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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Bohr–Einstein debates | 5/7 | https://en.wikipedia.org/wiki/Bohr–Einstein_debates | reference | science, encyclopedia | 2026-05-05T16:35:15.514856+00:00 | kb-cron |
=== Bohr's triumph === The triumph of Bohr consisted in his demonstrating, once again, that Einstein's subtle argument was not conclusive, but even more so in the way that he arrived at this conclusion by appealing precisely to one of the great ideas of Einstein: the principle of equivalence between gravitational mass and inertial mass, together with the time dilation of special relativity, and a consequence of these—the gravitational redshift. Bohr showed that, in order for Einstein's experiment to function, the box would have to be suspended on a spring in the middle of a gravitational field. In order to obtain a measurement of the weight of the box, a pointer would have to be attached to the box which corresponded with the index on a scale. After the release of a photon, a mass
m
{\displaystyle m}
could be added to the box to restore it to its original position and this would allow us to determine the energy
E
=
m
c
2
{\displaystyle E=mc^{2}}
that was lost when the photon left. The box is immersed in a gravitational field of strength
g
{\displaystyle g}
, and the gravitational redshift affects the speed of the clock, yielding uncertainty
Δ
t
{\displaystyle \Delta t}
in the time
t
{\displaystyle t}
required for the pointer to return to its original position. Bohr gave the following calculation establishing the uncertainty relation
Δ
E
Δ
t
≥
h
{\displaystyle \Delta E\Delta t\geq h}
. Let the uncertainty in the mass
m
{\displaystyle m}
be denoted by
Δ
m
{\displaystyle \Delta m}
. Let the error in the position of the pointer be
Δ
q
{\displaystyle \Delta q}
. Adding the load
m
{\displaystyle m}
to the box imparts a momentum
p
{\displaystyle p}
that we can measure with an accuracy
Δ
p
{\displaystyle \Delta p}
, where
Δ
p
Δ
q
{\displaystyle \Delta p\Delta q}
≈
h
{\displaystyle h}
. Clearly
Δ
p
≤
t
g
Δ
m
{\displaystyle \Delta p\leq tg\Delta m}
, and therefore
t
g
Δ
m
Δ
q
≥
h
{\displaystyle tg\Delta m\Delta q\geq h}
. By the redshift formula (which follows from the principle of equivalence and the time dilation), the uncertainty in the time
t
{\displaystyle t}
is
Δ
t
=
c
−
2
g
t
Δ
q
{\displaystyle \Delta t=c^{-2}gt\Delta q}
, and
Δ
E
=
c
2
Δ
m
{\displaystyle \Delta E=c^{2}\Delta m}
, and so
Δ
E
Δ
t
=
c
2
Δ
m
Δ
t
≥
h
{\displaystyle \Delta E\Delta t=c^{2}\Delta m\Delta t\geq h}
. We have therefore proven the claimed
Δ
E
Δ
t
≥
h
{\displaystyle \Delta E\Delta t\geq h}
. More recent analyses of the photon box debate questions Bohr's understanding of Einstein's thought experiment, referring instead to a prelude to the EPR paper, focusing on inseparability rather than indeterminism being at issue.
== Post-revolution: Second stage ==
The second phase of Einstein's "debate" with Bohr and the orthodox interpretation is characterized by an acceptance of the fact that it is, as a practical matter, impossible to simultaneously determine the values of certain incompatible quantities, but the rejection that this implies that these quantities do not actually have precise values. Einstein rejects the probabilistic interpretation of Born and insists that quantum probabilities are epistemic and not ontological in nature. As a consequence, the theory must be incomplete in some way. He recognizes the great value of the theory, but suggests that it "does not tell the whole story", and, while providing an appropriate description at a certain level, it gives no information on the more fundamental underlying level:
I have the greatest consideration for the goals which are pursued by the physicists of the latest generation which go under the name of quantum mechanics, and I believe that this theory represents a profound level of truth, but I also believe that the restriction to laws of a statistical nature will turn out to be transitory....Without doubt quantum mechanics has grasped an important fragment of the truth and will be a paragon for all future fundamental theories, for the fact that it must be deducible as a limiting case from such foundations, just as electrostatics is deducible from Maxwell's equations of the electromagnetic field or as thermodynamics is deducible from statistical mechanics. These thoughts of Einstein would set off a line of research into hidden variable theories, such as the Bohm interpretation, in an attempt to complete the edifice of quantum theory. If quantum mechanics can be made complete in Einstein's sense, it cannot be done locally; this fact was demonstrated by John Stewart Bell with the formulation of Bell's inequality in 1964. Although, the Bell inequality ruled out local hidden variable theories, Bohm's theory was not ruled out. A 2007 experiment ruled out a large class of non-Bohmian non-local hidden variable theories, though not Bohmian mechanics itself.
== Post-revolution: Third stage ==
=== The argument of EPR ===
In 1935 Einstein, Boris Podolsky and Nathan Rosen developed an argument, published in the magazine Physical Review with the title Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, based on an entangled state of two systems. Before coming to this argument, it is necessary to formulate another hypothesis that comes out of Einstein's work in relativity: the principle of locality. The elements of physical reality which are objectively possessed cannot be influenced instantaneously at a distance. David Bohm picked up the EPR argument in 1951. In his textbook Quantum Theory, he reformulated it in terms of an entangled state of two particles, which can be summarized as follows:
-
Consider a system of two photons which at time t are located, respectively, in the spatially distant regions A and B and which are also in the entangled state of polarization
| Ψ ⟩{\displaystyle \left|\Psi \right\rangle }
described below: