Entangled Clocks: Exploring Possibilities

[.Scott]

I just overheard an engineer saying "There are no two clocks in the world that tell identical time". She was describing a time syncing mechanism to another engineer, but it made me think...

In theory, can something large enough to be used as a clock become fully entangled with a copy of itself? For example, could a pair of unstable atomic isotopes be formed that are fully entangled with each other? Or perhaps something based on Neutrino oscillation? Or entangle mesons?

If so, it opens up another line of experimentation - since you don't need to query each member of the pair at the same time.

 

[PeterDonis]

can something large enough to be used as a clock become fully entangled with a copy of itself?

No, because you can't make an exact copy of a quantum state because of the no-cloning theorem.

you don't need to query each member of the pair at the same time

If you don't, how do you know they are both telling the exact same time?

 

[bhobba]

I just overheard an engineer saying "There are no two clocks in the world that tell identical time". She was describing a time syncing mechanism to another engineer, but it made me think...

Was it slow transport?

That one is often forgotten, and even Einstein forgot it in his original papers on relativity.

Its highly unlikely even two highly accurate atomic clocks will tell the same time over a long period - but how long is that if you use slow transport and the gravitational field doesn't vary much?

Interesting question to ask your engineering friend.

Thanks
Bill

 

[.Scott]

No, because you can't make an exact copy of a quantum state because of the no-cloning theorem.

There are such things as entangled particles that will always report the same result when measured appropriately. They share a common quantum state.
Why doesn't the no cloning rule prevent entanglement?

If you don't, how do you know they are both telling the exact same time?

You would start by verifying that if you did measure them at the same time, that you would get the same result. Then you could do Bell type experiments where you change the time difference in the measurement instead of the angle.

 

[PeterDonis]

There are such things as entangled particles that will always report the same result when measured appropriately.

For one measurement, yes. One example would be a pair of photons in the parallel polarization (PP) state, if you're measuring polarization. But the measurement destroys the entanglement, so results of measurements after the first one won't be correlated any more.

They share a common quantum state.

No, they form a combined system that has one, single, entangled quantum state. That is not the same as two copies of a quantum state.

Why doesn't the no cloning rule prevent entanglement?

See above.

You would start by verifying that if you did measure them at the same time, that you would get the same result.

And how would you do that?

 

[.Scott]

For one measurement, yes. One example would be a pair of photons in the parallel polarization (PP) state, if you're measuring polarization.

Can my one measurement be the flavor of the Neutrino?

 

[PeterDonis]

Can my one measurement be the flavor of the Neutrino?

What neutrino? I was talking about photons. What neutrino state are you considering?

 

[Strilanc]

Entangling the clocks doesn't guarantee that they will tell the same time. Entanglement allows you to learn something about A by measuring B, but it doesn't prevent A's state from evolving in the meantime and it doesn't guarantee that you will see A's state at some specific time during that evolution.

For example, suppose you produce an EPR pair $AB = |01\rangle - |10\rangle$, separate them, and begin rotating both around the X axis at 10 degrees per second. If you measure B and find that it's UP at t=10s, that tells you A is DOWN at t=10s. But if you measure A at t=28s, it will be UP instead because it was rotated by an extra 180 degrees in the 18s in between. In order to use B's measurement to infer A's current state, you have to know the time B was measured at and how that relates to the current time at A. Which is the same old clock synchronization problem.

Relatively still applies, too. If A is moving at high speeds relative to B, so that A's time passes half as quickly in B's frame of reference thereby causing A's rotation to also be half as fast, then when you need to wait until t=20s (in B's reference frame) instead of t=10s for A to be DOWN when you measure it (given that you measured B as UP at t=10s).

 

[.Scott]

For example, suppose you produce an EPR pair $AB = |01\rangle - |10\rangle$, separate them, and begin rotating both around the X axis at 10 degrees per second. If you measure B and find that it's UP at t=10s, that tells you A is DOWN at t=10s. But if you measure A at t=28s, it will be UP instead because it was rotated by an extra 180 degrees in the 18s in between. In order to use B's measurement to infer A's current state, you have to know the time B was measured at and how that relates to the current time at A. Which is the same old clock synchronization problem.

