Bell's theorem proof. Does it really proofs anything?

[zonde]

This formula is wrong.
N(+30°, -30°) ≤ N(+30°, 0°) + N(0°, -30°) (in my opinion of course.. ;) )

This formula is correct.

Say we take four pairs of entangled photons.
1A / 1B
2A / 2B
3A / 3B
4A / 4B
Alice performs measurement at some angle a, Bob performs measurement at some angle b.
The angle a and b are chosen so that we get perfectly correlated result, say.
1A=0 / 1B=0
2A=0 / 2B=0
3A=1 / 3B=1
4A=0 / 4B=0

Now Alice performs measurement at angle a+30°, Bob performs measurement at angle b.
So to get 25% match with Bob you can change only one measurement for Alice.
1A=1 / 1B=0
2A=0 / 2B=0
3A=1 / 3B=1
4A=0 / 4B=0

Now Alice performs measurement at angle a, Bob performs measurement at angle b-30°.
To get 25% match with Alice you can change only one measurement for Bob.
1A=0 / 1B=0
2A=0 / 2B=1
3A=1 / 3B=1
4A=0 / 4B=0

And now Alice performs measurement at angle a+30°, Bob performs measurement at angle b-30°.
1A=1 / 1B=0
2A=0 / 2B=1
3A=1 / 3B=1
4A=0 / 4B=0
And minimum we get is 50% match because definitely two pairs are left unchanged.

 

[DrChinese]

Then just to make clear - if i would replace twin-photon generator by simple photon generator (any laser), and add polarization filters on both sides, so both photons have same polarization and then repeat same example randomly changing both polarization filter orientation and calcium crystal direction, i would get these linear results, not cos function?

No, you will NOT get those results. The graph Avocado presents is the BEST CASE that a Local Realistic Theory can yield in the sense that it is as close to the Quantum Mechanical predictions as it gets. That is not what actually occurs in an experiment, because the best case is merely hypothetical for a reality that does not occur in our universe (but which would still follow classical thinking).

 

[DevilsAvocado]

HEY- maybe this experiment has already been produced??

Most probably, most probably... at least in theory in some genius brain...

You should know that spontaneous parametric down-conversion in BBO crystals is not a very effective process. Only one out of 10^6 photons converts into two entangled photons, one in a million.

This means that most photons that hit the detectors are "dummies". They don’t show any sign of QM correlations. I guess that this is a parallel to your "laser experiment"...

 

[DrChinese]

...

And now Alice performs measurement at angle a+30°, Bob performs measurement at angle b-30°.
1A=1 / 1B=0
2A=0 / 2B=1
3A=1 / 3B=1
4A=0 / 4B=0
And minimum we get is 50% match because definitely two pairs are left unchanged.

With this nice example, zonde is showing you what you would expect using classical/Local Realistic thinking. What you actually get, in an experiment, is something like:

1A=1 / 1B=0
2A=0 / 2B=1
3A=1 / 3B=0
4A=0 / 4B=0

So we actually get 25% match, when the minimum expected was 50%. So our assumption is wrong. Which is what Bell said.

 

[0xDEAD BEEF]

This means that most photons that hit the detectors are "dummies". They don’t show any sign of QM correlations. I guess that this is a parallel to your "laser experiment"...

Not exactly - there is no polarization filters between them and crystals! ;)
Beef
P.S. i still totally disagree and do not accept this idea, but i guess that is because of my incomplete knowledge!

BTW - so say i do conduct this experiment using normal light polarized using polarization fitlers (two polarizations filters polarizing light) - what results would i get?

 

[DevilsAvocado]

Not exactly - there is no polarization filters between them and crystals! ;)
Beef
P.S. i still totally disagree and do not accept this idea, but i guess that is because of my incomplete knowledge!

Well... some things you say... do make sense… (sorry bad joke )

BTW - so say i do conduct this experiment using normal light polarized using polarization fitlers (two polarizations filters polarizing light) - what results would i get?

