Is radioactive decay truly random?

[Braznor]

Since all atoms posses the same physical properties, what causes certain atoms(in a radioactive mass) to undergo decay and others don't? Is it pure random? i.e a certain atom decays without specific factors increasing the possibility or is there a known factor causing or yet, a completely factor?

Also, please list other random phenomena occuiring in nature.

 

[f95toli]

Yes, it is random.
At any given time the probabilty that a given atom will decay is constant; that is what leads to the exponential decay of radioactivity (i.e. the fact that an ensemble of atoms has a specfic half-life).

 

[CycloWizard]

Other random processes include mass diffusion and thermal conduction ('energy diffusion'). I'm sure there are many others, but those come to mind right away.

 

[BrownTown]

A solid argument can be made that nothing (at least so far as we have seen) is truely random. Our ability to model the interactions involved in theworld has steadily improved over the ages, and many things which were considered completely unpredictable, or "acts of god" can be easily determined nowadays. OF course at the same time new things are discovered which cannot be predicted. The agrument can simply be made that there are variables involved which are not known about by modern science which are causing the apparent randomness.

 

[cougar1]

Originally posted by: BrownTown
A solid argument can be made that nothing (at least so far as we have seen) is truely random. Our ability to model the interactions involved in theworld has steadily improved over the ages, and many things which were considered completely unpredictable, or "acts of god" can be easily determined nowadays. OF course at the same time new things are discovered which cannot be predicted. The agrument can simply be made that there are variables involved which are not known about by modern science which are causing the apparent randomness.

Randomness, or at least uncertainty, is a fundamental tenet of quantum theory, which is the best model of the Universe that we have at this time. So far, any and all attempts to discover such "hidden variables" as you describe have failed. Does that mean, they do not exist? Well, we can't be sure, since it is impossible to prove that something doesn't exist (perhaps we just can't detect it...). Nevertheless, Quantum Theory correctly predicts all known phenomena without the need to resort to such "hidden variables", so until they are discovered (disproving quantum theory), we must face the very real possibility that quantum theory is true and indeed some processes are truly random.

 

[cougar1]

Originally posted by: CycloWizard
Other random processes include mass diffusion and thermal conduction ('energy diffusion'). I'm sure there are many others, but those come to mind right away.

The "randomness" of diffusion processes, seems to stem more for the complex interaction of a large number of particles that is too difficult for us to track and uncertainty of initial conditions, than from something inherently random in the process. In other words, deterministic models using classical mechanics can adequately model most of these processes (except in special circumstances where quantum effects are significant).

By contrast, many quantum phenomena are truly random (ie. cannot be modeled deterministically). Such phenomena include radioactive decay, tunneling, Auger scattering, the Mossbauer effect, numerous excited state relaxation mechanisms, chemical reactions, etc... Of course in situations where these phenomena significantly effect atomic trajectories, they introduce additional randomness into the diffusion processes making them truly random as well.

 

[CycloWizard]

Originally posted by: cougar1
The "randomness" of diffusion processes, seems to stem more for the complex interaction of a large number of particles that is too difficult for us to track and uncertainty of initial conditions, than from something inherently random in the process. In other words, deterministic models using classical mechanics can adequately model most of these processes (except in special circumstances where quantum effects are significant).

We can model such systems to a high degree of accuracy on a molecular level by considering Brownian forces. However, there is some degree of stochastic behavior in real systems that deterministic models do not account for. Accordingly, some random components appear. I have a pretty well done thesis on this sort of thing in PDF format if you're interested. Someone in my department finished it about a year and a half ago and I went to his defense, which is the only reason I know anything about it.

edit: It could also be that these systems are deterministic but that, lacking an appropriate kinetic theory of liquids, the forces are not as well understood as those in the gas phase.

 

[cougar1]

In the case of a simulation of Brownian motion, my understanding is that you are treating the interaction between the solvent (small molecules) and the target substance (usually a large molecule or particle) in some average way to make the problem computationally tractable. In other words, you are not tracking the individual trajectories of the small molecules, but approximating their effects on the large molecule as the average of random events.

In reality the actual fluctuations depend on the trajectories of the individual molecules, however because these fluctuations average out over time, it is possible to get reasonable results considering only this average behavior, making the problem much simpler.

