I was listening to a Feynman lecture on the 2 slits experiment and he finished his talk by saying that it used to be thought that if a system was set up accurately enough then it was possible ,in theory to predict its subsequent evolution.

He then said that this could no longer be considered to be the case and that ,in another's words "nature does not herself know what comes next"(to paraphrase)

Might a reason for this be that no physical systems are identical even in theory?

(each system has its own unique place in the overall system)

So ,in practice no experimental setup can ever be precisely replicated -and no subsequent evolution of one system can ever be replicated by setting up another identical system and "prodding" it identically to the other.

A corollary might be that the mathematics used to describe any physical system is always going to be an approximation to what actually happens (which would be unwelcome "news" to anyone who believed mathematics to be fundamental to physical existence-rather than a very,very useful tool)

59 minutes ago, geordief said:

So ,in practice no experimental setup can ever be precisely replicated -and no subsequent evolution of one system can ever be replicated by setting up another identical system and "prodding" it identically to the other.

It depends what is meant by “precisely”. If you mean exactly, ie with no deviations at all, then I agree that this is probably not possible. In practice though it is often possible to minimize differences such that their effects on the evolution of the system are negligible, at least for some specified period of time.

Atoms of the same isotope are. They obey Bose-Einstein or Fermi-Dirac statistics depending on their spin, which assumes identical particles; the formulation of e.g. the Pauli exclusion principle assumes identical particles.

(Identical here refers to quantum states; you can’t apply a classical-physics-based notion of identical to the situation)

Experimental replication carries with it the notion of statistics and uncertainty. You can’t ignore that, because any physical process has noise

8 hours ago, geordief said:

I was listening to a Feynman lecture on the 2 slits experiment and he finished his talk by saying that it used to be thought that if a system was set up accurately enough then it was possible ,in theory to predict its subsequent evolution.

This would imply that it was possible to create multiple exact copies of the system - if you can do it once, then why not do it again and again?

It works in the classical world - we can design an operation that takes in arbitrary states of raw materials and converts them to multiple 'copies' of a predetermined state (Model T Ford, von Neumann probe etc).

But if we try shrinking this principle down to the quantum level, we start running into some issues with the mechanics. The erasure of arbitrary information in the input states implies eg a loss of entropy from the universe (see No-deleting theorem) and teleporting the output states to some storage destination has the potential to break causality (see No-cloning theorem).

And that's just the stuff that I think I can almost get my head around.

1 hour ago, swansont said:

Atoms of the same isotope are. They obey Bose-Einstein or Fermi-Dirac statistics depending on their spin, which assumes identical particles; the formulation of e.g. the Pauli exclusion principle assumes identical particles.

(Identical here refers to quantum states; you can’t apply a classical-physics-based notion of identical to the situation)

Experimental replication carries with it the notion of statistics and uncertainty. You can’t ignore that, because any physical process has noise

If we call those 2 atoms "systems" ,is there any sense in which they can be considered as "isolated systems" or does /can their quantum state incorporate the system in which they are "embedded"?

Edited 6 hours ago6 hr by geordief

25 minutes ago, sethoflagos said:

(see No-cloning theorem).

It should be noted that the no-cloning theorem says that an arbitrary quantum state can't be copied. It doesn't say that particular quantum states can't be copied. The no-cloning theorem is a consequence of the linearity of quantum mechanics.

9 hours ago, geordief said:

He then said that this could no longer be considered to be the case and that ,in another's words "nature does not herself know what comes next"(to paraphrase)

I believe R Feynman may have been referring to the demise of Determinism in modern Physics.

"Determinism is the philosophical view that all events, including human actions and decisions, are inevitable consequences of preceding causes and natural laws. It suggests that the past and present dictate a single, unavoidable future"

Determinism - Wikipedia

34 minutes ago, KJW said:

It should be noted that the no-cloning theorem says that an arbitrary quantum state can't be copied. It doesn't say that particular quantum states can't be copied. The no-cloning theorem is a consequence of the linearity of quantum mechanics.

