Exploring Randomness and Chaos in Classical & Quantum Physics

In summary, the comparison between electron spins and coin flips in classical and quantum physics raises questions about the true nature of randomness. While coin flips may appear random, they can be determined with certainty if all initial conditions are known. Gas molecules also exhibit random motion, but it is unclear if this is due to true quantum randomness or simply the sensitivity of initial conditions. The distinction between chaos and randomness in classical physics is a difficult one, and experimental evidence for microscopic chaos is inconclusive. In the quantum case, operational randomness can be certified through the use of hidden variables.
  • #1
Isaac0427
Insights Author
716
162
TL;DR Summary
In the scenarios of a coin flip and the motion of gas molecules, what is really at play: true randomness or chaos?
Note: This question involves both classical and quantum physics, so I didn't know where to put it.

I'll start with the coin flip:
People often compare electron spins to a coin flip, citing that coin flips are random. I am wondering if that is a true analogy, or just another faulty analogy between classical and quantum physics. My thinking is that while coin flips appear random, if you are given the the torque on the coin, the trajectory of the wind, and the initial state of the coin (including its position and whatnot), one could determine with certainty the result of the flip. This would be like a chaotic (local) hidden variable behind the result of the coin flip, which is forbidden in the case of electron spins. Given this, are coin flips purely random (like a quantum system), or do they just appear random due to underlying classical physics?

Now, with the gas:
Though there is an element of quantum mechanics at play here, I'm wondering if the "random motion" of a gas assumed in the kinetic theory is truly randomness. Say you zero in on each molecule and measure its position to an uncertainty of one micrometer, and then measure its momentum to the lowest uncertainty allowed. Though these may be large uncertainties for the size of the molecule, in terms of a 20L container, we know what that molecule is doing pretty well. Is the randomness here a result of true quantum randomness, or is it just due to the number of molecules that are all sensitive to initial conditions? That is, if I had to an allowed level of uncertainty the positions and momenta of every molecule, could I predict how the molecules would distribute over time?

Also, I'm not positive if I am using the term chaos correctly, but I think I am. Please correct me if I'm wrong.

Thank you in advance!
 
  • Like
Likes etotheipi
Physics news on Phys.org
  • #2
The nature of true randomness is always a very good question. Allow me to comment a bit on the coin flip part.

Coin flipping, die tossing and other similar experiments that after a short transient settles into one of several fixed point attractors and which can be modeled exclusively with classical physics are usually considered deterministic. If the dynamics contains many hard non-linearities (like a rolling die interacting with a roulette-like surface) the inherent uncertainties in initial state can of course quickly be amplified to macroscopic scale making a stochastic model for the steady-state (i.e. a mapping of the basins of attraction for each fixed point) more useful.

Such transient systems are usually not considered to be a chaotic system even if they have sensitivity to initial conditions and folding dynamics, as they lack the property of having dense periodic orbits. For instance, tossing a die onto a flat stationary plate is not considered chaotic system, but if you add drive the plate with a continuous periodical motion such that the die is kept in motion, then it may be characterized as chaotic (but since the die never settles calling it a die tossing experiment would then be misleading, I guess). A simple example of a mechanical system that do exhibit chaos is the driven double pendulum.
 
  • Like
Likes PeroK
  • #3
I think it is better to phrase the question in classical physics, so that there is no "true" randomness. Restricting ourselves to deterministic systems, one may ask whether random-looking behaviour is due to chaos or not. It turns out that the question is hard to answer experimentally. In theoretically well-defined deterministic systems, one can answer the question, and these same systems show that it is hard to experimentally tell what the "true" underlying theory is for real systems.

https://www.nature.com/articles/29721
Experimental evidence for microscopic chaos
Gaspard et al. Nature 394: 865–868(1998)

The above article by Gaspard was an interesting article that attempted to experimentally demonstrate that certain random-looking behaviour was due to chaos. However, commentators were not convinced:
https://www.nature.com/articles/44762
https://arxiv.org/abs/chao-dyn/9904041

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.79.031909
Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and-fire neurons
Rüdiger Zillmer, Nicolas Brunel, and David Hansel
Phys. Rev. E 79, 031909 – Published 18 March 2009

The article by Zillmer et al shows several theoretically defined deterministic systems, some chaotic and some not, but they all produce random-looking behaviour.
 
Last edited:
  • Like
Likes Pythagorean
  • #4
The separate question of how to determine whether something is operationally random in the quantum sense is addressed by

https://arxiv.org/abs/1708.00265
Certified randomness in quantum physics
Antonio Acín, Lluis Masanes

In the quantum case, it is allowed that there may be hidden variables such that the entire system is deterministic, but our ignorance of the state of the hidden variables means the system appears random to us. The system will be operationally random as long as no one has experimental control of the hidden variables. The above paper shows how one may certify such operational randomness.
 
Last edited:

Related to Exploring Randomness and Chaos in Classical & Quantum Physics

1. What is randomness and chaos in classical and quantum physics?

Randomness and chaos refer to the unpredictable behavior of systems in classical and quantum physics. In classical physics, randomness is often associated with the concept of entropy, which measures the disorder or randomness of a system. In quantum physics, randomness is a fundamental aspect of the probabilistic nature of the quantum world.

2. How do scientists study randomness and chaos in physics?

Scientists use mathematical models and experimental techniques to study randomness and chaos in physics. In classical physics, they may use chaos theory to study the behavior of complex systems, while in quantum physics, they may use statistical mechanics and quantum mechanics to analyze the probabilistic behavior of particles.

3. What are some real-world applications of studying randomness and chaos in physics?

The study of randomness and chaos in physics has many practical applications, such as in weather prediction, stock market analysis, and cryptography. Understanding the chaotic behavior of systems can also help us design more efficient and stable technologies.

4. Can randomness and chaos be controlled or predicted?

In classical physics, chaos theory suggests that even small changes in initial conditions can lead to drastically different outcomes, making it difficult to predict long-term behavior. In quantum physics, the probabilistic nature of particles makes it impossible to predict their exact behavior, but we can still make statistical predictions based on probabilities.

5. How does the study of randomness and chaos in physics relate to the concept of determinism?

Determinism is the idea that all events, including human actions, are ultimately determined by previous causes. The study of randomness and chaos in physics challenges this concept, as it suggests that some events may be inherently unpredictable due to the complex and chaotic nature of systems. However, some scientists argue that even in chaotic systems, there is still a level of determinism at play.

Similar threads

  • Classical Physics
Replies
4
Views
856
  • Quantum Physics
5
Replies
143
Views
6K
Replies
12
Views
758
Replies
16
Views
932
  • Quantum Physics
Replies
10
Views
2K
  • Beyond the Standard Models
Replies
1
Views
972
Replies
2
Views
739
  • Quantum Physics
Replies
16
Views
2K
Replies
15
Views
1K
Replies
7
Views
1K
Back
Top