But that would be a situation where the change was being applied by external events - something rotating one of particles in the EPR pair.
In the case on the neutrino, it may be changing flavors spontaneously. Can a neutrino EPR pair be created? Obviously there are practical consideration in working with neutrinos. But could the experiment be done in theory? And, in theory, would there be a "Bell Inequality" type correlation when measuring the flavor at different time offsets. Or do we simply not know enough about the flavor-changing process to model it this way.

 

[f95toli]

You still haven't explained what type of experiment you have in mind.

First of all, you need to realize that a "clock" is in reality a "thing" (atom, ion, resonant circuit etc) or a combination of "things" that work at a very well specified frequency (or several frequencies that somehow can be related to each other via e/g/. a comb). I don't understand how you would use a neutrino for this; it does not -as far as I know- have any useful Eucharistic frequency.

Secondly, there are already clocks that use entanglement in various ways; a good example would be clocks that use entangled "clock" and "logic" ions (see e.g. the NIST website).

 

[.Scott]

First of all, you need to realize that a "clock" is in reality a "thing" (atom, ion, resonant circuit etc) or a combination of "things" that work at a very well specified frequency (or several frequencies that somehow can be related to each other via e/g/. a comb). I don't understand how you would use a neutrino for this; it does not -as far as I know- have any useful Eucharistic frequency.

I don't understand your use of the term "Eucharistic". My wife is a Eucharistic minister, perhaps I should ask her?
In any case, neutrinos probably do have some inherent frequencies. From what I read, they are believed to oscillate because of the different masses of their component neutrino types:
https://en.wikipedia.org/wiki/Neutrino_oscillation
or
http://adsabs.harvard.edu/abs/1980PhRvD..22.2227S

Secondly, there are already clocks that use entanglement in various ways; a good example would be clocks that use entangled "clock" and "logic" ions (see e.g. the NIST website).

I am not looking for a method of syncing clocks or telling better time. I am simply wondering if, in theory, it is possible to have a clock or a timer that is entangled with an identical clock or timer such that measuring one would tell you what a corresponding measurement of the other would be. From there, you might be able to deduce something about limitations on how precisely the phase of the clock or time-constant on the timer is.

You still haven't explained what type of experiment you have in mind.

I think I have - but I will give a more specific case:
Say we have found a way to create an EPR pair of neutrinos. When each neutrino in the pair strikes an atomic nucleus, we can determine by the resulting decay particles whether the neutrino has its original identity or has changed. Although there are three possible flavors, for any given neutrino type, only two flavors are possible when detected.
So, with a continuous supply of entangled neutrinos, if they are entangled, I am hoping that whenever each of the is measured at the same time, we get the same decay results in each case - indicating that each neutrino in the pair was in the same phase.
We could then measure the each in each pair at different times to determine the level of correlation that exists as a function of time difference. My guess is that a Bell Inequality would be apparent - because the initial phase of the oscillation is subject to HUP and is only determined at the time of the measurement.

But this is not my area of expertise.
My real question is whether this type of entanglement is theoretically possible.

 

[f95toli]

I don't understand your use of the term "Eucharistic". My wife is a Eucharistic minister, perhaps I should ask her?
In any case, neutrinos probably do have some inherent frequencies. From what I read, they are believed to oscillate because of the different masses of their component neutrino types:
https://en.wikipedia.org/wiki/Neutrino_oscillation
or
http://adsabs.harvard.edu/abs/1980PhRvD..22.2227S

Sorry, not should have been characteristic. Auto-correct typo
The problem is that -as far as I know- the neutrino oscillations are probabilistic; they don't "tick" at a well specific frequency, and I don't think there is a way to probe the energy splitting (assuming there is one) between the states. It is worth remembering that what we are actually probing (in some sort of feedback loop) in when we build a real clock is the energy difference between two states, which can be then be "converted" to a frequency via W=hf. We are NOT measuring spontaneous transitions (in fact, we try to avoid them at all cost). Hence, a system that can spontaneously go from one state to another would be a bad clock.

I am not looking for a method of syncing clocks or telling better time. I am simply wondering if, in theory, it is possible to have a clock or a timer that is entangled with an identical clock or timer such that measuring one would tell you what a corresponding measurement of the other would be. From there, you might be able to deduce something about limitations on how precisely the phase of the clock or time-constant on the timer is.

