# Assumptions of the Bell theorem

I use the words "local" and "non-local" only in one proper mathematical meaning, i.e., that local observables in relativistic QFTs commute with the Hamilton density when their space-time arguments are space-like separated, i.e., ##[\hat{O}(x),\hat{\mathcal{H}}(y)]=0## for ##(x-y) \cdot (x-y)<0## (west-coast convention, i.e., ##\eta_{\mu \nu}=\mathrm{diag}(1,-1,-1,-1)##. Thus there cannot be any causal connections between space-like separated events.
Why is it not possible for the A measurement to cause the result at B if "local observables in relativistic QFTs commute with the Hamilton density when their space-time arguments are space-like separated"? How is this proven?

physika and Demystifier
Lynch101
Gold Member
I use the words "local" and "non-local" only in one proper mathematical meaning, i.e., that local observables in relativistic QFTs commute with the Hamilton density when their space-time arguments are space-like separated, i.e., ##[\hat{O}(x),\hat{\mathcal{H}}(y)]=0## for ##(x-y) \cdot (x-y)<0## (west-coast convention, i.e., ##\eta_{\mu \nu}=\mathrm{diag}(1,-1,-1,-1)##. Thus there cannot be any causal connections between space-like separated events.

For me an observable in Q(F)T has a predetermined value if and only if the system is prepared in a state such that the probability for measuring one of the possible values with 100% probability. Otherwise the value is indetermined before measurement and the state preparation only implies a certain probability for finding each of its possible values and nothing else. In which state the system is after the measurement depends on the construction of the measurement device, i.e., the specific interaction between the measured system and the measurement device. Since these interactions are just usual interactions described by local relativistic QFT there's no faster-than-light causal effect by a local measurement at one place and another space-like separated local measurement at another place. If the two space-like separated local measurements refer to entangled parts of a quantum system, then the observed correlations are not mutually caused by the local measurements but are due to the preparation of the system in the entangled state before any of the two measurements where done. By construction there is no contradiction between relativistic spacetime causality constraints and local relativistic QFT.

To confuse long-ranged correlations and inseparability of entangled systems with causal interactions at a distance is only misleading and contradicts the very foundational construction of local relativistic QFT.
But do you accept that some physicists use the term 'non-local' to refer to FTL causal influences?

vanhees71
Gold Member
I can't force people to use an understandable and consistent terminology, but if they use the term non-local in this sense, they don't talk about standard local relativistic QFT or they falsely name phenomena non-local when they talk about correlations of far-distant local observations.

Lynch101
Gold Member
I can't force people to use an understandable and consistent terminology, but if they use the term non-local in this sense, they don't talk about standard local relativistic QFT or they falsely name phenomena non-local when they talk about correlations of far-distant local observations.
So, just going back to the original point, whether the term 'non-local' or 'inseparability' is (mis)used, the (or an) issue of contention is whether or not there are FTL causal influences in nature which explain the observed correlations in quantum experiments.

Edit: again, it seems to come back to the question of completeness.

While quantum theory might not necessarily be FTL 'non-local' there are those who would say that nature must employ FTL causation to explain the outcomes of individual experiments.

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vanhees71
Gold Member
Again:

Locality: There are no FTL causal influcences according to local relativistic QFT (by construction)

Completeness: There's not one reproducible observation that contradicts the prediction of QFT. In this sense it's complete as a natural sciences.

Whether it's complete in a philosophical or religious sense, is subject to personal opinion, and this cannot be answered by the scientific method and as such not subject for discussion in a science forum.

Lynch101
Gold Member
Again:

Locality: There are no FTL causal influcences according to local relativistic QFT (by construction)
There are according to Bohemian Mechanics

Completeness: There's not one reproducible observation that contradicts the prediction of QFT. In this sense it's complete as a natural sciences.

Whether it's complete in a philosophical or religious sense, is subject to personal opinion, and this cannot be answered by the scientific method and as such not subject for discussion in a science forum.
So, interpretations of quantum theory which contradict the notion of 'no FTL causal influences' are not subject for discussion in a science forum?

physika
vanhees71
Gold Member
There is no convincing Bohmian reinterpretation of relativistic local QFT. So I don't know, what you are referring to.

Of course you can discuss models that contradict the so far observed facts and their descriptions by local relativistic QFT. Such models are per se "scientific" if they make clear predictions about observables which contradict the established theories and thus make them testable to decide whether they are better descriptions of the phenomena or the established theories.

Bell's inequality is a prime example for this: Making some assumptions, leading to observable predictions contradicting the established quantum theory (Bell's inequalities) makes it possible to test them and quantum theory against each other. The unanimous decision favors quantum theory by an amazing level of significance.

Lord Jestocost
If two 'ends' are spatially separated and an action performed one one end instantaneously affects the other end, then, by my reasoning, this would imply an FTL causal influence. Is there any alternative?
predefined values.

vanhees71
Gold Member
or correlations due to entanglement with maximally (!) undetermined values as described by Q(F)T.

