# B Can entangled particle pairs be measured at the same time?

#### Quantum Alchemy

Has there been an experiment where 2 particles that are entangled are measured at the same time? If so what was the result?

Can any observer occupy the same frame of reference down to an electron? Don't we all exist at different times based on our frame of reference so none of us can share the same present? Can we even talk about a frame of reference with an electron that's a point particle with zero volume?

Doesn't that also mean we're looking at entanglement in time as well as space if 2 entangled particle pairs can't share the same reference frame?

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#### Nugatory

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Has there been an experiment where 2 particles that are entangled are measured at the same time? If so what was the result?
The experiment has been done with the two measurement events being spacelike separated(and if you do the experiment with photons, as is usually done, it’s somewhat hard to do it any other way). “Spacelike separated” is the formal relativity-aware way of capturing your intuitive notion of “at the same time”: there is some inertial reference frame in which the the two events are simultaneous. So the answer to first question above is “yes”.

And when this was done, exactly the predicted entanglement effects were observed.

Can any observer occupy the same frame of reference down to an electron?
Yes, because....
Doesn't that also mean....entangled particle pairs can't share the same reference frame?
No. Everything is always in all frames; a frame is just a mathematical rule for assigning coordinates to points in spacetime (like latitude and longitude are a convention for assigning coordinates to points on the surface of the earth).

#### Quantum Alchemy

The experiment has been done with the two measurement events being spacelike separated(and if you do the experiment with photons, as is usually done, it’s somewhat hard to do it any other way). “Spacelike separated” is the formal relativity-aware way of capturing your intuitive notion of “at the same time”: there is some inertial reference frame in which the the two events are simultaneous. So the answer to first question above is “yes”.

And when this was done, exactly the predicted entanglement effects were observed.

Yes, because....No. Everything is always in all frames; a frame is just a mathematical rule for assigning coordinates to points in spacetime (like latitude and longitude are a convention for assigning coordinates to points on the surface of the earth).
Thanks for the response, also can you point me to the paper that carried out the experiment? I would like to read it.

Also, how can everything share the same reference frame when you're looking at everything as it were in the past. Even when you look in the mirror, you're looking at yourself in the past.

So if I'm standing in my kitchen at the fridge, my fridge is in a different past relative to me than my microwave across the room. The door is even further away, so it's in a different frame of spacetime in my past relative to me standing at the fridge.

So doesn't my fridge, microwave and door all share different frames of reference at different points of spacetime relative to my position standing in front of the fridge?

#### Nugatory

Mentor
Also, how can everything share the same reference frame when you're looking at everything as it were in the past. Even when you look in the mirror, you're looking at yourself in the past.
“Reference frame” doesn’t mean anything like what you’re thinking, but the quantum physics forum isn’t the place to work through this. The first few chapters of Taylor and Wheeler’s book “Spacetime Physics” explains the concept at a (barely) high school level, and someone reading this thread will probably know of a good online explanation.
But basically a reference frame is just a convention for putting numbers
into statements of the form “This event happened at position $x,y,z$ and time $t$”. I can say that a firecracker exploded three meters in front of me and five meters to my left at midnight EST, or I can say that it exploded at a particular latitude and longitude at 5 AM GMT - same explosion, same point in space and time, different numbers.

Further questions about reference frames #hould happen in the relativity forum .

#### Nugatory

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Thanks for the response, also can you point me to the paper that carried out the experiment? I would like to read it.
I can’t point you to “the” experiment because so many of this type have been done. Consider that if you start with the most naive version - a source generates a pair of entangled particles and sends them in opposite directions towards detectors - just putting the source exactly midway between the two detectors will give you your simultaneous measurements.

But if you’re only going to look at one experiment, you could do worse than https://arxiv.org/pdf/1508.05949.pdf which covers spacelike separation of the two measurements and a whole bunch of of stuff as well.

