with each other because this notion has existed when evolution produced our want to go forward brains. Life that actually contemplates the future based on present and past is bound to come up with causality.

We are very strange animals. Maxed out control freaks we are. Personally I am having fun with this struggle. For some reason it is satisfying. Maybe if it was not satisfying in some way we would not be here. (This is not a religious notion)

 

[FoxCommander]

I think you should place more emphasis on the difference between a governing equation and an initial condition. If you change the velocity, you will NOT change the equation used to determine the path of the ball. That equation is Newton's law for gravity, and is independent of initial conditions. All you do is get a different path, as different constants of integration.

Initial conditions ---> [Governing equations] ---> future state

Im talking about the equation of the motion not the equaitons used to find these motions. Take a ball thrown at an angle, the graph would look like a parabola, if you change the speed or direction of the ball you will change the path it takes and one equation of motion could not possibly determine them all

x²=y doesn't look like 2x²+2x+1=y Therefore you will need different equations of MOTION, however you will still use the same equations of gravity to determine this path

 

[FoxCommander]

Point is, we can't know it. Heck, we can't even *write down* most real numbers. There is only a subset of measure zero of the real numbers that we can write down, and by this I even mean all kinds of "notation" like square root, "solution{}" etc...



But that was already build in from the moment we postulated that positions were going to be triples of real numbers...

This is exactly what I am trying to say, Everyone keeps thinking i mean if some Human was to try and figure out all these numbers. We can not possibly know the exact value of them due to the infinite decimal places factor you guys/girls keep bringing up

I am talking about some Super intelligence, not neccessarily all-knowing, knew all the values of everything and then knew all the exact equations, then could it compute the future and past... To me I don't see how it could not... And no this person is not all knowing so he/she would have to actually work out the equations and figure it out him/her self.

Is there anything stopping this Being from finding the truth?

 

[diazona]

Im talking about the equation of the motion not the equaitons used to find these motions. Take a ball thrown at an angle, the graph would look like a parabola, if you change the speed or direction of the ball you will change the path it takes and one equation of motion could not possibly determine them all

x²=y doesn't look like 2x²+2x+1=y Therefore you will need different equations of MOTION, however you will still use the same equations of gravity to determine this path

This path is what we call a solution to the equation of motion. The equation of motion itself is something more general, something like F = ma or i\hbar \partial \psi/\partial t = H \psi (depends on which theory you're using). Probably what you're thinking of as "equation of gravity" corresponds to the equation of motion.

This is exactly what I am trying to say, Everyone keeps thinking i mean if some Human was to try and figure out all these numbers. We can not possibly know the exact value of them due to the infinite decimal places factor you guys/girls keep bringing up

I am talking about some Super intelligence, not neccessarily all-knowing, knew all the values of everything and then knew all the exact equations, then could it compute the future and past... To me I don't see how it could not... And no this person is not all knowing so he/she would have to actually work out the equations and figure it out him/her self.

Is there anything stopping this Being from finding the truth?

Maybe. That's kind of the definition of determinism - if the universe is deterministic, then this super-intelligent being would be able to compute the future; if not, then even a super-intelligent being, knowing everything there is to know about the universe at a single moment in time to infinite precision, would not be able to compute what would happen in the future. I believe the majority opinion right now is that physics is not deterministic (which is what quantum mechanics suggests).

 

[vanesch]

I am talking about some Super intelligence, not neccessarily all-knowing, knew all the values of everything and then knew all the exact equations, then could it compute the future and past... To me I don't see how it could not... And no this person is not all knowing so he/she would have to actually work out the equations and figure it out him/her self.

Is there anything stopping this Being from finding the truth?

Yes, but you are missing my point. What tells you that the "exact laws of nature" are of the evolutionary kind, that is "starting conditions + evolution equations" ? This is the way we like to build our theories which try to describe nature, but what tells you that this is the "right" way to describe nature ? What if the "true laws of nature" are simply the Book (the list of all events in the universe) - and that we can only find approximate theories with "evolution equations" which do in fact nothing else but describe approximate correlations between events in different time slices ?

