# Superposition vs. Causality

Hi, I'm new, both here and to the quantum world.

I understand that an entangled pair cannot violate causality, because by analyzing half of that pair, one cannot determine whether the particles are in a superposition of states or not. Since there is no way to determine if a given entangled pair is in a superposition of states, how do we even know that pairs can be in a superposition of states to begin with?

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DrChinese
Gold Member
Since there is no way to determine if a given entangled pair is in a superposition of states, how do we even know that pairs can be in a superposition of states to begin with?
Good question, and welcome to PhysicsForums!

The answer is that entangled pairs produce statistics that are different from mixed (product) state pairs. So they are demonstrated to be entangled after the fact by analysis of measurements.

Entangled pair production is something which can be predicted from quantum mechanics. There is no analog for this in the classical world - in which all particle pairs are always product state (also called factorizable).

It is somewhat subtle. The concept of a quantum state refers not only to the quantum system alone, but also to the "preparation procedure". Some preparation procedures will result in mixed states when applied many times. Imagine switching repeatedly between two different preparation procedures randomly, each of which separately would produce you a system in a pure state. You will get an ensemble described by a mixed state.

The concept of a quantum state refers not only to the quantum system alone, but also to the "preparation procedure". Some preparation procedures will result in mixed states when applied many times.
That makes sense. I suppose you can't prepare an already entangled particle without losing the entanglement?

That makes sense. I suppose you can't prepare an already entangled particle without losing the entanglement?
You can. The preparation instruction may read "Do nothing" or, weaker, "Do nothing evil". And there can be many ways of doing nothing evil. For instance you may try to carefully ("adiabatically") move your quantum device to another place in the lab, to let the cleaning lady to mope the floor.

For instance you may try to carefully ("adiabatically") move your quantum device to another place in the lab, to let the cleaning lady to mope the floor.
Hi, I noticed that you're online. I have a couple of questions for you (assuming that the OP's question has been more or less satisfactorily answered) that are slightly off topic. First, have you ever actually had to move anything for a cleaning lady (ok, not really a serious question, but I'm curious nonetheless). And, second, how do you, as a mathematical physicist, conceptualize an underlying reality? Do you think of it as being fundamentally waves in media and particles being emergent phenomena, or what? This isn't entirely off-topic since the OP is asking about superposition (a necessary component of any wave theory?) and causality. Anyway, just curious about your musings on reality.

Well, reality is a something that kicks back if you kick it. Some people are more sensitive than others, so they experience a richer reality. As for waves and particles - quantum theory is only about 100 years old. I don't think it is enough to fully comprehend its place and its role. So, I am inclined to think of it as of an efficient tool for describing, and partially controlling, a class of important phenomena. The apparent clash between relativity and quantum theory tells us that something very important is yet to be discovered. This something important may well include the proper understanding of the wavy part of the reality.

Concerning the cleaning lady part: in theory cleaning ladies are supposed not to touch or move anything in the lab. But when you see a dense and still growing spider web in the corner - you may be inclined to move your equipment a bit, adiabatically, to let the cleaning lady take some care of the sensitive motion detectors installed by the spiders.

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Well, reality is a something that kicks back if you kick it. Some people are more sensitive than others, so they experience a richer reality. As for waves and particles - quantum theory is only about 100 years old. I don't think it is enough to fully comprehend its place and its role. So, I am inclined to think of it as of an efficient tool for describing a class of important phenomena. The apparent clash between relativity and quantum theory tells us that something very important is yet to be discovered. This something important may well include the proper understanding of the wavy part of the reality.

Concerning the cleaning lady part: in theory cleaning ladies are supposed not to touch or move anything in the lab. But when you see a dense and still growing spider web in the corner - you may be inclined to move your equipment a bit, adiabatically, to let the cleaning lady take some care of the sensitive motion detectors installed by the spiders.
Thanks, that was enjoyable.