I Passing information faster than speed of light

[leonid.ge]

TL;DR Summary

Can two parties on remote planets instantly use same random number generator with entangled particles?

Say there is a lottery on Earth with 16 bit numbers (from 1 to 65535), i.e. 65535 lottery tickets are sold. Now, we take 16 pairs of entangled particles, 1st particle of each pair is kept on Earth, 2nd particle sent to Mars. The winning number is randomly chosen (on Earth) by checking the spin of each of the 16 particles and combining those zeros and ones into a number. Suppose the lottery draw takes place on Earth at 00:00 GMT. Then if astronauts on Mars check their particles at 00:01 Earth GMT time, they will know the lottery winning number just 1 second after the lottery was drawn, whilst the light travels from Earth to Mars say 20 minutes. Where is the mistake here?

 

[Dale]

No mistake.

They could even do their measurement 2 s earlier and then know the winning number a second before the lottery is drawn.

 

[Nugatory]

@leonid.ge There is even a practical application - cryptographic key exchange. Once the number is known to both sides, they can use it as the key for exchanging encrypted messages. It's like a sheet in a one-time-pad, but with no need to distribute the physical pads.
(Of course there is much more complexity involved in setting up a practical quantum key distribution system, but the general idea is pretty much what you describe).

 

[PeterDonis]

Where is the mistake here?

There's no mistake as far as your description of what happens. However, what happens does not count as transmitting information faster than light, because neither end (Earth or Mars) can control what the results of the spin measurements are; as you note, it's equivalent to randomly selecting 16 bits.

 

[PeterDonis]

cryptographic key exchange

It's worth noting, though, that the actual messages that get sent with this encryption system travel at ordinary light or slower than light speeds.

 

[martinbn]

TL;DR Summary: Can two parties on remote planets instantly use same random number generator with entangled particles?

Say there is a lottery on Earth with 16 bit numbers (from 1 to 65535), i.e. 65535 lottery tickets are sold. Now, we take 16 pairs of entangled particles, 1st particle of each pair is kept on Earth, 2nd particle sent to Mars. The winning number is randomly chosen (on Earth) by checking the spin of each of the 16 particles and combining those zeros and ones into a number. Suppose the lottery draw takes place on Earth at 00:00 GMT. Then if astronauts on Mars check their particles at 00:01 Earth GMT time, they will know the lottery winning number just 1 second after the lottery was drawn, whilst the light travels from Earth to Mars say 20 minutes. Where is the mistake here?

What if the Earth measurement was delayed and happened at 00:02. Do the Martians know the result before it happened? Did the Earth people send information back in time?

 

[phinds]

What if the Earth measurement was delayed and happened at 00:02. Do the Martians know the result before it happened? Did the Earth people send information back in time?

You're missing the point. I doesn't MATTER who measures first. When the Martians measure first, they record the results and then the Earth measurement is already determined. If the Earth measures first then they record the result and the Martian's measurement results is predetermined.

No information is being sent because neither side has any control of WHAT is measured. They are NOT making a setting, they are ONLY recording what happens, which is random.

 

[martinbn]

You're missing the point.

My questions were rhetorical.

 

[DaveC426913]

My questions were rhetorical.

Took me a moment.

martinbn agrees with the rest of you. He was directing this to the OP for consideration, in the hopes the OP would see the obvious flaw in it:

What if the Earth measurement was delayed and happened at 00:02. Do the Martians know the result before it happened? Did the Earth people send information back in time?

Did I get that right, martnbn?

 

[Nugatory]

My questions were rhetorical.

Indeed... I wrote a careful and thoughtful reply, then noticed that the quoted text I was replying to was you, not OP

 

[martinbn]

Indeed... I wrote a careful and thoughtful reply, then noticed that the quoted text I was replying to was you, not OP

Well, in situations like this I use my English as an excuse. It is very difficult to express yourself when you don't use your mother's tongue (the language of mathematics ).

 

[phinds]

My questions were rhetorical.

