Christine Webb
email: christinewebb@fas.harvard.edu

Peter Woodford
email: woodforp@union.edu

Elise Huchard
email: ehuchard@gmail.com

Animal Ethics and Behavioral Science: An Overdue Discussion

Keywords: animal behavior, behavioral biology, animal ethics, animal welfare

Animal ethics-the field of philosophy concerned with the moral status of animals-is experiencing a momentum unprecedented in its history. Surprisingly, animal behavior science remains on the sidelines, despite producing critical evidence on which many arguments in animal ethics rest. Here we explore the origins of the divide between animal behavior science and animal ethics, before considering whether behavioral scientists should concern themselves with it. We finally envision tangible steps that could be taken to bridge the gap, encouraging scientists to be aware of, and to more actively engage with, an ethical revolution that is partly fueled by the evidence they generate.

The moral status of animals is a longstanding question dating back at least to Aristotelian philosophy (see [START_REF] Regan | Animal Rights and Human Obligations[END_REF] for an overview of historical and contemporary writings on the topic). However, it has been brought into especially acute focus in recent decades. The modern development of the animal ethics debate is fueled by many factors-among them, novel scientific insights into the complexities of animal minds and emotions [START_REF] Bekoff | The Animals' Agenda: Freedom, Compassion, and Coexistence in the Human Age[END_REF]; the ever-increasing scale of industrial farming [START_REF] Harrison | Animal Machines: The New Factory Farming Industry[END_REF](Harrison, /1964)); and the Anthropocene, an era heralded by unprecedented human-induced changes to the earth's climate, environments, and resident wildlife [START_REF] Ceballos | Accelerated modern human-induced species losses: Entering the sixth mass extinction[END_REF]. The cumulative impact of these trends has raised the urgency of moral concerns over the nature of human-animal relationships, particularly in the context of our use, overuse, and misuse of animals. The exploitation of animals for food and other products represents just part of the prevailing narrative: a major shift is taking place in how people view the role of animals in research, entertainment, and even companionship. This turn was detectable in early publications like [START_REF] Ryder | Victims of Science: The Use of Animals in Research[END_REF] Victims of Science and Singer's (1975) seminal Animal Liberation, and later built upon by those of other scholars (e.g., [START_REF] Donaldson | Zoopolis: A Political Theory of Animal Rights[END_REF][START_REF] Francione | Animals, Property, and The Law[END_REF][START_REF] Jamieson | Morality's Progress: Essays on Humans, Other Animals, and the Rest of Nature[END_REF][START_REF] Korsgaard | Fellow Creatures: Our Obligations to Other Animals[END_REF][START_REF] Nussbaum | Working with and for animals: Getting the theoretical framework right[END_REF][START_REF] Regan | The Case for Animal Rights[END_REF][START_REF] Rollin | Animal Rights and Human Morality[END_REF]; see also [START_REF] Armstrong | The Animal Ethics Reader[END_REF] for a comprehensive anthology of readings on animal ethics). The last two decades have witnessed an exponential increase in literature and journals focusing on animal ethics-the field of philosophy concerned with the moral status of animals (Figure 1). This transition in ethical thinking about animals has been, at least in part, driven forward by evolutionary theory and discoveries made in the behavioral sciences. Darwin's theory of evolution by natural selection offered a new and powerful challenge to the anthropocentric assumption that humans are the pinnacle of creation-an assumption central to many historically and presently influential theological conceptions of the world [START_REF] Rachels | Created from Animals: The Moral Implications of Darwinism[END_REF]. As the earlier scientific revolution guiding human understanding of the natural order showed that the earth is not the center of the cosmos, this revolution more dramatically levelled human ontological status by insisting that humans are one of a countless variety of other animals. The disintegration of our pre-Darwinian understanding of nature, coupled today with the extent of anthropogenic changes faced by the environment and animals in the industrial world, has revealed deep-seated incompatibilities between dominant frameworks of value (still rooted in a pervasive sense of human superiority) and the current state of knowledge regarding the capacities of other species and their vulnerability to human actions (e.g., [START_REF] Bekoff | The Animals' Agenda: Freedom, Compassion, and Coexistence in the Human Age[END_REF][START_REF] Jones | Science, sentience, and animal welfare[END_REF][START_REF] Rachels | Created from Animals: The Moral Implications of Darwinism[END_REF].

Recent progress in scientific research on animal behavior has provided evidence used by animal ethics by documenting previously unknown aspects of animal life that have fundamental ethical implications. Studies on the cognitive, emotional, and social capacities of other species have discredited long-held assumptions about capacities thought to be unique to humans. Nonexclusively, this list includes the design and use of tools [START_REF] Sanz | Tool Use in Animals[END_REF]; the prevalence of animal cultures [START_REF] Laland | The Question of Animal Culture[END_REF] and the capacity to innovate [START_REF] Reader | Animal and human innovation: novel problems and novel solutions[END_REF]; the complexity and efficiency of animal vocal communication, including symbolic communication [START_REF] Seyfarth | Monkey responses to three different alarm calls: Evidence of predator classification and semantic communication[END_REF] and forms of protosyntaxes [START_REF] Ouattara | Campbell's monkeys concatenate vocalizations into context-specific call sequences[END_REF]; the capacity for self-awareness [START_REF] Gallup | The mirror test[END_REF], mental time-travel [START_REF] Raby | Planning for the future by western scrub-jays[END_REF], and a wide range of emotional experiences, including joy and grief (de Waal, 2019); reports of complex forms of consciousness such as empathy [START_REF] De Waal | Mammalian empathy: Behavioral manifestations and neural basis[END_REF], and of social intelligence such as the formation of reciprocal alliances and the active management of long-term social relationships [START_REF] Cheney | Baboon Metaphysics -The Evolution of a Social Mind[END_REF], systems of conflict resolution [START_REF] Aureli | Natural Conflict Resolution[END_REF], and the ability to impute mental states to others [START_REF] Call | Does the chimpanzee have a theory of mind? 30 years later[END_REF], including the strategic adjustment of one's own knowledge of what others know (Emery & Clayton, 2001). These findings have all blurred traditional divisions structuring historical discussions of human uniqueness-including the opposition between nature and culture, between animal objects and human subjects, and between instinctive and rational actions-consequently casting doubt on the anthropocentrism that has largely dominated the history of ethics as a field of philosophical inquiry.