Not that great I would say. Let’s assume we have the Source (S), Polarizer1 (P1), Polarizer2 (P2), and the Measuring apparatus (M), setup like this:

S----->-----P1----->-----P2----->-----M

Unpolarized normal light will go thru P1. Independent of the angle of P1, 50% of the light will pass thru. Let’s say we set P1 to 90º. Now P2 will have to 'relate' to the angle of P1. If P2 is set to 0º, no light will pass. If P2 is set to 45º, 25% of the (original) light will pass. If P2 is set to 90º, 50 % of the (original) light will pass.

You can play with different settings in this http://www.lon-capa.org/~mmp/kap24/polarizers/Polarizer.htm" , but I don’t think it will help you design a LHVT.

 

[zonde]

You should know that spontaneous parametric down-conversion in BBO crystals is not a very effective process. Only one out of 10^6 photons converts into two entangled photons, one in a million.

This means that most photons that hit the detectors are "dummies". They don’t show any sign of QM correlations. I guess that this is a parallel to your "laser experiment"...

There are not so much dummies. Pump photons are separated from downconverted photons (they usually have slightly different direction) and they do not arrive at detectors.
But if pump photon is downconverted there are always two downconverted photons leaving the source. Of course you can loose some along the way.
Anyways it's possible to make setup where more than 50% of detections at one detector are paired with detections at other detector (but not vice versa). Actually for me it's clearest demonstration that photons are particles (at macro scale).

 

[0xDEAD BEEF]

So I think is start to see the problem here!
All this proof is based on this formula output

N(+30°, -30°) ≤ N(+30°, 0°) + N(0°, -30°)

not matching measurements, right?

And this N function is function, which describes error (mismatch?). Right?

So - can i remove "two parameters" from this function and convert to one, since "error" is always calculated comparing output at Alise's detector to output at Bob's detector and absolute angle does not play role here, since polarization of photons is not known from very beginning?

So, should this also be true?
N(60°) ≤ N(30°) + N(30°)

Beef
EDIT: BTW - what is "two-channel polariser" and where do i get one! :)
EDIT2: two-channel polariser is same thing as "Wollaston prism" ?

 

[DevilsAvocado]

So I think is start to see the problem here!
All this proof is based on this formula output

N(+30°, -30°) ≤ N(+30°, 0°) + N(0°, -30°)

not matching measurements, right?

YES!

Not only measurements, it does not match the theoretical predictions of Quantum Mechanics (which is the most precise theory we have).

And this N function is function, which describes error (mismatch?). Right?

YES!

So, should this also be true?
N(60°) ≤ N(30°) + N(30°)

YES!

We could 'simplify' this even more and say:

50% = 25% + 25%

And more, by dividing by 25:

2 = 1 + 1

Or reversed, that works even for kids!

1 + 1 = 2

This is what we expect. This is the how "the normal world" should work. But, then comes the 'weird' QM-world and tell us that – This is how it works!

1 + 1 = 3

! !

EDIT: BTW - what is "two-channel polariser" and where do i get one! :)
EDIT2: two-channel polariser is same thing as "Wollaston prism" ?

This video explains the basics in EPR-Bell experiments:

https://www.youtube.com/watch?v=<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/c8J0SNAOXBg&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/c8J0SNAOXBg&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>

And here you find more info on the equipment: http://www.didaktik.physik.uni-erlangen.de/quantumlab/english/"

And if you really going to have a experimental shot at this, you should read this:

http://arxiv.org/abs/quant-ph/0205171"

 

[DevilsAvocado]

Hey DrC! Nice pink! (me want! )

 

[DevilsAvocado]

Anyways it's possible to make setup where more than 50% of detections at one detector are paired with detections at other detector (but not vice versa). Actually for me it's clearest demonstration that photons are particles (at macro scale).

Thanks for clarifying.

