Examples of systems that evolve deterministically

[Blue Scallop]

Please give examples of systems where the state evolves deterministically according to the Schroedinger equations where there are not yet measurements that can produce probabilistic outcomes.

I'd like to understand how big the systems can get where you can still entangle with the systems avoiding any measurements.

 

[PeterDonis]

I'd like to understand how big the systems can get where you can still entangle with the systems avoiding any measurements.

The only way to know whether you've produced an entangled state is to make measurements. So what you're asking isn't really answerable as you ask it.

A better question would be how large can systems be and still show quantum interference effects when measurements are made? For example, how large can systems be and still show an interference pattern in a double-slit experiment? AFAIK this experiment has been done successfully with buckyballs (60 carbon atoms), but I don't know if it has with anything larger.

 

[Blue Scallop]

The only way to know whether you've produced an entangled state is to make measurements. So what you're asking isn't really answerable as you ask it.

A better question would be how large can systems be and still show quantum interference effects when measurements are made? For example, how large can systems be and still show an interference pattern in a double-slit experiment? AFAIK this experiment has been done successfully with buckyballs (60 carbon atoms), but I don't know if it has with anything larger.

For molecular systems, they are entangled even if you don't make measurements.
Now if the molecular systems are entangled with the environment and decohered.. it doesn't mean there is measurement.
I'm trying to distinguish decoherence and measurements. Many confuse them together and thought decoherence is automatically measurements. But it is not. So I wonder what kind of systems can have decoherence with environment but no measurements done.. ? This inquiry is assuming the wave function has objective existence and it can evolve deterministically without our intervention to illustrate the concept better because for the formalism where the wave function is just device or tool used by humans, then my questions won't make any sense.

 

[PeterDonis]

For molecular systems, they are entangled even if you don't make measurements

That's not the point. The point is, how do we know this fact? By making measurements on these systems. From various measurements we can deduce what the states of the systems are in between measurements. So you can't "avoid any measurements" and still know anything about the systems.

what kind of systems can have decoherence with environment but no measurements done..

It depends on what you consider a "measurement"; that is not a precise concept in quantum mechanics. For example, any macroscopic object, like you or me or a table or chair, could be said to be constantly "measuring itself"--it is constantly undergoing decoherence simply because there are so many atoms in it and they are constantly interacting with each other. But nobody is actually recording any "measurements".

 

[Blue Scallop]

That's not the point. The point is, how do we know this fact? By making measurements on these systems. From various measurements we can deduce what the states of the systems are in between measurements. So you can't "avoid any measurements" and still know anything about the systems.
It depends on what you consider a "measurement"; that is not a precise concept in quantum mechanics. For example, any macroscopic object, like you or me or a table or chair, could be said to be constantly "measuring itself"--it is constantly undergoing decoherence simply because there are so many atoms in it and they are constantly interacting with each other. But nobody is actually recording any "measurements".

I know that in our world.. we can only access the orthogonal states and only the measurement results. No problem about that. But supposed, for sake of discussion, the wave function is objective like in the MWI variant where there are only state vectors.. and supposed in the chair, all the position bases (plural of basis) were nullified somehow (say by enclosing the chair with Hilbert bubble segretor and all bases nullified), what would become of the chair? Would it turn invisible? Let's say the chair become pure nonorthogonal states.. and if invisible can you still touch it?

And furthermore, after the position bases were brought back.. can the chair identity be recovered or would they become ashes or blob because the position bases can't be stored in the orthogonal states?

Again, this is to emphasize it's just for sake of discussion and not wildly speculating and it's just to understand the concept, and not saying it could occur. Thank you.

 

[PeterDonis]

supposed in the chair, all the position bases (plural of basis) were nullified somehow (say by enclosing the chair with Hilbert bubble segretor and all bases nullified)

Basis vectors are part of our mathematical model of reality, not reality itself. You can't change reality by changing your mathematical model.

Hilbert space is an abstract mathematical space, not a physical space. You can't "put" anything into a Hilbert space. It's part of the mathematical model.

it's just for sake of discussion and not wildly speculating

Sorry, but you are wildly speculating, whether you realize it or not. What you're describing makes no sense. See above.

