Quantum Entaglement and Relativity

[rickolasnice]

Why doesn't quantum entanglement violate relativity?

 

[rangrz]

Because it does not allow for faster than light information travel. The nature of quantum entanglement is statistical, not really causal. If I have two particles entangled, one of these particles will have a "up" spin and the other will have a "down" spin. That property is just intrinsic to them. I can then observe one of the particles and deduce the other particle's spin from that, but the other particle already had that spin and also, I can't transmit any information about my measurement of the spin of particle that I observed faster than light. So it does not violate relativity in the sense of propagating physical information faster than light.

 

[polymath]

If we were able to write down the wavefunction (state vector) of the whole universe, we would probably find out that all particles in the universe are entangled with each other at least to some extent... Therefore every measurement we make on anything will affect the whole quantum state of the universe. But as Rangrz said, there's no way to transmit any information through that effect. Information transfer between two particles requires that there's a coupling between the particles in the potential energy function of the two-particle system. Entanglement does not require this, it can occur even between non-interacting particles.

 

[rickolasnice]

But if you were to change the spin of one, does the others spin not instantly change with it?

 

[polymath]

But if you were to change the spin of one, does the others spin not instantly change with it?

The particle does not have to be in a state where the spin has a definite value (an eigenstate of spin operator). Denote state with spin up with symbol |up> and state with spin down with symbol |down>. These are not the only possible states. Also states

|up> + |down>

or

|up> - |down>

are possible, and if you measure the spin of the particle when it is in these states, you have a 50% change to find spin up and a 50% chance to find spin down (equal chances as the components both have coefficients with absolute value 1). The measurement causes 'collapse' of the state and removes from the state the term that is inconsistent with the result of the measurement. (suppose you measure state |up> - |down> and find spin down, after the measurement the state is -|down>).

A two-particle system can be represented as a product form state vector, like |up>|down> which describes a state where particle 1 has definite spin up and particle 2 definite spin down. An entangled state would be something like

|up>|down> + |down>|up> ,

where the particles have equal chances of either spin up or down, but you can be certain that they have opposite spins. If you measure the spin of one of the particles, also the spin of the other particle will have a definite value after the measurement. The collapse of the state happens instantly no matter how far the particles are form each other, but you can't transmit information in this manner.

Confusing? It certainly is, it took me 2 years of studying QM before I really understood these things...

 

[rangrz]

But if you were to change the spin of one, does the others spin not instantly change with it?

No, not once they are no longer coupled/interacting with each other. One way to entangle the is to create them from the same event...like photo pair production for e.g. (that's when a photon with >1.022MeV energy turns into an electron/positron pair) Those two particles are coupled at the time of the pair production event, and are entangled. However, once they are created, they can be treated as two separate particles and the state of one can change without affecting the other. Even to the point of one of the can be annihilated with another anti-particle (one not from the pair production event) and it won't affect the state of the other one at all.

 

[rickolasnice]

OK thanks guys, i get it now

 

[aussie101]

^ so if there was no living being to observe any of this, would it still exist?

 

[aussie101]

of course i exist, i exist amongst all this, which you do also.
/
yet, i cannot place my physical disruption, in the way of my psychological obstruction; which causes more interruption towards the thought of those to come, and my own preceding endeavors.

Thats very poetic, i like it.

But what I was asking was - what if there was no observer of matter/energy? Would it behave in the same way regardless? Or is that an impossible question to answer?

 

[rangrz]

Thats very poetic, i like it.

But what I was asking was - what if there was no observer of matter/energy? Would it behave in the same way regardless? Or is that an impossible question to answer?

Yes, observer in quantum mechanics has nothing to do a sentient/living being observing it. It just means another physical system that interacts with whatever is being "observed" i.e. an electron can observe a proton by being attracted to it's electric charge. A neutron can be observed by an atom when the neutron scatters off the atom after hitting it. When these events happen, the wave-function collapses and the super-positions of the properties of the systems involved take on a definite value.

 

[polymath]

The mechanism by which interaction with a measuring apparatus induces wavefunction collapse is probably very complex and there's no consensus about it AFAIK... I've never seen a textbook where there's an attempt to explain it.

