# Sustaining Open Data as a Digital Common – Design principles for Common Pool
Resources applied to Open Data Ecosystems

Johan Linåker<EMAIL_ADDRESS>0000-0001-9851-1404 RISE Research
Institutes of SwedenLundSweden and  Per Runeson<EMAIL_ADDRESS>0000-0003-2795-4851 Lund UniversityP.O. Box 118LundSweden

(2022)

###### Abstract.

_Motivation._ Digital commons is an emerging phenomenon and of increasing
importance, as we enter a digital society. Open data is one example that makes
up a pivotal input and foundation for many of today’s digital services and
applications. Ensuring sustainable provisioning and maintenance of the data,
therefore, becomes even more important. _Aim._ We aim to investigate how such
provisioning and maintenance can be collaboratively performed in the community
surrounding a common. Specifically, we look at Open Data Ecosystems (ODEs), a
type of community of actors, openly sharing and evolving data on a
technological platform. _Method._ We use Elinor Ostrom’s design principles for
Common Pool Resources as a lens to systematically analyze the governance of
earlier reported cases of ODEs using a theory-oriented software engineering
framework. _Results._ We find that, while natural commons must regulate
consumption, digital commons such as open data maintained by an ODE must
stimulate both use and data provisioning. Governance needs to enable such
stimulus while also ensuring that the collective action can still be
coordinated and managed within the frame of available maintenance resources of
a community. Subtractability is, in this sense, a concern regarding the
resources required to maintain the quality and value of the data, rather than
the availability of data. Further, we derive empirically-based recommended
practices for ODEs based on the design principles by Ostrom for how to design
a governance structure in a way that enables a sustainable and collaborative
provisioning and maintenance of the data. _Conclusion._ ODEs are expected to
play a role in data provisioning which democratize the digital society and
enables innovation from smaller commercial actors. Our empirically based
guidelines intend to support this development.

Open Data, Data Ecosystems, Digital Commons, Ostrom, Sustainability, Common
Pool Resources

††copyright: acmcopyright††journalyear: 2022††doi:
10.1145/1122445.1122456††conference: ; ; ††ccs: Software and its engineering
Open source model

##  1\. Introduction

With the emergence of a digital society, the concept of commons has been
applied to digital phenomena with applications ranging, from Open Source
Software (OSS) (Schweik and English, 2012; Benkler, 2014) to open data (Ruhaak
et al., 2021; Coyle et al., 2020) and online projects such as Wikipedia (Forte
et al., 2009; Viégas et al., 2007). A main reason for this relates to the
parallel between the sustainability of digital commons (Fuster Morell, 2014),
and the phenomenon referred to as “the tragedy of the commons”, where
individuals act in self-interest and over-utilize the common resource. The
“tragedy” is commonly exemplified through an open pasture where the rational
herder out of self-interest aims to maximize his (momentary) benefit from the
pasture by adding more animals, which in the end leads to over-grazing and
thereby reducing the benefit that can be gained from the pasture by any other
herder (Hardin, 1968).

The open pasture can in this sense be considered a Common Pool Resource (CPR),
implying a resource system where it is difficult (or costly) to exclude other
actors from benefiting from the use of its resource units (i.e., grass in the
herding example) (Ostrom, 1990). A second trait, also in the open pasture
example, is that a CPR is subtractable in the sense that over-utilization by
some actors may reduce the benefit to be obtained from others if the system is
not maintained.

To manage the tragedy, and the will to “free-ride” on the cost of others,
researchers have argued for central regulation or privatization of the CPR
being the only options forward. However, as explained by Ostrom (Ostrom,
1990), CPRs can very well be sustained (at least in small and local
communities). From her work, design principles, that characterize robust
institutions for managing CPRs, have emerged (Ostrom, 1990). These have later
been validated and extended by Cox et al. (Cox et al., 2010), empirically
confirming them being well supported.

Preliminary proposals of how to map Ostrom’s principles to digital commons
have been proposed (Coyle et al., 2020; Ruhaak et al., 2021; Forte et al.,
2009; Rozas, 2017). However, when mapping theory from general commons to
digital commons, it is worth noting a fundamental difference. Digital commons,
such as software and data, can be consumed by multiple consumers at the same
time without reducing the benefits extracted by each consumer as the marginal
production cost is close to zero (copying data or software (Benkler, 2014)),
implying that digital commons are non-rival (Coyle et al., 2020; O’Mahony,
2003). As a consequence, considering the ecosystem in which the digital common
is shared and maintained, the value increases – rather than the opposite –
since having more members raises the probability that the ecosystem stays
alive and the common resource is maintained (Iansiti and Levien, 2004).

The limitations are rather in labor and computing resources to maintain the
commons (Curto-Millet and Corsín Jiménez, 2022), and as in Hardin’s tragedy
and following streams of literature, free-riding is a large issue. Limited or
no maintenance of the digital common may result in vulnerabilities being
introduced, dependencies breaking, machine learning training-sets becoming
invalid, or business value being lost leading to users abandoning the common
to further deteriorate as a consequence (Curto-Millet and Corsín Jiménez,
2022).

In this paper, we investigate how the value of a digital common (Morell, 2010)
in the instance of open data (Ruhaak et al., 2021; Coyle et al., 2020) (i.e.,
not open hardware or software), can be sustained by its users and producers
organized in a surrounding ecosystem (Benkler, 2014; Fuster Morell, 2014).
Specifically, we explore how Ostrom’s design principles may be applied in the
context of ODEs to design a governance structure that sustains the
development, sharing, and quality of the open data, along with its boundary
resources, while still enabling open use and appropriation similar as to
Wikipedia (Viégas et al., 2007; Forte et al., 2009) and OSS commons in general
(Fuster Morell, 2014; Schweik and English, 2012; Rozas, 2017). For each of the
design principles, we analyze previously reported cases of open data (Runeson
et al., 2021; Viégas et al., 2007) and open software ecosystems (Forte et al.,
2009; Rozas, 2017), and observe how their governance has been set up to enable
joint maintenance of the data as well as its boundary resources. The analysis
is then validated against the earlier reported practice proposals of how to
map Ostrom’s principles to digital commons (Coyle et al., 2020; Ruhaak et al.,
2021).

We find, in the case of ODEs, that the governance is designed to _promote
participation and encourage contributions_ , rather than monitor and sanction
usage of a common, as the case with the original design principles.
Specifically, we propose for each principle, a recommendation for
orchestrators or members of ODEs in how they may design their governance in
such a way that it promotes the sustainability of open data and the potential
value it can provide in existing and future ecosystems.

##  2\. Background and related work

###  2.1. Open Data Ecosystems

The ecosystem lens, stemming from the biological setting, has been used both
on business (Iansiti and Levien, 2004) and technical levels (Jansen et al.,
2009) to describe how actors collaborate in a common context towards a common
goal while benefiting from the joint efforts more than what they would in
isolation. Software ecosystems, including OSS, is a well-explored area where
actors collaborate on the development and maintenance of a common software
platform, that actors in turn can reuse and extend in a common market or type
of use case (Alves et al., 2018). Recently, the lens had been adopted to data
ecosystems as well (S Oliveira et al., 2019).

Following work by Runeson et al. (Runeson et al., 2021; Linåker and Runeson,
2021), we define an Open Data Ecosystem as a networked _community of actors_
(organizations and individuals), which base their relations to each other on a
_common interest_. This interest is underpinned by a _technological platform_
that enables actors to process data (e.g., find, archive, publish, consume, or
reuse) as well as to foster innovation, create value, or support new
businesses. Actors _collaborate on the data and boundary resources_ (e.g.,
software and standards), through the exchange of information, resources, and
artifacts.

The technological platform, that enables and facilitates the collaboration, is
maintained and facilitated by a platform provider, who usually is the main
actor that initiated the ecosystem and orchestrates the overarching
collaboration (Linåker and Runeson, 2021). This actor is commonly constituted
by a public sector organization, as sharing of data from and between private
actors is still an emerging phenomenon (S Oliveira et al., 2019). In cases
where the data being shared openly is either produced or collected by a public
sector organization, the data is commonly referred to as open government data
(OGD) (Linåker and Runeson, 2021).

The ecosystem actors may be categorized based on their importance for the
ecosystem at large and the influence, formal or informal, that usually follows
regarding the platform and collaboration. This can be visualized using
Nakakoji et al.’s onion model, where those actors in the layers closest to the
center have a higher level of influence compared to those further out who are
usually more passive or inactive (Nakakoji et al., 2002). The center is made
up of the platform provider or group of actors (commonly referred to as
keystones) who are leading the decision-making.

On a functional level, actors in an ecosystem can take on one or multiple
roles, e.g., data providers, data brokers, infrastructure and tool providers,
service providers, application developers, and application users (Immonen et
al., 2014; Kitsios et al., 2017). They interact in what can be referred to as
value networks, where data is shared, enriched, and used as input to new and
improved products, services, or use cases that create value for the actors
(Lindman et al., 2015; Immonen et al., 2014). However, incentives may not
necessarily be tied to the data, but rather the knowledge and boundary
resources shared as a consequence of the collaboration (Runeson et al., 2021).

###  2.2. The emergence of digital commons

Commons is a broad term, seldom explicitly defined (Hess, 2008; Jullien and
Roudaut, 2020). According to Hess and Ostrom, commons conveys a “notion of
shared ownership, participation, and responsibility” (Hess and Ostrom, 2006).
Hess later proposes the definition of a common as a “resource shared by a
group where the resource is vulnerable to enclosure, overuse, and social
dilemmas. Unlike a public good, it requires management and protection in order
to sustain it.” Underpinning the definition, is a mapping of what types of
commons that has emerged, where Hess distinguishes between the traditional
commons (such as fisheries, forests, and grazing lands), and other types as
that of knowledge commons and its subset of online mass collaboration projects
(including Wikipedia, and OSS in general) (Hess, 2008).

The traditional type of commons aligns well with what Ostrom considers as
CPRs, i.e., a resource system that is large enough to be non-exclusive, yet
subtractable in terms of resource units within the system (Ostrom, 1990).
Knowledge commons on the other hand, and online mass collaboration projects
specifically, expand the understanding of what a common may imply. Benkler
characterizes this expansion with the distinction between bounded and open
commons (Benkler, 2014). The _bounded_ common resource is appropriated
exclusively and governed within a community as with traditional commons. The
_open_ common resource has no boundaries in terms of appropriation and is open
access (in full or part) to the public as with knowledge commons. Schweik and
English make an aligning distinction between environmental and OSS-based
commons, where the focus of the community in the latter is on co-creating a
public good for anyone to use rather than overuse as in the former (Schweik
and English, 2012), aligning with e.g., Jullien and Roudaut (Jullien and
Roudaut, 2020). Viégas et al. (Viégas et al., 2007) distinguishes between on-
line and off-line communities characterized by the works of Benkler (Benkler,
2014) and Ostrom (Ostrom, 1990) respectively.

Benkler describes the open and OSS-based commons as a product of commons-based
peer-production (Benkler, 2005), i.e., as the case when a publicly available
common is used as input to a collaborative and coordinated production process
between a number of individuals, and the output from the process is released
back to the originating common (Benkler, 2002). Fuster Morell describes the
communities, in which this peer-production takes place, as Online Creation
Communities where individuals collaborate through an online platform in
creating and sharing a CPR (Fuster Morell, 2014). These communities,
exemplified through Wikipedia and OSS, are open to anyone wishing to use or
contribute to the common development of the CPR.

These characteristics are highlighted by Fuster Morell (Morell, 2010) in her
definition of digital commons as “information and knowledge resources that are
collectively created and owned or shared between or among a community and that
tend to be non-exclusive, that is, be (generally freely) available to third
parties. Thus, they are oriented to favor use and reuse, rather than to
exchange as a commodity. Additionally, the community of people building them
can intervene in the governing of their interaction processes and of their
shared resources.”

