Is a-causality necessary for randomness?

[JPBenowitz]

To play devil's advocate - why do you believe that in a quantum universe best described by fields and operators, causality plays a fundamental role(except for ordering events so that they seem to make some sense to you)?

Causality plays a fundamental role as an emergent property on the macroscopic level as the arrow of time. The laws of physics are for the most part time-symmetric with the weak force and second law of thermodynamics being exceptions. QM is not entirely free from T-asymmetry. The larger question at hand is why is there an arrow of time on large scales but not on small scales?

 

[bhobba]

What it means to be be truly random is not well defined

I think you need to study some math - in math it is very well defined indeed - so well defined tests to determine randomness exist that are actually quite hard to pass for pseudo random number generators that try to mimic randomness. It can be done - but it aren't easy - even some highly sophisticated pseudo random number generators fail it. That's why those seriously into computer simulation use hardware random number generators based on QM and not pseudo generators - they are more reliable. I have done some simulation in the past and obtained some results in a queuing problem clearly at odds with theory - it took a while to sort out but the random number generator was not random - not random at all. You can choose to believe the randomness in QM is the result of some underlying deterministic process - no doubt about it such is an unassailable position - but it must be really good to pass the tests they have these days - I simply do not believe nature is that devious.

Thanks
Bill

 

[bhobba]

The larger question at hand is why is there an arrow of time on large scales but not on small scales?

In QM the arrow of time is a result of decoherence which is the interaction with the environment. Studies have shown it actually doesn't take much to do it - for example a collision with a dust particle - just one collision - is evidently enough to irreversibly decohere a quantum particle. Because of that it is there at small scales as well - which is why its actually hard to demonstrate quantum effects eg to demonstrate superconductivity you generally need very low temperatures so its not in thermal contact with the environment.

Thanks
Bill

 

[JPBenowitz]

I think you need to study some math - in math it is very well defined indeed - so well defined tests to determine randomness exist that are actually quite hard to pass for pseudo random number generators that try to mimic randomness. It can be done - but it aren't easy - even some highly sophisticated pseudo random number generators fail it. That's why those seriously into computer simulation use hardware random number generators based on QM and not pseudo generators - they are more reliable. I have done some simulation in the past and obtained some results in a queuing problem clearly at odds with theory - it took a while to sort out but the random number generator was not random - not random at all. You can choose to believe the randomness in QM is the result of some underlying deterministic process - no doubt about it such is an unassailable position - but it must be really good to pass the tests they have these days - I simply do not believe nature is that devious.

Thanks
Bill

Randomness in mathematics is defined only statistically not formally.

 

[JPBenowitz]

In QM the arrow of time is a result of decoherence which is the interaction with the environment. Studies have shown it actually doesn't take much to do it - for example a collision with a dust particle - just one collision - is evidently enough to irreversibly decohere a quantum particle. Because of that it is there at small scales as well - which is why its actually hard to demonstrate quantum effects eg to demonstrate superconductivity you generally need very low temperatures so its not in thermal contact with the environment.

Thanks
Bill

There is not apparent arrow of time on QM scales precisely because of the energy-time uncertainty principle which does not mean it requires a Δt to measure ΔE with a accuracy but means that the system with a ΔE requires Δt =$\pi$h/2ΔE to evolve into a distinguishable state; in other words there are time intervals where no information is present and thus causality cannot be determined, hence no arrow of time. Just as there exists discrete energy levels there also exists discrete information levels.

 

[bhobba]

Randomness in mathematics is defined only statistically not formally.

That makes no sense, since statistically is itself a concept involving probability. Can I ask exactly what books on probability theory you have studied? Can you explain the non formal nature of Kolmogorov’s axioms?

Books on axiomatic probability theory are extremely formal going to great lengths to prove things that are pretty obvious so they can rigorously prove things that are not such as the existence of a Wiener process - which actually has applications in QFT eg Hida distributions.

Tanks
Bill

 

[bhobba]

There is not apparent arrow of time on QM scales

I think you need to be clearer exactly what you mean by QM scales - usually decoherence occurs very very quickly - so quick that only under special contrived circumstances such as temperatures near absolute zero can it even be measured. Are you talking of time scales even below that - time scales so short present technology can't measure it? If so then I agree.

Thanks
Bill

 

[audioloop]

Randomness is really just chaos.

to be precise and concise:

chaos is highly sensitive to initial conditions, randomess is independent of initial conditions.