In principle, given sufficient computational resources, appropriate force field equations, and exact initial conditions, such a system could be modeled deterministically at least for short time periods. However, such results would require extreme amounts of computational resources and provide little additional insight than what can be gained from the simpler Brownian-force-based models.

Another factor in this discussion, is that the system you describe is probably a chaotic system. In other words, the exact trajectories of all particles are highly dependent on initial conditions and small errors in the calculation results due to rounding are quickly amplified into significant deviations in future simulation time-steps, essentially injecting another source of random "noise" into the simulation.

 

[CycloWizard]

Originally posted by: cougar1
In the case of a simulation of Brownian motion, my understanding is that you are treating the interaction between the solvent (small molecules) and the target substance (usually a large molecule or particle) in some average way to make the problem computationally tractable. In other words, you are not tracking the individual trajectories of the small molecules, but approximating their effects on the large molecule as the average of random events.

In reality the actual fluctuations depend on the trajectories of the individual molecules, however because these fluctuations average out over time, it is possible to get reasonable results considering only this average behavior, making the problem much simpler.

In principle, given sufficient computational resources, appropriate force field equations, and exact initial conditions, such a system could be modeled deterministically at least for short time periods. However, such results would require extreme amounts of computational resources and provide little additional insight than what can be gained from the simpler Brownian-force-based models.

Another factor in this discussion, is that the system you describe is probably a chaotic system. In other words, the exact trajectories of all particles are highly dependent on initial conditions and small errors in the calculation results due to rounding are quickly amplified into significant deviations in future simulation time-steps, essentially injecting another source of random "noise" into the simulation.

This just depends on what you're trying to model. The thesis I mentioned above used a multiscale technique in which a continuum-based approach was used to supply the boundary condition for a Brownian dynamic simulation in a smaller region of interest. There is a paper that addresses which of the various simulation methods are appropriate at various time/length scales:
Vvedensky, D. D. (2004) Multiscale modeling of nanostructures, Journal of Physics:
Condensed Matter, 16, R1537-R1576.

If you can access said paper, then you'll see that there is considerable interest in the computational world in looking at things on a much more detailed scale than Brownian dynamics simulations, with the smallest time/length scales being approachable only using ab initio methods, which rely on Schrodinger's equation (which, if you're not a physical chemist, governs the motions of electrons and nuclei). Moving up to larger time/length scales, we come to atomistic simulations, which encompass deterministic molecular dynamics simulations and Monte Carlo (stochastic) simulations. One further step up the ladder brings us, finally, to Brownian dynamic simulations and other mesoscopic techniques, such as dissipative particle dynamic methods.

Each larger time/length scale increases the number of assumptions you're making about the system. Simply because you choose a deterministic model does not mean the system that you're modeling is actually deterministic. Instead, if it is a good modeling assumption, it just means that the time/length scales of interest are sufficiently large that you may neglect the stochastic processes underlying the large-scale phenomena.

I'm not trying to argue that quantum mechanics is the end-all, be-all or that randomness is the underpinning of nature. I'm simply stating that, if you delve far enough into a diffusion problem, you can get at the movement of nuclei and protons that currently may only be well-modeled using quantum mechanics, which assumes random behavior. Whether this behavior is truly random is an open question for the scientific community and has drawn the attention of every great scientist for the last 100 years or so. Since I don't fit in that category, I'll not try to address the point further.

 

[cougar1]

The distinction that I'm really trying to make is that there are two types of randomness encountered in nature. The first, which I will call pseudo-randomness, arises due to our ignorance about the exact initial state of the system (eg. the positions and momenta of all particles in the system). The second, which I will call true randomness, arises as a direct consequence of the uncertainty principle of Quantum Theory, which says that we can only know both the position and momentum of a particle within a certain degree of accuracy and can never know the exact values of both.

For large particles, the level of quantum uncertainty is small and for many practical purposes can be neglected. In this case, which even applies to some molecular and atomic processes, classical mechanics can be used to adequately model the system. Since these processes are reasonably modeled by classical mechanics, which is deterministic (non-random), these processes, which include diffusion and Brownian motion are essentially deterministic as well. In other words, if we knew the initial state of the system and had sufficient computational resources, we could accurately model the trajectories of all particles in the system, meaning that no additional randomness enters the system (Neglecting, as stated above, uncertainties introduced by quantum effects).

