Do entangled systems have parts?

[PhilosNS1]

Some say that there are parts but their properties depend on the whole. But if we cannot assign properties to the 'parts' of an entangled system, what can it be to be a 'part' or any kind of entity in the first place? Can we say that there are parts but that they are not independent? What can 'part' mean in this situation?

Please assume that I know as much quantum mechanics and philosophy of same as you. If not, I will ask for clarification, but I am fairly well educated in them. Yet, still I am puzzled by it all. Alas.

 

[DrChinese]

Welcome to PhysicsForums!

An entangled system can be considered as a single something without well defined independent component parts.

 

[PhilosNS1]

Well, that is one way to answer. But what does it mean to be a component part if it is not well defined or independent?

 

[xts]

My positivistic nature demands to ask for definition of 'part' before answering such question.
I don't feel brave enough to propose defendably precise definition - let's stay with common meaning: less than a whole, but constituting self-contained, independent entity.
Don't pull me into dispute what 'entity' means!

Let's take a pair of spin-entangled electrons, one of them kept in lab, the second transported to friendly lab at Mars.
Our electron is just a normal electron, indistinguishable from any other we may separate from any atom. We may forget about its entangled sister and install it in some atom. It is self-contained entity by the same means as we could use about any other particle.
Independency - see below.
Do those electrons constitute any 'whole' - again question about definition. They definitely have something in common, more in common, than any of them have with any other electron of the universe.

Thus my taste fully accepts the term 'part' being used regarding entangled particles.

but their properties depend on the whole.
I can't agree. I would rather say that there are some properties of the whole, making no sense in regard of single part.
Actually those properties constitutes 'the whole' of entengled particles.

Can we say that there are parts but that they are not independent?
Yuck! Another word to be defined: 'independent'. As for my taste, two objects are independent if whatever happens to one of them has no influence on other. If we agree for that definition, entangled particles are independent.

What can 'part' mean in this situation?
My Occamian nature asks if we really need some special definition of 'part', other than common meaning (which should however be more precisely defined than I've done above):
wheels and engine are parts of the car, electron and proton are parts of hydrogen atom, etc.

 

[PhilosNS1]

1. Yes, the nuts and bolts of the question must be based on relevant and defensible definitions of 'part', 'independent' and such.

2. I don't think you can incorporate one pair of an entangled pair in an atom and retain the entanglement--the interaction will disentangle them.

3. Your definition of 'independent' suggests that when something happens to one of the pair then you can measure 'influence' on the other. Again, once you do something to the one, there is no more entanglement, correct? So the definition looses meaning, does it not?

4. A hydrogen atom is an entangled system, so this cannot be used in the definition of 'part'. Also, examples don't make a definition.

Sorry to be a stickler. No, actually, I am not--this is the important part.

 

[xts]

Ad.2 - True, but that was not my point. I wanted to illustrate, that an electron originating as a member of entangled pair is exactly the same as electron originating from any other process.

Ad.3 - my definition of 'independency' is a general one, based on common meaning. It doesn't utilize QM at all, but may be used also to QM phenomena. I'am not going to force that definition if you have better.
3.A. (Quantum Mechanical remark) You've fallen into pitfall of reality-without-measurement paradox. In order to say anything about particle you must do something to it. In order to see entanglement you must measure both particles and compare results. I see no sense to speak about any QM phenomenon assuming its reality in abstraco measurements.
3.B. Your definition of 'independent' suggests that when something happens to one of the pair then you can measure 'influence' on the other
Even stricter: if I manipulate one of the pair, then the effect of manipulation may be discovered examining the second of the pair. 'Manipulate' ::= do something which may be done on multiple ways, and the choice of the way is external to our system

Ad.4 - You are right, I gave examples, not a definition. And, as I told, I feel not brave enough to provide precise definition. I just illustrate what cases should be covered by any acceptable (for me) definition, to be consistent with my non-precise, colloquial meaning of the word.

Ad. being stickler - not a problem. Often I am the one too...