 

[Darwin123]

What is the relationship between a-causality and randomness?

Let's look at the argument below:

For something to be (truly/inherently) random there cannot be a cause.

Because, if there is a cause then the cause can be studied and the result/output can be predicted and hence there would no randomness.

True Randomness means something that cannot be predicted.

We can predict whether will be an interference pattern or not, however we cannot predict the location of any individual/single photon/electron on the screen.

We can, in principle, predict the results of a roll of a dice (or toss of a coin) if we took into account all the factors such initial forces on the dice during the toss, effect of air molecules etc. Since the roll of a dice has a cause its predictable.

The word “random” is not always used as meaning without a cause. Random is used in the sense that the correlation of two sets of numbers is zero. Random usually refers to the correlation between future events and a set of measurements. Nonzero correlation has a very precise meaning in mathematics, but loosely corresponds to a practical level of predictability. It has nothing to do with “cause”.
There is no such thing as an absolute measure of randomness. There is only randomness relative to a set of measurements or experiences. Events can be random with respect to one set of measurements, but not random with respect to another set of randomness. You are making the error of thinking there exists and absolute randomness.
I think this is the way physicists, mathematicians and actuaries define random. In the case of insurance, they use statistics on sickness and accidents. They know that each sickness and accident has a cause. In fact, two accidents on opposite sides of the globe may be connected by a series of causes. However, the actuary still considers these random events if the correlation between two sequences of such events is zero.
It really doesn’t matter to the actuary if that there are causes that can be uncovered with great difficulty. That is the job of the insurance detective. The insurance detective may be using a different criteria for random than the actuary. However, the actuary and the insurance detective have access to different types of measurement and experience. So “random” has to be defined relative to their job, not metaphysical causes.
Zero correlation occurs just as often in classical physics as in quantum physics. If there is no correlation between the numbers one can measure and future events, then it doesn’t matter if there is a perfectly understandable cause for the events. The events are random with respect to those measurements.
If there are other measurements that hypothetically can be made which have a nonzero correlation with future events, then the events are not random with respect to those other hypothetical measurements. However, not all hypothetical measurements can be done.
What I am referring to as random is related to what an electronics engineer calls noise. The electronics engineer can have problems with a fluctuating voltage, which he knows is “caused” by other users of electricity on the electronic grid. If he could know precisely what everybody in the world is doing with their electrical devices at the same time, and know the atmospheric electrical conditions all over the world, then he probably could predict electronic noise. He could subtract it. However, he can’t. The most that he could do is characterize the statistical moments of his electronic noise. What makes it noise is that it doesn’t correlate with itself given any sort of time delay. Whether it has a cause or not is irrelevant.
Here is a link concerning the definition of random as used by an electronic engineer.
http://en.wikipedia.org/wiki/White_noise
“A random vector is a white random vector if and only if its mean vector and autocorrelation matrix are the following:


That is, it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix. When the autocorrelation matrix is a multiple of the identity, we say that it has spherical correlation.”

Let me play devils advocate here. Suppose that we are using a definition of random that includes the concept of “cause”. Quantum mechanics is still a random theory even though there may be a hidden variables theory which is better.
Quantum mechanics is still a random theory because it does not include the hidden variables with which the calculations can be made. The final cause can not be measured. The final results relative to the measurements that can be made consistent with quantum mechanics can’t be used to calculate future events precisely. Therefore, quantum mechanics calculations are random with respect to all known measurement techniques. It may not be random with respect to measurement techniques that may be developed in the future. However, it is still random with respect relative to currently known causes.

Basically, acausal does not mean random. I think the concept of cause is not as well mathematically defined as the concept of random. As a physicist, I generally hear the word "acausal" referring to logical paradoxes or to hysteresis. If "history" can be "changed" in some fashion in a system, the system is considered acausal.
For instance, I often hear "acausal" referred to when discussing time travel. I also hear the word acausal referred to in terms of the Cramers-Kronig relations in optics. If a system is acausal, then supposedly the Kramers-Kronig relations are invalid. It turns our that the Kramers-Kronig relations are invalid if the system shows hysteresis. Hysteresis refers to a sensitivity to past history.
Cause has more to do with time ordering than to randomness. If the time ordering of a series of events is important, the earlier events are said to be the cause of the later events. However, there are hypothetical ways of creating a correlation even when the time ordering is not important.
<Spoiler for "A Sound of Thunder>
<Anyone who reads this should read the story anyway. It is more suspense than mystery.>