I think a system has to interact with something more complex than just another particle for wavefunction collapse to occur... Suppose we have an electron and a proton close enough to interact significantly. What's the observable that the proton measures when it interacts with the electron? In a more advanced treatment, the electron and proton can only observe local electromagnetic field strength and there's no 'action at a distance' between them. Their interaction happens indirectly through them both being coupled with the Fourier modes of the EM field between them. Does a 'measurement' happen at the moment when the electron excites a field mode, or at the moment when the proton interacts with this excited mode? Of course you can't have a totally free electron that isn't interacting with any other system, it's always constantly being observed by the EM field around it. Even a neutrino always interacts with the W and Z boson field...

 

[rangrz]

The wave function collapses when a virtual photon that makes that makes up the EM field interacts with one of the particles, thus conveying the physical information about the field/the particle/how the field has been affected by the particle. Say it's a neutron scattering...then it's when the neutron and the other particles probability amplitude of being at the same spot at the same time overlap and it conveys the physical information of it's kinetic energy and it's strong nuclear force charge is observed when a virtual meson from that neutron appears inside the nuclear region of the atom. The combination of it's kinetic energy vs the coupling of it's strong attraction determines how likely it is to be captured. It's Ke vs the binding energy of the nucleus in question determines the probability of induced fission. All of which collapse the wave-function as they are all events that involve observables and state transitions

That's about the best explanation I've seen/heard.

 

[Jabberwocky]

I can wrap my head around quantum mechanics, but gravity I simply just don't get.

 

[polymath]

The wave function collapses when a virtual photon that makes that makes up the EM field interacts with one of the particles, thus conveying the physical information about the field/the particle/how the field has been affected by the particle. Say it's a neutron scattering...then it's when the neutron and the other particles probability amplitude of being at the same spot at the same time overlap and it conveys the physical information of it's kinetic energy and it's strong nuclear force charge is observed when a virtual meson from that neutron appears inside the nuclear region of the atom. The combination of it's kinetic energy vs the coupling of it's strong attraction determines how likely it is to be captured. It's Ke vs the binding energy of the nucleus in question determines the probability of induced fission. All of which collapse the wave-function as they are all events that involve observables and state transitions

That's about the best explanation I've seen/heard.

You seem to take the viewpoint that the 'quantum measurement problem' is not really a problem at all... Well, of course the predictions of the theory don't depend on the interpretation of QM, so it really doesn't matter...

For those readers of this thread who don't have a background in physics, the QM measurement problem is explained from a philosophers point of view in: http://www.csus.edu/cpns/library/Epperson_QM and Logical Causality_Process Studies 38v2.pdf , and in the wiki: http://en.wikipedia.org/wiki/Measurement_problem .

One thing that puzzles me is the following paradox: The EM interaction between two charged particles depends on both their positions and velocities... Therefore, when particle A interacts with particle B, it in effect makes a measurement of the position, momentum and charge of particle B. In a quantum measurement, the wavefunction should collapse into an eigenstate of the observable that was measured. But there is no such thing as a state that is an eigenstate of both position and momentum. Therefore it's unclear whether the interaction between A and B can cause wavefunction collapse. On the other hand, if one thinks about the situation in the rest coordinate system of A, then the interaction depends only on the position of B (magnetic field does not affect a particle at rest), so maybe this is not a paradox after all...

 

[rangrz]

Yeah, I'm not really into the whole sitting in the armchair espousing about the untestable, unfalsifiable interpretations of QM. I'd rather be in the lab. I don't even concern myself with if wave-function collapse or decoherence are physically meaningful concepts, or if they are just unphysical mathematical abstractions that let me make predictions that correspond to empirical reality. It just doesn't matter, a shit load of the abstractions and concepts are obviously unphysical and bordering on absurd. But they work, bitches. That's good enough for me. http://en.wikipedia.org/wiki/Instrumentalism.

Also, the EM, being carried by virtual photons, one can only obtain information the position of where that photon originated from to no better than the wave-length of the photon. That also reduces the issue of observing exactly the position.

