This one is inspired by recent discussion of John Bell's
paper. It's easy/hard; non-obvious, yet simple once you see
the solution.
Given a pair of identical detectors, spaced far apart.
In between, a gun, which fires a pair of particles, one
at each detector. Each detector holds a bulb, which
flashes red or green upon receiving a particle.
It also holds a switch, with 3 positions. Prior to each
trial, the switch is set to an arbitrary position, randomly,
and independently of the other detector.
There exists no physical connection between the detectors.
You run 1000 trials, and observe the following:
I) Considering each detector in isolation, the bulb
flashes red/green, 50/50, with no apparent pattern,
it appears completely random. And no discernible
relation to the switch setting.
II) Considering the pair, things become more interesting:
i) When both switches are set to the same position, the
bulbs always flash the same color.
ii) When they are set differently, there is no apparent relation
between the colors.
There is no communication channel between the
detectors. However, a particle constitutes a possible
channel, from gun to detector. Therefore, you may
assume that a particle contains an internal state,
readable by the detector. No information is given
regarding the set of possible states.
How do you explain the operation of this apparatus?
Does it seem plausible and practical, in principle?
i.e. considering II (i). Does anything strike you as peculiar?
obvious hint: there IS something peculiar.
another hint:
https://www.nobelprize.org/prizes/physics/2022/press-release/
--
Rich
This one is inspired by recent discussion of John Bell'sII) Considering the pair:
paper. It's easy/hard; non-obvious, yet simple once you see
the solution.
Given a pair of identical detectors, spaced far apart.
In between, a gun, which fires a pair of particles, one
at each detector. Each detector holds a bulb, which
flashes red or green upon receiving a particle.
It also holds a switch, with 3 positions. Prior to each
trial, the switch is set to an arbitrary position, randomly,
and independently of the other detector.
There exists no physical connection between the detectors.
You run 1000 trials, and observe the following:
I) Considering each detector in isolation, the bulb
flashes red/green, 50/50, with no apparent pattern,
it appears completely random. And no discernible
relation to the switch setting.
i) When both switches are set to the same position, the
bulbs always flash the same color.
ii) When they are set differently, there is no apparent relation
between the colors.
There is no communication channel between the
detectors. However, a particle constitutes a possible
channel, from gun to detector. Therefore, you may
assume that a particle contains an internal state,
readable by the detector. No information is given
regarding the set of possible states.
How do you explain the operation of this apparatus?
Does it seem plausible and practical, in principle?
i.e. considering II (i). Does anything strike you as peculiar?
Yes, but only because what you describe is not equivalent to the
experiments that earned the Nobel prize.
It's easy/hard; non-obvious, yet simple once you see
the solution.
obvious hint: there IS something peculiar.
another hint:
https://www.nobelprize.org/prizes/physics/2022/press-release/
On September 18, Sylvia Else wrote:
This one is inspired by recent discussion of John Bell'sII) Considering the pair:
paper. It's easy/hard; non-obvious, yet simple once you see
the solution.
Given a pair of identical detectors, spaced far apart.
In between, a gun, which fires a pair of particles, one
at each detector. Each detector holds a bulb, which
flashes red or green upon receiving a particle.
It also holds a switch, with 3 positions. Prior to each
trial, the switch is set to an arbitrary position, randomly,
and independently of the other detector.
There exists no physical connection between the detectors.
You run 1000 trials, and observe the following:
I) Considering each detector in isolation, the bulb
flashes red/green, 50/50, with no apparent pattern,
it appears completely random. And no discernible
relation to the switch setting.
i) When both switches are set to the same position, the
bulbs always flash the same color.
ii) When they are set differently, there is no apparent relation
between the colors.
There is no communication channel between the
detectors. However, a particle constitutes a possible
channel, from gun to detector. Therefore, you may
assume that a particle contains an internal state,
readable by the detector. No information is given
regarding the set of possible states.
How do you explain the operation of this apparatus?
Does it seem plausible and practical, in principle?
i.e. considering II (i). Does anything strike you as peculiar?
Yes, but only because what you describe is not equivalent to the
experiments that earned the Nobel prize.
<wooooosh!>
This one is inspired by recent discussion of John Bell's
paper. It's easy/hard; non-obvious, yet simple once you see
the solution.
Given a pair of identical detectors, spaced far apart.
In between, a gun, which fires a pair of particles, one
at each detector. Each detector holds a bulb, which
flashes red or green upon receiving a particle.
It also holds a switch, with 3 positions. Prior to each
trial, the switch is set to an arbitrary position, randomly,
and independently of the other detector.
There exists no physical connection between the detectors.
You run 1000 trials, and observe the following:
I) Considering each detector in isolation, the bulb
flashes red/green, 50/50, with no apparent pattern,
it appears completely random. And no discernible
relation to the switch setting.