Alternative systems of ethical values developed in contemporary animal ethics often rely on empirical evidence to demonstrate the possession (or lack thereof) by a non-human individual of the relevant attribute conferring moral consideration [START_REF] Allen | Ethics and the science of animal minds[END_REF]. The main theories in animal ethics are pathocentric (i.e., centered on sentience and the capacity to suffer) and therefore hinge on empirical knowledge documenting the sentience of animals-such as recent work demonstrating that fish feel pain [START_REF] Brown | Fish intelligence, sentience and ethics[END_REF]. In addition, perceptions of animals as "subjects-of-a-life" are central to the deontological approach to animal ethics developed by Tom Regan that has also formed a critical part of the legal case for animal rights [START_REF] Regan | The Case for Animal Rights[END_REF].

Studies revealing the existence of personalities [START_REF] Sih | Behavioral syndromes: An ecological and evolutionary overview[END_REF], episodic memory [START_REF] Clayton | Episodic-like memory in animals[END_REF], intentionality [START_REF] Allen | Cognitive ethology and the intentionality of animal behaviour[END_REF], and rationality [START_REF] Hurley | Rational Animals?[END_REF] have thus been instrumental in revealing that animals have a subjective life, personal history, interests, and goal-oriented agency [START_REF] Jones | Science, sentience, and animal welfare[END_REF]. Taken together, this constellation of results from scientific research on animals has paved the way to changed (and changing) perspectives on the moral status of animals. Despite these critical contributions to animal ethics, animal behavior sciences like ethology, behavioral ecology, and comparative psychology have played a rather passive role in the progression and expansion of this movement. In other words, though animal behavior scientists' work has been integral, it is non-scientists who have primarily pioneered the integration of science and ethics. Here, we advance the argument that if the ethics of humananimal relationships are to be redefined, then more active participation on the part of animal behavior scientists has great potential-not just for moving animal ethics debates forward, but for scientists themselves. To be clear, in attempting to bridge the study of animal behavior and animal ethics, we are not just referring to the ethics of using animals in behavioral scienceswhich have already been the focus of thorough reviews (see Text Box 1). Further, although the scientific literature has recently highlighted how animal behavioral sciences can inform animal conservation (e.g., [START_REF] Caro | Behavior and conservation: A bridge too far?[END_REF][START_REF] Greggor | Research priorities from animal behaviour for maximising conservation progress[END_REF] and animal welfare science (e.g., [START_REF] Dawkins | A user's guide to animal welfare science[END_REF][START_REF] Fraser | Animal ethics and animal welfare science: Bridging the two cultures[END_REF], it has not yet extended to engage with the full realm of issues debated in animal ethics, which include questions about the fundamental ground of moral status. Our primary purpose in this article is to make that extension by addressing three key questions: What are the primary reasons for a gap between animal behavior science and animal ethics? Should behavioral scientists feel concerned about this growing disconnect? And how could they more actively contribute to the development of animal ethics?

Why the gap?

A primary reason for a frequent lack of communication between animal ethicists and behavioral scientists may reflect traditional difficulties in crossing disciplinary boundaries. Contemporary scientific culture remains largely disconnected from philosophy, which-unfortunately in our view-is not part of the regular academic training received by scientists; as a result, scientists may not be motivated or prepared to engage in broad ethical discussions that directly pertain to their scientific practice or results. The persistence of a gap is exacerbated institutionally by a lack of educational and career development opportunities that cross-over between behavioral science and philosophy. But it is also caused by fundamentally different theoretical and methodological orientations. Science aims to discover causal relationships between states of affairs and phenomena in the physical world, while ethics is an explicitly value-laden, normative field of inquiry that aims to defend our best judgments as to what we ought to do. We are not here proposing a solution to the "fact/value" relationship or to the problem of whether there are normative facts and how they might "fit" into nature, but rather proposing that differences in the basic questions and methods of scientists and ethicists underlie a prevalent, but divisive attitude that science is rigorous and "objective" while ethical theorizing is more "subjective."

Acquainting scientists with rigorous debate in normative ethics and ethical theory, as well as pointing them to the ways in which scientific research can be enmeshed within the values of the particular times and places in which it is carried out (Kincaid, Dupré, & Wylie, 2007), may help emphasize the benefits of interdisciplinary dialogue and research into the complex historical and logical relationship between science and ethics. Greater awareness of the various conceptual and normative assumptions that may come along with different conceptual frameworks can only improve the quality of scientific thinking [START_REF] Laplane | Opinion: Why science needs philosophy[END_REF].