Well, some say it’s particles, and some say wave/particles, and some only wave + a "click".

I have absolutely no idea what’s really true... (and I guess I’m not alone )

 

[0xDEAD BEEF]

So i wrote program which generates photons with random orientation and throws them at detectors. Now i got linear output comparing detectorA to detectorB. I wrote my detectors so, that they fire, if photon angle +- 45 degrees matches with detector angle. Is this correct detector setting?

So - if we assume, that measurement of one photon changes orientation of other... Why do we get random data output at Alisa's or Bob's detector? Why is not it so, that one detector returns more + than - or vice versa (thus - if detector has affected orientation of photon should not this detector fire more often, since photon's direction is changed to "suite" that(first) detector) ?

Beef

 

[DrChinese]

So i wrote program which generates photons with random orientation and throws them at detectors. Now i got linear output comparing detectorA to detectorB. I wrote my detectors so, that they fire, if photon angle +- 45 degrees matches with detector angle. Is this correct detector setting?

So - if we assume, that measurement of one photon changes orientation of other... Why do we get random data output at Alisa's or Bob's detector? Why is not it so, that one detector returns more + than - or vice versa (thus - if detector has affected orientation of photon should not this detector fire more often, since photon's direction is changed to "suite" that(first) detector) ?

Beef

First, 45 degree angles usually won't show much relative to Bell's Theorem. Second, it is very difficult to follow some of your questions - so I will try as best I can.

The general rule for a polarization entangled photon pair is that a measurement on Alice acts "AS IF" it causes a matching change to Bob. (Note the AS IF because no one is actually saying that can be proven. It is one of several possibilities. However it is useful for the rule, which is correct.) So if you measure Alice at 45 degrees, Bob will act as if he is likewise polarized at 45 degrees. Stats can then be calculated for any subsequent measurement on Bob (or Alice for that matter).

An important note because I think this can be confusing if it is not explicitly pointed out: Entangled photon pairs can be created either I) so Alice and Bob have the same polarization; or II) Alice and Bob have orientations 90 degrees apart. This is controlled by the choice of PDC crystals (called Type I or Type II).

Finally, any sequence of Alice will be random + and -, more or less equal, and Bob will be random too. Depending on the relative angle theta between then, their matches will show a pattern or not. Cos^2(theta) is the rule for Type I, Sin^2(theta) is for Type II. I always provide examples as Type I because it is easier to discuss.

 

[0xDEAD BEEF]

So how i now see this is that if instead of twin photons i would use simple photons with same polarization, then this same experiment would produce linear graph, not cos. Right?

So this would mean, that measurement on Alisa's photon has affected Bob's photon to be the same, BUT Alisa's photon somehow matches betters Alisa's detector? So we should see more + photons than - (or vice versa) photons at Alisa's detector?

Edit: or does this measurement says, that now that photons (both) know their polarization for Alisa's detector, they will respond with same value, but since they don't know polarization value for Bob's settings, they have not made that up yet so when Bob measures his photon, his photon wonders what value should it return to Bob, since Alisa did not measure exactly same "setting" so Bob's photon comes up with some new random value? :)

Edit2: And if so, should not those two photons have decided their polarization values earlier already (traveling through space and hitting various magnetic/electric fields or dust) ?

Beef

 

[DevilsAvocado]

I wrote my detectors so, that they fire, if photon angle +- 45 degrees matches with detector angle. Is this correct detector setting?

I’m not sure what you’re aiming at... do you mean the polarizing beam splitter?

This is 'just' to be able to measure all arriving photons (both Up/Down, +/-, 1/0, Yes/No), to get better 'precision'...

Why do we get random data output at Alisa's or Bob's detector? Why is not it so, that one detector returns more + than - or vice versa

Try to think of it like this: Basically at each end Alice & Bob receive unpolarized light that they run thru a polarizer. As you can test by yourself in the http://www.lon-capa.org/~mmp/kap24/polarizers/Polarizer.htm" , no matter what angle you set there will always be a 50% chance for the light (photon) to go thru, when the light is unpolarized.

