The Observer Effect

[Genady]

1 minute ago, geordief said:

 How do we know that a particle is in  a momentum eigenstate and not in a superposition of states?

Generally, we do not.

Physically, as @swansont has mentioned, momentum eigenstate is impossible. So, physically, it is always a superposition. But its range can be very narrow, concentrated very close to an eigenstate.

[geordief]

1 hour ago, Genady said:

Yes, if a particle has a definite momentum, measuring its momentum does not change its state. The same holds for its position

Coming back to you earlier post (hopefully with a better understanding)

So the particle is in a superposition of eigenstates  and you measure its momentum....

Are you saying that

none of the superimposed eigenstates are changed  by the measurement, 

or that jst the momentum eigenstate is unchanged 

or that all the other eigenstates (not including the momentum) are unchanged?

[Genady]

18 minutes ago, geordief said:

Coming back to you earlier post (hopefully with a better understanding)

So the particle is in a superposition of eigenstates  and you measure its momentum....

Are you saying that

none of the superimposed eigenstates are changed  by the measurement, 

or that jst the momentum eigenstate is unchanged 

or that all the other eigenstates (not including the momentum) are unchanged?

If the particle is in a superposition of momentum eigenstates and its momentum is measured, then its state changes and becomes one of the momentum eigenstates (physically, a narrow range around such eigenstate).

 

(It is after midnight here, so the follow up questions might need to wait.)

Edited December 9, 2023 by Genady

[Luc Turpin]

15 hours ago, Genady said:

I struggle to see how linearity or non-linearity can be applied to a world.

A simplistic way on my part of seing it; we use non-linear equations to obtain the weather and determine whether or not we go skiing

[Genady]

2 minutes ago, Luc Turpin said:

A simplistic way on my part of seing it; we use non-linear equations to obtain the weather and determine whether or not we go skiing

So, you mean that our models are non-linear, not our world.

[Luc Turpin]

14 hours ago, KJW said:

Just in case you don't, an operator L() is linear if and only if it satisfies:

L(ψ+ϕ)=L(ψ)+L(ϕ)

Linearity is essential to QM because quantum superposition demands it.

 

 

Helpful! Thank you for not leaving me behind in the discussion. 

Just now, Genady said:

So, you mean that our models are non-linear, not our world.

The opposite. world is non-linear and models linear.

Both should be non-linear.

However, with the discussion that I followed, it appears that non-linear models are readily in use.

My understanding is that weather models are non-linear and that the decision to go skiing or not depends on the precision of the forecast.  Today, I might go skiing because one day forecast are relatively good, while deciding to go skiing next week with forecast in hand, is frought with more imprecision. The forecast says nice weather, but it can change. Out in the world, everyone knows that forecasts have imprecision baked into them and that the more we advance in time, the more the imprecision grows.

This is the nature of weather in the world not predictable with absolute certainty. I may be attributing here a concept of certainty to non-linearity that may be incorrect. Still fumbling with words and their meanings.

[Genady]

40 minutes ago, Luc Turpin said:

world is non-linear and models linear.

In my understanding, world is neither. The concept of linearity is not applicable to world.

[joigus]

Linearity is applied to sets of variables and how they depend on each other. So it's not like a presence, "linearity is here" or "it smells of non-linearity".

 

[Luc Turpin]

28 minutes ago, Genady said:

In my understanding, world is neither. The concept of linearity is not applicable to world.

But, does the implications of linearity not  manifest themselves on the world? Imprecise measurement -imprecise world; we are not living in a clockwork world, even trains get delayed by the unexpected

[sethoflagos]

1 hour ago, Luc Turpin said:

This is the nature of weather in the world not predictable with absolute certainty. I may be attributing here a concept of certainty to non-linearity that may be incorrect. Still fumbling with words and their meanings.

From the Lorentz interpretion of chaos I mentioned above, it is possible for some number of associated parameters to evolve under the action of linear operations in entirely deterministic fashion and yet produce significantly unpredictable futures such as the weather phenomena you describe.

The (local) universe is not big enough to define general numbers with suffient absolute precision to prevent this from being the case.

However, it is not the full story. For example, it seems implausible for the above mechanism to produce all emergent properties not explicitly existing in the fundamental low level interactions. Yet, everyday experience tells us that we are likely to hear dull music in supermarkets.  