As an aside, the randomness you encounter in simulations using classical mechanics, like those you mention, arises due to the fact that in nature the vast majority of possible microstates (the exact positions and momenta of each particle) have approximately the same macroscopic properties (eg. temperature, pressure, volume, diffusion rates, etc...). Therefore, rather than modeling the exact trajectory of a single system, it is only necessary to identify the most probable microstates and then determine the macroscopic properties corresponding to these states. In molecular dynamics, the most probable microstates are determined by following the trajectory of a random initial system through time and assuming that after some equilibration period, most of the simulation time will be spent in the most probable microstates. In Monte Carlo simulations, microstates are randomly generated and the average microscopic properties determined for the various microstates sampled. Since the most likely states dominate the averages, the calculated properties will eventually converge to the properties for a real system. In practice, a Markov Chain is used to bias sampling toward the most likely states, so the simulation can converge more rapidly. In both of these cases, we inject the randomness into the model to compensate for our lack of knowledge about the actual microstates, but the processes themselves (again neglecting quantum uncertainty) are not inherently random.

BTW, I've spent the last eight years or so, modeling various phenomena, using molecular dynamics, Monte Carlo, continuum-based models and even quantum chemistry packages, so I know a little about these topics . Thanks for giving me the chance to "talk shop".

 

[CycloWizard]

Yeah, I think we're saying the same thing in two different ways.

 

[cougar1]

Agreed!

 

[QuantumPion]

Originally posted by: CycloWizard
I'm not trying to argue that quantum mechanics is the end-all, be-all or that randomness is the underpinning of nature. I'm simply stating that, if you delve far enough into a diffusion problem, you can get at the movement of nuclei and protons that currently may only be well-modeled using quantum mechanics, which assumes random behavior. Whether this behavior is truly random is an open question for the scientific community and has drawn the attention of every great scientist for the last 100 years or so. Since I don't fit in that category, I'll not try to address the point further.

Radioactivity is quantum mechanically random because the subatomic particle sizes and energies are of the same order as their wavelengths. The reason why diffusion is deterministic (although chaotic) is because the particles are much larger then their wavelengths. See: http://en.wikipedia.org/wiki/Thermal_de_Broglie_wavelength

 

[Born2bwire]

Originally posted by: cougar1

Originally posted by: BrownTown
A solid argument can be made that nothing (at least so far as we have seen) is truely random. Our ability to model the interactions involved in theworld has steadily improved over the ages, and many things which were considered completely unpredictable, or "acts of god" can be easily determined nowadays. OF course at the same time new things are discovered which cannot be predicted. The agrument can simply be made that there are variables involved which are not known about by modern science which are causing the apparent randomness.

Randomness, or at least uncertainty, is a fundamental tenet of quantum theory, which is the best model of the Universe that we have at this time. So far, any and all attempts to discover such "hidden variables" as you describe have failed. Does that mean, they do not exist? Well, we can't be sure, since it is impossible to prove that something doesn't exist (perhaps we just can't detect it...). Nevertheless, Quantum Theory correctly predicts all known phenomena without the need to resort to such "hidden variables", so until they are discovered (disproving quantum theory), we must face the very real possibility that quantum theory is true and indeed some processes are truly random.

Certain hidden variables have been disproven though, like with the EPR paradox and Bell's theorem.

 

[imported_iNGEN]

Wow, my brain is getting toasty. It's been a long time since I thought about this stuff. At the risk of dumbing down the conversation; Is it even fruitful to ask the question, "Is radioactive decay truly random?", when the uncertainty principle precludes awareness of a deterministic mechanism should one exist?

That is until there is some breakthrough that provides awareness without the impact of observation.

 

[CSMR]

Originally posted by: cougar1
The distinction that I'm really trying to make is that there are two types of randomness encountered in nature. The first, which I will call pseudo-randomness, arises due to our ignorance about the exact initial state of the system (eg. the positions and momenta of all particles in the system). The second, which I will call true randomness, arises as a direct consequence of the uncertainty principle of Quantum Theory, which says that we can only know both the position and momentum of a particle within a certain degree of accuracy and can never know the exact values of both.

Yes but these are two types of ignorance involved within a theory not in nature.