To make more precise measurements, we take care of both "thru" & "stopped" by a polarizing beam splitter. This means there is always 50/50 chance for the photon to be detected at each detector after the beam splitter.

The EPRB 'mystery' lays in the correlations in the sequence of photons between Alice & Bob.

For example, let’s say we have a relative angle of 60º between Alice & Bob, meaning there’s a 75% mismatch. When counting 8 photon pairs, we could get this:

Alice: 0000 0000
Bob..: 1111 1100

But, more probably we will see something like this:

Alice: 0101 0101
Bob..: 1010 0011

Get it?

 

[DrChinese]

1. So how i now see this is that if instead of twin photons i would use simple photons with same polarization, then this same experiment would produce linear graph, not cos. Right?

2. So this would mean, that measurement on Alisa's photon has affected Bob's photon to be the same, BUT Alisa's photon somehow matches betters Alisa's detector? So we should see more + photons than - (or vice versa) photons at Alisa's detector?

Edit: or does this measurement says, that now that photons (both) know their polarization for Alisa's detector, they will respond with same value, but since they don't know polarization value for Bob's settings, they have not made that up yet so when Bob measures his photon, his photon wonders what value should it return to Bob, since Alisa did not measure exactly same "setting" so Bob's photon comes up with some new random value? :)

3. Edit2: And if so, should not those two photons have decided their polarization values earlier already (traveling through space and hitting various magnetic/electric fields or dust) ?

Beef

1. No, it is a completely different formula that involves 3 variables but follows classical rules (Malus).

2. I cannot follow your question. I assume English is not your native language so if you could rephrase that would be helpful. There is no reason you would see more + than - anywhere, not sure what your thinking is on that but it is not correct.

3. Free space fields generally will not affect photon polarization in any way. Many times the effects cancel out. Now, if you go through an optical device such as a polarizing beam splitter or a wave plate you can see effects.

 

[0xDEAD BEEF]

Sorry! I don't get it! :)
I would really apreciate, if you could answer this question-

->>
So this would mean, that measurement on Alisa's photon has affected Bob's photon to be the same, BUT Alisa's photon somehow matches betters Alisa's detector? So we should see more + photons than - (or vice versa) photons at Alisa's detector?

Edit: or does this measurement says, that now that photons (both) know their polarization for Alisa's detector, they will respond with same value, but since they don't know polarization value for Bob's settings, they have not made that up yet so when Bob measures his photon, his photon wonders what value should it return to Bob, since Alisa did not measure exactly same "setting" so Bob's photon comes up with some new random value? :)
<<-

What i mean is - where does it start to make difference between twin-photons and photons with same polarization. How would this change results of experiment. Let's say - i have black-box device which creates "twin-photons", which actualy are not twin photons, but simply photons with same polarization. Where would this change output of these measurements.

--
The big idea behind this theory/experiment is, that polarization of these photons becomes "known" only as they get measured (pass thru polarization filter (Wollaston prism?)).
Am i right?

Beef
P.S. english is not my native language, sorry.

 

[zonde]

So how i now see this is that if instead of twin photons i would use simple photons with same polarization, then this same experiment would produce linear graph, not cos. Right?

No, it would produce cos^2(a)*cos^2(b) where a and b are angle between polarization axis of photons and polarization axis of respective polarizer.

In case of entanglement you get something like:
cos^2(a)*cos^2(b)+sin^2(a)*sin^2(b)+1/2*sin2a*sin2b=cos^2(a-b)
this third term (1/2*sin2a*sin2b) is called interference term and it's the one that complicates things.