#### Quantum Alchemy

“Reference frame” doesn’t mean anything like what you’re thinking, but the quantum physics forum isn’t the place to work through this. The first few chapters of Taylor and Wheeler’s book “Spacetime Physics” explains the concept at a (barely) high school level, and someone reading this thread will probably know of a good online explanation.
But basically a reference frame is just a convention for putting numbers
into statements of the form “This event happened at position $x,y,z$ and time $t$”. I can say that a firecracker exploded three meters in front of me and five meters to my left at midnight EST, or I can say that it exploded at a particular latitude and longitude at 5 AM GMT - same explosion, same point in space and time, different numbers.

Further questions about reference frames #hould happen in the relativity forum .
Yes, but three meters in front of you are at a different point in spacetime because you're seeing it as it were in the past so how can you and the explosion share the same reference frame?

For instance, if the Sun exploded, you will see it 8 minutes later. So you would see the explosion of the sun at a different reference frame on earth than the actual explosion which occurred 8 minutes earlier.

You then look at entanglement in time:

Entanglement Swapping between Photons that have Never Coexisted

ABSTRACT
The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the nonlocality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spacelike separation, but also to particles with timelike separation. In order to demonstrate these principles, we generated and fully characterized an entangled pair of photons that have never coexisted. Using entanglement swapping between two temporally separated photon pairs, we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed two-photon state demonstrates that entanglement can be shared between timelike separated quantum systems.

Doesn't this show that entangled particles can be correlated even if they share different reference frames? (My last question on reference frames)

#### PeroK

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Yes, but three meters in front of you are at a different point in spacetime because you're seeing it as it were in the past so how can you and the explosion share the same reference frame?

For instance, if the Sun exploded, you will see it 8 minutes later. So you would see the explosion of the sun at a different reference frame on earth than the actual explosion which occurred 8 minutes earlier.

You then look at entanglement in time:

Entanglement Swapping between Photons that have Never Coexisted

ABSTRACT

Doesn't this show that entangled particles can be correlated even if they share different reference frames? (My last question on reference frames)
A prerequisite to learning physics is to accept when you have misunderstood something. You've been told clearly and simply (several times) that you have misunderstood the concept of a reference frame.

Simply asking the same misguided question over and over again gets you nowhere.

#### Quantum Alchemy

A prerequisite to learning physics is to accept when you have misunderstood something. You've been told clearly and simply (several times) that you have misunderstood the concept of a reference frame.

Simply asking the same misguided question over and over again gets you nowhere.
What are you talking about? What misguided question?

We were having a cordial conversation and I don't misunderstand anything. This is why I talked about time entanglement. Here's another recent paper that supports what I said.

Entanglement-assisted communication in the absence of shared reference frame

Alice wants to convey the value of a parameter to Bob with whom she does not share a reference frame. What physical object can she use for this task? Shall she encode this value into the angle between two physical vectors such as the angle between two spins? Can she benefit from using entanglement? We approach these questions here and show that an entangled state of two qubits has three parameters that are invariant under changes of the reference frame. We also calculate the average information gain, when each one of these parameters is used for communication. We compare our result with the special case of separable states and find that entanglement enhances the information gain.
https://arxiv.org/abs/1901.01503

"With whom she does not share a reference frame."

So everything isn't always in the same reference frame. They can't be because everything you see is in a different time than you are. You're seeing everything as it were in the past.

Optical Clocks and Relativity

https://www.ncbi.nlm.nih.gov/pubmed/20929843

I put the thread in this forum because I was talking about entanglement as it relates to different reference frames. Here's another paper.

Quantum Entanglement of Moving Bodies

We study the properties of quantum information and quantum entanglement in moving frames. We show that the entanglement between the spins and the momenta of two particles can be interchanged under a Lorentz transformation, so that a pair of particles that is entangled in spin but not momentum in one reference frame, may, in another frame, be entangled in momentum at the expense of spin-entanglement. Similarly, entanglement between momenta may be transferred to spin under a Lorentz transformation. While spin and momentum entanglement each is not Lorentz invariant, the joint entanglement of the wave function is.
https://arxiv.org/abs/quant-ph/0205179

This is about reference frames and entanglement.