Ad.1 (at the end, as it is a kind of summary). My common-sense-empiric nature tells me that it is not so important. We may accept such definition or another. It does not affect our knowledge about the world, nor our Weltanschauung.
Its importance is similar to the problem if 'turquoise' is 'green' or 'blue'. (Oh, that's soooo important! Don't I care if my shirt is blue or green?)
Sometimes (pretty often) we use non-precise words. If the precission is required - we don't use such words like 'part', 'existence', 'dependence', etc. - then we use the language of mathematics and strict scientific terms and we buy shirts of the RGB=(48, 214, 200).

 

[atyy]

There is a related discussion in http://arxiv.org/abs/quant-ph/0312059, section IIIA "Resolution into subsystems".

 

[PhilosNS1]

Perhaps speaking in mathematics is the way to proceed.

 

[PhilosNS1]

Thanks, atyy.

 

[xts]

Well, mathematics and strict scientific languiage is too far from our everyday experience to be sufficient to create our intuitions, understanding, Weltanschauung. It is even insufficient to teach us how to use its own precise terms. Euclid had to define 'point' as 'is that which has no part'. You must anchor precise language in colloquial one.
So I see attempts to find perfect definitions of terms like 'part' as unimportant. They may - in the best case - move us a step further on the never-ending path of defining words.
As long, as we understand what happens in experiments, and we are able to analyze thought-experiments (e.g. we are able to answer if entanglement phenomena may be used to construct the machine allowing me to inform my yesterday's me what was/will be the lottery numbers), we are gathering some knowledge and understanding.
If we dispute which sentence of 'entangled particles are parts of the entangled systems' / 'entangled system is an indivisible wholly holistic whole' is true, we learn nothing about the worLd. We learn only what meaning we had assigned to words, we use in the dispute (and only in this dispute, as the same words we use in colloquial talks in different meanings)

 

[MrDementao]

As for my taste, two objects are independent if whatever happens to one of them has no influence on other. If we agree for that definition, entangled particles are independent.[\i]

If we agree in this definition, entangled particles are dependent. A measurement in one side changes the quantum state (description, properties, etc) of the other side. That is precisely the point in quantum entanglement.

About the original question, you should treat an entangled particle as a single indivisible entity, otherwise you fall in paradoxes and ambiguities. Read Asher Peres book, Quantum Theory Concepts and Methods.

 

[xts]

A measurement in one side changes the quantum state (description, properties, etc) of the other side. That is precisely the point in quantum entanglement.

That is precisely the point of "spooky action" assuming reality model.
Propose please an experiment (not requiring any communication with the other branch) allowing to determine if the state got changed or not as a result of measurement done in the other branch.

As long as there is no such recipe it is not a particle affected by 'the influence' but only your mathematical model you use to describe it. Nothing empirically verificable is influenced.

 

[MrDementao]

That is precisely the point of "spooky action" assuming reality model.
Propose please an experiment (not requiring any communication with the other branch) allowing to determine if the state got changed or not as a result of measurement done in the other branch.

As long as there is no such recipe it is not a particle affected by 'the influence' but only your mathematical model you use to describe it. Nothing empirically verificable is influenced.

Nope, any experiment that observes the violation of a Bell-inequality precisely verifies the "spooky" influence of one particle into another.

But I can describe one for you. If you take the spin-singlet state (maximally entangled), initially the local states (Alice and Bob states) are maximally entropic states (nonpure, mixed states). But, if you perform a local measurement in, say, Alice's state, Bob's will colapse to a pure state. All physical properties of Bob's state change. No superluminal stuff here, because Bob don't know into which state he has collapsed. The change can be verified doing quantum tomography afterwards.

Mathematically, take a bipartite-entangled state, apply a local projection operator on the joint state, take the partial trace of Alice's subsystem and see that Bob's state is not the same.

 

[xts]

Nope, any experiment that observes the violation of a Bell-inequality precisely verifies the "spooky" influence of one particle into another.

But I can describe one for you. If you take the spin-singlet state (maximally entangled), initially the local states (Alice and Bob states) are maximally entropic states (nonpure, mixed states). But, if you perform a local measurement in, say, Alice's state, Bob's will colapse to a pure state. All physical properties of Bob's state change. No superluminal stuff here, because Bob don't know into which state he has collapsed. The change can be verified doing quantum tomography afterwards.

