Physics Letters B 739 (2014) 451–456
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Is string interaction the origin of quantum mechanics?
Itzhak Bars
∗
, Dmitry Rychkov
Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
10 August 2014
Received
in revised form 23 September
2014
Accepted
23 October 2014
Available
online 27 October 2014
Editor:
M. Cveti
ˇ
c
String theory was developed by demanding consistency with quantum mechanics. In this paper we wish
to reverse the reasoning. We pretend that open string field theory is a fully consistent definition of the
theory – it is at least a self-consistent sector. Then we find in its structure that the rules of quantum
mechanics emerge from the non-commutative nature of the basic string joining/splitting interactions.
Thus, rather than assuming the quantum commutation rules among the usual canonical variables we
derive them from the physical process of string interactions. Morally we could apply such an argument
to M-theory to cover quantum mechanics for all physics. If string or M-theory really underlies all physics,
it seems that the door has been opened to an explanation of the origins of quantum mechanics from the
physical processes point of view.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP
3
.
1. Introduction
Quantum mechanics (QM) works amazingly well in all known
parts of microscopic physics. One can deduce classical physics as
the limit of QM for large quantum numbers (or equivalently the
small
¯
h limit). Hence the general belief is that QM is the only rule
for all types of mechanics. Despite the tremendous success of QM,
the fundamental commutation rules from which all QM is derived,
namely [x, p] = i
¯
h for every degree of freedom, need to be put
in mysteriously “by hand” without any underlying reasoning. It is
well established that, if the quantization rule is accepted, then all
of the amazing and correct consequences of quantum mechanics
follow. The success of QM is of course a justification to accept the
mysterious rule as correct, but it leaves us begging for an underly-
ing
explanation.
In
this paper we will present arguments that there may be a
physical explanation for where the QM rules come from. We will
show that there is a clear link between the commutation rules of
QM operators and the non-commutative string joining/splitting in-
teractions
[1] that were expressed in the language of the Moyal
star formulation of string field theory (MSFT) [2] in a recently
improved and more intuitive version [3]. Except for the mathe-
matical
similarity, the Moyal in MSFT has nothing to do with
the Moyal product [4] that reproduces
1
QM, because the basic
*
Corresponding author.
E-mail
address: bars@usc.edu (I. Bars).
1
For the explanation of how the well known Moyal product [4] for classical phase
space functions reproduces all the details of quantum mechanics, read Section III
in [3] which
summarizes the essentials of this correspondence.
non-commuting quantities in the string in MSFT are very differ-
ent
than the canonical conjugates indicated by quantum mechan-
ics.
Nevertheless, we found how to link the basic QM commutators
to the string and derive the QM rules only from the rules of string
joining/splitting. This link suggests that there is a deeper physi-
cal
phenomenon, namely string interactions, underlying the usual
quantum rules of QM, thus providing a possible explanation for
where they come from.
The
essential arguments for the thesis of this paper can be
adequately presented in a simplified model that captures the nec-
essary
ingredients of MSFT. The simplified model, which we call
mini-MSFT, consists basically of the phase space system of two
particles, rather than the full phase space of an infinite number
of particles that make up all the points on a string. The two par-
ticles
may be thought of as the end points of an open string, but
it is also possible not to think of the string concept at all to dis-
cuss
the main ideas. This is because only the properties of phase
space, rather than the property of the dynamics of the two par-
ticles
enter in the main part of the discussion. Hence to keep our
discussion as simple as possible, we will define the mini-MSFT sys-
tem
in Section 3 and discuss how to derive the QM properties from
“string” interactions. The mini-MSFT may be a useful model in its
own right to discuss some physically interesting systems, as in the
examples we outline at the end of Section 3.
Even
though we will not use the full machinery of MSFT in
this paper, we begin our discussion in Section 2 with a brief de-
scription
of its setup so that the reader, even without knowing
much about string theory, can see the connection between the full
string field theory and the simplified 2-particle model in Section 3,
and be able to deduce easily that the arguments for the thesis
http://dx.doi.org/10.1016/j.physletb.2014.10.053
0370-2693/
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by
SCOAP
3
.