###  2.3. Governance of digital commons related to software and data

Governance, as with commons, also comes with multiple definitions. Markus
defines it in the context of OSS as “the means of achieving the direction,
control, and coordination of wholly or partially autonomous individuals and
organizations on behalf of an OSS development project to which they jointly
contribute” (Markus, 2007). De Laat in turn considers governance as
configurations primarily based on democratic or autocratic principles (De
Laat, 2007). Configurations that can be nuanced even further (De Noni et al.,
2013; Germonprez et al., 2014), evolve with time (O’Mahony and Ferraro, 2007),
and even co-exist (Shaikh and Henfridsson, 2017). In a similar context, Alves
et al. (Alves et al., 2018) define governance mechanisms as “managerial tools
of participants in software ecosystems, i.e., orchestrators and platform
extenders that have the goal of influencing an ecosystem’s health. Ecosystems
are healthy when they exhibit longevity and propensity for growth.” A
definition further contextualized in the case of data ecosystems by Oliviera
et al. (S Oliveira et al., 2019).

The connection between governance and health aligns with the intention of
Ostrom regarding her design principles of a governance structure that enables
a sustainable CPR, i.e., a scenario where its resources are neither depleted
nor degraded (Ostrom, 1990). The applicability of the design principles in
terms of digital commons such as open data and OSS has, however, only been
explored to a limited extent (with notable exceptions (Viégas et al., 2007;
Forte et al., 2009; Rozas, 2017; Ruhaak et al., 2021; Coyle et al., 2020)).
One reason for this may be that the CPR framework aligns more with the
traditional commons, rather than knowledge and digital commons (Hess, 2008).
However, as hinted by Benkler (Benkler, 2014), work on CPR may still provide
input to the governance within the community where the commons-based peer-
production takes place.

This is illustrated by Viégas et al. (Viégas et al., 2007) and Forte et al.
(Forte et al., 2009) who apply Ostrom’s design principles to the governance of
Wikipedia. Forte et al. state that the principles fit as the “[Wikipedia]
community is not only managing a resource, it is striving to encourage
collaboration and cooperation among volunteers” (Forte et al., 2009). They
found that the governance is upheld and facilitated through social norms
developed by the community through time (Forte et al., 2009), aligning with
Ostrom’s suggestion that norms have a higher impact and long-term acceptance
than external rules imposed on a community (Ostrom, 2000).

Rozas (Rozas, 2017) performed a similar study on self-organization carried out
in the Drupal OSS community. Rozas used the design principles by Ostrom to
describe and capture related organizational changes in the Drupal OSS
community as it has grown and adopted a decentralized governance and decision-
making process. The connection between OSS commons and CPRs is further
explored by O’Mahony who confirms that the two share certain characteristics
in terms of regulating the balance between provisioning and appropriation
(O’Mahony, 2003), where licences are central in the digital domain. O’Mahony
specifically investigates how copyleft license obligations are enforced to
make (especially) commercial appropriators contribute back modifications or
additions to the OSS (i.e., the common) to preserve its quality.

In terms of open data, Coyle et al. make the analogy of how an upstream farmer
may need to share water with a downstream community to improve harvest so that
everyone can benefit from (Coyle et al., 2020). According to Coyle et al.,
“the holder of data may need to sacrifice some private economic benefits by
sharing data to unlock potentially much larger benefits for their sector or
supply chain.” In their report, Coyle et al. further highlight how Ostrom’s
design principles for CPRs can guide the regulation and governance of the
data, by contextualizing the principles from a data economy perspective.
Ruhaak et al. make a similar translation of Ostrom’s design principle to the
context of data commons (Ruhaak et al., 2021).

##  3\. Research Approach

###  3.1. Methodology

The research is a deepened and refocused analysis of existing literature and
empirical studies of ODEs (Runeson et al., 2021; Forte et al., 2009; Rozas,
2017), using Ostrom’s design principles as an analytical lens (Ostrom, 1990).
For each of the design principles, we contrast previously reported cases of
digital commons and how the governance has been set up to enable joint
maintenance of the data, as well as its boundary resources. The analysis is
then contrasted with the earlier reported proposals of how to map Ostrom’s
principles to open data as a digital common. We specifically address the
questions of (RQ1) how Ostrom’s design principles may be applied in the
context of ODEs to help sustain the shared data, and (RQ2) what the
fundamental differences are between natural and digital commons.

Figure 1. Overview of research method, based on Stol and Fitzgerald (Stol and
Fitzgerald, 2015). Grey boxes refer to Runeson and Linåker’s study (Runeson et
al., 2021) and white boxes to the current one.

Conceptually, we follow Stol and Fitzgerald’s theory-oriented software
engineering process (Stol and Fitzgerald, 2015), as outlined in Fig. 1. In
Runeson et al’s previous work, focus group interviews were conducted, and
observations were made in three ODE practice cases (ESS–CSDL, RoDL, and
JobTech), which were conceptualized into a general conceptual model of ODE
(Runeson et al., 2021). The model consists of four higher-level themes:
_value, intrinsics, governance_ , and _evolution_. Of these, _governance_ is
of particular interest for this study.

Using Ostrom’s eight design principles for commons as a lens, we revisit the
analysis and the underpinning empirical data of the conceptual ODE model and
its governance theme specifically. For each of the eight principles, we
firstly contextualize other researchers’ interpretations and application of
the principles, both in terms of a) case studies of Wikipedia (Forte et al.,
2009; Viégas et al., 2007) and Drupal (Rozas, 2017), and b) two sets of
existing practice guidelines, related to Ostrom’s guidelines and open data as
a digital common; one set by Coyle et al. (Coyle et al., 2020) and one
published by the Mozilla foundation (Ruhaak et al., 2021). However, as the
derivation of these guidelines is not transparently reported, we consider them
to be directly practice-based rather than theoretically founded (labeled as a
“shortcut” by Stol and Fitzgerald (Stol and Fitzgerald, 2015)). Secondly, each
principle is contextualized in terms of ODE governance, followed by an
analysis and comparison between the ODE contextualization and that of the
related work. Thirdly, we derive recommendations for how governance of ODEs
can be performed in a way that promotes and enables sustainable maintenance of
the digital commons overseen by an ODE.

###  3.2. Cases

In our analysis, we consider three cases from our previously reported work
(Runeson et al., 2021) where further details are available.

Case 1 concerns the The Road Data Lab (RoDL), a joint industry–academia
project focused on sharing and collaborating on image and sensor data related
to roads. The goal is to provide a basis for machine-learning-based
applications related to autonomous driving, but also to explore challenges
related to the sharing of data and how these can be addressed.

Case 2 regards the ESS Control System Data Lab (ESS–CSDL), part of The
European Spallation Source (ESS) consortium, which is responsible for managing
data from the control systems of the consortium’s multi-disciplinary research
facility. The ecosystem’s scope is to share and collaborate on alarm data,
stemming from the control systems and provide a basis for joint innovation and
knowledge sharing on how the data can be leveraged to improve the security and
operations of the research facility (and related contexts).

Case 3 focus on JobTech Development (JobTech), an ODE initiated and
orchestrated by the Swedish Public Employment Service focused on sharing and
collaborating on data that can help improve the digital match-making between
job seekers and employers in Sweden. Data includes job ads, personal resumés,
and a taxonomy of skills and work titles.

##  4\. Results and Analysis

###  4.1. Principle 1: Clearly defined boundaries

“Individuals or households who have rights to withdraw resource units from the
CPR must be clearly defined, as must the boundaries of the CPR itself”
(Ostrom, 1990).

####  4.1.1. Related interpretations on Digital commons:

Forte et al. note that the principle, in terms of traditional commons, is
focused on defining who has the right to withdraw resource units from a common
that is consumable (Forte et al., 2009). In terms of Wikipedia, which output
can be classified as open-access, the principle is re-interpreted to define
who is included and has the right to contribute to the commons-based peer-
production. This is considered especially important since anyone is eligible
to participate without being familiar with the processes of the peer-
production.

This interpretation was further adopted by Rozas in the case of the Drupal OSS
community, who noted an increased formalization and definition of these
boundaries as the community grew (Rozas, 2017). The interpretations of Rozas
and Forte et al., hence, mainly focus on who can _contribute_ to the common,
and as a consequence with whom to communicate norms and processes related to
the peer-production. In essence, this aligns rather well with the intention of
Ostrom who considers the principle as a means to help members of a community
know “who is in and who is out of a defined set of relationships and thus with
whom to cooperate” (Ostrom, 2000).

From a data economy perspective, provided by Coyle et al., the principle also
covers the appropriation aspects as highlighted in the original definition:
“Clarity on the rights of different entities to control, access, use and share
data” (Coyle et al., 2020). Ruhaak et al. align in their interpretation
concerning data commons as the boundaries should help to “determine who can
contribute, access, and use the data resource or make decisions about it. [The
boundaries] also [help] determine the shape and context of the data resource
itself” (Ruhaak et al., 2021)

####  4.1.2. Contextualization on ODEs:

Actors within an ODE base their interrelations on a common interest with the
rationale that working together and sharing resources creates more value than
standing alone. The common interest, which implicitly leads to defining the
boundaries, is the basis for a common vision and purpose for the ODE, and
thereby what type of resources should be shared and collaborated on, i.e., the
type of data and related boundary resources. The boundaries and vision for the
ecosystem is commonly defined by the platform provider and keystone actors
closest to the core of the ecosystem (see Section 2.1).

Among the cases studied, we could differentiate between three types of driving
forces among these core groups of actors that help to shape the common vision
and way forward. One type concerns the _business-driven_ ODEs where there is
an emphasis on creating commercial value and opportunities for companies
involved in the ecosystem (exemplified by ESS–CSDL and RoDL). _Public-driven_
ODEs (as in the case of JobTech) are a second type where the main focus is on
creating value for the society at large. In the third type, the _community-
driven_ ODEs, the driving force is not necessarily limited to a public or
business-centered incentive, but may also include personal or group-wise
incentives for individuals and organizations, either co-located or
decentralized. Although not studied as a case, OpenStreetMap may be considered
as an example. Among the three types mentioned, however, it should be noted
that they are not mutually exclusive. An ODE may very well have commercial
goals while the overall purpose can be classified as public-driven.

####  4.1.3. Analysis and recommendation:

As in all related cases, the output of the commons-based peer production in
the ODEs is available as open access. Yet, there is still value in defining
who will benefit from and use the data as this can be considered part of the
ecosystem’s common goal and vision. While the cases of Wikipedia (Forte et
al., 2009) and Drupal (Rozas, 2017) mainly consider boundaries in terms of
contributing and engaging in the peer-production, Coyle et al. (Coyle et al.,
2020) and Ruhaak et al. (Ruhaak et al., 2021) also consider the use and
appropriation perspective of the data as important to define as well. In an
ODE, the boundaries are implicitly defined by the common vision and goal of
the ecosystem. Especially in public- and business-driven ODEs, this is set in
the beginning by the platform provider and potentially also keystone actors.
However, to build a sustainable and attractive ecosystem, the voices of the
actors also need to be considered, as often done implicitly in community-
driven ODEs like Wikipedia and Drupal where consensus is a driving norm for
decision-making (Viégas et al., 2007; Forte et al., 2009).

Recommendation #1 for ODEs: Boundaries of the ecosystem and its underpinning
common (e.g., in terms of control, access, use, and sharing of data) follow as
a consequence of the overarching vision of the ecosystem, which should be
inclusive and shaped with the input of the whole ecosystem.