 

[Blue Scallop]

Basis vectors are part of our mathematical model of reality, not reality itself. You can't change reality by changing your mathematical model.

Hilbert space is an abstract mathematical space, not a physical space. You can't "put" anything into a Hilbert space. It's part of the mathematical model.

I mean physical objects are simply state vectors with bases.. is it not? state vectors form the Hilbert space.. so maybe I use wrong language that one can put anything in the Hilbert space, it is the object itself. I was just asking what would happen if the bases were temporarily disable and the object become pure nonorthogonal state, instead of orthogonal states..

Sorry, but you are wildly speculating, whether you realize it or not. What you're describing makes no sense. See above.

 

[PeterDonis]

physical objects are simply state vectors with bases.. is it not?

No. Physical objects are physical objects. State vectors are mathematical objects that appear in mathematical models. They are not the same.

I was just asking what would happen if the bases were temporarily disable

And my response is that there is no physical action you can perform that does this. So it's nonsense to ask what happens if you do it, since you can't do it, not even in principle. Choosing basis vectors, or refusing to choose them, is something you do in the mathematical model, and it doesn't correspond to anything you can do in the actual, real, physical world.

 

[Blue Scallop]

No. Physical objects are physical objects. State vectors are mathematical objects that appear in mathematical models. They are not the same.

Is it not wave function is related to the state vector? They say physical object is wave function that becomes orthogonal when measurements are made.. so how can physical object not be wave function (state vector)??

And my response is that there is no physical action you can perform that does this. So it's nonsense to ask what happens if you do it, since you can't do it, not even in principle. Choosing basis vectors, or refusing to choose them, is something you do in the mathematical model, and it doesn't correspond to anything you can do in the actual, real, physical world.

 

[PeterDonis]

Is it not wave function is related to the state vector?

They are both mathematical objects that appear in mathematical models.

They say physical object is wave function

Who says? Please give a reference to a textbook or peer-reviewed paper that says that. Pop science sources don't count.

 

[Blue Scallop]

They are both mathematical objects that appear in mathematical models.
Who says? Please give a reference to a textbook or peer-reviewed paper that says that. Pop science sources don't count.

What are physical object then if not mathematical object?

In Bohmian, physical objects are the local particles being pushed by quantum potential and wave function.
In MWI, physical objects are state vectors.
In Copenhagen or the Orthodox. Physical objects appear ruled by born rule.

So it depends on your thought of them. If the above is not right. What then are physical object? About reference. I thought the textbook or peer reviewed paper expand on the above basic. In a brief paragraph. Please share what is a physical object or particle if the above are all wrong. Thanks.

 

[PeterDonis]

What are physical object then if not mathematical object?

Um, isn't the difference obvious?

Physical objects are the things you and I are made of; the things we make measurements of; the things that cause the phenomena we observe.

Mathematical objects are abstractions that we use, among other things, to build models in physics. If you honestly can't tell the difference between a mathematical model of something and the thing itself, I'm not sure we can even have a discussion.

 

[Blue Scallop]

Um, isn't the difference obvious?

Physical objects are the things you and I are made of; the things we make measurements of; the things that cause the phenomena we observe.

Mathematical objects are abstractions that we use, among other things, to build models in physics. If you honestly can't tell the difference between a mathematical model of something and the thing itself, I'm not sure we can even have a discussion.

What's the matter. I thought it was universally accepted now that physical objects can only be modeled by math. The relationship is so intimate that many believe physical object is the mathematical vectors themselves (like Tegmark who wrote the Mathematical Universe). And the reason we see objects as solid is because our body particles are modeled and possibly made of math too (wave functions).. so math interacting with math has it's own world.

If you don't believe physical object are not only modeled by math but they are nothing but the math equations themselves. What then are physical object? Can you show any reference about your claim that a particle is not a wave function? What is it then if not a wave function??

 

[PeterDonis]

@BlueScallop, at this point we are discussing philosophy, not physics, and this is a physics forum so such a discussion is off topic. Thread closed.