Gold Member
There is no convincing Bohmian reinterpretation of relativistic local QFT.
How do you know that? Did you actually read some of the existing Bohmian reinterpretations of relativistic QFT?

Gold Member
Locality: There are no FTL causal influcences according to local relativistic QFT (by construction)
Nonlocality: There are FTL causal influences according to Bohmian relativistic QFT (by construction)

Completeness: There's not one reproducible observation that contradicts the prediction of QFT. In this sense it's complete as a natural sciences.
Completeness: There's not one reproducible observation that contradicts the prediction of Bohmian QFT. In this sense it's complete as a natural sciences.

Whether it's complete in a philosophical or religious sense, is subject to personal opinion, and this cannot be answered by the scientific method and as such not subject for discussion in a science forum.
Whether Bohmian QFT is convincing in a philosophical or religious sense, is subject to personal opinion, and this cannot be answered by the scientific method and as such not subject for discussion in a science forum.

There is no convincing Bohmian reinterpretation of relativistic local QFT. So I don't know, what you are referring to.

Of course you can discuss models that contradict the so far observed facts and their descriptions by local relativistic QFT. Such models are per se "scientific" if they make clear predictions about observables which contradict the established theories and thus make them testable to decide whether they are better descriptions of the phenomena or the established theories.

Bell's inequality is a prime example for this: Making some assumptions, leading to observable predictions contradicting the established quantum theory (Bell's inequalities) makes it possible to test them and quantum theory against each other. The unanimous decision favors quantum theory by an amazing level of significance.
Tumulka

Gold Member
Tumulka
Tumulka what?

Tumulka what?

Bohmian relativistic...

vanhees71
Gold Member
How do you know that? Did you actually read some of the existing Bohmian reinterpretations of relativistic QFT?
Yes, you pointed to some once, and I didn't find them convincing.

vanhees71
Gold Member
Nonlocality: There are FTL causal influences according to Bohmian relativistic QFT (by construction)
That's why it's not convincing, because a relativistic theory shouldn't violate the very foundations of relativistic physics, among them the causality structure implemented in the spacetime model.
Completeness: There's not one reproducible observation that contradicts the prediction of Bohmian QFT. In this sense it's complete as a natural sciences.
So you say, there's an unanimous observation in accordance with FTL causal influences?
Whether Bohmian QFT is convincing in a philosophical or religious sense, is subject to personal opinion, and this cannot be answered by the scientific method and as such not subject for discussion in a science forum.
My religious believes are unaffected by anything science finds out about Nature, because these are completely disjoint realms of human experience, and indeed religious believes shouldn't be discussed in a science forum (imho also philosophy is only confusing the science either).

martinbn
Nonlocality: There are FTL causal influences according to Bohmian relativistic QFT ( by construction).
Let me guess. The two of you mean different things by FTL causal influences.

Demystifier, Lynch101 and vanhees71
Gold Member
That's why it's not convincing, because a relativistic theory shouldn't violate the very foundations of relativistic physics, among them the causality structure implemented in the spacetime model.
OK, so it's not convincing in the sense that it doesn't fit some philosophical prejudices. (Not in the sense that it doesn't fit observations, because Bohmian and standard QFT make the same measurable predictions.) Your arguments against Bohmian QFT are philosophical (not scientific) as much as my arguments for it are philosophical.

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Gold Member
So you say, there's an unanimous observation in accordance with FTL causal influences?
Yes. For instance, violation of Bell inequalities is in Bohmian mechanics explained by FTL causal influences.

Gold Member
imho also philosophy is only confusing the science either
Then why do you repeatedly use philosophical arguments against Bohmian mechanics? Or, for that matter, against all interpretations of QM that differ from your favored one?

physika
Gold Member
Let me guess. The two of you mean different things by FTL causal influences.
The difference is in entities between which the influences are supposed to happen. Standard quantum theory talks about causal influences between states in the Hilbert space of different subsystems. Bohmian quantum theory talks about causal influences between ontic states (particle positions or field configurations), which are not states in the Hilbert space. Standard quantum theory does not even talk about ontic states, so it cannot see nonlocality that ontic theories can.

vanhees71
Gold Member
OK, so it's not convincing in the sense that it doesn't fit some philosophical prejudices. (Not in the sense that it doesn't fit observations, because Bohmian and standard QFT make the same measurable predictions.) Your arguments against Bohmian QFT are philosophical (not scientific) as much as my arguments for it are philosophical.
I consider causality the prerequisite of all science. If there were no causality we wouldn't have any natural sciences, because there were no natural laws to be discovered.

physika
Lord Jestocost
Gold Member
Regarding quantum mechanics, I would speak of “statistical causality”.

vanhees71
martinbn