B Why don't two double pendulum apparatus follow the same paths? / Chaos

[Filip Larsen]

If we anylize fluid turbulence deep enough, atoms/molecules moves random so fluid turbulence must be also random system?

If you are thinking about quantum mechanics randomness being amplified to macroscopic scale by chaos, then that is in principle possible, but note that even though every physical system has an underlying quantum mechanic "reality", different chaotic systems may have different time scales for this.

For example, in electronic systems like Chua's circuit it is far more likely that electronic noise can be amplified fast, whereas systems with turbulent mixing likely would take much longer since quantum effects has far less direct influence on the dynamics. For the double pendulum system mentioned at the start, it is also not obvious (to me at least) exactly what quantum interaction eventually will have an effect on the macroscopic position of the arms.

Part of the issue is of course also that in order to analyse a system is has to be modeled with enough detail to capture the essential dynamics and quantum effects will thus only be included in the model to the extend they are understood and considered essential for the dynamics. If you consider quantum noise in Chua's circuit I would expect that it would not be essential for the dynamics in the sense that the attractor will look the same with or without quantum noise, even if the precise state trajectory for the two will diverge at some point. Add to this that specific chaotic system are almost exclusively analysed with numerical methods which in itself adds round-off and truncation "noise" to the trajectory that likely far out-weight any quantum effect for an otherwise classical system.

 

[John Mcrain]

Atoms and molecules do no actually move randomly; they move quite deterministically, it only seems random to us.

That is also true for smaller particles from atoms?
How we know they move deterministic, but scientist allways say that this small praticles moves randomly?

 

[John Mcrain]

If you are thinking about quantum mechanics randomness being amplified to macroscopic scale by chaos, then that is in principle possible, but note that even though every physical system has an underlying quantum mechanic "reality", different chaotic systems may have different time scales for this.

For example, in electronic systems like Chua's circuit it is far more likely that electronic noise can be amplified fast, whereas systems with turbulent mixing likely would take much longer since quantum effects has far less direct influence on the dynamics. For the double pendulum system mentioned at the start, it is also not obvious (to me at least) exactly what quantum interaction eventually will have an effect on the macroscopic position of the arms.

Part of the issue is of course also that in order to analyse a system is has to be modeled with enough detail to capture the essential dynamics and quantum effects will thus only be included in the model to the extend they are understood and considered essential for the dynamics. If you consider quantum noise in Chua's circuit I would expect that it would not be essential for the dynamics in the sense that the attractor will look the same with or without quantum noise, even if the precise state trajectory for the two will diverge at some point. Add to this that specific chaotic system are almost exclusively analysed with numerical methods which in itself adds round-off and truncation "noise" to the trajectory that likely far out-weight any quantum effect for an otherwise classical system.

So fluid turbulance is not random effects?

 

[Filip Larsen]

So fluid turbulance is not random effects?

No, the cause of turbulence is not random effects. It is an instability (i.e. sensitivity to initial conditions) that folds back on itself (i.e. topological mixing). Classical systems that exhibit chaotic motion do so without the "need" of any source of "true randomness". As mentioned, this means the general behavior with and without "true randomness" is likely the same, only the actual precise state will diverge over time.

 

[John Mcrain]

No, the cause of turbulence is not random effects. It is an instability (i.e. sensitivity to initial conditions) that folds back on itself (i.e. topological mixing). Classical systems that exhibit chaotic motion do so without the "need" of any source of "true randomness". As mentioned, this means the general behavior with and without "true randomness" is likely the same, only the actual precise state will diverge over time.

Does true randomness exist?

 

[DaveC426913]

How we know they move deterministic,

Atoms don't move of their own accord; they move as a result of being knocked about by other atoms. That is not random; it's classical Newtonian (or Brownian) motion.

but scientist allways say that this small praticles moves randomly?

It's a simplification. If pressed for accuracy, any physicist will acknowledge use of the word "random" is sloppy.

 

[DaveC426913]

Does true randomness exist?

That is a question under active research.

 

[sophiecentaur]

Does true randomness exist?

A truly random process can be defined as having zero correlation with itself except at one instant. Wiki has something to say about the topic. "In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information."

Many quantum systems exhibit a high level of (or true?) randomness and. for instance, the delay in photon emission from an energised atom appears to be totally random.

The behaviour of a chaotic system can appear to be random when the initial conditions are random. Most naturally occurring chaotic systems are too complicated to use the fact / belief that their behaviour is deterministic.

 

[Lord Jestocost]

Does true randomness exist?

Maybe, the following might be of help. It’s a section from the introduction of Robert C. Bishop’s book “CHAOS THEORY A Quick Immersion” (Tibidabo Publishing, Inc. New York, 2023):

“Randomness

Before we begin that journey, it is important to clear up one confusion about randomness or random behavior. In everyday talk, our tendency is to use the word random to mean a lawless or completely unordered behavior. Scientists never use the term random to mean this for an important reason: There are no examples of lawless disorder in any of the physical phenomena we study.

Confusion arises because systems behaving randomly appear to lack any order when we’re watching their behavior. Scientists call this apparent randomness when a system looks random to us but has an underlying deterministic order to it. Think of a roulette wheel. The outcome of each spin with the ball landing in a particular numbered slot looks like there is no order. Yet suppose we were able to know the speed of the wheel’s spinning, the initial velocity of the ball as it enters the wheel, the friction slowing the wheel down, the friction the ball experiences as it rolls around the wheel and eventually bounces into a slot, among several other factors. Given these factors, the final slot the ball settles in is fully determined. We might not be able to calculate this due to the many factors involved and the limits on our knowledge, but there is an underlying order to the system determining where the ball will land. It appears random to us because we cannot track all the factors involved. Nevertheless, the ball’s behavior is fully determined in an ordered way.

There is a second form of randomness scientists study known as irreducible randomness. When the full set of physical conditions determine the probability for outcomes, but not the specific outcome in a system at a particular time, it is irreducibly random. Nonetheless, the irreducible randomness of these outcomes still conforms to fixed probabilities. These probabilities are constrained by statistical laws rather than deterministic laws. This means irreducible randomness is a different form of order than the deterministic order we experience with mechanical systems such as engines and computers. It definitely is not lawless chaos.

An example of irreducible randomness is radioactive decay. All the relevant factors in a sample of a radioactive element, such as uranium, will not determine when any specific nucleus in the sample will undergo a decay event. Nevertheless, the sample will behave as described by a statistical law constraining how many nuclei will decay on average during a given time interval. Scientists make use of such irreducible randomness all the time in medical treatments for cancer and in nuclear power plants.”

 

[PeterDonis]

The OP question has been sufficiently addressed. Thread closed.