II) Considering the pair:
i) When both switches are set to the same position, the
bulbs always flash the same color.
ii) When they are set differently, there is no apparent relation
between the colors.
There is no communication channel between the detectors.
How do you explain the operation of this apparatus?
Does it seem plausible and practical, in principle?
i.e. considering II (i). Does anything strike you as peculiar?
Yes, but only because what you describe is not equivalent to the
experiments that earned the Nobel prize.
<wooooosh!>
I don't think so. You're just trying to cover up your blunder.
On September 18, Sylvia Else wrote:
This one is inspired by recent discussion of John Bell's
paper. It's easy/hard; non-obvious, yet simple once you see
the solution.
Given a pair of identical detectors, spaced far apart.
In between, a gun, which fires a pair of particles, one
at each detector. Each detector holds a bulb, which
flashes red or green upon receiving a particle.
It also holds a switch, with 3 positions. Prior to each
trial, the switch is set to an arbitrary position, randomly,
and independently of the other detector.
There exists no physical connection between the detectors.
You run 1000 trials, and observe the following:
I) Considering each detector in isolation, the bulb
flashes red/green, 50/50, with no apparent pattern,
it appears completely random. And no discernible
relation to the switch setting.
II) Considering the pair:
i) When both switches are set to the same position, the
bulbs always flash the same color.
ii) When they are set differently, there is no apparent relation
between the colors.
There is no communication channel between the detectors.
How do you explain the operation of this apparatus?
Does it seem plausible and practical, in principle?
i.e. considering II (i). Does anything strike you as peculiar?
Yes, but only because what you describe is not equivalent to the
experiments that earned the Nobel prize.
<wooooosh!>
I don't think so. You're just trying to cover up your blunder.
Most excellent! Your juvenile response highlights the instructional value. Let's see, there's reference to John Bell, and the Nobel... we have two particles which interact, then separate, then an ambiguous property is measured... does that remind you of anything?
The problem is likely too tricky, no one will solve it. I'll offer a few hints.
II (i) is the vital point. No connections between the detectors, how do they coordinate their outputs? There must be messages carried by the particles, that's the only reasonable hypothesis. What are these messages, is this insoluble? Not at all: 3 switch positions, 2 colors, the particle's state
represents a specific instruction... how many states, what are they? This is easy, use binary, it's CS 101.
That's the first step. The next step is the tricky part. Eventually, with the
given numbers, which model real reality, it leads to something peculiar -
Anyone who solves it, kudos! You have derived Bell's theorem. If not,
take consolation, it eluded the entire physics community for 20 years.
--
Rich
On 20-Sept-23 4:25 am, RichD wrote:
On September 18, Sylvia Else wrote:
This one is inspired by recent discussion of John Bell's
paper. It's easy/hard; non-obvious, yet simple once you see
the solution.
Given a pair of identical detectors, spaced far apart.
In between, a gun, which fires a pair of particles, one
at each detector. Each detector holds a bulb, which
flashes red or green upon receiving a particle.
It also holds a switch, with 3 positions. Prior to each
trial, the switch is set to an arbitrary position, randomly,
and independently of the other detector.
There exists no physical connection between the detectors.
You run 1000 trials, and observe the following:
I) Considering each detector in isolation, the bulb
flashes red/green, 50/50, with no apparent pattern,
it appears completely random. And no discernible
relation to the switch setting.
II) Considering the pair:
i) When both switches are set to the same position, the
bulbs always flash the same color.
ii) When they are set differently, there is no apparent relation
between the colors.
There is no communication channel between the detectors.
How do you explain the operation of this apparatus?
Does it seem plausible and practical, in principle?
i.e. considering II (i). Does anything strike you as peculiar?
Yes, but only because what you describe is not equivalent to the
experiments that earned the Nobel prize.
<wooooosh!>
I don't think so. You're just trying to cover up your blunder.
Most excellent! Your juvenile response highlights the instructional value. Let's see, there's reference to John Bell, and the Nobel... we have two particles which interact, then separate, then an ambiguous property is measured... does that remind you of anything?
The problem is likely too tricky, no one will solve it. I'll offer a few hints.
II (i) is the vital point. No connections between the detectors, how do they coordinate their outputs? There must be messages carried by the particles, that's the only reasonable hypothesis. What are these messages, is this insoluble? Not at all: 3 switch positions, 2 colors, the particle's state
represents a specific instruction... how many states, what are they? This is easy, use binary, it's CS 101.
That's the first step. The next step is the tricky part. Eventually, with the
given numbers, which model real reality, it leads to something peculiar -
Anyone who solves it, kudos! You have derived Bell's theorem. If not,
take consolation, it eluded the entire physics community for 20 years.