While scientists should all be aware of the spectrum of ethical discussions related to their daily scientific practice, they may sometimes fail to see that animal ethics is a broad and fastgrowing area of philosophical inquiry and normative debate concerning the nature of humananimal relationships that is built on rational argumentation. It is important to realize that philosophers working on animal ethics may adopt a diversity of nuanced positions, and do not uniformly defend specific political or policy agendas. Scientists may sometimes lump the term "animal ethics" with other domains, in particular with the set of ethical regulations that rule their research activities (Text Box 1); with the emergence of animal welfare or conservation as scientific fields using research to assess and improve the animal condition; or even with the activism incited by animal rights associations. Conversely, while ethicists may be more aware of scientists' work than the reverse, they may not be up-to-date with the most current research and debates in the field. Nor do ethicists necessarily have experience rigorously observing animal behavior. Disciplinary segregations between animal welfare scientists, conservation biologists, and (some) animal ethicists are particularly telling examples of the oddity that the divide between these so-called "two cultures" persists even in the context of obviously shared ethical concerns [START_REF] Fraser | Animal ethics and animal welfare science: Bridging the two cultures[END_REF]. While the integration of normative and empirical approaches to animal welfare and conservation sciences have eventually gained advocates (i.e., welfare [START_REF] Dawkins | A user's guide to animal welfare science[END_REF][START_REF] Fraser | Animal ethics and animal welfare science: Bridging the two cultures[END_REF][START_REF] Würbel | Ethology applied to animal ethics[END_REF]conservation: Ramp & Bekoff, 2015), scientific discussions of ethical issues have focused on a rather specific set of questions with limited attention to foundational reflection on ethical frameworks and on how normative and empirical approaches relate [START_REF] Dawkins | A user's guide to animal welfare science[END_REF].

The gap between ethicists and behavioral scientists has further been maintained by mutual defiance and skepticism. If and how animals should be used in science has been a core question of animal ethics since its inception, and behavioral research has immediately been the focus of severe criticism for conducting painful and unnecessary experiments [START_REF] Ryder | Victims of Science: The Use of Animals in Research[END_REF][START_REF] Singer | Animal Liberation: A New Ethics for Our Treatment of Animals[END_REF]. Ethicists subsequently became suspicious towards, or dismissive of, any scientific procedure involving animals to study their behavior [START_REF] Fraser | Animal ethics and animal welfare science: Bridging the two cultures[END_REF]. Meanwhile, animal behavior scientists naturally feared condemnation surrounding their research, and may have perceived the gradual development of ethical regulations on the use of animals in research (Text Box 1) as an extra source of constraints and bureaucracy in their work. This divide has likely been furthered by several aspects of the predominant disciplinary culture of animal behavior. Many animal behavior researchers have traditionally adopted the attitude of stifling empathy towards their study subjects in the interest of preserving scientific objectivity and avoiding behavioral interferences with the study subject [START_REF] Kennedy | The New Anthropomorphism[END_REF]. Such detachment in the name of objectivity may have contributed to the notion that an ethical sensibility towards subjects of research is "unscientific" and "subjective," and may still prevent many researchers from perceiving open engagement with current debates in animal ethics as an integral part of, or at least as compatible with, scientific thinking and practice.

New points of tension have arisen in the course of contemporary discussions in animal ethics, which have for the most part been dominated by two competing approaches: utilitarian welfare-based and deontological rights-based approaches. Whereas both approaches share the idea that animal welfare is worthy of protection for its own sake and not for the sake of humans, the welfare approach insists that moral duties related to the humane treatment of animals come from animals' capacity to feel pain and pleasure. It stems from a utilitarian and consequentialist approach to animal ethics, according to which the aggregate benefits of any intervention into animal lives must exceed any harmful costs [START_REF] Singer | Animal Liberation: A New Ethics for Our Treatment of Animals[END_REF]. In contrast, theories of animal rights are based in deontological ethics, pursuant to which duties to animals come from the respect that they deserve as agents with their own unique interests, aims, and goals. Theorists in this school consider animals' lives to be intrinsically valuable and propose to grant them basic rights-such as the right to life, freedom, and not to be tortured-to prevent them from being treated as "mere means" such that their interests are sacrificed to human interests [START_REF] Donaldson | Zoopolis: A Political Theory of Animal Rights[END_REF][START_REF] Francione | Animals, Property, and The Law[END_REF][START_REF] Regan | The Case for Animal Rights[END_REF]. This generates a critical tension with welfare approaches, according to which animals retain an instrumental value in situations in which benefits (to the human community) might outweigh harm (to the animals). It is clear that when animal scientists do engage with ethical debates, the prevailing utilitarian, welfare-based approach is often adopted by default, probably due-at least in part-to the use of animals in scientific research.

However, many ethicists have instead favored theories of animal rights [START_REF] Donaldson | Zoopolis: A Political Theory of Animal Rights[END_REF], though they have not uniformly condemned the use of animals in research within this framework. Thus, although the practical implications of such divergences in underlying ethical theory may be profound, rights-based theories do not necessarily exclude the possibility of research on animals. For example, just as human volunteers can participate in scientific experiments, it may be possible to envision a research protocol that respects the dissent of a nonhuman subject (e.g., [START_REF] Fenton | Can a chimp say "no"? Reenvisioning chimpanzee dissent in harmful research[END_REF], especially in behavioral research where experiments can be designed in which animals are free to participate.

Should animal behavior scientists concern themselves with animal ethics?

A greater integration between animal ethics and the animal behavior scientific community is desirable for ethical and pragmatic reasons. Foremost, there is an ethical reason in that scientists fulfill a social responsibility when they engage with and help others understand ethical implications of research. Yet there are also pragmatic benefits for science, including helping scientists examine sources of historical and cultural bias that may limit scientific questions and approaches, and so further enrich and broaden scientific understanding. Some of these benefits may admittedly arise from interactions with philosophical discussions about the nature of animals that are broader than animal ethics, for example philosophical work on animal minds, perception and representation, social learning and culture, altruism and cooperation, and rationality [START_REF] Andrews | The Animal Mind: An Introduction to the Philosophy of Animal Cognition[END_REF]Andrews & Beck, 2018). Nonetheless, the recent renewal of the philosophy of animals as a sub-field within the philosophy of science has played and continues to play a major role in the expansion of animal ethics insofar as it has also challenged anthropocentric approaches that have dominated classical philosophy. While the recognition of animal consciousness and subjectivity is growing, it is not unanimous in philosophy (cf [START_REF] Carruthers | Phenomenal Consciousness: A Naturalistic Theory[END_REF]Tye, 2016, for instance). These important debates that are relevant to animal ethics, but are also broader, draw on and require science and should, therefore, be inspiring to animal scientists as well.