Mathematically, take a bipartite-entangled state, apply a local projection operator on the joint state, take the partial trace of Alice's subsystem and see that Bob's state is not the same.

Could you say the same in simple words, understandable to a humble peasant?
What Alice should measure on her photon in order to know if Bob performed measurement on his one or if Bob's photon is still in 'unmeasured' state?

 

[MrDementao]

With a single photon she can't say anything. This is an important point. She can't tell if Bob obtained + or - in his measurement, unless Bob tells her his outcome.

But there is the influence, since repeating the experiment many times you observe a statistical deviation (Bell-inequality violation) of what would be seen assuming no influence. See wikipedia on Bell's Theorem.

This is the standard explanation. There is a long debate about this nowadays and maybe there is not an actual influence. Maybe everything is masked by the detection efficiency, that is still low in the experiments. But with the data we have today, and with different approaches like contextuality, the physicists tend to agree that there is the influence.

Questions much appreciated so far :)

 

[xts]

With a single photon she can't say anything.

That's what I call 'lack of influence'

She can't tell if Bob obtained + or - in his measurement, unless Bob tells her his outcome.

She even can't tell if Bob obtained any result.
Alice cannot analysing her photon determine if Bob measured his photon or not.
So why do you claim that act of measurement on Bob's side influenced anything on Alice's side?

But there is the influence, since repeating the experiment many times you observe a statistical deviation

I call it correlation. But why influence?
Is the fact that I see the sun shining (I live in Europe) influences night/day condition in Australia?
These are correlated, but I would never say, that the fact I am looking out the window has 'influence' on Australia!
And the fact that correlation between entangled pair is more complex than between Europe/Australia day/night doesn't change the difference between 'influence' and 'correlation'.
'Influence' implies detectable causality - 'correlation' doesn't.

 

[MrDementao]

The quantum state of Alice has changed after Bob's measurement. So, its physical properties, like spin, have changed. Alice can't determine this alone, but the change occurred. If Bob say to her his outcome, she knows that her state changed. And it was not the communication that changed the state, it was the measurement of Bob on his state. For me this is an influence.

Okay, I agree that the best name is correlation, but it is not a classical correlation like you described. With this kind of quantum correlation you can, for example, teleport a quantum state. You can't influence Australia by looking in the window, because Australia is a macroscopic classical state.

 

[xts]

And it was not the communication that changed the state, it was the measurement of Bob on his state.

Why do you think so (say it in empirically verifyable words, not using metaphysical prassumptions) if that may be checked only after Bob communicates his results?

Take an experiment with Alice and Bob in relative motion, making measurements such that from each other perpective he/she makes it first. (e.g.: http://arxiv.org/abs/quant-ph/0002031v3)

Does Alice's measurement "influences" Bob's photon, or maybe Bob's measurement "influences" Alice's photon?

 

[MrDementao]

Why do you think so (say it in empirically verifyable words, not using metaphysical prassumptions) if that may be checked only after Bob communicates his results?

Take an experiment with Alice and Bob in relative motion, making measurements such that from each other perpective he/she makes it first. (e.g.: http://arxiv.org/abs/quant-ph/0002031v3)

Does Alice's measurement "influences" Bob's photon, or maybe Bob's measurement "influences" Alice's photon?

Oh man, I didnt think you would go this far XD.

I have thought before in a kind of paradox with observers going away from each other at light-speed. With a third observer, the one in which the detections are simultaneous, you have some quantitative surprises...

You can't tell which one influenced the other. In relativistic scenario this is meaningless. But I would say you can tell there is an influence. I stop here, is beyond my current power.

 

[xts]

You can't tell which one influenced the other. [...] But I would say you can tell there is an influence. I stop here, is beyond my current power.

OK then - I'll leave you for a weekend with purely lexical problem:
can you, being consistent with common meaning (Oxford dictionary, Webster's...) say that 'A influences B' if event B is earlier than A.