Do you have an example of a truly random phenomenon?

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I tried to think of a truly random phenomena thatis not related to quantum physics, and i can't. Let's take heads or tails as an example, if you had all of the data about the throwing of the coin you could tell on which side it will land.

So does anyone know a random phenomena?
 

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  • #2
Dale
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What do you mean by “truly random”?
 
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What do you mean by “truly random”?
I mean that if we had all of the data we could have on the phenomena, then even theortically it will still be random.
 
  • #4
Dale
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I mean that if we had all of the data we could have on the phenomena, then even theortically it will still be random.
That is circular.

And presumably “all of the data” would include quantum data, so the “not related to quantum physics” restriction in the OP becomes problematic.

The topic of randomness is difficult to pin down.
 
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Radiodecay? Or is that quantum because it's in Schrödinger's box
 
  • #6
Lord Jestocost
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I tried to think of a truly random phenomena thatis not related to quantum physics, and i can't. Let's take heads or tails as an example, if you had all of the data about the throwing of the coin you could tell on which side it will land.

So does anyone know a random phenomena?
A truly random phenomena means that an event occuring in space and time can in principle not be undone. Here is the essential difference between the views of classical and quantum physics.
 
  • #7
Nugatory
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I mean that if we had all of the data we could have on the phenomena, then even theoretically it will still be random.
If the dynamics of a system are accurately and completely described by a deterministic theory, then its phenomena will not be "truly random" as you mean that (unexpectedly slippery) term; only if the theory is complete (as far as we know) and non-deterministic can we get what you're looking for. At the moment quantum mechanics is the only candidate theory, so all examples of "true" randomness we can come up with will be quantum mechanical in origin.

But be aware that I am counting on that parenthesized note about slipperiness to do a lot of work hiding sloppy thinking. One of the more important caveats is that the apparent determinism of classical mechanics emerges (analogous to how the ideal gas law emerges from the statistical behavior of large numbers of atoms) from the collective behavior of enormous numbers of particles each governed by non-deterministic quantum mechanics. Thus, your quest for "true randomness" comes down to considering:
A completely random theory (using your definition) might, given some initial conditions, assign a probability of ##1-10^{-500}## to outcome A and a probability of ##10^{-500}## to outcome B. The outcomes predicted by this theory are indistinguishable in every way from the outcomes predicted by a non-deterministic theory in which for those initial conditions the probability of outcome A is one and outcome B zero; and that in turn is indistiguishable from a deterministic theory that predicts outcome A.
Thus it is not clear that the distinction between "true" randomness and the randomness that comes from incomplete information is meaningful.
 
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  • #8
sophiecentaur
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A random process has an autocorrelation function of zero everywhere, except at one point (or value). Physics is all about measurement and I would like to know how one would know what that point is. So you could only discuss randomness in terms of 'random enough', I think.
 
  • #9
Filip Larsen
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Would "unpredictable events" based on deterministic chaotic motion count as an example of deterministic "true randomness"? For example, is the position of the particle within the Lorenz-attractor, e.g. is it in left or right branch, after a very long time truely random or not. For a practical (physical) system this is effectively unpredicable so does that make it truly random?

To me it sounds like the OP is not likely to let such "deterministic unpredictability" imply "true randomness" because unpredictability through chaos in a physical system in a sense is rooted at quantum randomness with deterministic chaos "just amplifying" this quantum randomness to macroscopic scale, but I thought I would mention it anyway.
 
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The theories of probability and randomness had their origin in gambling and games more general. A "truly random phenomena" in that context would be one producing outcomes that are completely unpredictable. And not just unpredictable for you and me, but for anybody, including the most omniscient opponent. But we need more, we actually need to "know" that our opponent cannot predict it, and if he could predict it nevertheless, then he has somehow cheated.

But the most omniscient opponent is a red herring. What is important are our actual opponents. A box with identical balls with numbers on them that get mixed extensively produces truly random phenomena, at least if we can ensure that our opponents have not manipulated things to their advantage. And the overall procedure must be such that also all other possibilities for manipulation (or cheating more generally) have been prevented. The successes of secret services in past wars indicate that this is extremely difficult to achieve.
 
  • #11
phinds
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A box with identical balls with numbers on them that get mixed extensively produces truly random phenomena
No, it is only random in the practical game-playing situation you describe. In physics theory it would just be a classical set of movements and would not be random.
 
  • #12
sophiecentaur
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A truly random process is no more obtainable in Physics than Infinity or Zero. Randomness is a mathematical concept and Maths is based on axioms. This discussion cannot get us anywhere useful.
 
  • #13
Baluncore
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What objection is there to two independently amplified Johnson white noise sources. Limit one to frequencies above 10 MHz, the other to frequencies below 10 kHz. Amplify, digitise and divide the data streams by two, to make them square with 50% duty cycle, then bring the streams together to use the slow one as a clock to sample the fast one. That will produce a stream of unpredictable bits.
 
