Does Randomness Exist?

slipss

Inspired by a post in After Hours I've been trying to read up on this question and get some sort of a grasp on the arguments. So I thought I'd open it up for debate here and see what people have to say. Any physics I know myself I know from juniour cert science, the discovery channels and late night wikipedia surfing so unfortunately won't be able to add a huge amount to the discussion myself, hopefully others here will. I find the question fascinating in and of itself and also for the implications the answer would have on philosophical subjects such as the idea of free will, fate, determination and fatalism and also for concepts like evolution being partially driven by "random" mutations or predicting the future being an impossibility. Thanks in advance for any opinions or information put forward.

thecornflake

well quantum mechanics deals with the probability of finding particles and the like , so we can never be 100 % on certain aspects. This could be interpretated as random such as electrons tunneling ect , it is this probabilistic outcome that einstein famously replied to with " God does not play dice "

slipss

thecornflake wrote: »

well quantum mechanics deals with the probability of finding particles and the like , so we can never be 100 % on certain aspects. This could be interpretated as random such as electrons tunneling ect , it is this probabilistic outcome that einstein famously replied to with " God does not play dice "

That would be the "uncertainty princible" theorys? But do they not deal with the ability to predict future events rather than wether or not those events are truely random?

thecornflake

say there is a 50% chance of a particle being in a box or tunneling out , to be outside.
what determines if it is in or out ? It is random as if you repeated the test , it could be the same answer or different to your first observation. on a whole , we predict that if 100 test were carried out , we would hope to observe the particle in the box 50 times and out 50 times. Thus the outcome is confined to being in or out , but as for for what the actual answer is ( in or out ) it is simply random ( as it is a random due to 50/50 chance)

slipss

Maybe my difficulty here is that I'm looking for the answers to a different question. Does randomness just mean unpredictability? If so maybe the question I want to ask in this thread is: Does everything have a cause? If everything does have a cause then wouldn't it mean if we could identify the cause we could identify the outcome that would be produced by the causes?

Professor_Fink

Hi slipss,

Let me have a shot at answering your question. As far as we can tell, the evolution of closed systems is completely deterministic. When we measure a quantum system, however, we can not measure all possible states. Our measurement outcome must be one of a set of so called orthogonal states. If we measure a system which is not in one of the orthogonal states measured by our device, then we will measure it to be in one of the states, where the outcome is random, with the probability determined by how close each orthogonal state is to the actual state being measured.

Here is an example: We can prepare a state |+> = 1/sqrt(2)(|0> + |1>), where |0> and |1> represent orthogonal states. Clearly, |+> is neither of these states, and lies midway between the two states. This means that is I measure the |+> state in the {|0>,|1>} basis, the measurement outcome will give me either 0 or 1 with equal probability.

The result of this is that we can indeed experience random outcomes from an experiment. This does not, however, imply that the universe must be random, since the universe can be regarded as a closed system, and quite likely does evolve deterministically. This is a rather subtle point, so rather than trying to explain the mechanism that would allow this, I will refer you to the wikipedia entry on the Everett Interpretation of quantum mechanics.

thecornflake

Professor_Fink wrote: »

Hi slipss,

Let me have a shot at answering your question. As far as we can tell, the evolution of closed systems is completely deterministic. When we measure a quantum system, however, we can not measure all possible states. Our measurement outcome must be one of a set of so called orthogonal states. If we measure a system which is not in one of the orthogonal states measured by our device, then we will measure it to be in one of the states, where the outcome is random, with the probability determined by how close each orthogonal state is to the actual state being measured.

Here is an example: We can prepare a state |+> = 1/sqrt(2)(|0> + |1>), where |0> and |1> represent orthogonal states. Clearly, |+> is neither of these states, and lies midway between the two states. This means that is I measure the |+> state in the {|0>,|1>} basis, the measurement outcome will give me either 0 or 1 with equal probability.

The result of this is that we can indeed experience random outcomes from an experiment. This does not, however, imply that the universe must be random, since the universe can be regarded as a closed system, and quite likely does evolve deterministically. This is a rather subtle point, so rather than trying to explain the mechanism that would allow this, I will refer you to the wikipedia entry on the Everett Interpretation of quantum mechanics.

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and thats why he gets paid the big bucks . . . . . . . . . . . ( i think ? ) , but yeah i actually couldnt have said it beter myself.

Professor_Fink

thecornflake wrote: »

and thats why he gets paid the big bucks . . . . . . . . . . . ( i think ? )

I wouldn't say "big" bucks...

thecornflake

Professor_Fink wrote: »

I wouldn't say "big" bucks...

well then you get payed the medium to big bucks, more than most can say

Kevster

I had a brief few lectures at the end of last year on quantum chemistry and was intrigued by it (having a purely 'biology' background). I am aware that the Schrodinger eqn. has only been solved for the Hydrogen and Helium atoms, but is this related in any way to what we are talking about here? To expand, if we had the computing power - and computed the Schrodinger eqn (energy state) for larger and complex molecules - could we then predict the future of these molecules in a given closed system?

Kevin (<- non-physicist/chemist!)

thecornflake

Kevster wrote: »

I had a brief few lectures at the end of last year on quantum chemistry and was intrigued by it (having a purely 'biology' background). I am aware that the Schrodinger eqn. has only been solved for the Hydrogen and Helium atoms, but is this related in any way to what we are talking about here? To expand, if we had the computing power - and computed the Schrodinger eqn (energy state) for larger and complex molecules - could we then predict the future of these molecules in a given closed system?