If you read the Ray Bradbury's story, a "Sound of Thunder", you will know what I mean. A time traveler votes for a certain candidate who wins. He then steps on a butterfly in the Mesozoic. When he gets back to his own time, the other candidate has won.
The choice of which candidate won is random with respect to the lifespan of butterflies in the Mesozoic. There was no way to tell that stepping on that butterfly will cause the other candidate to win. However, killing the butterfly was obviously the cause of the other candidate winning. If he stepped on another butterfly, maybe the first candidate would have won. Or maybe he would have come back to a kingdom rather than a democracy. The butterfly in this case is definitely a cause, but it still has a random effect on the election.
Note that the hunter who steps on the butterfly is still responsible for his actions. He didn't know what the consequences would be. However, he knew that it would cause something. The fact that he had no way to predict what would happen makes him MORE responsible for doing it because it could have been a lot worse. Therefore, randomness is NOT free will at least in this story.

 

[JPBenowitz]

That makes no sense, since statistically is itself a concept involving probability. Can I ask exactly what books on probability theory you have studied? Can you explain the non formal nature of Kolmogorov’s axioms?

Books on axiomatic probability theory are extremely formal going to great lengths to prove things that are pretty obvious so they can rigorously prove things that are not such as the existence of a Wiener process - which actually has applications in QFT eg Hida distributions.

Tanks
Bill

Of course there are formal proofs in probability what I am saying is that no pure mathematical equation can generate a truly random number. All true random number generators utilize a random physical system.

 

[JPBenowitz]

to be precise and concise:

chaos is highly sensitive to initial conditions, randomess is independent of initial conditions.

I am making a speculation that there exists an error in computing the initial conditions of a chaotic system that exceeds a fundamental physical computational limit thereby rendering it impossible to compute the initial conditions of the system. This "true randomness" is not independent of initial conditions but at the time of the initial conditions to the time it reaches this limit we can say no information has survived.

 

[Maui]

But aside from such theoretical considerations physics is an experimental science and QM and QFT are fully in accord with experiment.

Thanks
Bill

I agree about the BI but my point about causality, which seems to have been lost, was that you get 'causaility' after solving the equations of motion, i.e. there are no pre-existing classical Lagrangians. In this view, both causality and classicality are emergent(and also the apparent randomness), the trade-off is that there appears to be just one possible worldview(if one must have such) - reality probably has to be a projection?

 

[bhobba]

I think this is the way physicists, mathematicians and actuaries define random. In the case of insurance, they use statistics on sickness and accidents

Formally they define it usually by Kolmogorov's axioms. Intuitively it is usually thought of as the limiting proportions of a long sequence of trials.

Thanks
Bill

 

[bhobba]

I agree about the BI but my point about causality, which seems to have been lost, was that you get 'causaility' after solving the equations of motion, i.e. there are no pre-existing classical Lagrangians. In this view, both causality and classicality are emergent(and also the apparent randomness), the trade-off is that there appears to be just one possible worldview(if one must have such) - reality probably has to be a projection?

You get causality in the following way. The fundamental principle is an infinitesimal change in time leads to an infinitesimal change in state. From this, probability invariance and Wigners theorem the transformation must be unitary. Stones theorem implies it has a generator that by definition is called energy. Thus knowledge of energy uniquely determines the time evolution of a quantum system. Galilean invariance of probabilities implies the form of the energy operator has exactly the same form as the Hamiltonian in classical mechanics which in fact is Schrodinger's equation - for a proof of this see Chapter 3 of Ballentine.

Thanks
Bill

 

[JPBenowitz]

You get causality in the following way. The fundamental principle is an infinitesimal change in time leads to an infinitesimal change in state. From this, probability invariance and Wigners theorem the transformation must be unitary. Stones theorem implies it has a generator that by definition is called energy. Thus knowledge of energy uniquely determines the time evolution of a quantum system. Galilean invariance of probabilities implies the form of the energy operator has exactly the same form as the Hamiltonian in classical mechanics which in fact is Schrodinger's equation - for a proof of this see Chapter 3 of Ballentine.

Thanks
Bill

Which is why the time-energy uncertainty principle is correctly interpreted as the energy required to drive the evolution of a quantum system to an orthogonal and hence distinguishable state.