... so a particular unitary operator cannot switch between Model Ts, As, Bs etc in the same production line?

10 hours ago, geordief said:

I was listening to a Feynman lecture on the 2 slits experiment and he finished his talk by saying that it used to be thought that if a system was set up accurately enough then it was possible ,in theory to predict its subsequent evolution.

He then said that this could no longer be considered to be the case and that ,in another's words "nature does not herself know what comes next"(to paraphrase)

Might a reason for this be that no physical systems are identical even in theory?

(each system has its own unique place in the overall system)

So ,in practice no experimental setup can ever be precisely replicated -and no subsequent evolution of one system can ever be replicated by setting up another identical system and "prodding" it identically to the other.

A corollary might be that the mathematics used to describe any physical system is always going to be an approximation to what actually happens (which would be unwelcome "news" to anyone who believed mathematics to be fundamental to physical existence-rather than a very,very useful tool)

This must surely depend upon your definition of identical ?

I suggest the best way to approach this situation is a pragmatic one, like the definition of a point particle.

"Identical for my specified purposes"

1 hour ago, studiot said:

This must surely depend upon your definition of identical ?

I suggest the best way to approach this situation is a pragmatic one, like the definition of a point particle.

"Identical for my specified puirposes"

I think I mean for all(physical) purposes.

We know that no matter to what degree of identity we prepare any two systems they will evolve differently.

I wonder if this is due to the "embedding system" ,a property of any two "identical" pairs or a(non-linear?)combination of both.

2 hours ago, MigL said:

I believe R Feynman may have been referring to the demise of Determinism in modern Physics.

"Determinism is the philosophical view that all events, including human actions and decisions, are inevitable consequences of preceding causes and natural laws. It suggests that the past and present dictate a single, unavoidable future"

Determinism - Wikipedia

Yes ,that is how I took it.

3 hours ago, sethoflagos said:

This would imply that it was possible to create multiple exact copies of the system - if you can do it once, then why not do it again and again?

It works in the classical world - we can design an operation that takes in arbitrary states of raw materials and converts them to multiple 'copies' of a predetermined state (Model T Ford, von Neumann probe etc).

But if we try shrinking this principle down to the quantum level, we start running into some issues with the mechanics. The erasure of arbitrary information in the input states implies eg a loss of entropy from the universe (see No-deleting theorem) and teleporting the output states to some storage destination has the potential to break causality (see No-cloning theorem).

And that's just the stuff that I think I can almost get my head around.

Will have to look at those theorems.They seem relevant

33 minutes ago, geordief said:

I think I mean for all(physical) purposes.

We know that no matter to what degree of identity we prepare any two systems they will evolve differently.

I wonder if this is due to the "embedding system" ,a property of any two "identical" pairs or a(non-linear?)combination of both.

Yes ,that is how I took it.

Will have to look at those theorems.They seem relevant

The for all is a problem, the for all physical even more so.

Can two physical things occupy exactly the same space ?

Is orientation important important ?
Say I have two allegedly identical mirrors and I stand them side by side, one with the mirror face towards me the other with its back to me.
If I shine a torch on them I will observe two totally different responses to my light.

3 hours ago, geordief said:

If we call those 2 atoms "systems" ,is there any sense in which they can be considered as "isolated systems" or does /can their quantum state incorporate the system in which they are "embedded"?

They can be, because we can create Bose-Einstein condensates and Fermi gases, which rely on the particles being identical, and do not behave like a mixture of gases under similar conditions. Whether they incorporate the embedding system would likely depend on how strong of an interaction there was between them; making these isolated systems is not easy to do, and they can be disrupted fairly easily

9 minutes ago, studiot said:

Can two physical things occupy exactly the same space ?

Exactly needs to be well-defined here, but I’ve mentioned Bose-Einstein condensates which do that.

44 minutes ago, studiot said:

The for all is a problem, the for all physical even more so.

Can two physical things occupy exactly the same space ?

Is orientation important important ?
Say I have two allegedly identical mirrors and I stand them side by side, one with the mirror face towards me the other with its back to me.
If I shine a torch on them I will observe two totally different responses to my light.