We show that the entanglement between the spins and the momenta of two particles can be interchanged under a Lorentz transformation, so that a pair of particles that is entangled in spin but not momentum in one reference frame, may, in another frame, be entangled in momentum at the expense of spin-entanglement.

Why is that taboo? You have never read a paper about reference frames and entanglement? You have never read about entanglement in time? These topics aren't new.

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#### DarMM

Gold Member
What @Nugatory is saying is that a given event can be assigned coordinates in any frame. Thus any event is in any reference frame.

When you say reference frame, I think what you're trying to say is rest frame.

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#### Quantum Alchemy

What @Nugatory is saying is that a given event can be assigned coordinates in any frame. Thus any event is in any reference frame.

When you say reference frame, I think what you're trying to say is rest frame.
I think he means that the laws of physics are the same in all inertial reference frames. Clearly, we don't all share the same reference frames down to quantum entangled particles.

Here's an example that blows my mind.

If the Sun blows up at 1 PM, I will not see it until 1:08. Why is that, it's because we have different reference frames and it takes light from the Sun 8 minutes to reach the Earth.

Say I'm mowing the lawn and at 1 PM, I pass by the tree in my front yard and look up at the sun. I will see the Sun like I usually see it and continue cutting the grass.

At 1 PM though, the Sun will be exploding.

Ask yourself, why don't I know this. At 1 PM, I should know that a huge explosion occurred if we all share the same reference frame. It's like we're in 2 different scenes in a movie. At 1 PM, I'm in a scene where I'm cutting my grass and I pass by the tree and look up at the Sun.

The Sun is in a different movie at 1 PM and it explodes. The strange thing is, why can't I know it explodes at 1 PM if we share the same reference frame? It's almost like we're in 2 different universes. My universe is my own subjective reference frame. It's my own movie that doesn't include the Sun exploding but again, if we shared the same reference frame or the same movie at 1 PM, I should know the Sun exploded.

It's like I only know what's in my reference frame at 1 PM even though this huge explosion is occurring at 1 PM but in my reference frame, I'm enjoying the Sun.

#### PeroK

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Gold Member
2018 Award
I think he means that the laws of physics are the same in all inertial reference frames. Clearly, we don't all share the same reference frames down to quantum entangled particles.

Here's an example that blows my mind.

If the Sun blows up at 1 PM, I will not see it until 1:08. Why is that, it's because we have different reference frames and it takes light from the Sun 8 minutes to reach the Earth.

Say I'm mowing the lawn and at 1 PM, I pass by the tree in my front yard and look up at the sun. I will see the Sun like I usually see it and continue cutting the grass.

At 1 PM though, the Sun will be exploding.

Ask yourself, why don't I know this. At 1 PM, I should know that a huge explosion occurred if we all share the same reference frame. It's like we're in 2 different scenes in a movie. At 1 PM, I'm in a scene where I'm cutting my grass and I pass by the tree and look up at the Sun.

The Sun is in a different movie at 1 PM and it explodes. The strange thing is, why can't I know it explodes at 1 PM if we share the same reference frame? It's almost like we're in 2 different universes. My universe is my own subjective reference frame. It's my own movie that doesn't include the Sun exploding but again, if we shared the same reference frame or the same movie at 1 PM, I should know the Sun exploded.

It's like I only know what's in my reference frame at 1 PM even though this huge explosion is occurring at 1 PM but in my reference frame, I'm enjoying the Sun.
If you really believe and are telling us that you know what a reference frame is and we don't, then how can we answer your physics questions? If that were the case, you would be answering our questions on relativity and QM.

All of what you have said above is based on a fundamental misunderstanding. If you don't accept that, then you can't learn any physics,I'm sorry to say.