Edited December 9, 2023 by sethoflagos
artistic license

[Luc Turpin]

Is everything in the world not dependent on initial conditions?

[joigus]

1 minute ago, Luc Turpin said:

Is everything in the world not dependent on initial conditions?

Not necessarily. Thermal equilibrium isn't.

[Luc Turpin]

And outcome not predictable with absolutely certainty?

[Genady]

16 minutes ago, Luc Turpin said:

But, does the implications of linearity not  manifest themselves on the world? Imprecise measurement -imprecise world; we are not living in a clockwork world, even trains get delayed by the unexpected

No, it they do not. All your references - measurements, clockwork, unexpected - refer to our use of models. They say nothing about the world.

[joigus]

1 minute ago, Luc Turpin said:

And outcome not predictable with absolutely certainty?

Outcome of what? Thermodynamics of system can be predicted under certain circumstances. Where molecule X is going to be, no.

Absolute certainty doesn't exist.

[swansont]

10 hours ago, Genady said:

Yes, it is completely uncertain before and after the measurement. I call this, "does not change."

If you don’t know where it is, how do you know it hasn’t changed position?

[joigus]

x-posted with @Genady

[Luc Turpin]

4 minutes ago, joigus said:

Not necessarily. Thermal equilibrium isn't.

Noted

3 minutes ago, Genady said:

No, it they do not. All your references - measurements, clockwork, unexpected - refer to our use of models. They say nothing about the world.

Noted, need to think before answering

[Genady]

2 minutes ago, swansont said:

If you don’t know where it is, how do you know it hasn’t changed position?

It is not that it is somewhere, but we don't know where. We know that it does not have a definite position.

[Luc Turpin]

4 minutes ago, joigus said:

Outcome of what? Thermodynamics of system can be predicted under certain circumstances. Where molecule X is going to be, no.

Absolute certainty doesn't exist.

Is it not what i am trying to say that absolute certainty does not exist

[joigus]

1 minute ago, Luc Turpin said:

Noted

I really don't want to butt in on the very interesting discussion you were having with Seth. But here's an interesting point: It is precisely because microscopic variables are so extremely sensitive to initial conditions, these systems (called ergodic) become highly indifferent to initial conditions (reach thermal equilibrium quite efficiently) macroscopically.

How about that for pointing out that nothing is as simple as it might seem in physics?

[Luc Turpin]

9 minutes ago, Genady said:

No, it they do not. All your references - measurements, clockwork, unexpected - refer to our use of models. They say nothing about the world.

What is your definition of world?

[Genady]

8 minutes ago, Luc Turpin said:

What is your definition of world?

I don't have a definition. I refer with this word to an object of scientific studies.

[Luc Turpin]

1 hour ago, Genady said:

I don't have a definition. I refer with this word to an object of scientific studies.

And i use world as the one that surround.use, still need to think before answering

[sethoflagos]

1 hour ago, joigus said:

I really don't want to butt in on the very interesting discussion you were having with Seth. But here's an interesting point: It is precisely because microscopic variables are so extremely sensitive to initial conditions, these systems (called ergodic) become highly indifferent to initial conditions (reach thermal equilibrium quite efficiently) macroscopically.

Please feel free to butt in! I was hoping someone would raise the topic of ergodicity as it is relevant,

Thermodynamic equilibrium is often presented as a dull, featureless system state, but it seems quite the opposite to me.

If it is interpreted as the condition of maximum quantum entanglement of its constituent parts, each of those linkages existing as superpositions all of their possible outcome states, then in at least some limited sense, thermodynamic equilibrium can be seen as a superposition of all possible arrangements of its constituent parts consistent with its geometry, chemical makeup and total energy content. That is, that all structures that can possibly exist within that state do so simultaneously at least within the non-material abstractions of the mathematical space wherein the superpositions reside prior to 'being looked at' (ahem).  

Ergodicity (the limitation that in the concrete, individual microstates can only be accessed by stepwise progression from a neighbour) places limits on this picture, but I hope there is some truth in it as it helps me get my head around quite a few practical situations that are otherwise difficult to comprehend.

For instance, abiogenesis becomes considerably less problematic if all necessary component building blocks continuously coexist at least to some degree when conditions render it a non-zero possibility, even if that space is temporarily abstract rather than concrete.