Filling our social responsibility. Many scientists are naturally interested in how their results inform and inspire societal debates-one obvious reason for animal behavioral scientists to engage with the literature on animal ethics. In addition to this natural curiosity, and despite commonly holding the view that scientific findings have no intrinsic normative value, scientists still usually support ideas of moral progress that follow from scientific progress in our rational understanding of the natural world. For example, where progress in understanding the neurologic development of infants uncovered the capacity for pain [START_REF] Anand | Pain and its effects in the human neonate and fetus[END_REF], it became an ethical duty for scientists to advocate against neonatal surgeries without anesthesia. The parallels to our understanding of animal pain are obvious, and scientists could play an important role in advocating against farming or research practices that involve suffering in the form of pain as well. More generally, ethics makes a claim on scientists to engage with public debates on ethical issues that are related to their scientific activities (and sometimes even raised by their results) [START_REF] Pain | The social responsibilities of scientists[END_REF][START_REF] Siekevitz | Scientific responsibility[END_REF]. At a time when researchers in science and technology are often consulted to set the direction and values of society, and often occupy leadership roles on decision-making bodies, this obligation must increasingly be emphasized. For example, a communication from Mark S. Frankel, director of the Scientific Responsibility, Human Rights, and Law Program at the American Association for the Advancement of Science (AAAS), argues that students and scientists should put less emphasis on their internal responsibility regarding how research should be conducted, and more on their external responsibility by being "vitally concerned" with the influence that their work and knowledge can have on society [START_REF] Pain | The social responsibilities of scientists[END_REF].

Scientists are increasingly required to justify the benefits of their research to society-this is notably the case for individual applications to research positions or funding, as well as for research evaluations at the institutional level-and growing debates on animal moral status spark public interest in animal behavior science. In this context, active engagement with animal ethics could translate to a new and promising applied dimension of scientists' work-one that is both instrumentally beneficial and aligned with social responsibilities.

Opening the "black box" of animal minds. Following the vast accumulation of knowledge on animal behavior, scientists are faced with new questions about the nature of animal minds, a crucial topic also at the center of philosophical debate today [START_REF] Andrews | The Animal Mind: An Introduction to the Philosophy of Animal Cognition[END_REF]Andrews & Beck, 2018;[START_REF] Lurz | The Philosophy of Animal Minds[END_REF]. Nonetheless, the lingering conviction that animal mental states are unknowable-a "black box" that is inaccessible to science-or irrelevant to the explanation of behavior (e.g., [START_REF] Dawkins | Animal welfare and the paradox of animal consciousness[END_REF] has limited scientifically-informed ethical reasoning about animals. For example, [START_REF] Griffin | From cognition to consciousness[END_REF] call to bring the study of consciousness to the fore of ethology nearly two decades ago is continually met with considerable resistance (for a historical overview on cognitive ethology, see: [START_REF] Allen | Animal minds, cognitive ethology, and ethics[END_REF], and some contemporary scientists deny that documenting the degree of animal consciousness is useful in the science of comparative cognition [START_REF] Shettleworth | Cognition, Evolution, and Behavior[END_REF]. In addition to this fundamental debate on whether animal consciousness can and should be studied by scientists, some major explanatory frameworks in animal behavior science have downplayed the explanatory significance of animal mental and emotional lives. In particular, behavioral ecologists are traditionally trained to focus on the adaptive value of a trait, favoring ultimate over proximate explanations for behavior. As one example, infanticide is often framed exclusively in terms of evolutionary costs/benefits, rather than any underlying emotion or proximate motivation (e.g., see van Schaik & Janson, 2009). Although these functional evolutionary explanations are valuable in their own right, they offer only a very limited view of animal emotions, capabilities, and agency, and little to no insight into perceptions, intentionality, rationality, or consciousness residing "inside" of animal minds. This poses a deeper, more fundamental epistemological problem in the sense that building a whole field of scientific inquiry around what is currently a "black box" inherently hampers ultimate explanatory and predictive efforts. This shortcoming in turn reveals how explanatory frameworks in the behavioral sciences can quickly overlook or render invisible the very "object" of moral concern-the organism itself as a potentially sentient entity that can be benefited or harmed-or, at the very least, relegate the organism to secondary status [START_REF] Walsh | Organisms, Agency, and Evolution[END_REF].

The language that animal behavior scientists habitually employ reflects this deeply entrenched practice [START_REF] Crist | Images of Animals: Anthropomorphism and Animal Mind[END_REF]. Reducing animal behavior to mechanistic, causal descriptions has reinforced the view of animals as "mere" objects or "vehicles" of their genes and environment, preempting any inferences to their mental life or agency (it is noteworthy that in the writings of early naturalists such as Darwin, animals were commonly portrayed as individuals with an array of meaningful subjective experiences and aims). For example, scientists have traditionally used terms such as "innate releasing mechanism" while habitually relegating complex behavioral phenomena-usually those linked with cognitive or affective capacities-to more "parsimonious" explanations, further distancing themselves from the animals they study.

However, this presupposes that such technical, parsimonious descriptions are also unbiased, and it would behoove scientists to realize that the theoretical language they employ is built on an inherently skeptical bias towards animal subjective and agential traits. The animal ethics literature, which puts animal subjectivity and agency at the heart of its argumentation, places an ethical urgency and burden of proof on mechanistic views of animal behavior in the behavioral sciences to show that animals are not sentient [START_REF] Birch | Animal sentience and the precautionary principle[END_REF][START_REF] Birch | Animal cognition and human values[END_REF], and to develop more solid inferences about the existence and character of animal subjectivity (e.g., see [START_REF] Godfrey-Smith | Other minds: The octopus, the sea, and the deep origins of consciousness[END_REF][START_REF] Smuts | Encounters with animal minds[END_REF].