I don't think this would work even in principle. Note that entanglement will give you correlations; it can't be used to transfer information; which - unless I am misunderstanding something- is what you are proposing.

 

[.Scott]

I don't think this would work even in principle. Note that entanglement will give you correlations; it can't be used to transfer information; which - unless I am misunderstanding something- is what you are proposing.

I am only looking for correlation. And I would then want to continue examining those correlations under different timing conditions.

The notion that neutrino correlations are probabilistic is essential. If they were not, there would be no possibility that the underlying phase was restricted by HUP, and there could be no "entangled flavor phase".

And perhaps that's the key. Presuming that the flavor phase is constrained by HUP, we need to entangle the flavor phase between two neutrinos.

 

[PeterDonis]

the neutrino oscillations are probabilistic; they don't "tick" at a well specific frequency

More precisely: since a typical neutrino state created by a nuclear reaction (e.g., in the Sun) is a superposition of different mass eigenstates (because a typical reaction creates a neutrino in a flavor eigenstate, and flavor eigenstates are not mass eigenstates), and the phase of each mass eigenstate oscillates at a different frequency (the frequency corresponding to its mass), a neutrino that starts out in a given flavor eigenstate will not stay in a flavor eigenstate, and there will be no single frequency at which it oscillates between flavor eigenstates.

 

[Strilanc]

But that would be a situation where the change was being applied by external events - something rotating one of particles in the EPR pair.

The same logic applies if the rotation is just an inherent part of the system. The entanglement can tell you how the state at two abstract times relate to each other, but it won't tell you how to relate those abstract times into what you're actually doing and seeing. So it's not very useful as a clock.

 

[Vanadium 50]

This thread has gone in about a million different directions. Let me try and sweep away some of the brush.

Let's drop neutrinos for the moment, and figure out what we are trying to accomplish before how we are trying to accomplish it. Besides, neutrino oscillations are, despite the name, not primarily an oscillation phenomenon. It's an inteference phenomenon.

The definition of an entangled clock isn't given, but it seems to be a device that will tell you what time a distant clock is reading at that instant. In a Newtonian world, such a device is trivial, as all clocks possesses it. In an Einsteinian world, such a device is impossible, as "at the same instant" is not defined.

 

[l0st]

No, because you can't make an exact copy of a quantum state because of the no-cloning theorem.

Irrelevant to the topic's main question, but is cloning theorem really applicable here? Doesn't no-cloning theorem say, that you can't build a machine to clone arbitrary existing quantum system? That does not seem to prohibit in any way an ability to make some specific system twice.

Also, for practical purposes, does it actually prohibit creation of a clock, that is not an exact copy of original system in some single aspect, but that aspect being irrelevant for the working of a clock? E.g. a clock made of antimatter will work the same (assuming no weird symmetry breaking effect alters the clock behavior as a clock).

 

[PeterDonis]

That does not seem to prohibit in any way an ability to make some specific system twice.

You can run the same preparation procedure multiple times, yes, and thereby produce multiple quantum systems which are in the same state.

I'm not sure at this point how relevant the no-cloning theorem (or the statement you've made about what it doesn't say) is to the OP question; it seems like the issue with the OP may be more an improper understanding of what entanglement means.

does it actually prohibit creation of a clock, that is not an exact copy of original system in some single aspect, but that aspect being irrelevant for the working of a clock?

Obviously we can create multiple clocks that have the same principle of operation, yes. (For example, we have created multiple cesium atomic clocks that all work the same way.) This works because there is no requirement that all of the clocks are in exactly the same quantum state. All that is required is that they all have the same principle of operation (in the case of cesium clocks, they all depend on the same hyperfine transition in the cesium atom).

 

[l0st]

Obviously we can create multiple clocks that have the same principle of operation, yes. (For example, we have created multiple cesium atomic clocks that all work the same way.) This works because there is no requirement that all of the clocks are in exactly the same quantum state. All that is required is that they all have the same principle of operation (in the case of cesium clocks, they all depend on the same hyperfine transition in the cesium atom).

What I meant is that you can in principle create an entangled pair of clocks, one made of matter, another of antimatter. The clocks do not necessarily have to share the same quantum state to behave identically (as clocks).

P.S. I am not trying to answer OP's question. Just clarifying your statement about cloning theorem and its relevance.