 

[cougar1]

Originally posted by: CSMR

Originally posted by: cougar1
The distinction that I'm really trying to make is that there are two types of randomness encountered in nature. The first, which I will call pseudo-randomness, arises due to our ignorance about the exact initial state of the system (eg. the positions and momenta of all particles in the system). The second, which I will call true randomness, arises as a direct consequence of the uncertainty principle of Quantum Theory, which says that we can only know both the position and momentum of a particle within a certain degree of accuracy and can never know the exact values of both.

Yes but these are two types of ignorance involved within a theory not in nature.

But, the theory implies that such ignorance or randomness may be an integral part of nature (not just a consequence of our ignorance or the incompleteness of a theory).

 

[CycloWizard]

Originally posted by: CSMR
Yes but these are two types of ignorance involved within a theory not in nature.

Like cougar said, we don't yet know whether 'true' randomness actually is random. It seems to be one of the long-standing debates in the physics community. Einstein didn't seem to believe that true randomness existed ('God doesn't roll dice', or something similar). Several prominent scientists have disagreed with him. I'm not in a position, intellectually or otherwise, to disagree with Einstein or anyone who might disagree with him. While it might be nice for us to think that nothing is random, I don't think any evidence has been (or even, perhaps, can be) attained that tells us one way or the other. So, it's my understanding that whether such 'true randomness' exists is still an open question.

 

[Gannon]

The truth is man is too inferior at the present time to model the universes complexity, where the complexity stops is anyones guess, but as soon as we start accelerating our ability to measure and process information we'll find things less and less random about the universe, the inherent "randomness" just comes from the universe having so many things known and unknown interacting at once. There may be some sort of fundamental knowledge wall of nature we may never be able to penetrate without extreme danger to ourselves... but we won't know that in our lifetimes.

 

[CycloWizard]

Originally posted by: Gannon
The truth is man is too inferior at the present time to model the universes complexity, where the complexity stops is anyones guess, but as soon as we start accelerating our ability to measure and process information we'll find things less and less random about the universe, the inherent "randomness" just comes from the universe having so many things known and unknown interacting at once. There may be some sort of fundamental knowledge wall of nature we may never be able to penetrate without extreme danger to ourselves... but we won't know that in our lifetimes.

Nothing like a little begging the question to solve one of science's greatest riddles, eh? Interesting hypothesis, but a hypothesis is not proof of itself.

 

[Blouge]

>Since all atoms posses the same physical properties

The very first line of the OP's post is wrong. Atoms have different properties. There are different elements and isotopes. They have differing mass, charge, position, velocity, and angular momentum. Then the electrons can be in different energy states, with various spins. Also the nucleons, quarks, gluons, and virtual particles contained within the atom have numerous properties. A particular atom might be entangled with a distant particle. Then there are the particles and hidden variables we don't know about, because we aren't advanced enough. And if you think we know everything, note that yet another particle (the axion) was just discovered only a couple months ago. BTW, "Atom" comes from the greek for "indivisible". What a laugh that definition turned out to be. Let's not repeat that mistake again!

>Yes, it is random.

That's not a scientific statement. It's not possible to measure a process and establish that its random. You can only establish that the process obeys a given statistical model. QM, for example, is a deterministic theory that yields precise statistical distributions, which are backed up by experiment. You might go further and claim there's randomness yielding the distribution, but that's only for reasons of convenience. For example, Einstein used randomness in his model of Brownian motion, yet he remained a staunch determinist. To jump to conclusions and embrace QM and randomness as the foundation of the universe is foolhardy, in light of QM's flaws (intractable GR incompatibility) and our primitive state of knowledge. There's no laboratory equipment to distinguish "randomness" from pseudorandomness, human conciousness, God's will, each particle has its own free will (heard this one recently), Everett's many worlds, and who knows what else.Perhaps we'll find nonlocal hidden variables, a possibility which could actually be scientifically verified. For now, I suggest using Occam's razor and admitting that the answer is just our own plain ignorance.

 

[cougar1]

> The very first line of the OP's post is wrong.

Technically, you are right, but assuming the poster meant atoms of the same isotope in their ground state (which is usually implied in such a statement), he is basically correct about their being indistinguishable.

> QM, for example, is a deterministic theory that yields precise statistical distributions, which are backed up by experiment.