--So what? It still bears no resemblance to the work that earned the Nobel prize. Bell's analysis, and the subsequent experimental verification,
Rich
This one is inspired by recent discussion of John Bell's
paper. It's easy/hard; non-obvious, yet simple once you see
the solution.
Given a pair of identical detectors, spaced far apart.
In between, a gun, which fires a pair of particles, one
at each detector. Each detector holds a bulb, which
flashes red or green upon receiving a particle.
It also holds a switch, with 3 positions. Prior to each
trial, the switch is set to an arbitrary position, randomly,
and independently of the other detector.
There exists no physical connection between the detectors.
You run 1000 trials, and observe the following:
I) Considering each detector in isolation, the bulb
flashes red/green, 50/50, with no apparent pattern,
it appears completely random. And no discernible
relation to the switch setting.
II) Considering the pair, things become more interesting:
i) When both switches are set to the same position, the
bulbs always flash the same color.
ii) When they are set differently, there is no apparent relation
between the colors.
There is no communication channel between the
detectors. However, a particle constitutes a possible
channel, from gun to detector. Therefore, you may
assume that a particle contains an internal state,
readable by the detector. No information is given
regarding the set of possible states.
How do you explain the operation of this apparatus?
Does it seem plausible and practical, in principle?
i.e. considering II (i). Does anything strike you as peculiar?
obvious hint: there IS something peculiar.
another hint:
https://www.nobelprize.org/prizes/physics/2022/press-release/
--
Rich
Let's see, there's reference to John Bell, and the Nobel... we have two
particles which interact, then separate, then an ambiguous property is
measured... does that remind you of anything?
II (i) is the vital point. No connections between the detectors, how do
they coordinate their outputs? There must be messages carried by the
particles, that's the only reasonable hypothesis. What are these messages, >> is this insoluble? Not at all: 3 switch positions, 2 colors, the particle's state
represents a specific instruction... how many states, what are they? This
is easy, use binary, it's CS 101.
That's the first step. The next step is the tricky part. Eventually, with the
given numbers, which model real reality, it leads to something peculiar -
Anyone who solves it, kudos! You have derived Bell's theorem. If not,
take consolation, it eluded the entire physics community for 20 years.
It still bears no resemblance to the work that earned the Nobel prize.
Bell's analysis, and the subsequent experimental verification,
showed that a hidden variable solution does not work.
On September 19, Sylvia Else wrote:
Let's see, there's reference to John Bell, and the Nobel... we have two >> particles which interact, then separate, then an ambiguous property is
measured... does that remind you of anything?
II (i) is the vital point. No connections between the detectors, how do >> they coordinate their outputs? There must be messages carried by the
particles, that's the only reasonable hypothesis. What are these messages,
is this insoluble? Not at all: 3 switch positions, 2 colors, the particle's state
represents a specific instruction... how many states, what are they? This >> is easy, use binary, it's CS 101.
That's the first step. The next step is the tricky part. Eventually, with the
given numbers, which model real reality, it leads to something peculiar - >> Anyone who solves it, kudos! You have derived Bell's theorem. If not,
take consolation, it eluded the entire physics community for 20 years.
It still bears no resemblance to the work that earned the Nobel prize.You missed the landing pad by so many miles, you splash
landed near the Titanic. Good job.
This simple example, followed to the end, leads DIRECTLY to
Bell's theorem.
Bell's analysis, and the subsequent experimental verification,So you can regurgitate something your read in a pop science
showed that a hidden variable solution does not work.
book. Impressive.
Regurgitation isn't derivation.
Echoing isn't understanding.
"exercise for the student", "work it out for yourself",
"take up the challenge"... do these phrases mean anything
to you? Evidently we have someone who doesn't understand
why teachers assign homework!
This is a physics board, presumably there are subscribers
who wish to delve into this topic Solving this puzzle, which
appears mundane, gives insight into Bell's accomplishment.
You have all the answers? Great. First, define "hidden
variable" and "does not work". Then, via this example,
show that a hidden variable solution does not work.
SHOW YOUR WORK.
PS "hidden variables" is mushy, I prefer nonlocal reality, as
more descriptive.
--
Rich
On September 19, Sylvia Else wrote:
Let's see, there's reference to John Bell, and the Nobel... we have two
particles which interact, then separate, then an ambiguous property is
measured... does that remind you of anything?
II (i) is the vital point. No connections between the detectors, how do
they coordinate their outputs? There must be messages carried by the
particles, that's the only reasonable hypothesis. What are these messages, >>> is this insoluble? Not at all: 3 switch positions, 2 colors, the particle's state
represents a specific instruction... how many states, what are they? This >>> is easy, use binary, it's CS 101.
That's the first step. The next step is the tricky part. Eventually, with the
given numbers, which model real reality, it leads to something peculiar - >>> Anyone who solves it, kudos! You have derived Bell's theorem. If not,
take consolation, it eluded the entire physics community for 20 years.