 

[PeroK]

My questions were rhetorical.

IMO, it's a British versus American thing. Your post seemed obvious to me.

 

[PeroK]

TL;DR Summary: Can two parties on remote planets instantly use same random number generator with entangled particles?

Say there is a lottery on Earth with 16 bit numbers (from 1 to 65535), i.e. 65535 lottery tickets are sold. Now, we take 16 pairs of entangled particles, 1st particle of each pair is kept on Earth, 2nd particle sent to Mars. The winning number is randomly chosen (on Earth) by checking the spin of each of the 16 particles and combining those zeros and ones into a number. Suppose the lottery draw takes place on Earth at 00:00 GMT. Then if astronauts on Mars check their particles at 00:01 Earth GMT time, they will know the lottery winning number just 1 second after the lottery was drawn, whilst the light travels from Earth to Mars say 20 minutes. Where is the mistake here?

In addition to everything else, there's also a fundamental ambiguity about what GMT means for an event on Mars. There is not an absolute simultaneity convention that allows you to say that an event on Mars occurs at the same time as an event on Earth.

Note that is also true for events separated across the Earth, but the magnitude of the ambiguity is generally not significant.

 

[PeterDonis]

What if the Earth measurement was delayed and happened at 00:02. Do the Martians know the result before it happened? Did the Earth people send information back in time?

The measurements are spacelike separated, which means their time ordering is frame dependent, and therefore has no physical meaning. In other words, there is no invariant fact of the matter about which one occurs first. The results just have to be correlated in the appropriate way for the state of the entangled particles. And since there is no actual information being sent, there is no issue about which direction in time information goes.

 

[FactChecker]

The measurements are spacelike separated, which means their time ordering is frame dependent, and therefore has no physical meaning. In other words, there is no invariant fact of the matter about which one occurs first.

I have always been under the impression that the special relativity effect on clocks was never enough to change a cause-effect relationship between two events. In other words, all inertial reference frames would agree on which event in a cause-effect relationship with another event happened first.

CORRECTION: I made an elementary mistake. I didn't realize the significance of "spacelike-separation".

 

[PeterDonis]

I have always been under the impression that the special relativity effect on clocks was never enough to change a cause-effect relationship between two events. In other words, all inertial reference frames would agree on which event in a cause-effect relationship with another event happened first.

That's a common viewpoint, although it actually is not required by SR. But if you take that viewpoint, then you must also accept that there is no cause-effect relationship between spacelike separated measurements on entangled particles. And this makes sense in terms of standard QM, since standard QM predicts that the results of the measurements are the same regardless of the order in which they occur. That's not something one would expect from two events that are in a cause-effect relationship.

 

[FactChecker]

That's a common viewpoint, although it actually is not required by SR. But if you take that viewpoint, then you must also accept that there is no cause-effect relationship between spacelike separated measurements on entangled particles.

I agree that is a dilemma. But I would hate to give up all time sequencing in spatially separated events because of entanglement in QM.

The measurements are spacelike separated, which means their time ordering is frame dependent, and therefore has no physical meaning.

This just seems like too much to me in the general case.

CORRECTION: I made an elementary mistake. I didn't realize the significance of "spacelike-separation".

 

[Nugatory]

In other words, all inertial reference frames would agree on which event in a cause-effect relationship with another event happened first.

Yes, and if two events are spacelike-separated then there can be no cause-effect relationship between them - and that is when “which happened first” is frame-dependent.

We avoid all of this by stating the relationship in invariant terms: causes lie in the past light cone of effects. This formulation works in non-inertial frames and even physically reasonable curved spacetimes.

 

[PeterDonis]

I would hate to give up all time sequencing in spatially separated events

You have to give that up regardless of entanglement in QM. It's a basic principle of relativity.

 

[FactChecker]

Yes, and if two events are spacelike-separated then there can be no cause-effect relationship between them - and that is when “which happened first” is frame-dependent.

Sorry. I made an elementary mistake. I didn't realize the significance of "spacelike-separation".