I discuss a hypothetical historical context in which a Bohm-like deterministic interpretation of the Schrödinger equation is proposed before the Born probabilistic interpretation and argue that in such a context the Copenhagen (Bohr) interpretation would probably have not achieved great popularity among physicists.

1.
See, for example, the recent book by
D.
Lindley
,
Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science
(
Doubleday
,
New York
,
2007
).
2.
L. E.
Ballentine
, “
The statistical interpretation of quantum mechanics
,”
Rev. Mod. Phys.
42
,
358
381
(
1970
).
3.
D.
Bohm
, “
A suggested interpretation of the quantum theory in terms of ‘hidden variables.’ I
,”
Phys. Rev.
85
(
2
),
166
179
(
1952
);
D.
Bohm
, “
A suggested interpretation of the quantum theory in terms of ‘hidden variables.’ II
,”
Phys. Rev.
85
(
2
),
180
193
(
1952
).
4.
E.
Nelson
, “
Derivation of the Schrödonger equation from Newtonian mechanics
,”
Phys. Rev.
150
,
1079
1085
(
1966
).
5.
G. C.
Ghirardi
,
A.
Rimini
, and
T.
Weber
, “
Unified dynamics for microscopic and macroscopic systems
,”
Phys. Rev. D
34
,
470
491
(
1986
).
6.
G.
Birkhoff
and
J.
von Neumann
, “
The logic of quantum mechanics
,”
Ann. Math.
37
,
823
843
(
1936
).
7.
The information-theoretic interpretation gradually developed from the Copenhagen interpretation, so it is difficult to specify the first paper in which this interpretation was proposed. For a review, see, for example,
A.
Peres
and
D.
Terno
, “
Quantum information and relativity theory
,”
Rev. Mod. Phys.
76
,
93
123
(
2004
).
8.
R. B.
Griffiths
, “
Consistent histories and the interpretation of quantum mechanics
,”
J. Stat. Phys.
36
,
219
272
(
1984
).
9.
H.
Everett
, “
Relative state interpretation of quantum mechanics
,”
Rev. Mod. Phys.
29
,
454
462
(
1957
).
10.
C.
Rovelli
, “
Relational quantum mechanics
,”
Int. J. Theor. Phys.
35
,
1637
1678
(
1996
).
11.
A similar thesis with somewhat different arguments has been advocated by
J. T.
Cushing
,
Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony
(
Univ. of Chicago
,
Chicago
,
1994
).
12.

Remarks concerning the actual history of quantum mechanics are given in the references.