###  4.2. Principle 2: Congruence between appropriation and provision rules
and local conditions

“Appropriation rules restricting time, place, technology, and/or quantity of
resource units are related to local conditions and to provision rules
requiring labor, material, and/or money.” (Ostrom, 1990)

####  4.2.1. Related interpretations on Digital commons:

In the case of Wikipedia, the growing community has created a decentralized
structure of local groups that are responsible for distinct WikiProjects.
Grouping within these projects form what can be referred to as local
jurisdictions, “within which local leadership, norms, and standards for
writing are agreed upon by editors familiar with a particular topic” (Forte et
al., 2009). Forte et al., in their reinterpretation, highlight the need to
consider these aspects even though central editing and policy guidelines from
Wikipedia must still be considered (Forte et al., 2009). They further
highlight the perspective that these local norms may change over time.

The need for a large and decentralized community such as Wikipedia to consider
local conditions is confirmed by Viégas et al. who highlight that “instead of
relying on ”one-size-fits-all” regulation, rules must be intimately associated
with the particularities of the resources they regulate” (Viégas et al.,
2007). Rozas further notes, in the case of the Drupal OSS community, an
“emergence of autonomous spaces with regards to local decision-making in
contributed projects and local institutions to avoid a “one-size-fits-all”
regulation” (Forte et al., 2009).

Coyle et al. interpret this principle slightly differently, focusing on
transparency and understanding, rather than adaptations to local conditions:
“Transparency and better understanding of both rights and how value from data
returns to people and organisations” (Coyle et al., 2020).

####  4.2.2. Contextualization on ODEs:

The diversity of actors and the relationships in-between them affect the
conditions and form how data and related resources are shared and shaped
through the joint contributions (cf. “labor, material, and/or money” (Ostrom,
1990)). Benefits need to be weighed against the potential risks and costs of
sharing data or any boundary resource (Linåker and Regnell, 2020). Companies,
for example, commonly associate the risk of giving away differentiating value
to competitors through data sharing. A more general, but also overlapping risk
concerns that of sharing integrity and confidentiality-related information.

To manage these risks, licenses can be defined to balance how the data is
permitted to be shared while still enabling opportunities for individual and
collective value creation. Among the cases studied, we have noted four ways in
which the data can be transformed before publication to address concerns and
perceived risks among ecosystem actors (aligning with e.g., (Enders et al.,
2020)): 1) Adapting the _currentness_ of the data, e.g., by only sharing
historical data when the real-time data is considered sensitive. 2) Adapting
the _level of processing_ of the data, e.g., by only providing the raw data
when processing and enrichment are considered as differentiating steps. 3)
Adapting the _granularity_ of the data, e.g., by abstracting, anonymizing, or
removing certain fields in the published data. 4) Adapting the _level of
openness_ of the data, e.g., if it should be shared internally within the
ecosystem or openly with an open data license.

####  4.2.3. Analysis and recommendation:

The related studies of Wikipedia (Viégas et al., 2007; Forte et al., 2009) and
Drupal (Rozas, 2017) focus on the need to adapt rules, especially for the
contribution and collaborative aspects, to local needs. Both cases have very
large communities where sub-projects have emerged as a consequence, hence the
specific need to consider local conditions. The studied cases of ODEs,
however, are rather small and do not have this specific concern in their
current stage of evolution. Still, they need to define feasible licenses for
use and sharing, to ensure that actors in the ecosystem feel that perceived
risks are managed and that the potential for value creation persists. As
highlighted by Coyle et al. (Coyle et al., 2020), these rules and processes
need to be transparent and generally understood, e.g., in how they address the
concerned risks.

Recommendation #2 for ODEs: Licenses and processes related to consumption and
contribution to the common (i.e., data and related boundary resources) should
address perceived risks while persisting potential for value creation for the
members of the ecosystem. As the ecosystem evolves, local needs must be
considered and addressed accordingly.

###  4.3. Principle 3: Collective-choice arrangements

“Most individuals affected by the operational rules can participate in
modifying the operational rules.” (Ostrom, 1990)

####  4.3.1. Related interpretations on Digital commons:

Forte et al. generally align in their interpretation of this principle: “In
order to best accomplish the congruence called for in principle 2, principle 3
suggests that people who are affected by the rules of the community can
participate in changing them.” (Forte et al., 2009) Viégas et al. further add
that “the cost of altering rules should be kept low” (Viégas et al., 2007). In
terms of Wikipedia, both aforementioned studies describe a decision-making
process that is generally based on consensus building among those interested
(Forte et al., 2009; Viégas et al., 2007). Rozas notes in the case of Drupal
that there is a continuous ongoing process in the community in terms of
inventing “ways to increase participation in the elaboration of rules by those
affected by them” (Rozas, 2017). A similar interpretation is echoed by Ruhaak
et al. (Ruhaak et al., 2021).

####  4.3.2. Contextualization on ODEs:

Rules and rights for using and sharing data, as well as contributing to its
evolution are ultimately decided by the platform provider. However, the
platform provider must still recognize and consider the opinions of the
ecosystem actors, especially the keystones as they are pivotal for the success
and health of the ecosystem (see principles 4–6 for discussion on the mutual
monitoring, sanctioning, and conflict-resolution mechanisms).

Among our cases, we have noted both formal and informal means for setting up
such governance structures and thus we differentiate between three types of
ecosystem governance structures. In _organization-centric_ ODEs (e.g. ESS–CSDL
and JobTech), the governance is concentrated on one single organization, also
constituting the platform provider. Here, the platform provider needs to build
relationships and means for the ecosystem to influence, e.g., what data is
shared. In _consortium-based_ ODEs (e.g RoDL), several actors (often
keystones) share the role of the platform provider through a joint
organization. Here, governance is set up more formally with e.g., statutes and
committees that enable collective decision-making. In _community-based_ ODEs
(e.g. OpenStreetMap), the role of a platform provider is taken on by a
community at large where governance is decentralized directly to the actors
within the ecosystem whom themselves decide on how to organize the decision-
making.

####  4.3.3. Analysis and recommendation:

All related cases are clear in that those affected by a decision should be
able to influence the decision. In Wikipedia (Forte et al., 2009) and Drupal
(Rozas, 2017), this is a consensus-based process which aligns with their
community-driven approach. For the ODEs studied, this was mainly the role of
the platform provider, yet taking the input of the ecosystem, primarily based
on their level of importance for the success of the ecosystem and general
level of activity. The structure and ownership of the platform provider
(considering the cases of organization-centric, consortium-based, and
community-based ODEs) further affect how the collective-choice arrangements
are made.

Recommendation #3 for ODEs: Rules and overall governance structure should
ideally be shaped through dialogue among the ecosystem members, and enable
influence, formal or informal, for the members both concerning the governance,
as the general collaboration related to the common.

###  4.4. Principle 4: Monitoring

“Monitors, who actively audit CPR conditions and appropriator behaviour, are
accountable to the appropriators or are the appropriators.” (Ostrom, 1990)

####  4.4.1. Related interpretations on Digital commons:

Forte et al. interpret the principle much in line with Ostrom as do Viégas et
al., stating that “Individuals who monitor the commons should be accountable
to the rest of the community”. This definition aligns well with observations
in the case of Wikipedia where “[t]he entire community monitors content and if
a dispute arises, it is generally resolved through discussion by the people
involved in the situation” (Forte et al., 2009). In the case of Drupal, Rozas
observed the “[e]mergence of explicit roles and processes related to quality
assurance so that certain individuals, accountable to the community, [can]
monitor the commons” (Rozas, 2017).

Ruhaak et al. interpret the principle for data commons and how it “includes
monitoring of data production processes — ongoing validation of data
integrity, verification of data quality, — as well as monitoring data access
and use” (Ruhaak et al., 2021).

####  4.4.2. Contextualization on ODEs:

Monitoring in terms of how rules and governance is followed is not conducted
by any external actors but is a responsibility shared between the platform
provider and the ecosystem in general. The platform provider may use
diagnostics and statistics connected to the platform to monitor how the data
is used, as employed by the Swedish Public Employment Service in the case of
JobTech. By also mandating use of API keys, they can further monitor e.g., the
amount of calls to API:s to a specific user, and require acceptance of any
terms and conditions.

From the ecosystem perspective, actors can collectively monitor how the
platform provider abides by the defined rules and governance structure, and
how they can exercise their influence on e.g., what data is shared.

####  4.4.3. Analysis and recommendation:

In the communities of Wikipedia (Forte et al., 2009) and Drupal (Forte et al.,
2009), the community monitors itself through the transparent and consensus-
based collaboration and governance processes. Similar observations regard the
ODEs studied. Although, there may not necessarily be equal conditions in terms
of monitoring each other, both the platform provider and the members of the
ecosystem both have the possibility to monitor and check up on each other, and
act accordingly. Traits that are important for a common trust to reside
between the members, which is especially central in smaller ecosystems where
co-opetition is present, i.e., collaboration between competitors. As Ruhaak et
al. point out, monitoring should also include the production and collaboration
regarding the common (Ruhaak et al., 2021).

Recommendation #4 for ODEs: Monitoring concerning the orchestration, as well
as the consumption, and general collaboration and production related to the
common should be performed equally by both those facilitating an ecosystem
(i.e., the platform provider), and the members of the ecosystem.

###  4.5. Principle 5: Graduated sanctions

“Appropriators who violate operational rules are likely to be assessed
graduated sanctions (depending on the seriousness and context of the offence)
by other appropriators, by officials accountable to these appropriators, or
both.” (Ostrom, 1990)

####  4.5.1. Related interpretations on Digital commons:

The interpretation by Forte et al. highlights how “community members actively
monitor and sanction one another when behavior is found to conflict with
community rules”. (Forte et al., 2009)

In the Wikipedia community, “[w]hen behavior-related policy is broken, a
series of graduated sanctions can be imposed that begin with the posting of
warnings and can lead to being banned from the site” (Forte et al., 2009). If
the dispute can not be resolved locally in the specific project, the case is
transferred and managed by a central entity. In the Drupal community, a code
of conduct listing different sanctions has been developed and is enforced
collectively by the community. Tweeting derogatory comments about a presenter
at a community event may e.g., result in banning from the event (Rozas, 2017).

Coyle et al. emphasize concrete examples of sanctions related to misuse of the
data: “Enforcement of a range of consequences for the misuse of data, ranging
from the withdrawal of access permissions to fines and other penalties” (Coyle
et al., 2020). The interpretation by Ruhaak et al. aligns with the original
definition (Ruhaak et al., 2021).

####  4.5.2. Contextualization on ODEs:

As with monitoring, graduated sanctions can be exercised both from the
platform provider and ecosystem actors, respectively. The platform provider
has the option of disabling or limiting access to the data shared via their
platform, especially if they have enforced the use of API keys. In the case of
JobTech, API keys have, however, mainly been introduced to communicate any
events that might affect the users, e.g., the deprecation or revision of an
API that might affect business-critical applications among its users. Another
means is to limit the influence that a specific actor may have.

The ecosystem actors, on the other hand, may enforce informal sanctions by
individually or collectively voicing their opinions, or ultimately leaving the
ecosystem. This would hurt the platform provider who is dependent on an
ecosystem of actors that use and add value to its platform. The actors may,
e.g., choose to join an existing ecosystem, or create a new ecosystem, similar
to the concept of forking in terms of OSS (Gamalielsson and Lundell, 2014), a
maneuver that is associated with many risks and costs. An alternative sanction
is to limit any contribution to the platform and shared resources, e.g., in
terms of data – in our cases alarm data in ESS–CSDL, image data in RoDL or job
ads in JobTech.

