[From Bill Powers (2005.04.03.14129 MDT)]

So proof of violations of Bell’s

Inequality seem to be based on not doing experiments. If anybody had ever

just gone ahead and done the experiments and written down the results in

a table, and then analyzed the table, Bell’s Inequality would have been

shown to be true.

Unfortunately, many people have done the experiments, using different

kinds of entities, incuding photons, electrons, and ions. And the

inequality has been shown always to fail.

Let me backtrack. When you say the inequality has been shown to fail, has

this been done by making measurements and filling in a table like the one

shown in Rae on page 37, and then counting the occurrances of up and down

spins in the table? If so then there is something extremely wrong,

because as Rae says, and I can’t contradict him, there is NO WAY those

relationships can violate the basic inequality. That inequality will hold

for ANY arrangement of ups and downs in the table, including

experimentally determined arrangements.

To show me I am wrong, all you have to do is present a table showing the

measured spins in the three columns, and demonstrate that the numbers of

combinations of +'s and -'s do not obey Bell’s Inequality.

Perhaps the problem is that in fact it is impossible to fill in the table

that Rae describes. Maybe that’s what he’s saying that I interpreted to

mean that the experiments weren’t done. But the way he described it, it

would certainly be possible.

New point. On pages 39-40 where he describes the experiments, he seems to

be describing experiments in which only two of the three spins can be

obtained at any given time. Thus in any table of results, one of the

entries for each triplet would be blank. That’s different, of course,

from saying that all three relationships hold at the same time – the two

on the left of the inequality and the relationship between their sum and

the quantity on the right. The counts that Rae talks about couldn’t be

done if there were blanks in the table.

Just to make it clear what we’re talking about, here is the table I’ve

been talking about, with up and down spins being indicated by + and

-:

```
Condition
1 2 3
+ + -
- - +
- + -
```

and so on, in any random arrangment.

The Bell Inequality is then simply

n[1+,2+] + n[2-,3+] >= n[1+,3+],

where n[1+,2+] (for example) means number of rows in which

spin is up in both condition 1 and condition 2.

Since this inequality holds for any arrangement of +'s and -'s

whatsoever, it is not false for any arrangement. Therefore if this table

is filled in with experimental determinations, whether done

simultaneously or in any sequence, the inequality must hold true. Rae’s

description of how to obtain the numbers precludes any dependence on

assumptions or experimental conditions or anything else. The inequality

is simply a mathematical fact about tables of this kind and has nothing

to do with reality or experiments. Is that a misunderstanding on my part?

If so, Rae seems to be under the same impression.

That is so obvious it makes me

think that something is missing from these explanations that everybody

knows but nobody bothers to mention.

Do you think the same is true in the quantum eraser experiment?

As I read Harrison’s paper about Bell’s theorem in the link, it says that

if there are three classes of something, with possible properties A, B,

and C, the classes being Class X (those that have A and not B), Y (those

that have B and not C), and Z (those that have A and not C), the total

number of the members of Classes X and Y is at least as great as the

number of class Z. This is consistent with classical logic. The problem

is that in the actual experiment, the “logically necessary”

result doesn’t hold.

Martin, try to answer this simple question. How are the results of the

experiments tabulated? Are they in a table showing triples of results, as

in the Rae table above? If they are, then the inequality holds. There is

simply no way it can not hold, because this is a property of the table

and has nothing to do with how the table was constructed. It is true of

all possible tables of this kind.

The only guess I can make is that such tables have never been constructed

– that the results have been presented in some other way, and never

written down in a table of triplets of + and - spins.

## Harrison says:

We have made two assumptions in the proof. These are:

l*Logic is a valid way to reason.**l*Parameters exist whether they are measured or not. For example, when

we collected the terms **Number(A, not B, not C) + Number(A, B, not**

C) to get **Number(A, not C)**, we assumed that either **not**

B or **B** is true for every member.

Why do we have to assume anything? Aren’t these three quantities EACH the

results of experimental determinations? In other words, we measure A, B,

and C, noting down whether the spins are + or - after each determination.

That completes one row of the table. Then we repeat as many times as we

like, and finally sum up the numbers of + and - marks for each condition.

Isn’t that the way it’s done?

You may call it spooky, perhaps,

but if you accept the experimental observations, I think you have to deal

with the apparent spookiness.

Since we’re talking about perceptions here and not external reality, the

spookiness is relative to what we expect. The spookiness is in the

explanation we offer, not in nature. I’m not yet convinced that we don’t

have an internal contradiction here, which is the only kind of spookiness

we have to disallow unconditionally.

Best,

Bill P.