 

[0xDEAD BEEF]

zonde! regarding

No, it would produce cos^2(a)*cos^2(b) where a and b are angle between polarization axis of photons and polarization axis of respective polarizer.

as i said, i would use black-box, so, whatever "polarization axis of respective polarizer" is, i can no know that! So - what output would i get?
Beef

 

[DevilsAvocado]

What i mean is - where does it start to make difference between twin-photons and photons with same polarization. How would this change results of experiment. Let's say - i have black-box device which creates "twin-photons", which actualy are not twin photons, but simply photons with same polarization. Where would this change output of these measurements.

--
The big idea behind this theory/experiment is, that polarization of these photons becomes "known" only as they get measured (pass thru polarization filter (Wollaston prism?)).
Am i right?

Well, now we are talking!

First, two photons with the same "pre-polarization" will not do any good in EPRB = dead end. Just check the math.

The second part is touching the real juicy stuff in EPRB! This almost makes me throw up! And I know that it 'troubled' John Bell as well...

Who decide, Alice or Bob??

According to Einstein’s Special Relativity, BOTH DECIDE! In different frame of reference!

It doesn’t make sense, right? Only one can decide, anything else is just pure stupidity, right?

But this is the way it is, in current science, and to me this is more shocking than any locality or reality... the future is probably going to show us some real interesting "features" of nature...

 

[0xDEAD BEEF]

DevilsAvocado: "Bubuubibeebuu. Bububeee! Babubabubee?"
0xDEAD BEEF: "Eat this porridge son, it is good for your teeth!"

:)

OK - that was just a joke!

I just really did not get your idea here..

EDIT: we allways have one, who decided first, don't we? But if this decison affected results of other - should not it affect the results of first one as well?

 

[DevilsAvocado]

Part one or two?

 

[DevilsAvocado]

EDIT: we allways have one, who decided first, don't we?

Nope!

But if this decison affected results of other - should not it affect the results of first one as well?

The problem here is that from the perspective of observer Chris, Alice will always measure her photons first, thus Alice is not forced by any rules of EPRB to make correlations with Bob. Alice should always have random 50/50 evenly spread out.

From the perspective of observer Dave, Bob will always measure his photons first, thus Bob is not forced by any rules of EPRB to make correlations with Alice. Bob should always have random 50/50 evenly spread out.

This is pure madness!

Get it??

 

[0xDEAD BEEF]

Ok ok!
0xDEAD BEEF: "Bubuubibeebuu. Bububeee! Babubabubee?"
DevilsAvocado: "Eat this porridge son, it is good for your teeth!"

;)

I really would like to understand this case, because - i have come up with one cool experiment. And i, of courese, will share it with you (but only, if it makes sense)!

So - my question still remains - where is the catch! What is the difference between simple photons having same polarization, but not linked together and twin photons?

In fact - here is my idea:

--- simple case ---
Polairty of two photons is same before they enter Anna's and Bob's polarity detectors. Those photons were generated by our black-box, which generates 2 photons having same polarization, BUT, to match experiment with twin-photons, we have placed our apparatus in black box, so no one can actually see, what is that polarization of those photons.

--- wtf is going on case ---
twin-photons, same polarization (maybe) hitting Anna's and Bob's detectors.

As I understand - it does not matter, what was polarization of those two photons (but it was same), BUT after Annas detector photon has changed. But - it is still not determined, because, if it would be, then this case would be same as "simple case".

Now - the funky experiment which allows data to be exchanged faster than light. (Of course not!, but just idea).

So - let's have this configuration -

Bob has same detector as allways and he is measuring photon orientation at 45 degrees.
Anna has boosted her detector! Instead of one detector, she has 3 detectors(not 3 detectors but 4! she has 3 polarization crustals) with same angle now.
So -
first photon hits Anna's A detector (set at angle 0), next it hits Bob's detector (45). Now - here the tricky part - Anna has 2 more detectors after detector A. She has detector A1 and A2. These detectors are exactly same as detector A, but they are located so in time, that photon first hits A, then B, then A1/A2.