####  4.5.3. Analysis and recommendation:

As noted in relation to monitoring, definition, and provisioning of sanctions
are done collectively by the communities in Wikipedia (Forte et al., 2009) and
Drupal (Rozas, 2017). In the ODEs studied, the types of sanctions that can be
provided differ between the platform provider and the rest of the ecosystem
members. However, relating to Principle #3, there should be a common
discussion and understanding of what sanctions apply and under what
conditions. As highlighted by Ruhaak et al. (Ruhaak et al., 2021), sanctions
should consider misconduct both regarding the consumption, and general
collaboration and production related to the common.

Recommendation #5 for ODEs: Graduated sanctions should be discussed and
decided on collectively by those facilitating an ecosystem (i.e., the platform
provider), and the members of the ecosystem. However, different sanctions may
still be available to each side even though these should be considered a last
resort.

###  4.6. Principle 6: Conflict-resolution mechanisms

“Appropriators and their officials have rapid access to low cost local arenas
to resolve conflicts among appropriators or between appropriators and
officials.” (Ostrom, 1990)

####  4.6.1. Related interpretations on Digital commons:

The interpretation by Forte et al. aligns with the original definition, as
does Viégas et al. who more concisely say that “community members should have
rapid access to low-cost local arenas to resolve conflicts”. In Wikipedia,
most disputes are managed in a decentralized and local setting, a trend that
is considered a consequence given the rapid growth of the community (Forte et
al., 2009). In Drupal, there are mechanisms to facilitate conflict resolution
which is also managed primarily in the local working groups (Rozas, 2017).

Ruhaak et al. phrase the principle as: “When conflict arises in a data
commons, there needs to be an effective, inexpensive, and otherwise accessible
way to handle that conflict. In addition, a data commons needs to decide and
make clear which conflicts will be handled internally and which ones should be
resolved externally, for instance by going to court”. (Ruhaak et al., 2021)

####  4.6.2. Contextualization on ODEs:

To enable conflict resolution as well as rulemaking and collaboration in
general, there is a need for trust, both between the actors and towards the
shared data and its related resources. This can be especially important in
ecosystems where there are direct or indirect competitors (as in JobTech and
RoDL). Among the cases studied, we have noticed the importance of a neutral
platform provider with the possibility to build this trust within the
ecosystem. In JobTech, the Swedish Public Employment Service has taken on this
role in the context of an organization-centric governance structure. In RoDL
and its consortium-based governance structure, an independent body through
which multiple actors interact provided a neutral ground for discussions and
conflict resolutions.

In ODEs with a community-based governance structure, conflicts are managed
through community-defined norms and processes. OpenStreetMap has a consensus-
based approach to addressing any disputes, e.g., regarding a certain edit to
their map data. Data trusts is another solution proposed by Coyle et al.
(Coyle et al., 2020), which provides a legal structure that can host any
shared data for its users. The OpenStreetMap foundation can be likened to a
data trust as it holds the intellectual property rights for the OpenStreetMap
community but is not part of the governance structure, as is commonly the case
for open source software-focused foundations.

####  4.6.3. Analysis and recommendation:

Both Wikipedia (Forte et al., 2009) and Drupal (Rozas, 2017) manage most
conflicts in local settings due to their size and decentralized organization,
similar to the example of OpenStreetMap. In the ODEs studied, which are
considerably smaller in size, conflicts are managed centrally by, or through
the platform provider, both in the case of organization-centric and
consortium-based ODEs. Ruhaak et al. stress that it should also be defined
what conflicts are managed internally and which ones should be managed
externally, e.g., in court (Ruhaak et al., 2021) although the latter is
somewhat alien to the community context.

Recommendation #6 for ODEs: A neutral actor or common body (potentially the
platform provider) can help in establishing a common trust and resolving
potential conflicts in the ecosystem. As an ecosystem evolves, a more
decentralized process may need to be considered.

###  4.7. Principle 7: Minimal Recognition of rights to organize

“The rights of appropriators to devise their own institutions are not
challenged by external governmental authorities.” (Ostrom, 1990)

####  4.7.1. Related interpretations on Digital commons:

Forte et al. reinterpret the principle as: “Local jurisdiction to create and
enforce rules should be recognized by external, central authorities.” (Forte
et al., 2009) Interestingly, Forte et al. consider this principle in the
context of the local projects (or “jurisdictions”) within the overarching
Wikipedia project in contrast to Ostrom et al., who in traditional commons
consider the external government and local authorities. In Drupal, there is an
“[e]mergence of local jurisdiction and acknowledgment by the most centralised
authorities of creation and enforcement of local rules” (Rozas, 2017). This
development can be observed both in the language-specific communities, as well
as among the contributed modules that connect to the Drupal Core OSS project.

Coyle et al. emphasize the need for a “comprehensive data strategy and
institutional/regulatory framework” (Coyle et al., 2020). In the context of
data commons, as per Ruhaak et al., “this principle encourages us to
understand how far the decisions we make about the collection and use of data
are in line with, for instance, data protection regulations” (Ruhaak et al.,
2021).

####  4.7.2. Contextualization on ODEs:

An ODE needs legitimacy to attract actors and stay competitive with other
ecosystems. The legitimacy, as well as attractiveness, relates to the value an
ODE can offer its actors, e.g., through the data being shared, and the related
collaboration. For ODEs focused on open government data, public organizations
(as with JobTech) can provide the legitimacy and foundation for the trust
needed to establish a sustainable and long-term ecosystem. An ODE must also
respect regulations and aspects that might limit the kind of data that may be
shared, or how.

####  4.7.3. Analysis and recommendation:

This principle is contextualized both in the case of Wikipedia (Forte et al.,
2009) and Drupal (Rozas, 2017) inside each community. This comes naturally
given the size and decentralized nature of the communities, creating the
dynamics and need for respect between central and local governance. The
contexts of the studied ODEs align more with the original definition by Ostrom
in terms of a need to be recognized by the external environment (not
necessarily local authorities as stated by Ostrom). Such recognition may be
built by including necessary parties as members of the ecosystem, e.g., public
sector organizations or actors who could be considered potential keystones. As
highlighted by Ruhaak et al., one also needs to consider the relevant
regulations, e.g., in terms of data protection regulations (Ruhaak et al.,
2021). Further, as highlighted by Principle #2, an ecosystem also needs to
consider risks perceived by the members and how these can be addressed.

Recommendation #7 for ODEs: External recognition is connected to the
attractiveness of the ecosystem and its underpinning common, and the value
they can provide to new and existing members. The ecosystem must also ensure
that regulations are met and perceived risks from its members are addressed as
highlighted in Principle #2.

###  4.8. Principle 8: Nested enterprises (for CPRs that are part of larger
systems)

“Appropriation, provision, monitoring, enforcement, conflict resolution, and
governance activities are organized in multiple layers of nested enterprises.”
(Ostrom, 1990)

####  4.8.1. Related interpretations on Digital commons:

This principle only relates to CPRs that are part of the larger ecosystem and
overarching governance. Forte et al. define it as: “By forming multiple nested
layers of organization, communities can address issues that affect resource
management differently at broader and very local levels.” (Forte et al., 2009)

Again, this principle can be contextualized in the context of the overarching
Wikipedia community, and how its governance structure considers the local
projects within (Forte et al., 2009). In Drupal, Rozas noted an “[o]verall
emergence of socio-technical systems of contribution to address issues that
affect the common resources differently at wider and local levels”, e.g.,
through the emergence of international, regional, and local conferences and
meetups where members of the community and concerned sub-communities can meet
and discuss matters of importance (Rozas, 2017).

Concerning data commons, “this principle can refer to a possible need for one
data commons to interoperate with another, or to break up one large commons
into smaller, nested commons that interoperate with one another. Doing so
would allow each smaller commons to make decisions that better reflect their
circumstance and match a narrowly defined purpose” (Ruhaak et al., 2021).

####  4.8.2. Contextualization on ODEs:

It is not uncommon that an ODE is part of a larger and more nested ecosystem.
In the case of JobTech, the taxonomy of skill and work titles on one hand
relates to other data sets such as those defining types of education
maintained by the National Agency for Education. On another hand, the taxonomy
data set makes up a Swedish translation and contextualization of a more
abstract taxonomy data set for the European Union, which in turn relates to an
even more abstract international taxonomy.

####  4.8.3. Analysis and recommendation:

In both the Wikipedia (Forte et al., 2009) and the Drupal communities (Rozas,
2017), this principle is contextualized as the different layers that emerge
due to their large size and decentralized nature. Again, for the ODEs studied,
which are all considerably smaller in size, this principle rather refers to
how an ODE relates to connecting ODEs, on a similar or differing level of
abstraction as with the example of public transport data. This aspect is also
highlighted by Ruhaak et al. (Ruhaak et al., 2021) as the potential need to
interoperate with other ODEs, or even break one up into smaller ones. In some
sense, similar to what has happened in Wikipedia and Drupal, where smaller
sub-communities have emerged forming new and lower levels within the
overarching community. An ODE may, hence, as it matures turn into a nested
enterprise itself with layers, and local jurisdictions emerging underneath.

Recommendation #8 for ODEs: Interoperability and collaboration should be
sought out by connecting ecosystems with aligning commons. Ecosystems should
further be open to internal sub-groupings emerging as the ecosystem evolves,
or even breaking up an ecosystem if appropriate, e.g., enabling smaller
commons with a narrower focus.

##  5\. Discussion and Conclusions

###  5.1. Natural and digital commons

When reanalyzing the ODE cases as digital commons (Morell, 2010), in relation
to natural commons, one difference sticks out, namely whether the resource is
subtractable as hinted by Ostrom’s definition of a CPR (Ostrom, 2000). A
subtractable resource is reduced through the consumption by one on the cost of
others. If non-renewable, the resource may risk depletion. A non-subtractable
resource, on the other hand, can be consumed by multiple stakeholders without
being diminished.

For natural commons, e.g water supply in a well or creek, the dilemma of the
commons is clearly prevalent. If one landowner along the creek taps too much
water for irrigation, the creek will dry out for the downstream land owners.
The same phenomenon is observable at multiple levels, from the small village
well, to huge-scale power dam projects, e.g. in Ethiopia (Wikipedia, [n.d.]).
Consequently, commons must focus on regulating consumption, and sanctions
taken against those who break the regulations. Natural commons resources may
also suffer from under-consumption, e.g. if too few creatures graze a common
pasture, bushes may take over the land or the ground may be malnourished due
to lack of fertilization from the creep if too small herds use the pastures.
However, the primary concern is over-consumption.

For digital commons, e.g. OSS (Schweik and English, 2012; Jullien and Roudaut,
2020) and open data (Coyle et al., 2020; Ruhaak et al., 2021), the dilemma of
the commons is different. Digital commons are primarily non-subtractable.
Software is not worn out by being run, and data is not consumed by being
copied to new databases. On the contrary, OSS and open data are improved by
utilization. More users of an OSS means that more eyes spot potential faults,
and more stakeholders have an interest in having these faults fixed. Thus the
probability that some stakeholders actually will provide labor to fix the
fault is higher. For open data, similar patterns can be seen, e.g. when users
of OpenStreetMap spot faults in the map data and propose corrections. Further,
they map the unchartered territory and make this data available to other
consumers.

However, this highlights another aspect of digital commons that is very much
subtractable. That is the labor needed for the collective action to properly
maintain the digital common. For example, if digital preservation efforts such
as the Software Heritage (Di Cosmo and Zacchiroli, 2017) would fail if a lack
in preservation efforts arises. Equally, if an OSS is not maintained properly
by the community, vulnerabilities may risk being introduced and dependencies
break. In the case of open data, ML training sets may risk becoming invalid,
or map data incorrect as its physical counterpart is altered.

As a community grows, and so the appropriation of a common, the demand grows
for maintenance labor that can provide support for the community, e.g., by
answering questions (Eghbal, 2016). Effort required to manage and coordinate
collective action for maintaining the common may also risk to scale out of
proportion. Or as put by Jullien and Roudaut, “the available brain time of
peers is not extensible, therefore rival, even if it is a renewable resource”
(Jullien and Roudaut, 2020). The collective action producing and maintaining
the common, may in this sense itself be considered as a CPR where the “brain
time” makes up the resource system that needs governing and oversight.