 

[rangrz]

Suppose a measurement of an electron's spin component along some direction is being measured. The result can either be "up" or "down". The result of the measurement is automatically communicated to a printer that can either print "up" or "down". If human consciousness is what causes the collapse to the observed state, then the collapse would only occur when someone read the printout, and not before. Now suppose that the printer has just enough ink to print "up", and not enough ink to print "down". Furthermore, if the printer runs out of ink, a bell sounds in a secretary's office. If the secretary hears the bell, a collapse to "down" has clearly occurred before the bell sounded. If the secretary does not hear the bell, a collapse to "up" must have occurred--and no human interaction was necessary at all.

Yeah, pretty much this.

 

[polymath]

Also, the EM, being carried by virtual photons, one can only obtain information the position of where that photon originated from to no better than the wave-length of the photon. That also reduces the issue of observing exactly the position.

I think we'd need a model for a measurement that gives only incomplete information about an observable, and causes only incomplete collapse of the quantum state...

Let's say we have some particle on the x-axis and its wavefunction is a gaussian wavepacket: y(x) = exp(-a(x-x₀)²) (I omit normalization factors for simplicity). Then we make a hypothetical, infinitely accurate measurement of the particle's position by scattering something with very short de Broglie wavelength off the particle. If the measured position is x_m, then after the measurement the state has collapsed to a position eigenstate y(x) = d(x-x_m).

Next we do the same experiment, but measure the position imprecisely by scattering something with a nonzero de Broglie wavelength l. The result of the measurement is now x_m ± dx , where the error dx is of the same order of magnitude as wavelength l. I'd hypothesize that this imprecise measurement does not collapse the wavefunction into an exact position eigenstate, but rather an approximate one: y(x) = exp(-b(x-x_m)²) , where the width parameter b is proportional to 1/l ... Of course this function approximates the Dirac delta function very accurately if the wavelength is very short.

One could probably define a 'fuzzy' position operator whose eigenfunctions are not exact position eigenstates but sharp gaussian spikes centered on some position...

 

[rangrz]

I think we'd need a model for a measurement that gives only incomplete information about an observable, and causes only incomplete collapse of the quantum state...

That makes a good deal of sense, at least intuitively, to me. For the reason that one can argue that every particle in the universe is entangled to some (small) degree, so it should also make sense that a measurement only observes partial information and only causes a partial collapse of a universal wave-function.

As all physical experiments involve scattering particles with non-zero DeBroglie wavelengths, it's always the case that we have at least that much error.

 

[rickolasnice]

Just read this:

When most people describe this interesting process, they’ll describe the information transfer as ‘instantaneous’ or ‘near-instantaneous’. Several research teams have attempted to measure the actual speed seen in the transfer of information in entangled systems, but have failed in one way or another, usually resulting from flawed methodology dealing in quantum nonlocality.

Of course, this violates relativity in the sense that nothing can travel faster than light. At the moment, relativity is clear because you can’t send useful data using quantum entanglement as of yet. Even then, a ton of work is being done in this field and a growing number of physicists believe we’ll achieve faster-than-light communication by cleverly using quantum entanglement to our advantage.

In order to get this measurement, the Chinese physicists entangled pairs of photons, then transmitted half of the pair to receiving units. These receiving units, named Alice and Bob, were positioned 15.3 km apart in an east-west orientation – the receivers were oriented in this fashion to minimize interference from Earth’s rotation, which is a significant factor at this scale. The team then observed the first half of the entangled pair and waited to see how quickly the other half assumed the same state. They repeated this process for over 12 hours to help ensure accuracy of their measurements.

So what were their results? The team came back and said that quantum entanglement transfers information at around 3-trillion meters per second – or four orders of magnitude faster than light. This is a lower speed limit, meaning as we collect more precise data, you can expect that number to get larger. At the moment, our technology and methodologies aren’t sensitive enough to measure speeds at this scale.

http://www.extremetech.com/extreme/...stance-at-least-10000-times-faster-than-light

Edit: Quote is from a post about the link (source).. It's not from the actual source.. although it says the same thing.

 

[rickolasnice]

Anybody wanna help me out here?

That last post seems to think that quantum entanglement is capable of sending information far faster than the speed of light.