For sure, this is the way physics has worked since its beginnings and the paradigm "starting conditions + evolution equations" is pretty successful. In fact, it is probably the only *practical* way of doing physics. The fact that it seems to work doesn't necessarily mean that this is the way the "machinery of nature" works, but for sure it describes strong correlations between events in different, successive time slices. We seem to think of these correlations as "causal relationships", and if they are univocal, we call them "deterministic". I also argued that such correlations are necessary - up to a point - in order for some form of intelligent life to emerge: if there are NO correlations between events at a certain time, and the next set of events, then it is hard to imagine how you can "start to understand" this world, and it is hard to imagine how you could have intelligent life (or even life for short - as there can be no "actions with a purpose" given that nothing you do "now" will determine whatever in "now + epsilon seconds"). So in any case, any universe in which there is "some mechanism with a purpose" (like life, and certainly, intelligent life) needs to have correlations between events in different time slices, and finding out these correlations will give rise to theories which have {initial conditions + evolution equations}, which are nothing else but means to describe these correlations.

But again, nature doesn't have to "work" that way although, based upon our theories, we can mentally *picture* it that way. If spacetime is nothing but a bag of events, in between, as we saw, there are correlations between events in different time slices, then so be it. How it "came to be" that way (which is then nothing else but the question of "how the machinery of nature works") is an entirely different question (and most probably unanswerable) than the question of "what the correlations are" (our scientific theories), even though the mental picture we might associate with a given scientific theory is of course a *possible* way of telling us how "it came to be that way".

Think of a good fiction book, or a cartoon. Here too, we have correlations between the different "time slices" (Coyote running after Roadrunner) and we could think of "laws of coyote-physics", but how the successive events in the cartoon *came to be* (on the drawing table of the cartoonist in this case) has nothing to do with the correlations between the time slices in the movie which constituted our coyote-physics. Even though you might have found differential equations describing the motion of the queue of Roadrunner, and you might wonder how the movie projector "worked this out real-time during the projection of the motion picture while your super-duper computer couldn't converge to a solution in one hour", this is simply because that's not "how the movie works". It works by projecting different slices of "the Book" (here, the motion picture) on the screen.
This is a poor analogy of course, but I try to make you think about the concepts of "laws of nature" in the form of {initial conditions + evolution equations), causality and determinism in a broader frame.

The paradigm {initial conditions + evolution equations} is probably the only *practical way* to find out laws of nature, and they indicate correlations between events in successive time frames. They suggest causal relationships. Whether nature works that way, through genuinly causal mechanisms, or not, is a totally different question. In order to "understand" (that is, get some intuition) the theory with the evolution equations, it is very useful to set up a mental picture of a universe where nature DOES work that way. But that doesn't mean actual nature is working that way. Maybe it does, maybe it doesn't. Your mental picture is then just a conceptual construction based upon the theory at hand.

 

[mikeph]

That "book" would be almost as displeasing than the "multiverse" theory used to explain fine-tuning of constants..

But you are right, who knows whether the local area of spacetime we experiment in corresponds to a few pages which have a remarkable correlation. Why does anything have to be like it is at 391.49 bn years after the big bang? Who knows if there was a big bang, maybe the book is infinitely long and at current time the pages contain a "trace" that would make us believe there is a big bang.

Seems to be bordering metaphysics! I think we need to assume governing laws exist in order to make any progress.

 

[vanesch]

Seems to be bordering metaphysics! I think we need to assume governing laws exist in order to make any progress.

That's because concepts such as causality and determinism are metaphysical concepts (they say something ABOUT physics and physical theories). As well as "exist", btw. So no wonder we're talking metaphysics when dealing with them.

I don't know if it is necessary to assume that governing laws "exist" (of course they exist,as an idea, in a Platonian sense!) to make progress although I can see its utility. However, even if it is a good idea to take on certain working hypotheses, I also think it is very useful to be aware of what assumptions we've been making and what could have been different - even though for practical purposes we prefer to think it isn't.

 

[mikeph]

In any case it has given me a new perspective!

 

[FoxCommander]

OHHHH I get it now vanesch, That makes good sense. I thought when you said Book you meant just like a list of information or something, not like an actual book.

You have given me a new way of looking at this whole thing, which is cool. Thanks!

Well Thank you guys very very much for all of your opinions, I loved an appreciated them all.
This was actually my first Thread post and you guys have made it very successful
Also, Happy Thanksgiving(for those in America)


FoxCommander