Questioning the anthropocentric legacy of behavioral studies. The slow development of cognitive ethology is not merely a consequence of empirical limitations in accessing animal minds or a predominant focus on ultimate explanation in studies of animal behavior. The avoidance of attributing-or even studying-morally-relevant traits like agency, interests, or motivations and goals to non-human animals reflects a more pervasive bias, namely the perceived dangers of anthropomorphism (e.g., [START_REF] Wynne | The perils of anthropomorphism[END_REF]. In addition to shaping research questions, experimental settings and interpretations of results traditionally tend to disfavor anthropomorphic hypotheses, according to which similar mechanisms underlie the behavioral similarities observed between humans and non-humans. This occurs even when studying species that are closely related to us, a revelatory context regarding such a bias, referred to as "anthropodenial" by de Waal (1999). According to basic evolutionary principles, the most parsimonious explanation in such cases is the one assuming that similar processes in closely related species emerge from common ancestry ("phylogenetic parsimony"). A scenario in which the evolution of distinct cognitive processes generates similar behavioral manifestations in closely related species is, in fact, improbable. It is also revealing to note that simple mechanistic explanations are generally favored over phylogenetic parsimony when discussing cognitive capacities, as opposed to physiological or anatomical traits, for which scientists have no problem invoking human-animal similarity [START_REF] De Waal | Anthropomorphism and anthropodenial: Consistency in our thinking about humans and other animals[END_REF]. This bias appears to be a direct, pervasive legacy of the famous Morgan's Canon proposed at the end of the 19th century, which states that:

'In no case may we interpret an action as the outcome of the exercise of a higher psychical faculty, if it can be interpreted as the outcome of the exercise of one which stands lower in the psychological scale' (Morgan, 1894, p. 53). A large philosophical literature has recently accumulated around related methodological issues [START_REF] Buckner | Rational inference: The lowest bounds[END_REF][START_REF] Fitzpatrick | Doing away with morgan's canon[END_REF][START_REF] Halina | There Is no special problem of mindreading in nonhuman animals[END_REF][START_REF] Keeley | Anthropomorphism, primatomorphism, mammalomorphism: Understanding cross-species comparisons[END_REF][START_REF] Mikhalevich | A critique of the principle of cognitive simplicity in comparative cognition[END_REF][START_REF] Sober | Anthropomorphism, parsimony, and common Ancestry[END_REF], and scientists can benefit from deeper reflection on any bias toward simplicity that is motivated by worries about the dangers of anthropomorphism.

Another upshot of this approach is that the threshold of evidence needed to provide support for a particular cognitive or emotional faculty in other species is much higher than in our own. For example, the definition of animal teaching initially proposed by [START_REF] Caro | Is there teaching in nonhuman animals?[END_REF] has proven so strict that it would exclude many occurrences of human teaching as employed in common parlance [START_REF] Laland | Do animals have culture ?[END_REF]. This anthropocentric perspective has also figured prominently in debates about animal emotions [START_REF] Bekoff | Animal emotions and animal sentience and why they matter: Blending 'science sense' with common sense, compassion and heart[END_REF][START_REF] De Waal | Mama's Last Hug[END_REF]; it is not just a remnant of the behaviorist era but still alive today in the form of categorical rejections of anthropomorphism and anecdote. However, when the animal's perspective is carefully considered, anthropomorphic and anecdotal accounts have an important role to play in informing and inspiring rigorous science [START_REF] Bates | Creative or created : Using anecdotes to investigate animal cognition[END_REF][START_REF] Burghardt | Cognitive ethology and critical anthropomorphism: A snake with two heads and hognose snakes that play dead[END_REF][START_REF] De Waal | Anthropomorphism and anthropodenial: Consistency in our thinking about humans and other animals[END_REF][START_REF] Godfrey-Smith | Other minds: The octopus, the sea, and the deep origins of consciousness[END_REF], particularly when it comes to animal mental capacities and emotions [START_REF] Bekoff | Animal emotions and animal sentience and why they matter: Blending 'science sense' with common sense, compassion and heart[END_REF]. While this form of anthropocentric reductionism is very entrenched in the Western scientific culture in animal behavior, an independent academic tradition emerged in Japan, where anecdotes were valued, and where anthropomorphism was not considered a threat [START_REF] Asquith | Japanese science and western hegemonies: Primatology and the limits set to questions[END_REF][START_REF] De Waal | Silent invasion: Imanishi's primatology and cultural bias in science[END_REF]. Despite intense criticisms by Western scientists, Japanese primatologists used individually-based observations-which are now the standard in ethological studies-and made fundamental discoveries in socio-ecology, such as the existence of tight family bonds structuring animal societies, and the diffusion of socially-learnt behaviors throughout animal groups, long before these questions crystallized interest in Western research [START_REF] Asquith | Japanese science and western hegemonies: Primatology and the limits set to questions[END_REF][START_REF] De Waal | Silent invasion: Imanishi's primatology and cultural bias in science[END_REF]. This example illustrates the potential benefits of raising scientists' awareness of the cultural and cognitive biases that may hamper progress in their discipline. And even though the fear of anthropomorphism may be less present in today's scientific culture than it used to be, the critical stance adopted by thinkers in animal ethics regarding anthropocentric values, combined with their fresh and attentive eye towards animal minds and subjectivity, encourages behavioral scientists who have not already done so to inspect the deeply entrenched sources of biases that inevitably affect their discipline.