It still bears no resemblance to the work that earned the Nobel prize.
You missed the landing pad by so many miles, you splash
landed near the Titanic. Good job.
This simple example, followed to the end, leads DIRECTLY to
Bell's theorem.
Bell's analysis, and the subsequent experimental verification,
showed that a hidden variable solution does not work.
So you can regurgitate something your read in a pop science
book. Impressive.
Regurgitation isn't derivation.
Echoing isn't understanding.
"exercise for the student", "work it out for yourself",
"take up the challenge"... do these phrases mean anything
to you? Evidently we have someone who doesn't understand
why teachers assign homework!
This is a physics board, presumably there are subscribers
who wish to delve into this topic Solving this puzzle, which
appears mundane, gives insight into Bell's accomplishment.
You have all the answers? Great. First, define "hidden
variable" and "does not work". Then, via this example,
show that a hidden variable solution does not work.
SHOW YOUR WORK.
PS "hidden variables" is mushy, I prefer nonlocal reality, as
more descriptive.
Bell's analysis, and the subsequent experimental verification,
showed that a hidden variable solution does not work.
So you can regurgitate something your read in a pop science book.
Regurgitation isn't derivation.
Echoing isn't understanding.
PS "hidden variables" is mushy, I prefer nonlocal reality, as more descriptive.
Ah, changing the terminology - a sure sign of a crank.
This one is inspired by recent discussion of John Bell's
paper. It's easy/hard; non-obvious, yet simple once you see
the solution.
Given a pair of identical detectors, spaced far apart.
In between, a gun, which fires a pair of particles, one
at each detector. Each detector holds a bulb, which
flashes red or green upon receiving a particle.
It also holds a switch, with 3 positions. Prior to each
trial, the switch is set to an arbitrary position, randomly,
and independently of the other detector.
There exists no physical connection between the detectors.
You run 1000 trials, and observe the following:
I) Considering each detector in isolation, the bulb
flashes red/green, 50/50, with no apparent pattern,
it appears completely random. And no discernible
relation to the switch setting.
II) Considering the pair, things become more interesting:
i) When both switches are set to the same position, the
bulbs always flash the same color.
ii) When they are set differently, there is no apparent relation
between the colors.
There is no communication channel between the
detectors. However, a particle constitutes a possible
channel, from gun to detector.
How do you explain the operation of this apparatus?
Does it seem plausible and practical, in principle?
On September 18, RichD wrote:
This one is inspired by recent discussion of John Bell'sAssuming anyone is interested in this topic...
paper. It's easy/hard; non-obvious, yet simple once you see
the solution.
Given a pair of identical detectors, spaced far apart.
In between, a gun, which fires a pair of particles, one
at each detector. Each detector holds a bulb, which
flashes red or green upon receiving a particle.
It also holds a switch, with 3 positions. Prior to each
trial, the switch is set to an arbitrary position, randomly,
and independently of the other detector.
There exists no physical connection between the detectors.
You run 1000 trials, and observe the following:
I) Considering each detector in isolation, the bulb
flashes red/green, 50/50, with no apparent pattern,
it appears completely random. And no discernible
relation to the switch setting.
II) Considering the pair, things become more interesting:
i) When both switches are set to the same position, the
bulbs always flash the same color.
ii) When they are set differently, there is no apparent relation
between the colors.
There is no communication channel between the
detectors. However, a particle constitutes a possible
channel, from gun to detector.
How do you explain the operation of this apparatus?
Does it seem plausible and practical, in principle?
II (i) is the vital point. No connections between the detectors, how do
they coordinate their outputs? There must be messages carried by the particles, that's the only reasonable hypothesis.
So we postulate that the particles contain instructions.
3 switch positions, and 2 colors ==> a particle contains 3 bits,
one for each position. A bit dictates the color, R/G, for the
corresponding position. Therefore 8 possible states, thus:
RRR
RRG
...
GGG
Each pair must carry identical states, in order to achieve II (i).
The states are uniformly distributed, per the observations.
So far, so mundane, nothing interesting. Now the trick: there's
a vital piece of data missing from the original note, call it (III).
The student must experience this insight, to see its relevance.
Strictly speaking, it's unnecessary to provide this information,
it's easily derived.
III) Considering only the pair of bulbs, ignoring the switches,
there are 4 possible color states. Obviously, from (I) and (II),
these are uniformly distributed.
Put I, II, and III together, using freshman level combinatorics,
one can discover something startling, Nobel worthy -
--
Rich
| Sysop: | Keyop |
|---|---|
| Location: | Huddersfield, West Yorkshire, UK |
| Users: | 325 |
| Nodes: | 16 (2 / 14) |
| Uptime: | 83:02:48 |
| Calls: | 7,164 |
| Files: | 12,542 |
| Messages: | 5,534,271 |