Communities, hence, need to design their governance in a way that manages a
potential increase in effort as appropriation and provisioning grows (as in
the examples of Wikipedia (Forte et al., 2009; Viégas et al., 2007) and Drupal
(Rozas, 2017)), while also reducing barriers to entry and enabling new members
of a community to engage and start contributing to the collective action as
frictionless as possible (Jullien and Roudaut, 2020). We synthesize our
findings into two propositions:

P1) As appropriation of a digital common grows, so does the demand for labor
required to contribute to and manage the contributions to the collective
action, underpinning the common.

P2) To enable sustainability of a digital common, governance must consider
both how to promote and manage contributions, within the available frame of
maintenance labor of a community.

###  5.2. Design principles for digital commons

As a consequence of the difference between natural and digital resources, we
have tailored some of Ostrom’s design principles conceptually, while others
only have to be contextualized into the digital domain.

Two principles remain principally the same for digital commons, #1 defined
boundaries, and #3 collective-choice arrangements. In both natural and digital
commons, there is a need for clear scope definitions and the democratic
aspects of influencing the common. The principles may be implemented
differently: the boundaries of the artificially created artifacts of digital
commons are scoped by their vision, while boundaries of the natural commons
are related to physical entities and stakeholders (Benkler, 2014). Similarly,
the mechanisms for enabling influence from stakeholders are different in the
digital and the physical world. Still, in both cases, the dialogue, not its
medium is the key.

Another three of the principles are also principally the same, but since the
digital media are so different, the principles are conceptually modified with
respect to what is local and what is global. For principles #6, conflict
resolution, #7, rights to organize, and #8, nested enterprises, the commons
are technically global (via the internet) but there is little global-wide
jurisdiction to align to. Thus, local working groups are created e.g. within
the global Wikipedia community, to decentralize the governance (Forte et al.,
2009; Viégas et al., 2007). This is in contrast to natural commons, where the
scope of the common is physically bound to a country or a region (Hess, 2008).
Principally, also natural commons are global, e.g. $CO_{2}$ and water
resources, but we have not seen commons principles applied at this scale.

The remaining three principles are conceptually different. Principle #2 on
appropriation and provision is for natural commons focused on over-
consumption, while governance of digital commons must monitor under-
consumption and ensure the incentives for new contributions to the commons,
whether it is software or data. For principles #4 on monitoring and #5 on
sanctions, the platform provider in the digital common has a central role,
since monitoring and sanctions are technically connected to features of the
platform. The APIs of the platform may handle access rights, and sanctions can
be implemented as withdrawn API keys, giving the platform provider’s powerful
tools to manage the common (Linåker and Runeson, 2021). However, since the
stakeholders are needed for new contributions to the common, this helps
balance the power between the facilitators (platform providers) and members
(users) of the common.

###  5.3. Limitations and Future work

The applicability of Ostrom’s design principles to digital commons may be
questioned as they were originally elicited for small and locally based
natural commons. However, as proposed by Benkler (Benkler, 2014), and explored
by others (Viégas et al., 2007; Forte et al., 2009; Rozas, 2017; Coyle et al.,
2020; Ruhaak et al., 2021), they may very well prove applicable to digital
commons, although with some modifications as hinted by this study.

A further aspect concerns when open data can be considered a digital common,
and by extension, to which ODEs that our recommendations are applicable. Many
authors (e.g., (Morell, 2010; Benkler, 2014; Jullien and Roudaut, 2020))
highlight the characteristics of co-creation and co-ownership. A
(hypothetical) case of an organization-centric business-driven ODE where a
company release open data as part of their business model for public
consumption may hence be questioned. However, per our definition of an ODE, if
there is no collaborative component, or networked group of actors present with
a common vision (see Section 2.1), it is questionable if this hypothetical
case can be considered as an ODE. Our recommendations may instead be
considered as guidance for how such a company can organize an ODE and tailor
its governance structure to transform the open data into (or resemble aspects
of) a “digital common” and thereby extract the potential benefits that (may)
follow. Research into the gray area of what constitutes a digital common is a
topic warranting further attention.

It should further be noted that our review of related interpretations of
Ostrom design principles is limited to the referred works (Forte et al., 2009;
Viégas et al., 2007; Rozas, 2017), and their application of the principles
when describing the governance of their respective cases. We hence acknowledge
that our coverage of, e.g., social and cultural aspects that also affect the
governance, i.e., the social norms practiced, are not extensively covered, and
is considered as a topic for future research.

## Acknowledgement

Thanks to professor Krister Andersson, University of Colorado at Boulder, for
advice and encouragement in applying the commons concept to the digital
domain.

## References

  * (1)
  * Alves et al. (2018) Carina Alves, Joyce Oliveira, and Slinger Jansen. 2018\.  Understanding Governance Mechanisms and Health in Software Ecosystems: A Systematic Literature Review. In _Enterprise Information Systems_ , Slimane Hammoudi, Michał Śmiałek, Olivier Camp, and Joaquim Filipe (Eds.). Springer International Publishing, Cham, 517–542.  https://doi.org/10.5220/0006269402150226
  * Benkler (2002) Yochai Benkler. 2002\.  Coase’s penguin, or, linux and ”the nature of the firm”.  _Yale law journal_ 12, 3 (2002), 369–446.  https://doi.org/10.2307/1562247
  * Benkler (2005) Yochai Benkler. 2005\.  Common Wisdom: Peer Production of Educational Materials, Center for Open and Sustainable Learning.  http://nrs.harvard.edu/urn-3:HUL.InstRepos:37077901
  * Benkler (2014) Yochai Benkler. 2014\.  Between Spanish huertas and the open road: a tale of two commons?  _Governing knowledge commons_ 69 (2014).  https://doi.org/10.1093/acprof:oso/9780199972036.001.0001
  * Cox et al. (2010) Michael Cox, Gwen Arnold, and Sergio Villamayor Tomás. 2010\.  A review of design principles for community-based natural resource management.  _Ecology and Society_ 15 (2010), 38.  Issue 4. http://www.ecologyandsociety.org/vol15/iss4/art38/
  * Coyle et al. (2020) Diane Coyle, Stephanie Diepeveen, and Julia Wdowin. 2020\.  _The Value of Data summary report_.  Technical Report. The Bennett Institute, Cambridge.
  * Curto-Millet and Corsín Jiménez (2022) Daniel Curto-Millet and Alberto Corsín Jiménez. 2022\.  The sustainability of open source commons.  _European Journal of Information Systems_ (2022), 1–19.  https://doi.org/10.1080/0960085X.2022.2046516
  * De Laat (2007) Paul B. De Laat. 2007\.  Governance of open source software: State of the art.  _Journal of Management & Governance_ 11, 2 (2007), 165–177.  https://doi.org/10.1007/s10997-007-9022-9
  * De Noni et al. (2013) Ivan De Noni, Andrea Ganzaroli, and Luigi Orsi. 2013\.  The evolution of OSS governance: A dimensional comparative analysis.  _Scandinavian Journal of Management_ 29, 3 (2013), 247–263.  https://doi.org/10.1016/j.scaman.2012.10.003
  * Di Cosmo and Zacchiroli (2017) Roberto Di Cosmo and Stefano Zacchiroli. 2017.  Software heritage: Why and how to preserve software source code. In _iPRES 2017-14th International Conference on Digital Preservation_. 1–10.
  * Eghbal (2016) Nadia Eghbal. 2016\.  Roads and bridges.  _The Unseen labor behind our digital infrastructure_ (2016).  https://www.fordfoundation.org/media/2976/roads-and-bridges-the-unseen-labor-behind-our-digital-infrastructure.pdf
  * Enders et al. (2020) Tobias Enders, Clemens Wolff, and Gerhard Satzger. 2020\.  Knowing What to Share: Selective Revealing in Open Data. In _European Conference on Information Systems 2020 Research-in-Progress Paper_.  https://aisel.aisnet.org/ecis2020_rip/11
  * Forte et al. (2009) Andrea Forte, Vanesa Larco, and Amy Bruckman. 2009\.  Decentralization in Wikipedia governance.  _Journal of Management Information Systems_ 26, 1 (2009), 49–72.  https://doi.org/10.2753/MIS0742-1222260103
  * Fuster Morell (2014) Mayo Fuster Morell. 2014\.  Governance of online creation communities for the building of digital commons: Viewed through the framework of the institutional analysis and development. In _Governing knowledge commons_ , Brett M. Frischmann, Michael J. Madison, and Katherine J. Strandburg (Eds.). Oxford University Press, 281\.  https://doi.org/10.2139/ssrn.2842586
  * Gamalielsson and Lundell (2014) Jonas Gamalielsson and Björn Lundell. 2014.  Sustainability of Open Source software communities beyond a fork: How and why has the LibreOffice project evolved?  _Journal of Systems and Software_ 89 (2014), 128–145.  https://doi.org/10.1016/j.jss.2013.11.1077
  * Germonprez et al. (2014) Matt Germonprez, Julie E. Kendall, Kenneth E. Kendall, and Brett Young. 2014.  Collectivism, creativity, competition, and control in open source software development: Reflections on the emergent governance of the SPDX working group.  _International Journal of Information Systems and Management_ 1, 1-2 (2014), 125–145.  https://doi.org/10.1504/IJISAM.2014.062290
  * Hardin (1968) Garrett Hardin. 1968\.  The Tragedy of the Commons.  _Science_ 162, 3859 (1968), 1243–1248.  https://doi.org/10.1126/science.162.3859.1243
  * Hess (2008) Charlotte Hess. 2008\.  Mapping the new commons. In _The Twelfth Biennial Conference of the International Association for the Study of the Commons_ (14-18 July). Cheltenham, UK.  https://doi.org/10.2139/ssrn.1356835
  * Hess and Ostrom (2006) Charlotte Hess and Elinor Ostrom. 2006.  A framework for analysing the microbiological commons.  _International Social Science Journal_ 58, 188 (2006), 335–349.  https://doi.org/10.1111/j.1468-2451.2006.00622.x
  * Iansiti and Levien (2004) Marco Iansiti and Roy Levien. 2004.  _The keystone advantage: what the new dynamics of business ecosystems mean for strategy, innovation, and sustainability_.  Harvard Business Review Press, Boston.
  * Immonen et al. (2014) Anne Immonen, Marko Palviainen, and Eila Ovaska. 2014\.  Requirements of an open data based business ecosystem.  _IEEE Access_ 2 (2014), 88–103.  https://doi.org/10.1109/ACCESS.2014.2302872
  * Jansen et al. (2009) Slinger Jansen, Anthony Finkelstein, and Sjaak Brinkkemper. 2009\.  A sense of community: A research agenda for software ecosystems. In _31st International Conference on Software Engineering - Companion Volume_ _(ICSE’09)_. IEEE, Vancouver, BC, Canada, 187–190.  https://doi.org/10.1109/ICSE-COMPANION.2009.5070978
  * Jullien and Roudaut (2020) Nicolas Jullien and Karine Roudaut. 2020.  Digital knowledge commons: Definition and conditions of existence.  _Innovations_ 63, 3 (2020), 69–93.  https://doi.org/10.3917/inno.063.0069 Quote in translation from French.
  * Kitsios et al. (2017) Fotis Kitsios, Nikolaos Papachristos, and Maria Kamariotou. 2017\.  Business models for open data ecosystem: challenges and motivations for entrepreneurship and innovation. In _19th Conference on Business Informatics_ , Vol. 1. IEEE, 398–407.  https://doi.org/10.1109/CBI.2017.51
  * Linåker and Regnell (2020) Johan Linåker and Björn Regnell. 2020.  What to share, when, and where: balancing the objectives and complexities of open source software contributions.  _Empirical Software Engineering_ 25, 5 (2020), 3799–3840.  https://doi.org/10.1007/s10664-020-09855-2
  * Linåker and Runeson (2021) Johan Linåker and Per Runeson. 2021.  How to Enable Collaboration in Open Government Data Ecosystems: A Public Platform Provider’s Perspective.  _JeDEM - eJournal of eDemocracy and Open Government_ 13, 1 (2021), 1–30.  https://doi.org/10.29379/jedem.v13i1.634
  * Lindman et al. (2015) Juho Lindman, Tomi Kinnari, and Matti Rossi. 2015\.  Business roles in the emerging open-data ecosystem.  _IEEE Software_ 33, 5 (2015), 54–59.  https://doi.org/10.1109/MS.2015.25
  * Markus (2007) M Lynne Markus. 2007\.  The governance of free/open source software projects: monolithic, multidimensional, or configurational?  _Journal of Management & Governance_ 11, 2 (2007), 151–163.  https://doi.org/10.1007/s10997-007-9021-x
  * Morell (2010) Mayo Fuster Morell. 2010\.  _Governance of online creation communities: Provision of infrastructure for the building of digital commons_.  Ph.D. Dissertation. European University Institute Fiesole.  http://hdl.handle.net/1814/14709
  * Nakakoji et al. (2002) Kumiyo Nakakoji, Yasuhiro Yamamoto, Yoshiyuki Nishinaka, Kouichi Kishida, and Yunwen Ye. 2002\.  Evolution patterns of open-source software systems and communities. In _Proc. int. workshop on Principles of software evolution_. ACM, Orlando, Florida, 76–85.  https://doi.org/10.1145/512035.512055
  * O’Mahony and Ferraro (2007) Siobhán O’Mahony and Fabrizio Ferraro. 2007.  The emergence of governance in an open source community.  _Academy of Management Journal_ 50, 5 (2007), 1079–1106.  https://doi.org/10.5465/amj.2007.27169153
  * Ostrom (1990) Elinor Ostrom. 1990\.  _Governing the commons: the evolution of institutions for collective action_.  Cambridge University Press, Cambridge, UK.
  * Ostrom (2000) Elinor Ostrom. 2000\.  Collective action and the evolution of social norms.  _Journal of economic perspectives_ 14, 3 (2000), 137–158.  https://doi.org/10.1257/jep.14.3.137
  * O’Mahony (2003) Siobhán O’Mahony. 2003\.  Guarding the commons: how community managed software projects protect their work.  _Research policy_ 32, 7 (2003), 1179–1198.  https://doi.org/10.1016/S0048-7333(03)00048-9
  * Rozas (2017) David Rozas. 2017\.  _Self-organisation in Commons-Based Peer Production. Drupal: “the drop is always moving”_.  Ph.D. Dissertation. University of Surrey, United Kingdom.  https://openresearch.surrey.ac.uk/esploro/outputs/doctoral/Self-organisation-in-commons-based-peer-production--Drupal--the-drop-is-always-moving/99512497702346
  * Ruhaak et al. (2021) Anouk Ruhaak, Greg Blooma, Angie Raymond, Willa Tavernier, Divya Siddarth, Gary Motz, and Melanie Dulong de Rosnay. 2021.  A Practical Framework for Applying Ostrom’s Principles to Data Commons Governance.  https://foundation.mozilla.org/en/blog/a-practical-framework-for-applying-ostroms-principles-to-data-commons-governance/ last visited 2021-12-17.
  * Runeson et al. (2021) Per Runeson, Thomas Olsson, and Johan Linåker. 2021\.  Open Data Ecosystems – an empirical investigation into an emerging industry collaboration concept.  _Journal of Systems and Software_ 182 (2021), 111088.  https://doi.org/10.1016/j.jss.2021.111088
  * S Oliveira et al. (2019) Marcelo Iury S Oliveira, Glória de Fátima Barros Lima, and Bernadette Farias Lóscio. 2019\.  Investigations into data ecosystems: a systematic mapping study.  _Knowledge and Information Systems_ 61, 2 (2019), 589–630.  https://doi.org/10.1007/s10115-018-1323-6
  * Schweik and English (2012) Charles M Schweik and Robert C English. 2012.  _Internet success: a study of open-source software commons_.  MIT Press.
  * Shaikh and Henfridsson (2017) Maha Shaikh and Ola Henfridsson. 2017.  Governing open source software through coordination processes.  _Information and Organization_ 27, 2 (2017), 116–135.  https://doi.org/10.1016/j.infoandorg.2017.04.001
  * Stol and Fitzgerald (2015) Klaas-Jan Stol and Brian Fitzgerald. 2015.  Theory-oriented software engineering.  _Science of Computer Programming_ 101 (2015), 79–98.  https://doi.org/10.1016/j.scico.2014.11.010
  * Viégas et al. (2007) Fernanda B Viégas, Martin Wattenberg, and Matthew M McKeon. 2007.  The hidden order of Wikipedia. In _International conference on Online communities and social computing_. Springer, 445–454.  https://doi.org/10.1007/978-3-540-73257-0_49
  * Wikipedia ([n.d.]) Wikipedia. [n.d.].  Grand Ethiopian Renaissance Dam.  https://en.wikipedia.org/wiki/Grand_Ethiopian_Renaissance_Dam last visited 2022-06-14.


# PROPOSAL TO REPEAT THE ABRAHAM FORCE EXPERIMENT USING GIANT PERMITTIVITY
MATERIALS

Iver<EMAIL_ADDRESS>Department of Energy and Process
Engineering, Norwegian University of Science and Technology, N-7491 Trondheim,
Norway

###### Abstract

In the more than 100 years-old Abraham-Minkowski problem in macroscopic
electrodynamics, the issue of how to observe the so-called Abraham term ${\bf
f}^{\rm Aterm}=[(\varepsilon\mu-1)/c^{2}]\partial/\partial t({\bf E}\times{\bf
H})$ has been a main point. Such a measurement is rather delicate. Recent
years have seen a number of beautiful experiments in radiation optics, but
these experiments usually give no information about the Abraham term as this
term simply fluctuates out. So one is left with somewhat indirect
verifications of this force, as in the radiation pressure of Jones et al. in
the 1950’s, testing the radiation pressure on a mirror immersed in a
dielectric liquid. Now, there is a different way to test the existence of
${\bf f}^{\rm Aterm}$, namely to work with low (quasi-stationary) frequencies
enabling one to observe the sinusoidal variation of the force directly. These
kind of experiments were actually done by Walker et al. in 1he 1970’s, using
BaTiO3 as a high-frequency dielectric (permittivity $\varepsilon\sim 3600$).
The outcome of these experiments was convincing. Now, in recent years there
have appeared dielectric materials with giant permittivities, of order
$10^{5}$ or even higher. It is therefore natural to consider the idea of
Walker et al. anew, in order to test if this demanding experiment can be
facilitated and give better accuracy. That is the main topic of the present
paper. The positive outcome of these kinds of experiments clearly supports the
Abraham energy-momentum tensor at low frequencies. The Minkowski tensor is
unable to predict a torque at all. The low-frequency and the high-frequency
regimes are in this way highly contrasted, as it is obvious that in optical
experiments the Minkowski tensor is by far the simplest and most convenient
one to use. We end this note by commenting upon the use of the Einstein-Laub
tensor (1908) in explaining this experiment, and discuss also the influence
from air friction.

###### pacs:

98.80.-k, 95.36.+x

##  I Introduction

The classic Abraham-Minkowski problem (for some original references see [1, 2,
3]), focuses on what is the correct, or at least the most convenient,
expression for photon momentum propagating an a dielectric medium. To give a
proper background for the present investigation, let us begin with the general
expression for the basic electromagnetic force density ${\bf f}$ in an
isotropic dispersive fluid with mass density $\rho_{m}$, [4, 5, 6],

$\displaystyle{\bf f}=$ $\displaystyle\rho{\bf E}+{\bf J\times
B}-\frac{1}{2}\varepsilon_{0}E^{2}{\bf\nabla}\varepsilon-\frac{1}{2}\mu_{0}H^{2}{\bf\nabla}\mu+\frac{1}{2}\varepsilon_{0}{\bf\nabla}\left[E^{2}\rho_{m}\frac{\partial\varepsilon}{\partial\rho_{m}}\right]+\frac{1}{2}\mu_{0}{\bf\nabla}\left[H^{2}\rho_{m}\frac{\partial\mu}{\partial\rho_{m}}\right]$
$\displaystyle+\frac{n^{2}-1}{c^{2}}\frac{\partial}{\partial t}{\bf(E\times
H)}.$ (1)

Here the constitutive relations are written in the form ${\bf
D}=\varepsilon\varepsilon_{0}{\bf E},\,{\bf B}=\mu\mu_{0}{\bf H}$, so that
$\varepsilon$ and $\mu$ become nondimensional. The refractive index is
$n=\sqrt{\varepsilon\mu}$. If the medium is nonpolar, the partial derivatives
$\partial\varepsilon/\partial\rho_{m}$ and $\partial\mu/\partial\rho_{m}$ will
be independent of whether they are taken at constant entropy or at constant
temperature. The Clausius-Mossotti relation is the applicable in the
nonmagnetic case.

In the following we assume that the charge density $\rho$ and the current
density $\bf J$ are zero, and that the medium is nonmagnetic. The force
expression above simplifies to

$\displaystyle{\bf
f}=-\frac{1}{2}\varepsilon_{0}E^{2}{\bf\nabla}n^{2}+\frac{1}{2}\varepsilon_{0}{\bf\nabla}\left[E^{2}\rho_{m}\frac{\partial
n^{2}}{\partial\rho_{m}}\right]+$
$\displaystyle\frac{n^{2}-1}{c^{2}}\frac{\partial}{\partial t}{\bf(E\times
H)},$ (2)

with $n^{2}=\varepsilon$. The first term in the above expression is the one
usually detected in radiation experiments in optics. As in such cases $n>1$,
it means that radiation forces acting in inhomogeneous regions in the fluid
act toward the optically thinner region. This kind of experiments, started by
Ashskin and Dziedzic back in 1973 [7], has later been repeated under different
circumstances, and are showing the effect very clearly. Some recent papers can
be consulted in Refs. [8, 9, 10, 11, 12, 13, 14, 15]. This kind of force is
evidently of importance, both from a fundamental and a practical viewpoint,
especially in microfluidic contexts.

The second term in Eq. (2) is the electrostriction term. This force gives rse
to a local pressure increase in the fluid, but is usually not of practical
importance since being spatial gradient it can be transformed into a surface
integral giving zero total force if the body is surrounded by a vacuum.

The classic experiment of Hakim and Higham [16] is here important. They
measured the refractive index increase in a dielectric fluid when located in
the region between two plates in the presence of a strong electric field.
Theoretical considerations of this effect can be found at various places; cf.
[5, 17, 18, 19, 20]. An interesting recent experimental confirmation of the
dispersive effect is recently reported [21]. These authors exploited the lack
of axial symmetry in a single-mode optical fiber, and were able to measure the
radiation force, including the electrostriction force, very accurately.

The third member in Eq. (2) is the famous Abraham term. It plays a central in
the discussions about the preferable energy-momentum tensor. Experimental
verifications of the Abraham term are scarce. There exist several claims in
the literature, based upon experimental observations, about ”solving” the
Abraham-Minkowski problem, but many of these are over-interpreting the
importance of the observations. They can often be described using only the
first term (the surface force) in Eq. (2) (a closer discussion given in Ref.
[6]).