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What objection is there to two independently amplified Johnson white noise sources. Limit one to frequencies above 10 MHz, the other to frequencies below 10 kHz. Amplify, digitise and divide the data streams by two, to make them square with 50% duty cycle, then bring the streams together to use the slow one as a clock to sample the fast one. That will produce a stream of unpredictable bits.
To quote an answer from a more knowledgeable person than myself on the topic, given to me from a question I posed as, "Can you generate a random number from a machine?"
This is in fact one of the tri[c]kiest jobs to do in computing.
An actual random number has some qualities that are impossible to emulate nowadays, and this numbers are needed in fields like cryptograpy.
In the analogic world, the ramdom signals generators where always based on quantum phenomena, like the tuneling of a diode for white noise generation. Even today the hardware random number generators are based on that phenomena.
Roger Penrose did a fantastic job stressing the limitations of the computational systems, a[nd] wrote a book about that "The Emperor new mind", among other issues.
...
Not sure that's all relevant, or that I can support the assertion, but that is the mostly complete answer. He seemed to be aware of something similar vis a vis white noise generators for randomness.

I want to also reiterate that I believe radioactive decay is considered stochastic (random?) at the individual atomic level. From the wikipedia on radioactive decay, we can see there are some applied methods that work from the premise that radioactive decay is random:

On the premise that radioactive decay is truly random (rather than merely chaotic), it has been used in hardware random-number generators. Because the process is not thought to vary significantly in mechanism over time, it is also a valuable tool in estimating the absolute ages of certain materials. For geological materials, the radioisotopes and some of their decay products become trapped when a rock solidifies, and can then later be used (subject to many well-known qualifications) to estimate the date of the solidification. These include checking the results of several simultaneous processes and their products against each other, within the same sample. In a similar fashion, and also subject to qualification, the rate of formation of carbon-14 in various eras, the date of formation of organic matter within a certain period related to the isotope's half-life may be estimated, because the carbon-14 becomes trapped when the organic matter grows and incorporates the new carbon-14 from the air. Thereafter, the amount of carbon-14 in organic matter decreases according to decay processes that may also be independently cross-checked by other means (such as checking the carbon-14 in individual tree rings, for example).
from: https://en.wikipedia.org/wiki/Radioactive_decay
 
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  • #15
Filip Larsen
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What objection is there to two independently amplified Johnson white noise sources. Limit one to frequencies above 10 MHz, the other to frequencies below 10 kHz. Amplify, digitise and divide the data streams by two, to make them square with 50% duty cycle, then bring the streams together to use the slow one as a clock to sample the fast one. That will produce a stream of unpredictable bits.
I guess no one would argue that such a bit stream in principle can have unpredictable bits in the sense that there would be no way for anyone, based on measurements of the state of the initial system, to produce a predicted stream that would stay correlated with the actual stream over time.

But I also guess that Johnson noise is a very clear example of "directly amplified" thermodynamic noise, i.e. quantum noise. I think it is an interesting question if it is possible to make an unpredictable system where the source of uncertainty is not quantum noise, not directly at least. Since classical deterministic theory makes everything predictable with perfect knowledge, its seem to follow rather directly that unpredictability of the dynamics of a closed system has to be introduced either as a lack of perfect knowledge (i.e. non-perfect measurements of the initial state), a lack of full dynamic determinism (i.e. part of the dynamic is a "truly" stochastic processes), or by the system not being fully closed after all (i.e. some external disturbances sneaking in).

By the way, when the last condition is relaxed (non-closed systems) you can also get phenomenons like undecidability in an otherwise fully deterministic (computational) system, but while undecidability do seem to lead to (a certain kind of) unpredictability it does so in a different way than a "true random" process would.
 
  • #16
PeroK
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No, it is only random in the practical game-playing situation you describe. In physics theory it would just be a classical set of movements and would not be random.
That assumes that in some sense classical physics provides an accurate description of the physical system.

That classical physics is not random does not imply that the system itself is not random.

For example, you may assume that infinitely precise positions and momenta are known for all objects in the system. That assumption may be true of the physical model, but is not necessarily true of the physical system.

I might argue that even theoretically the initial conditions cannot be indefinitely precisely known. And, therefore, the question of whether the system is random is not decided by the model that classical physics provides.
 
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  • #17
sophiecentaur
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What objection is there to two independently amplified Johnson white noise sources. Limit one to frequencies above 10 MHz, the other to frequencies below 10 kHz. Amplify, digitise and divide the data streams by two, to make them square with 50% duty cycle, then bring the streams together to use the slow one as a clock to sample the fast one. That will produce a stream of unpredictable bits.
I don't think that gets you anywhere, in fact. Two deterministic processes can't generate randomness - although there may be practical reasons for using your system in some situations.

But we're just chasing our tails. If we are not allowed to use QM to introduce randomness then we are stuck with deterministic situations. But this is essentially an Engineering problem and, for Engineers, near enough is good enough. (And that doesn't imply sloppiness in any way.) Autocorrelation is the ultimate test for randomness and the sharper the spike, the better the randomness. Signal to noise ratio raises its head here.
 