13.
R.
Tumulka
, “
Understanding Bohmian mechanics: A dialogue
,”
Am. J. Phys.
72
(
9
),
1220
1226
(
2004
).
14.
D. F.
Styer
 et al, “
Nine formulations of quantum mechanics
,”
Am. J. Phys.
70
(
3
),
288
297
(
2002
).
15.
Such an interpretation was proposed in 1926:
E.
Madelung
, “
Quantentheorie in hydrodynamischer form
,”
Z. Phys.
40
,
322
326
(
1926
).
16.
These arguments might have looked similar to those in
D.
Dürr
,
S.
Goldstein
, and
N.
Zanghì
, “
Quantum equilibrium and the origin of absolute uncertainty
,”
J. Stat. Phys.
67
,
843
907
(
1992
);
A.
Valentini
, “
Signal-locality, uncertainty, and the subquantum H-theorem
,”
Phys. Lett. A
156
,
5
11
(
1991
).
17.
This interpretation is known today as the Bohm interpretation, while the status of the orthodox interpretation is enjoyed by a significantly different interpretation. De Broglie proposed the same equation for particle trajectories much earlier than Bohm, but de Broglie did not develop a theory of quantum measurements, so he could not reproduce the predictions of standard quantum mechanics for observables other than particle positions, such as particle momenta. For more historical details see
G.
Bacciagaluppi
and
A.
Valentini
,
Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference
(
Cambridge U.P.
,
Cambridge
, to be published),
18.
Such arguments might have looked similar to those in
H.
Nikolić
, “
Classical mechanics without determinism
,”
Found. Phys. Lett.
19
,
553
566
(
2006
). In this paper it is shown that classical statistical physics can be represented by a nonlinear modification of the Schrödinger equation, in which classical particle trajectories may be identified with special solitonic solutions. A Bohr-like interpretation of general (not solitonic) solutions suggests that even classical particles might not have trajectories when they are not measured, while a measurement of the previously unknown position may induce an indeterministic wave-function collapse to a solitonic state.
19.
For a review of the theory of decoherence with emphasis on the interpretational issues, see
M.
Schlosshauer
, “
Decoherence, the measurement problem, and interpretations of quantum mechanics
,”
Rev. Mod. Phys.
76
,
1267
1305
(
2004
).
20.
Tachyons were actually introduced in physics somewhat later. See
O. M. P.
Bilaniuk
,
V. K.
Deshpande
, and
E. C. G.
Sudarshan
, “
Meta’ relativity
,”
Am. J. Phys.
30
(
10
),
718
723
(
1962
);
O. M. P.
Bilaniuk
and
E. C. G.
Sudarshan
, “
Particles beyond the light barrier
,”
Phys. Today
22
(
5
),
43
51
(
1969
).
21.
It is well known that a wave equation describing the propagation of sound with velocity cs, in a fluid has the same form as a special-relativistic wave equation describing the propagation of light with the velocity c, in vacuum. Consequently, such a wave equation of sound is invariant with respect to Lorentz transformations in which the velocity c, is replaced by cs,. A fluid analogy of curved spacetime may also be constructed by introducing an inhomogeneous fluid. For more details, see, for example,
M.
Visser
, “
Acoustic black holes: Horizons, ergospheres, and Hawking radiation
,”
Class. Quantum Grav.
15
,
1767
1791
(
1998
).
22.
This proof is now usually attributed to Bell, although other versions of this proof exist. For a pedagogic review see
F.
Laloë
, “
Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems
,”
Am. J. Phys.
69
(
6
),
655
701
(
2001
).
23.

Many of the current interpretations of quantum mechanics mentioned in Sec. I are of this form.

24.
String theory also contains evidence against locality at the fundamental level. Although the theory was originally formulated as a local theory, nonlocal features arise in a surprising and counterintuitive manner. It turns out that string theories defined on different background spacetimes may be mathematically equivalent, which suggests that spacetime is not fundamental. Without a fundamental notion of spacetime, there is no fundamental notion of locality and relativity. It is believed that a more fundamental formulation of string theory should remove locality more explicitly, and known local laws of field theory should emerge as an approximation. See, for example,
G. T.
Horowitz
, “
Spacetime in string theory
,”
New J. Phys.
7
,
201
213
(
2005
);
N.
Seiberg
, “
Emergent spacetime
,” arXiv:hep-th/0601234.
25.
It is known that relativistic quantum mechanics based on the Klein-Gordon equation and quantum field theory does not contain a position operator. Therefore, the conventional interpretation of quantum theory does not have clear predictions for probabilities of particle positions in the relativistic regime. The fundamentally deterministic Bohmian interpretation may lead to clearer predictions, which means that it may be empirically richer than (and thus nonequivalent to) the conventional formulation. For more details, see, for example,
H.
Nikolić
, “
Relativistic quantum mechanics and the Bohmian interpretation
,”
Found. Phys. Lett.
18
,
549
561
(
2005
);
H.
Nikolić
, “
Is quantum field theory a genuine quantum theory? Foundational insights on particles and strings
,” arXiv:0705.3542. Unfortunately, experiments that could confirm or reject such a formulation have not yet been performed. This version of the Bohmian interpretation, which is not empirically equivalent to the conventional interpretation, is considered controversial even among the proponents of the Bohmian interpretation. Nevertheless, in an alternative history of quantum mechanics in which the conventional probabilistic interpretation never became widely accepted, such a fundamentally deterministic Bohmian interpretation might have seemed more natural.
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