It is now convenient to write down the Minkowski and Abraham energy-momentum
tensors $S_{\mu\nu}^{M}$ and $S_{\mu\nu}^{A}$ (cf., for instance, Ref. [22]).
The spatial part of Minkowski’s tensor is

$S_{ik}^{\rm M}=-E_{i}D_{k}-H_{i}B_{k}+\frac{1}{2}\delta_{ik}({\bf E\cdot
D+H\cdot B}),$ (3)

the energy flux density (Poynting vector) and momentum density are

${\bf S}^{\rm M}={\bf E\times H},\quad{\bf g}^{\rm M}={\bf D\times B},$ (4)

and the energy density is

$w^{\rm M}=\frac{1}{2}{\bf(E\cdot D+H\cdot B)}.$ (5)

The Minkowski force density for a nonmagnetic medium thus becomes

${\bf f}^{\rm M}=-\frac{1}{2}\varepsilon_{0}E^{2}{\bf\nabla}n^{2}.$ (6)

In the Abraham case we have $S_{ik}^{\rm A}=S_{ik}^{\rm M},\,{\bf S}^{\rm
A}={\bf S}^{\rm M}={\bf E\times H},\,w^{\rm A}=w^{\rm M}$. The difference from
the foregoing case occurs in the force density, which becomes

${\bf f}^{A}={\bf f}^{M}+\frac{n^{2}-1}{c^{2}}\frac{\partial}{\partial
t}{\bf(E\times H)}\mathrm{}.$ (7)

The core of the Abraham-Minkowski problem thus lies in the Abraham term. As
mentioned, this term is under optical circumstances small, and rapidly
fluctuating, and difficult to detect experimentally. As in the Minkowski case,
the Abraham theory is unable to encompass the electrostriction forces.

The expression (1) is thus the Abraham force density, with the
electrostriction and magnetostriction forces added. It is often called the
Helmholtz force density.

##  II Updated version of the experiment of Walker et al. [23, 24]

We will henceforth be concerned with the Abraham term, called ${\bf f}^{\rm
Aterm}$, under quasi-stationary conditions, when the permittivity of the test
medium is very large. It is then natural to revert to the symbol $\varepsilon$
instead of the optical symbol $n^{2}$, for the permittivity. Thus,

${\bf f}^{A}={\bf f}^{M}+{\bf f}^{\rm Aterm},$ (8)

with

${\bf f}^{\rm Aterm}=\frac{\varepsilon-1}{c^{2}}\frac{\partial}{\partial
t}{\bf(E\times H)}.$ (9)

The experiment of Walker et al. [23, 24] measured the torque on a torsional
pendulum (annular cylinder) suspended in the gravitational field. The
frequencies were low, $\omega/2\pi\sim 0.4~{}$Hz, in resonance with the
applied Abraham term (9) in order to maximize the torque and the angular
deflection here called $\phi$. A strong vertical constant magnetic field,
$B_{0}=\mu_{0}H_{0}\sim 1~{}$T, was created by an electromagnet, and a
harmonically varying radial electric field

$E=\frac{V_{0}}{r\ln(b/a)}\sin\omega t$ (10)

was imposed between the aluminium-coated inner and outer cylindrical surfaces
$r=a$ and $r=b$. Here $V_{0}\sim 260~{}$V was the voltage across the disk. The
material in the disk (height $L$) was BaTiO3, with permittivity
$\varepsilon=3620$. The suspended system was heavy, in total about 800 kg
including the magnet. The pendulum was suspended by a thin tungsten fiber. The
experiment was performed at a low pressure, $10^{-5}~{}$torr.

We can now from Eqs. (9) and (10) write the axial torque $T$ in the form

$T=K\omega\cos\omega t,$ (11)

where

$K=\frac{\pi\varepsilon_{0}(\varepsilon-1)L}{\ln(b/a)}(b^{2}-a^{2})B_{0}V_{0}.$
(12)

When applied to the pendulum, $T$ can be written as

$T=I(\ddot{\phi}+2\lambda\dot{\phi}+\Omega^{2}\phi),$ (13)

where $I$ is the moment of inertia, $I=(1/2)\rho_{m}L(b^{4}-a^{4})$, $\lambda$
is the damping coefficient, and $\Omega$ is the eigenfrequency in the absence
of any damping. (For comparison purposes, note that the symbols $\delta$ and
$\gamma$ in Ref. [23] correspond to $\delta=2I\lambda$ and
$\gamma=I\Omega^{2}$.)

We will seek only the stationary solution of the equation of motion

$\ddot{\phi}+2\lambda\dot{\phi}+\Omega^{2}\phi=\frac{K}{I}\omega\cos\omega t.$
(14)

Assuming the form

$\phi=b\cos(\omega t+\delta),$ (15)

with $b$ and $\delta$ as constants, we derive

$b=\frac{(K/I)\omega}{\sqrt{(\Omega^{2}-\omega^{2})^{2}+4\lambda^{2}\omega^{2}}},\quad\tan\delta=\frac{2\lambda\omega}{\omega^{2}-\Omega^{2}}.$
(16)

In general, the deflection $\phi$ lags behind the applied torque $T$. The
angle $\delta$ is negative. Far from resonance on the side $\omega<\Omega$,
one gets $\delta\rightarrow 0$, whereas on the other side $\omega>\Omega$,
$\delta\rightarrow-\pi$. The passage of $\delta$ through $-\frac{1}{2}\pi$
occurs when $\omega=\Omega$.

Of main interest is the region near resonance. We put $\omega=\Omega+\xi$ with
$|\xi|\ll 1$, and assume that $\lambda\ll\Omega$. Then approximately

$b=\frac{K/2I}{\sqrt{\xi^{2}+\lambda^{2}}},\quad\tan\delta=\frac{\lambda}{\xi},$
(17)

showing that the amplitude $b$ does not now depend on the driving frequency
$\omega$. In the actual experiment, two values of the driving frequency were
investigated, $\omega/2\pi=0.24$ and $0.48~{}$Hz. In the present analysis, we
shall simplify to the case $\xi=0$, $\delta=-\frac{1}{2}\pi$, whereby from the
formulas above we get the following expression for the deflection,

$\phi=\frac{K}{2I\lambda}\sin\omega t.$ (18)

It is convenient to insert the same geometric data as in the experiment,
$b=2.63~{}$cm, $a=0.40~{}$cm, $L=1.99~{}$cm, cylinder mass $M=217~{}$g,
$I=779~{}$ gcm2, time constant $\tau=1/\lambda=1~{}$hour, $B_{0}=1~{}$T,
$V_{0}=260~{}$V, keeping $\varepsilon$ and $\omega$ unspecified. That leads to

$K=5.16(\varepsilon-1)\times 10^{-14}~{}\rm{N~{}m~{}s},$ (19)

and so

$\phi=1.2(\varepsilon-1)\times 10^{-6}\sin\omega t.$ (20)

Thus with $\varepsilon=3620$, the permittivity used in the experiment, we get
a maximum deflection of $\phi_{0}=4.3\times 10^{-3}~{}$rad. The maximum torque
is given by Eq. (11) as $T_{0}=K\omega$. Assuming $\omega/2\pi=0.4~{}$Hz, this
yields $T_{0}=4.7\times 10^{-10}~{}$Nm. These are theoretical formulas. The
experimenters, carefully taking into account corrections, were able to get
agreement with the theoretical prediction to within $\pm 10\%$.

This is an important classic experiment, showing unambiguously the existence
of the Abraham force. Note that the prediction from the Minkowski force (6) is
quite different, as it corresponds to a radial force, with no component in the
azimuthal direction at all, thus no torque.

We have now come to a main point of this paper, namely to propose a repetition
of the experiment of Walker et al. taking advantage of the impressive
improvements in the fabrication of high-permittivity materials in recent
years. They are often called colossal permittivity materials (CP), where the
permittivities can exceed $10^{3}$ by far. They are of obvious interest for
modern electronics and energy storage systems. A useful reference is the
review article of Wang et al. [25]. The most well-known nonferroelectric CP
material is CaCu3Ti4O12 (called CCTO), being stable under a wide temperature
range including room temperatures, and being practically constant at the
frequencies of interest here. (There are even other types of materials called
supercapacitors, containing liquid electrolytes, where the permittivities can
be as large as about $10^{9}$ [26].)

For definiteness, assume a CCTO single crystal with $\varepsilon=10^{5}$ (Fig.
11 in Ref. [25]) used in the Walker et al. experiment, the other parameters
being the same as above. It then follows that

$\phi=0.12\sin\omega t,$ (21)

and with $\omega/2\pi=0.4~{}$Hz,

$T_{0}=1.2\times 10^{-8}~{}\rm{Nm}.$ (22)

This indicates an essential simplification of the classic experiment: the
angular deflection, as well as the torque, become amplified by a factor of
about 27. In our opinion this significant change makes a repetition of the
experiment highly worth considering.

##  III Final remarks

Whereas the conclusion of the present investigation is obvious from the
previous section, we will add three remarks.

1\. Comparison with the Enstein-Laub prediction. In addition to the best known
Abraham and Minkowski alternatives for the electromagnetic energy-momentum
tensor in media, there exist also other alternatives, like the one proposed by
Peierls, for instance [27]. A more well-known alternative is the proposal of
Einstein and Laub back in 1908 [28]. Calling this energy-momentum tensor
$S_{\mu\nu}^{\rm E}$, we have for its spatial part

$S_{ik}^{\rm
E}=-E_{i}D_{k}-H_{i}B_{k}+\frac{1}{2}\delta_{ik}(\varepsilon_{0}E^{2}+\mu_{0}H^{2}),$
(23)

and its energy flux density and momentum density are

${\bf S}^{\rm E}={\bf E\times H},\quad{\bf g}^{\rm E}=\frac{1}{c^{2}}{\bf
E\times H}.$ (24)

We define the corresponding energy density as

$w^{\rm E}=\frac{1}{2}(\varepsilon_{0}E^{2}+\mu_{0}H^{2}),$ (25)

although this quantity was not explicitly given by Einstein and Laub. (In this
way we make the energy-momentum tensor identical to one of the alternatives
derived by de Groot and Suttorp [29].)

The general expression for the energy density ${\bf f}^{E}$ is, when
$\rho={\bf J}=0$ (cf. also Sec. 1.2 in [5]),

${\bf
f}^{E}={\bf(P\cdot\nabla)E}+\mu_{0}{\bf(M\cdot\nabla)H}+\mu_{0}{\bf\dot{P}\times
H}+\frac{1}{c^{2}}{\bf E\times\dot{M}},$ (26)

where ${\bf D}=\varepsilon_{0}{\bf E}+{\bf P}$. If the medium is isotropic and
nonconducting, the following rewriting is useful,

${\bf f}^{E}={\bf f}^{A}+\frac{1}{2}{\bf\nabla(E\cdot P}+\mu_{0}{\bf H\cdot
M)}.$ (27)

In the present case where ${\bf M}=0$, the expression (26) is reduced to two
terms. The first term containing ${\bf E}$ has no azimuthal component, and so
we are left with the single effective term

${\bf f}^{E}=\mu_{0}{\bf\dot{P}\times
H}=\frac{\varepsilon-1}{c^{2}}\frac{\partial}{\partial t}{\bf(E\times H)},$
(28)

since $\bf H$ is assumed constant. Thus ${\bf f}^{\rm E}={\bf f}^{\rm Aterm}$,
where the last quantity given by Eq. (9). The Abraham and the Einstein-Laub
expressions predict the same result in this case. Also, in the recent
experiment of angular symmetry of the radiation force in a solid dielectric
[21], the investigators give preference to the Einstein-Laub formulation.