Enriching scientific practices. A greater consideration of animal interests and subjectivity may be beneficial pragmatically by changing the way scientists ask questions, design protocols, and interpret animal reactions to experimental conditions. Integrating information about the firstperson perspective of the animal is increasingly recognized as important in evolutionary modelling of the effects of natural selection on behavior (e.g., [START_REF] Akçay | A theory for the evolution of other-regard integrating proximate and ultimate perspectives[END_REF]. When designing experiments, careful attention to the animal's perspective on a proposed task can reduce some biases-such as experimenter effects [START_REF] Despret | Thinking Like a Rat[END_REF]. For example, laboratory mice perceive gender of the experimenter and may consequently modify their behavioral response in an experiment, with male experimenters eliciting a greater stress response than females [START_REF] Sorge | Olfactory exposure to males, including men, causes stress and related analgesia in rodents[END_REF]. Along similar lines, earlier scholars appreciated that animals live in meaningful and complex worlds, and that adopting the animal's sensory perspective was a necessary precondition for the successful study of behavior [START_REF] Von Uexküll | A stroll through the worlds of animals and men: A picture book of invisible worlds[END_REF](von Uexküll, /1957)). In contrast, subsequent behavioral studies have sometimes failed to adopt such a perspective by designing studies linked to species-specific daily environmental challenges, and so are at risk of making erroneous inferences about animal capacities. For example, dogs were once thought to lack self-awareness due to their failure to pass the mirror self-recognition task, which is strongly biased towards visual species, but they were subsequently found to succeed in passing an "olfactory mirror" test (e.g., [START_REF] Gatti | Self-consciousness: Beyond the looking-glass and what dogs found there[END_REF]. The role of perspective-taking in animal behavior research is also central to the influential work of philosopher Merleau-Ponty (1998), who first established a link between animal behavior and phenomenology-which can arguably make a major contribution to both animal ethics [START_REF] Painter | Phenomenology and the Non-Human Animal: At the Limits of Experience[END_REF] and scientific research on animal behavior [START_REF] Ruonakoski | Phenomenology and the study of animal behavior[END_REF] by offering additional insights into animal subjectivity.

When it comes to studying animal behavior, Merleau-Ponty (1998) questions the behaviorist way of interpreting the scientist's role, requiring the scientist's detachment from the study subject.

Rather than rejecting anthropomorphism and denying their own sensitivity towards the behavior of study subjects, scientists could acknowledge that human experience, careful observation, and even engaged interaction with animals are the only possible starting points for their investigations, because absolute detachment is impossible in practice (e.g., see [START_REF] Candea | I fell in love with carlos the meerkat: Engagement and detachment in humananimal Relations[END_REF][START_REF] Ruonakoski | Phenomenology and the study of animal behavior[END_REF][START_REF] Smuts | Encounters with animal minds[END_REF].

An interdisciplinary dialogue between philosophers, ethicists, and scientists may promote changes in paradigms that could usefully complement traditional approaches and open productive, more holistic avenues to study and understand animal behavior without compromising scientific rigor. In particular, research in cognitive ethology on concepts rooted in classical, anthropocentric philosophy (e.g., self-awareness, empathy, free will, or culture) would benefit from such discussions, which may facilitate the establishment of more inclusive definitions (i.e., applicable to studying non-human animals) that retain theoretical and empirical traction. It would further encourage reflection on the most efficient research approaches and the criteria that would provide supporting evidence for the existence of such phenomena in other species. As one example, some philosophers reexamined the state of knowledge regarding behaviors long thought to be human-unique, such as the capacity to commit suicide (e.g., Peña-Guzmán, 2017), by lending more weight to animal subjectivity than many scientists traditionally have. These exercises illustrate the potential power of such interdisciplinary dialogues for enriching the perspectives of scientists working on animal behavior, while making them more aware of the fact that a collection of scientific observations can lead to divergent interpretative frameworks.

In sum, interactions between the science of animal behavior and animal ethics could have a greater and mutually beneficial scope, addressing questions about what animals are, how we should treat them, and how to envision potential futures for human-animal interactions. The possibility of such a productive exchange between science and philosophy has a strong precedent in the relationship between the science of ecology and environmental philosophy. By generating new scientific knowledge on the interconnectedness and dependence amongst various forms of life, the field of ecology has also influenced ethical thought. Though not uniformly defended by ethicists, ecology has led to calls to regard supra-individual processes, such as ecosystems themselves, as intrinsically valuable and as objects of ethical concern-particularly concerning planetary health criteria grounded in the capacity to sustain and generate biodiversity. Just as in the case of animal behavior science and animal ethics, ecology too has been a source for combating anthropocentrism and generating a more balanced, indeed scientifically informed, worldview regarding the place of humans as one species embedded within deeply interconnected, interdependent living systems [START_REF] Callicott | Whither conservation ethics?[END_REF].

How can animal behavior scientists engage with philosophy and animal ethics?

In turn, animal behavior scientists can contribute to animal ethics in various ways. Their potential contributions to animal ethics span the full spectrum of scientific activities-not only in offering original evidence that fuels theoretical progress in animal ethics, but shaping its practical applications, lending pertinent expertise, and communicating effectively with the wider public. There are, however, boundary conditions to what they can offer to ethicists; one prerequisite is that some research involving animals is tolerated-itself a source of disagreement even within the animal ethics community-provided that its costs are minimal and outweighed by clear benefits. As a result, behavioral scientists should carefully take ethical considerations into account when designing their research (Text Box 1).

Foster productive interdisciplinary exchanges. An essential first step in this integration could be for behavioral scientists to familiarize themselves with the field of animal ethics [START_REF] Armstrong | The Animal Ethics Reader[END_REF] provide a comprehensive anthology of readings on animal ethics), which will also cultivate mutual respect and awareness across fields. However, at least to our knowledge, animal ethics, and philosophy more generally, are often absent from animal behavior educational programs and curricula. Reciprocally, academic departments in animal studies are typically housed in social science or humanities faculties, and often lack scientists. This structural separation limits cross-disciplinary exchanges, which could be encouraged by the development of joint teaching, reading groups, research programs, and conferences. Mutual engagement and integrative theory-building could be further fostered by hosting philosophers and ethicists in scientific labs and research groups. Further, several interdisciplinary journals now provide a forum wherein scholars across these disparate fields can comment on topics of mutual interest ranging from animal emotions to the most sound approaches to animal protection legislation (e.g., see Birch, 2017 along with associated commentaries).