#### DarMM

Gold Member
I think he means that the laws of physics are the same in all inertial reference frames. Clearly, we don't all share the same reference frames down to quantum entangled particles.
We don't all share the same rest frame.
Any of us can make use of any particular reference frame, but there is (ignoring details not important here) only one frame in which given object is at rest. That rest frame will describe the locations and timings of events as measured by "clocks and rulers" at rest with respect to the object.

The rest of your post doesn't really concern Relativity and would be true of events in a purely Newtonian world where there was a delay in your being informed of them, e.g. a train whistle goes off in the distance and I only hear it later.

#### PeterDonis

Mentor
"With whom she does not share a reference frame."
This paper is using the term "reference frame" in a highly non-standard way. Their use of this term has nothing whatever to do with your scenario about the Sun exploding and it taking 8 minutes (in the Earth's rest frame) for that information to reach Earth. What you say about that scenario is wrong, because your understanding of reference frames as that term is standardly used in relativity is wrong, as others have pointed out. But that usage of the term has nothing to do with the highly non-standard usage of that term in the paper you linked to.

In the paper, the term "shared reference frame" means that, if repeated measurements on pairs of entangled qubits are made at spacelike separated events, in order to compare the actual results of the measurements with the predictions of QM (or in order to realize processes like "quantum teleportation", as the paper describes), there has to be some way of knowing the angle between the directions in which the two measuring devices point. The paper is using the term "shared reference frame" to describe a situation where the directions can be directly compared--but that would require the two measuring devices to be co-located. In cases where the measuring devices are not co-located, you can't directly compare their directions to find the angle between them; that is what the paper means when it says the two measuring devices do not "share a reference frame". The paper then discusses how you might indirectly compare the two directions in such cases.

#### Quantum Alchemy

This paper is using the term "reference frame" in a highly non-standard way. Their use of this term has nothing whatever to do with your scenario about the Sun exploding and it taking 8 minutes (in the Earth's rest frame) for that information to reach Earth. What you say about that scenario is wrong, because your understanding of reference frames as that term is standardly used in relativity is wrong, as others have pointed out. But that usage of the term has nothing to do with the highly non-standard usage of that term in the paper you linked to.

In the paper, the term "shared reference frame" means that, if repeated measurements on pairs of entangled qubits are made at spacelike separated events, in order to compare the actual results of the measurements with the predictions of QM (or in order to realize processes like "quantum teleportation", as the paper describes), there has to be some way of knowing the angle between the directions in which the two measuring devices point. The paper is using the term "shared reference frame" to describe a situation where the directions can be directly compared--but that would require the two measuring devices to be co-located. In cases where the measuring devices are not co-located, you can't directly compare their directions to find the angle between them; that is what the paper means when it says the two measuring devices do not "share a reference frame". The paper then discusses how you might indirectly compare the two directions in such cases.
This is wrong.

The paper is using the term shared reference frame to highlight local observations in an entangled system. There's like a thousand papers on Arxiv that make this point. Here's another one.

Testing nonlocality of a single photon without a shared reference frame

The question of testing the nonlocality of a single photon has raised much debate over the last years. The controversy is intimately related to the issue of providing a common reference frame for the observers to perform their local measurements. Here we address this point by presenting a simple scheme for demonstrating the nonlocality of a single photon which does not require a shared reference frame. Specifically, Bell inequality violation can be obtained with certainty with unaligned devices, even if the relative frame fluctuates between each experimental run of the Bell test. Our scheme appears feasible with current technology, and may simplify the realization of quantum communication protocols based on single-photon entanglement.

Are you saying all of these Authors just don't understand what a reference frame is? This is why I asked for any papers that say all observers share the same reference frame. I have never seen that in a paper and I would like to read it. What's wrong with that?

#### PeterDonis

Mentor
This is wrong.
You are mistaken. See below.

Are you saying all of these Authors just don't understand what a reference frame is?
No, I am saying that they are using the term "reference frame" in a different way than you think they are.

This is why I asked for any papers that say all observers share the same reference frame. I have never seen that in a paper and I would like to read it.
Go read any textbook on Special Relativity.

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