Does this imply that the Einstein-Laub formulation is fully equivalent to the
Abraham formulation? The answer is no. This is seen if we go back to the
electrostrictive generalization of the Abraham theory, that means, to the
Helmholtz force ${\bf f}^{\rm H}$, which follows from Eq. (1) as

${\bf f}^{\rm
H}=-\frac{1}{2}\varepsilon_{0}E^{2}{\bf\nabla}\varepsilon+\frac{1}{2}\varepsilon_{0}{\bf\nabla}\left[E^{2}\rho_{m}\frac{\partial\varepsilon}{\partial\rho_{m}}\right].$
(29)

As already mentioned, in the Hakim-Higham experiment [16] the electrostrictive
excess pressure $\Delta p$ was measured in a dielectric liquid in the strong
field region between two plates completely immersed in the liquid. From Eq.
(29) it follows that the Helmholtz pressure $\Delta p^{\rm H}$ in the interior
homogeneous region where ${\bf\nabla}\varepsilon=0$ is

$\Delta p^{\rm
H}=\frac{1}{6}\varepsilon_{0}E^{2}(\varepsilon-1)(\varepsilon+2),$ (30)

where use has been made of the Clausius-Mossotti relation. The corresponding
Einstein-Laub excess pressure $\Delta p^{\rm E}$ follows directly from Eq.
(27) as

$\Delta p^{\rm E}=\frac{1}{2}\varepsilon_{0}E^{2}(\varepsilon-1).$ (31)

The experiment showed agreement with the prediction (30), to $\pm 5$ per cent,
and disagreed with (31). The Abraham alternative, when in an electrostrictive
situation extended to the Helmholtz expression, thus stands out as the
preferable option on the fundamental level.

2\. Influence from air friction. In air surroundings, there will be viscous
damping forces from the air viscosity. It is of interest to estimate the
magnitude of this correction. We go back to the Abraham theory, and assume for
simplicity the viscous shear stress on the surface of the sample can be
evaluated as if the cylinder were long ($\L\rightarrow\infty$). Moreover, we
assume in connection with friction the cylinder to be uniformly rotating with
constant angular velocity $\dot{\phi}$.

From the Navier-Stokes equation we find the angular velocity $v$ of air
outside and inside the annular test body to be

$v=\frac{\dot{\phi}b^{2}}{r},\quad r\geq b,$ (32) $v=\dot{\phi}r,\quad r\leq
a.$ (33)

The inner air volume $0<r<a$ thus rotates as a solid body, and there is no
shear stress on the surface $r=a$. The shear stress $\sigma_{r\phi}$ on the
surface $r=b$ is

$\sigma_{r\phi}=\eta\left(\frac{\partial v}{\partial
r}-\frac{v}{r}\right)_{r=b}=-2\eta\dot{\phi},$ (34)

where $\eta$ is the shear viscosity for air. The viscous torque on a length
$L$ of the cylinder thus becomes

$T_{\rm viscous}=-4\pi\eta\dot{\phi}b^{2}L.$ (35)

The expression for (13) for the torque now gets modified, and can be written
as

$T=I[\ddot{\phi}+2(\lambda+\lambda_{\rm viscous})\dot{\phi}+\Omega^{2}\phi],$
(36)

with

$\lambda_{\rm viscous}=\left(\frac{2\pi\eta}{I}\right)b^{2}L.$ (37)

The equation of motion becomes

$\ddot{\phi}+2(\lambda+\lambda_{\rm
viscous})\dot{\phi}+\Omega^{2}\phi=\frac{K}{I}\omega\cos\omega t,$ (38)

and the solution is given by Eqs. (16) and (17) with $\lambda$ replaced by
$(\lambda+\lambda_{\rm viscous})$.

Assume first atmospheric pressure, for which $\eta=1.8\times 10^{-5}~{}$Pa s
$=1.8\times 10^{-4}~{}$dyn s cm-2. Taking as before $I=779~{}$g cm2,
$L=1.99~{}$cm, $b=2.63~{}$cm, we obtain

$\lambda_{\rm viscous}=2.0\times 10^{-5}~{}\rm{s}^{-1}.$ (39)

As mentioned above, the authors estimated the time constant to be
$\tau=1/\lambda=1~{}$hour. With these values,

$\frac{\lambda_{\rm viscous}}{\lambda}=0.072.$ (40)

This is a quite small correction. As pointed out in their paper, the time
constant might in reality have been higher, perhaps around 2 hours. That would
in case double the ratio (40). As is shown by Eq. (37), the running of the
experiment at the low pressure of $10^{-5}~{}$torr, as was actually done, was
beneficial as a lower air density implied a lower viscosity $\eta$, thus a
lower $\lambda_{\rm viscous}$.

3\. An optical analog: use of whispering gallery modes. As mentioned, at
optical frequencies the direct observation of Abraham’s fluctuating force is
practical impossible; the fluctuations become averaged out. As our last
remark, we wish however to emphasize that a critical experimental of this
force can be achievable after all, by an intensity modulation of a laser beam.
This topic was actually considered in some detail earlier, in Ref. [30], but
we will comment briefly on it also here. The subject involves ordinary
dielectric media of refractive index $n$ only; thus has no relationship to
giant permittivities. The reason why we nevertheless consider it here, is for
comparison purposes.

In practice, the optical variant of our problem involves dielectric
microresonators, primarily of spherical form. Let us consider such a compact
sphere with radius $a\sim 50-100~{}\mu$m. When fed by an external source ,
whispering gallery modes can be built up in the interior with large
azimuthically circulating power, of order $P\sim 100~{}$W or more,
concentrated near the rim. If the sphere is suspended in the gravitational
field, it can execute torsional oscillations, essentially in the same way as
above. Assume $P=P_{0}\cos\omega_{0}t$, where $\omega_{0}$ is the modulation
frequency. The circulating energy flux density varies in the same way,

$S=S_{0}\cos\omega_{0}t,$ (41)

where the complicated expression for $S_{0}$ as a function of the input
parameters is given in Ref. [30]. The Abraham term (9) predicts an azimuthal
force density component

$f=-\frac{n^{2}-1}{c^{2}}\omega_{0}S_{0}\sin\omega_{0}t,$ (42)

and a corresponding axial torque on the sphere,

$T=\int rf\sin\theta dV,$ (43)

with $dV=r^{2}\sin\theta drd\theta d\phi$.

We now omit corrections from air friction, and put for definiteness
$a=100~{}\mu$m, $P_{0}=100~{}$W. The moment of inertia about the $z$ axis is
$I=(2/5)Ma^{2}$, where $M=4~{}\mu$g is the mass. From earlier experimental
tests of the equivalence principle [31, 32], we adopt the relationship
$I\Omega^{2}\sim 10^{-9}~{}$N m/rad, where $\Omega$ as before is the undamped
angular frequency of the test body. This leads to

$\Omega\sim 10^{3}\,\rm{rad\,s}^{-1}.$ (44)

The torque varies with time as $T=T_{0}\sin\omega_{0}t$, and with the given
data we estimate for the amplitude

$T_{0}\sim 10^{-23}\omega_{0}~{}\rm{N\,m\,s}.$ (45)

This is very small. Realistic values for the modulation frequency are
moderate; even with the relatively high value of $\omega_{0}=10^{6}~{}$rad/s
we would obtain only

$T_{0}\sim 10^{-17}~{}\rm{N\,m}.$ (46)

This is one order of magnitude smaller than the value $10^{-16}~{}$N m
obtained by Beth [33] in his classic experiment on photon angular momentum.

The corresponding values of the angular deflection are also small; we estimate
for the amplitude

$\phi_{0}\sim 10^{-8}~{}\rm{rad}.$ (47)

In conclusion, we find a comparison between Eqs. (21), (22) in the macroscopic
case, and Eqs. (46), (47) in the microscopic case, to be instructive. The two
cases aim at measuring the same Abraham force, but under widely different
conditions.

## References

  * [1] M. Abraham, Rend. Circ. Matem. Palermo 28, 1 (1909).
  * [2] M. Abraham, Rend. Circ. Matem. Palermo 30, 33 (1910).
  * [3] H. Minkowski, Math. Annaln. 68, 472 (1910).
  * [4] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinemann, Oxford, 1984).
  * [5] I. Brevik, Phys. Rep. 52, 133 (1979).
  * [6] I. Brevik, Mod. Phys. Lett. A 33, 1830006 (2018).
  * [7] A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 30, 19 (1973).
  * [8] A. Casner and J. P. Delville, Phys. Rev. Lett. 90, 144503 (2003).
  * [9] R. Wunenburger, B. Issenmann, E. Brasselet, C. Loussert, V. Houstane and J. P. Delville, J. Fluid Mech. 666, 273 (2011).
  * [10] N. G. C. Astrath, L. C. Malacarne, M. L. Baesso, G. V. B. Lukasievicz and S. E. Bialkowski, Nature Commun. 5, 4363 (2014) [DOI: 10.1038/ncomms5363].
  * [11] O. A. Capeloto, V. S. Zanuto, L. C. Malacarne, M. L. Baesso, G. V. B. Lukasievicz, S. E. Bialkowski, and N. G. C. Astrath, Scient. Rep. 6, 20515; doi:10.11038/srep20515(2016).
  * [12] J. Z. Zhang and R. K. Chang, Opt. Lett. 13, 916 (1988).
  * [13] A. Kundu, R. Rani, and K. S. Hazra, Scient. Reports 7, 42538 (2017); doi:10.1038/srep42538.
  * [14] L. Zhang, W. She, N. Peng and U. Leonhardt, New J. Phys. 17, 053035 (2015).
  * [15] H. Choi, M. Park, D. S. Elliott, and K. Oh, Phys. Rev. A 95, 053817 (2017).
  * [16] S. S. Hakim and J. B. Higham, Proc. Phys. Soc. London 80, 190 (1962).
  * [17] H. M. Lai, P. T. Leung, K. L. Poon, and K. Young, J. Opt. Soc. Am. B 6, 2430 (1989).
  * [18] G. A. Zimmerli, R. A. Wilkinson, R. A. Ferrell, and M. R. Moldover, Phys. Rev. E 59, 5862 (1999).
  * [19] S. Å. Ellingsen and I. Brevik, Phys. Fluids 23. 096101 (2011).
  * [20] M. Partanen and J. Tulkki, Phys. Rev. A 96, 063834 (2017).
  * [21] X. Xi, J. Ma, Z.-H. Zhou, X.-X. Hu, Y. Chen, C.-L. Zou, C.-H. Dong and X. Sun, Optica 8, 1435 (2021).
  * [22] C. Møller, The Theory of Relativity, 2nd ed. (Clarendon Press, Oxford, 1972).
  * [23] G. B. Walker, D. G. Lahoz and G. Walker, Can. J. Phys. 53, 2577 (1975).
  * [24] G. B. Walker and D. G. Lahoz, Nature (London) 253, 339 (1975).
  * [25] Y. Wang, W. Jie, C. Yang, X. Wei and J. Hao, Adv. Funct. Mater. 29, 1808118 (2019).
  * [26] F. J. Q. Cortes and J. Phillips, Materials 8, 6208 (2015).
  * [27] R. Peierls, Proc. Roy. Soc. A 347, 475 (1976).
  * [28] A. Einstein and J. Laub, Annalen der Physik 26, 541 (1908).
  * [29] S. R. de Groot and L. G. Suttorp, Foundations of Electrodynamics (North-Holland Publ. Comp. , Amsterdam, 1972).
  * [30] I. Brevik and S. Å. Ellingsen, Phys. Rev. A 81, 063830 (2010).
  * [31] L. S. Hou, W. T. Ni and Yu-Chum Li, Phys. Rev. Lett. 90, 201101 (2003).
  * [32] S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach and E. G. Adelberger, Phys. Rev. Lett. 100, 041101 (2008).
  * [33] R. A. Beth, Phys. Rev. 50, 115 (1936).