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phinds
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That assumes that in some sense classical physics provides an accurate description of the physical system.

That classical physics is not random does not imply that the system itself is not random.

For example, you may assume that infinitely precise positions and momenta are known for all objects in the system. That assumption may be true of the physical model, but is not necessarily true of the physical system.

I might argue that even theoretically the initial conditions cannot be indefinitely precisely known. And, therefore, the question of whether the system is random is not decided by the model that classical physics provides.
I have no argument at all w/ what you are saying. My point was that in the kind of game of chance he's talking about, it was random in the sense that colloquial English defines random (e.g. "drawing a card at random" kind of thing). None of the players would have any possible way to determine the outcome in advance.
 
  • #19
sophiecentaur
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I tried to think of a truly random phenomena thatis not related to quantum physics, and i can't.
I don't think any of us can.
That classical physics is not random does not imply that the system itself is not random.
In the context of classical physics it does. Classical Physics is not adequate to describe even the simplest phenomena to a 'satisfactory' level, once we scratch the surface so the answer to the OP is that we basically agree with him but that many classical based 'machines' have enough significant QM effects to treat them as behaving randomly.
The only truth about non random / random distinction is that a mathematical based attempt at a RN generator will have to be a Pseudo Random Number Generator.

Remember ERNIE? In those days (especially) they needed a non-digital source of randomness because computers were far too limited to have even a reasonably good PRNG. I wonder if a PRNS from Deep Blue would be 'distinguishable' from ERNIE's output.
 
  • #20
Dale
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A truly random phenomena means that an event occuring in space and time can in principle not be undone.
I have been thinking about this response and have decided that is a good one. If you think about it in phase space, an event that cannot be undone would be a place where the phase space lines converge such that two different initial states lead to a single final state. I think that a good definition of “truly random” would be the reverse of that. So one phase space line would diverge such that one initial state leads to two final states.

Then, Liouville’s theorem proves that classical physics forbids “truly random” systems.

Note: I am not aware if there is already literature on this topic
 
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  • #21
I tried to think of a truly random phenomena thatis not related to quantum physics, and i can't. Let's take heads or tails as an example, if you had all of the data about the throwing of the coin you could tell on which side it will land.

So does anyone know a random phenomena?
Crumpling a sheet of paper. It is HUGELY complicated/impossible to mathematically model.
 
  • #22
Filip Larsen
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Note: I am not aware if there is already literature on this topic
Branches in state space sounds similar to symmetry breaking, and that at least has some literature. As I understand it symmetry breaking in an otherwise symmetric system is only considered to be a result of quantum effects (spontaneous or dynamical symmetry breaking) or, for in case of purely classical system, due to the system not being precisely symmetric after all.
 
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As some folks point out, randomness is slippery because there are independent definitions. I refer you to the book by the late I. Prigogine: "The End of Certainty". Following its logic, you are left without practically no fully non-random events.

As I see it, the difference between random events and non-random events is information. An event/outcome is random to the extent that you lack information on the event. And it is random in terms of objective reality, to the extent that information existing in the universe does not exist, as opposed to the information that is available to you. If enough information exists to determine how your coin toss works, then the outcome might be random to you, but the universe would "know", and "determine" the outcome in advance.

But information is finite. Now, consider symmetry-breaking. Someone mentioned crumpling paper: a large part of its unpredictable nature is because it involves a lot of symmetry breaking, much of it only roughly, but some of it beyond any probable information available. Even the universe could not tell you exactly how it would crumple.

Let's choose a different form of symmetry breaking: the needle test. Imagine a horizontal rigid surface in a vacuum in neutral gravitational and electromagnetic fields. You have a device that tosses the needle so that at least sometimes that needle lands balanced on its tip. The game is to bet on which way it eventually will topple. Laplace does not forbid such a possibility, and offers no prediction.

The needle and surface offer no information to the universe about how that symmetry will break. To the extent that information on any bias exists, it will affect the direction and reduce the randomness accordingly, and affect the precision of the outcome..

If you happen not to like the needle, try the ball test: start with a rigid surface and vacuum as already described. Take a vertical, symmetrical stack of rigid, notionally perfect spheres of excellent coefficient of restitution, and drop them. As long as there is no information on any asymmetrical bias (not just your ignorance, and ignoring any quantum asymmetry, those balls, in obedience to F=ma, will bounce vertically for a long time till they stop and remain balanced. Right?

Wrong.
For that to happen there would have to be infinite information determining the symmetry of the system. It follows from the nature of the geometry of the balls. But we live in an observable universe that lacks capacity for infinite information.

It follows that, QM or no QM, there could not be a completely non-random system in our universe. And your personal capacity for information is a good deal smaller than that of the universe.
 
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  • #24
Dale
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Is information finite classically?
 
  • #25
PeroK
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Is information finite classically?
A "typical" real number contains an infinite amount of information. There was a thread a couple of years ago about whether physics could be done using only the computable numbers. In any case, using a real continuum for position of a particle, say, creates a conundrum.
 
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