No! QM is not a deterministic theory, which is why Einstein had such a hard time accepting it. While it does yield precise statistical distributions describing the behavior of a group of particles, it tells nothing about the instantaneous behavior of a single particle. It cannot predict the exact position and trajectory of a single particle, only the probability density for that particle (the probability of finding the particle at a particular location in space and time). QM can predict what fraction of a large number of atoms will undergo radioactive decay, but it tells nothing about if and when a single atom will undergo such decay.

Whether QM accurately describes reality is an open question. It's possible that there are unknown factors (hidden variables) causing the apparent randomness described by QM. However, such variables have never been found, so until they are found, which would require QM to be significantly modified or even rejected, we must be prepared to accept that such variables in fact may not exist and that at least at some scales, nature truly is random.

In short, while QM cannot prove the universe is random, it does show that a random universe could produce the order we observe in nature and by extension that our universe could in fact be random.

 

[smack Down]

Is the randoms a result of a property of QM or due to unknown initial conditions?

 

[f95toli]

Originally posted by: smack Down
Is the randoms a result of a property of QM or due to unknown initial conditions?

It is a property of QM. QM only allows us to calculate the probabilty that an atom will decay at any given moment; it it impossible to calculate the exact moment this will happen no matter how well you know the initial conditions .

 

[f95toli]

Originally posted by: Blouge

>Yes, it is random.

That's not a scientific statement. It's not possible to measure a process and establish that its random. You can only establish that the process obeys a given statistical model. QM, for example, is a deterministic theory that yields precise statistical distributions, which are backed up by experiment. You might go further and claim there's randomness yielding the distribution, but that's only for reasons of convenience. For example, Einstein used randomness in his model of Brownian motion, yet he remained a staunch determinist. To jump to conclusions and embrace QM and randomness as the foundation of the universe is foolhardy, in light of QM's flaws (intractable GR incompatibility) and our primitive state of knowledge. There's no laboratory equipment to distinguish "randomness" from pseudorandomness, human conciousness, God's will, each particle has its own free will (heard this one recently), Everett's many worlds, and who knows what else.Perhaps we'll find nonlocal hidden variables, a possibility which could actually be scientifically verified. For now, I suggest using Occam's razor and admitting that the answer is just our own plain ignorance.

Techically you are almost right, but you are again confusing philosophy with science.
The problem with your argument is that it makes it impossible to "know" anything.

QM does, as you say, make it possible to calculate the distribution function of a certain process. Now, if I then perform a measurement and the result does indeed agree with the QM prediction I would say that QM was correct, the process is random (remember that the "randomness"-property was used when I calculated the disitribution.

Now, of course I can't be sure of this in the "philosophical" sense, since it enirely possible that I will get a result that does not agree with QM if I repeat the same experiment the following day but that is true for all theories. It is impossible to PROVE a theory, you can only prove it wrong.
Hence, from a "philopsophical" point of view we can never know anything for sure but that does not stop us from using QM or any other good theories in e.g. engineering and when we do that we generally speak about results being correct or not: which is why I gave the answer "yes, it is random".
While saying "we don't know anything" might be interesting from a philosophical standpoint it doesn't really help if you want to e.g. calculate how much concrete you need to build a bridge ("According to the theory I need 10 tons, but since we can't be sure the theory is correct I will use 3 instead")

Also, note that I said "almost" in my first sentence. There are ways to test QM (and local realism in particular) which DO NOT direcly rely on calculating distributions.

In the latest issue of Nature (vol 445, pp. 723) there is an interesting article by Gregor Weihs where he is commenting on some recent experiment using neutron diffraction to test "quantum realism" (Hasegawa et al, Phys. Rev. Lett vol 97, 230401). The experiment is relevant here since it directly test for local variables (in this case non-contextual variables, which are more general than "ordinary" hidden variables) and specifically "randomness" (using Kochen-Specker inequalities).
Not surprissingly, the QM predictions are correct.

I can reallly recommend Weihs article for those of you who have access to Nature, there is no math involved so it is relatively easy to read.
Hasegawas paper is on the other hand quite techical so unless you have a background in neutron diffraction (I don't) it is not very helpfull.

The conclusion by Weihs based on this (and other earlier experiements) is that the world is "fundamentally random", at least in the scientific sense.