Everything ,including orientation would be important but I was interested as to whether quantum objects/systems in particular could be identical in every regard or whether this could be ruled out in all circumstances.

As Leonard Susskind used to say, "If one electron is in Massachusetts and another is in California, they are not in the same state."

3 hours ago, sethoflagos said:

  4 hours ago, KJW said:

It should be noted that the no-cloning theorem says that an arbitrary quantum state can't be copied. It doesn't say that particular quantum states can't be copied. The no-cloning theorem is a consequence of the linearity of quantum mechanics.

... so a particular unitary operator cannot switch between Model Ts, As, Bs etc in the same production line?

A simple mathematical way to illustrate the no-cloning theorem is as follows:

Suppose one can clone state [math]|\psi\!\!>[/math] as well as state [math]|\varphi\!\!>[/math].

Cloning state [math]|\psi\!\!>[/math] produces tensor product state [math]|\psi\!\!>\!|\psi\!\!>[/math]:

[math]|\psi\!\!>\ \longrightarrow \ |\psi\!\!>\!|\psi\!\!>[/math]

Similarly, cloning state [math]|\varphi\!\!>[/math] produces tensor product state [math]|\varphi\!\!>\!|\varphi\!\!>[/math]:

[math]|\varphi\!\!>\ \longrightarrow \ |\varphi\!\!>\!|\varphi\!\!>[/math]

Linearity of quantum mechanics requires that cloning state [math]|\psi\!+\!\varphi\!\!>[/math] produces:

[math]|\psi\!+\!\varphi\!\!>\ \longrightarrow\ |\psi\!\!>\!|\psi\!\!>\! +|\varphi\!\!>\!|\varphi\!\!>[/math]

But, a clone of state [math]|\psi\!+\!\varphi\!\!>[/math] is actually the tensor product:

[math]|\psi\!+\!\varphi\!\!>\ \longrightarrow\ |\psi\!+\!\varphi\!\!>\!|\psi\!+\!\varphi\!\!>[/math]

[math]= |\psi\!\!>\!|\psi\!\!>\! +|\psi\!\!>\!|\varphi\!\!>\! +|\varphi\!\!>\!|\psi\!\!>\! +|\varphi\!\!>\!|\varphi\!\!>[/math]

[math]\ne |\psi\!\!>\!|\psi\!\!>\! +|\varphi\!\!>\!|\varphi\!\!>[/math]

The above is not saying that states [math]|\psi\!\!>[/math] and [math]|\varphi\!\!>[/math] can't be cloned. But if these two states can be cloned, then the sum state [math]|\psi\!+\!\varphi\!\!>[/math] can't be cloned, proving that arbitrary states cannot be cloned.

45 minutes ago, swansont said:

hey can be, because we can create Bose-Einstein condensates and Fermi gases, which rely on the particles being identical, and do not behave like a mixture of gases under similar conditions. Whether they incorporate the embedding system would likely depend on how strong of an interaction there was between them; making these isolated systems is not easy to do, and they can be disrupted fairly easily

Does that mean that no constituent part of a BE condensate can have any interaction with a neighbouring system but can only interact with it as a group?

Would that in anyway involve faster than light(or instantaneous) transmission of information ?

Or does the BE condensate unravel like a ball of wool when disrupted?

11 minutes ago, geordief said:

Does that mean that no constituent part of a BE condensate can have any interaction with a neighbouring system but can only interact with it as a group?

I think so; as long as it’s a BEC you can’t distinguish individual constituents

11 minutes ago, geordief said:

Would that in anyway involve faster than light(or instantaneous) transmission of information ?

It never does.

11 minutes ago, geordief said:

Or does the BE condensate unravel like a ball of wool when disrupted?

I don’t know about the unravel part; it would act like a cold gas

54 minutes ago, KJW said:

A simple mathematical way to illustrate the no-cloning theorem is as follows:

Unfortunately, your 'simple' involves a notation system that didn't make it into Chem Eng courses in the '70s.

Think crayons and picture books. That's more my level. 😄