Anna's detector setup would look like this
A1+
A1-
...A
A2+
A2-


So - what we would expect is, that Anna almost allways gets either A1+ or A2-. How ever - if this all strange quantum stuff is reall, then as soon as Bob turns his detector away from 0 (same as Anna), Anna should start receiving also (more than before) A1- and/or A2+.

This would be totally cool. I agree! Faster than light communication!

However - would that happen? If no. What is the difference totally twin-photons and simple photons with same polarization?
Beefs

 

[0xDEAD BEEF]

here picture.
- goes down,
+ goes up

So - does this theory says, that after Bobs measurement (taking place in time between A and A1/A2) we could get A1- or A2+ or we allways will see A1+ or A2-

EDIT: it would make more sense to call A1 A+ and A2 A- :)

 

[DevilsAvocado]

0xDEAD BEEF: "Bubuubibeebuu. Bububeee! Babubabubee?"
DevilsAvocado: "Eat this dead beef son, it is good for your teeth!"

However - would that happen?

With two photons that have a fixed polarization from start, this will happen (at best! ):

Alice polarized 0º
Bob polarized 0º

Alice hit the detector at 0º, and she passes thru 100% of the time.
Bob hit the detector at 30º, and he passes thru 75% of the time.

The relative angle between Alice & Bob is 30º and the mismatch is 25% which seems OK, right?

Next test:

Alice hit the detector at 30º, and she passes thru 75% of the time.
Bob hit the detector at 60º, and he passes thru 25% of the time.

The relative angle between Alice & Bob is now also 30º... but the mismatch is now 50%!? This is not OK!

Babubabubee? Get it?

 

[0xDEAD BEEF]

Thats because you were firing photons at angle about 0.
To be honest - i don't get it. If i would - would i start this weird (nonsense) topic from very begining? By the way - what do you think of my experiment setup with 3 polarizers and 4 detectors at Anna's place?
Beef
Edit: Nope - i got your experiment! That was exactly what my program outputed. Only - i tried out all different options of photon polarization. Now the question is - where is the catch!

 

[DevilsAvocado]

What is it?? Julian Assange’s contact network!?

(terribly sorry, extremely bad joke! )

 

[DevilsAvocado]

Edit: Nope - i got your experiment! That was exactly what my program outputed. Only - i tried out all different options of photon polarization. Now the question is - where is the catch!

The catch (that I have tried to inform you for TWO WHOLE DAYS) is – QM does not behave in the expected classical way, it’s weird; 1 + 1 = 3! ()

Seriously, I have to leave now. You've got some reading to do. I’m sure it will come to you.

Good luck and Cheers!

 

[0xDEAD BEEF]

Ha ha! (irony, but maybe not).

So, how i see this-
Anna got polarization filter and Bob has. Standart setup.
What if we further extend this setup, so that Anna has 3 polarization filters all set at same angle.

So, Anna would have 4 detectors. 2 for each "second" filter like this -
dA++
... pA+
dA+-
...
...... pA
...
dA-+
... pA-
dA--

So pA (first polarization filter) decides polarization and redirects photon to either pA+ or pA- polarization filters. In the mean time twin-photon hits Bob's polarizer, which is set at 45 degree angle.
If we forget about this QM weird stuf, no mater what/when/ever second twin-photon hit Bob's polarization filter, Anna should always get either dA-- or dA++, because, if photon once choose to go through Anna's 0 polarizer in + direction (up), why shoul it choose differnetly, when facing second one pA+ (or vice versa - facing pA-).

In this case standart physics predict, that Anna should only get dA-- or dA++ output! How ever - if this QM stuff is real and Bob's detector has given new properties to photon, while it was traveling through Bob's polarizer set at very different angle than Anna's was - we should see Anna's dA-+ and dA+- detectors fire as well!

This really would prove everything! Scienitifcal brekathrough - i would say. Otherwise... sorry guys, but we are just creating our own virtual reality to play with (wich ain't that bad, since we can learn new thing from it as well).

Beef