Kevin (<- non-physicist/chemist!)

the S.W.E. predicts probability density i.e. the probability of where a particle is likely to be , we cannot be certain of it due to the wave natue of particles ( via uncertainty principal ). You are refereing to the " particle in a box " theme. It was once thought that if you were somehow able to know the location and forces acting on every particle in the universe , then you would be able to predict the future and know all about the past , however it is due to the uncertainty principal that we can never know exactly the outcome of a system with 100% accuracy . including the system you mentioned. ( many people find this hard to believe as we are used to thinking in terms of a claasical framework , however a quatum framework is very different ).

however for large items ( the molecule would need to be very large ) , we are able to predict these things beter as the wave lenght of the particle becomes smaller the larger the mass of the " particle " in question , and thus the uncertainty reduced.

Kevster

Yes, there was some French scientists who claimed that everything could be predicted through mathematics, right? I don't recall his name, but he was mentioned in A brief history of time. I knew about the uncertainty principal too, but wasn't sure if it was relatd to the Schrodinger eqn.

In response to your last paragraph, is that reduced uncertainty for real?; and is it possibly due to the greater amount of 'unbonding' electrons that would exist in much larger systems? (i.e. These electrons wouldn't have to be computed because they don't interact with anything... ...)

Kevin

thecornflake

Kevster wrote: »

Yes, there was some French scientists who claimed that everything could be predicted through mathematics, right? I don't recall his name, but he was mentioned in A brief history of time. I knew about the uncertainty principal too, but wasn't sure if it was relatd to the Schrodinger eqn.

In response to your last paragraph, is that reduced uncertainty for real?; and is it possibly due to the greater amount of 'unbonding' electrons that would exist in much larger systems? (i.e. These electrons wouldn't have to be computed because they don't interact with anything... ...)

Kevin

no , electrons in a finite well or " box " , are conputed individualy if they do not interact with each other and due to quatummechanics , they can only take on descrete amount of energy , it is larger mass things i am refering to such as a human , or like a question i studied a few days ago a grain of sand. The sand grain is very tiny but still massive in terms of quantum mechanics and only has a particle wavelenght on the order on small nano meters, This means the uncertainty in its position and momentum is extremely small , where as an electrons uncertainty in postion and momentum is high compared to the grain due to it's tiny mass.

Podge_irl

Kevster wrote: »

I had a brief few lectures at the end of last year on quantum chemistry and was intrigued by it (having a purely 'biology' background). I am aware that the Schrodinger eqn. has only been solved for the Hydrogen and Helium atoms, but is this related in any way to what we are talking about here? To expand, if we had the computing power - and computed the Schrodinger eqn (energy state) for larger and complex molecules - could we then predict the future of these molecules in a given closed system?

Kevin (<- non-physicist/chemist!)

Has it been solved for the Helium atom? I didn't realise it had been (at least not analytically). It's not a question of computing power, that's only useful in doing numerical calculations. Solving anything above the hydrogen atom brings the same complications that solving 3-body problems in gravity bring - namely that its difficult to bring the back-reactions into the equation (difficult to the point of being currently impossible).

Professor_Fink

Kevster wrote: »

I am aware that the Schrodinger eqn. has only been solved for the Hydrogen and Helium atoms, but is this related in any way to what we are talking about here?

Actually it has been solved for a huge variety of systems. I think you are confusing the issue of numerical calculations vs an analytic solution with our ability to actually make predictions from the equation.

Many common mathematical equations do not have analytic solutions, but that does not mean they are unsolvable, or unsolved.

That said, it is computationally difficult to solve the general SWE for large systems, but this is simply due to the simulations requiring enormous memory to represent quantum states.

Kevster wrote: »

To expand, if we had the computing power - and computed the Schrodinger eqn (energy state) for larger and complex molecules - could we then predict the future of these molecules in a given closed system?

We can, and do. For large systems we often try to make approximations to cut down on the computing time required, but this doesn't really change matters. Certainly, I myself have simulated the quantum evolution of spin chains of 20,000+ spins (which can be done efficiently due to a very nice mathematical trick).

Professor_Fink

Kevster wrote: »

In response to your last paragraph, is that reduced uncertainty for real?;

There seems to be some confusion here. We can solve the state of the particle in the box deterministically using the Schroedinger equation. This is more than a probability distribution (as cornflake claimed), it is the exact state of the particle.

The problem that arises, however is that that general quantum states can be formed from an orthogonal basis consisting of different positions, but can in general be any linear combination of these position states. In my earlier post I mentioned the |+> state, which is a linear combination of the states |0> and |1>. We could choose |0> and |1> to be two different positions. Thus a system prepared in the state |+> does not really have a localised position, since when measured it will be found to be in either |0> or |1>. We are making a fundamental mistake in trying to ascribe definite values to properties such as position or momentum for a quantum system. This is what gives rise to the uncertainty principal, and to uncertainty in general in quantum mechanics. It is not that we cannot predict the state of a particle, but merely that for any quantum state there is some measurement basis for which the state is not one of the orthogonal basis states, and so does not meaningfully have a value.