Upon gaining meaningful exposure to the basic purview of animal ethics, scientists of animal behavior can further update some of their conceptual frameworks and research practices (as elaborated in the previous section), which may simultaneously foster the endorsement of their findings by non-scientists pursuing related questions. Among the most notable successes in this regard is pioneering work in the area of compassionate conservation, which attempts to appease tensions between scientists who conventionally focus on species and populations and ethicists who typically focus on individuals [START_REF] Ramp | Compassion as a practical and evolved ethic for conservation[END_REF].

Produce relevant original evidence. As highlighted above, original evidence stemming from the natural course of animal behavior science has already played a role in inspiring important developments in animal philosophy. Of course, while detailed knowledge concerning the cognitive, affective, and social lives of animals can contribute to our understanding of what is "painful" to an animal, its degree of sentience and consciousness, the optimal environments in which it thrives, etc., it certainly cannot tell us what is right or wrong-the central concepts that structure ethical theory and practice. Nevertheless, biological knowledge on the natural behavior of different species, in relation to their phylogenetic position and ecology, can help in setting species-specific criteria for animal ethics agendas. It also has a hand in proposing modes of interactions with animals that are respectful of their physiology and psychology, consistent with a new theory of animal rights that borrows concepts from political philosophy (including citizenship or sovereignty) to envision a new legal frame applicable to the complexity and diversity of animal-human relationships [START_REF] Donaldson | Zoopolis: A Political Theory of Animal Rights[END_REF].

In addition, as has already occurred in conservation practice, there is growing pressure for policy decisions concerning animal ethics to be evidence-based, and animal behavior scientists are positioned to contribute data and knowledge that can, at a minimum, inform political decisions regarding the assignment of diverse taxonomic groupings to particular moral categories [START_REF] Jones | Science, sentience, and animal welfare[END_REF]. The diversity of species that animal behavior scientists study-many of which are beneath the radar of philosophers in favor of a focus on higher vertebrates (with notable exceptions, e.g., [START_REF] Godfrey-Smith | Other minds: The octopus, the sea, and the deep origins of consciousness[END_REF][START_REF] Tye | Tense Bees and Shell-Shocked Crabs: Are Animals Conscious?[END_REF]-can raise new ethical concerns and priorities. For example, combined with novel insights on behavioral and cognitive complexity, accumulating scientific evidence that fish feel pain has supported the argument that they be granted similar legal protections to other vertebrates [START_REF] Brown | Fish intelligence, sentience and ethics[END_REF]. Similarly, legal personhood campaigns, generally devised to grant legal protections to large mammals, are contingent on evidence concerning capacities like self-awareness and autonomy [START_REF] Andrews | Chimpanzee Rights: The Philosophers' Brief[END_REF][START_REF] Wise | Rattling the Cage: Toward Legal Rights for Animals[END_REF]. [START_REF] Thompson | Supporting ape rights: Finding the right fit between science and the law[END_REF] recently outlined how scientists' work could better position lawyers to build personhood cases, citing four domains-innovativeness, altruism, self-control, and defiance-that would more demonstrably provide evidence for autonomy to the court system.

Despite philosophical disagreement over the personhood defense of animal rights (e.g., see [START_REF] Korsgaard | Fellow Creatures: Our Obligations to Other Animals[END_REF][START_REF] Nussbaum | Working with and for animals: Getting the theoretical framework right[END_REF], such communications are important given that scientists do not naturally design their research in light of legal principles and questions.

The need for evidence-based animal ethics frameworks is not to overlook the veritable limits of scientific knowledge. It is important to note that the pace and reach of scientific progress is not always compatible with more immediate ethical decisions, necessitating guidance on what to do in the absence of convincing scientific evidence for aspects of animal sentience (e.g., see [START_REF] Birch | Animal sentience and the precautionary principle[END_REF]. Further, burden of proof frameworks must weigh the relative consequences of under-versus over-attributing particular mental states to animals, as such estimations can immediately impact welfare and related policy decisions-in particular, the implications of our systematic use of skepticism as the default position should be carefully evaluated [START_REF] Birch | Animal sentience and the precautionary principle[END_REF][START_REF] Birch | Animal cognition and human values[END_REF]. It is also important to acknowledge the diversity of ethical stances towards the weight of scientific evidence-not merely in terms of what is accepted/tolerated, but what is encouraged as the optimal way to understand the complexity of the world around us.

There are important philosophical discussions about the sources of our judgment as to whether or not animals have minds and mental lives, with some defending non-inferential approaches based on direct experience (see [START_REF] Jamieson | Science, knowledge, and animal minds[END_REF]; see also [START_REF] Bekoff | Animal emotions and animal sentience and why they matter: Blending 'science sense' with common sense, compassion and heart[END_REF] for an interesting discussion of scientific vs. common-sense approaches, which are likely best considered in tandem when it comes to animal ethics).

Regardless of one's position here, many scientists in the field of animal behavior spend considerable time observing animals, and thus have a wealth of direct "real world" experiences in this regard. A deep understanding of evolutionary theory, allied with the intimate experiences that people who work extensively with animals have, can translate to a unique perspective on animals and human-animal relationships that ethical debate should capitalize on (see [START_REF] Godfrey-Smith | Other minds: The octopus, the sea, and the deep origins of consciousness[END_REF][START_REF] Smuts | Encounters with animal minds[END_REF] for pertinent examples). Phenomenologists are particularly interested in such perspectives given their potential to elucidate new realms of being and experience, challenging traditional philosophical views on animal natures and intersubjectivity [START_REF] Merleau-Ponty | The Structure of Behavior (Translatio)[END_REF].

Provide scientific expertise. Scientists' ability to synthesize and scrutinize academic knowledge has the potential to further guide the public and policymakers in their interpretation of scientific evidence. For example, The Cambridge Declaration on Consciousness [START_REF] Low | The Cambridge Declaration on Consciousness[END_REF]prompted by the accumulation of data revealing that humans are not unique in possessing the neurological substrates that generate consciousness-was written by a group of neuroscientists to challenge previously held standards. Animal behavior scientists could similarly consider synthesizing information about species' intellectual, emotional, and social lives in a format that can be used by decision-makers when drafting and/or updating ethics policies and legislation, preferably through quantitative meta-analyses and systematic reviews. Conservation and animal behavior scientists recently convened to identify research priorities in animal behavior that promote progress in applied conservation [START_REF] Greggor | Research priorities from animal behaviour for maximising conservation progress[END_REF]; a similar exercise could benefit the translation of animal ethics into practical actions. Court cases on animal legal personhood are arising in a growing number of countries, providing a new context where animal behavior scientists may be expected to act as experts. However, unlike scientists who regularly intervene in court cases and are well aware of the legal culture, such as criminologists or psychiatrists, animal behavioral scientists are generally unprepared for such an exercise. At a smaller scale (and if not already the case), behavioral scientists can join ethics committees to ensure independent representation of animal interests in other scientific fields, and ascertain that ethical concerns are carefully weighed when reviewing articles and grant applications in their own field.

Add a scientific credit to animal ethics in outreach efforts. Finally, scientists are often perceived as the authorities on animal behavior, and therefore have the opportunity to inform and engage the public about animal interests. Yet while it is commonplace for animal behavior scientists to emphasize the conservation implications of their work, other broader impacts related to the moral standing of animals are emphasized relatively less in their public outreach. Increasingly, research on animal behavior has mass public appeal, which opens the door for animal behavior scientists to more actively engage with contemporary animal ethical or philosophical debates and discussions-following the recent tracks of some behavioral scientists [START_REF] Balcombe | Pleasurable Kingdom: Animals and the Nature of Feeling Good[END_REF][START_REF] Bekoff | Animal emotions and animal sentience and why they matter: Blending 'science sense' with common sense, compassion and heart[END_REF][START_REF] Brown | Fish intelligence, sentience and ethics[END_REF][START_REF] Smuts | Encounters with animal minds[END_REF].

Concluding remarks

Animal behavioral scientists have much to gain from their academic community's engagement with animal ethics. By jumping into the discussion, scientists also engage more directly with a revolution that has been in part stimulated by their work. Given the rapid rise and foreseeable progress of debates around animal ethics, it is certain that the current generation of animal behavior scientists will have to confront the questions that it raises in the coming decade(s), both as scientists and as citizens. Developing a stronger, more informed and engaged stance that aims to build consensus surrounding questions raised in animal ethics becomes critical to ensure the long-term importance and contribution of their scientific field, to fulfill their moral obligations, and to meet societal expectations by taking part in debates that they are well-positioned to inform. We hope that this paper will encourage this pressing and overdue discussion.

Figure 1 .

 1 Figure 1. Web-based search results (grey bars correspond to total number of hits) for the search terms (a) "animal ethics" as well as

Acknowledgments

We would like to extend our thanks to many colleagues for insightful comments at various stages of this manuscript's preparation, especially: Alice Baniel, Alecia Carter, Marie Charpentier, Becca Franks, Jennifer Jacquet, Alex Lee, and Harry Marshall. We are further grateful to several anonymous reviewers, who provided thorough and constructive feedback, as well as Marc Bekoff for his advice and encouragement. Finally, we would like to express our gratitude to the non-human animals with whom we have worked over the years. Those experiences inspired this paper and most importantly, cultivated a personal and professional concern for animal ethics.

Text Box 1: The ethics of using animals in behavioral science

In this paper, we emphasize potential interactions between the philosophical field of animal 2010)). The main scientific journals in psychology and behavioral ecology require that these standards be met to publish a paper. It certainly does not mean that all ethical issues associated with animal behavior sciences have been thoroughly resolved, and future work should strive to keep ethics questions central to its interests. Empirical work attempting to measure the stress, pain, and mortality caused by study protocols is an emerging field of research (e.g., [START_REF] Hämäläinen | Evaluating capture stress in wild gray mouse lemurs via repeated fecal sampling: Method validation and the influence of prior experience and handling protocols on stress responses[END_REF][START_REF] Maho | An ethical issue in biodiversity science: The monitoring of penguins with flipper bands[END_REF], and several recent reviews have been dedicated to these and other ethical issues [START_REF] Costello | Field work ethics in biological research[END_REF][START_REF] Field | Publication reform to safeguard wildlife from researcher harm[END_REF][START_REF] Mackinnon | Field primatology of today: Current ethical issues[END_REF].


Keywords: Information quantique, causalité, super-luminique, rétro-information, intrication

Relayages spatio-temporels et principe de causalité dans l'information

Résumé :

Nous analysons la connexion entre le principe de causalité et théorie de l'information. Nous montrons qu'une lecture basique de la théorie de l'information peut amener à d'crire le phénomène quantique d'intrication comme un transfers d'information super-luminique. Nous montrons comment l'introduction du concept de routage spatio-temporel résoud partiellement ce paradoxe de transfers d'information non causal. De manière surprenante la causalité del'information dépend du principe d'unitarité quantique, celui-ci étant un principe physique plus faible que celui de la causalité.

Introduction

Since the early ages men have sent their messages on pieces of matter or on energy flows, e.g. on stones, paper, flags, smokes, messengers, electrical signals, radio waves. In the near future, the quantity of mass or energy needed to carry the same amount of information will certainly continue to decay, closing to quantum limits, but this will still be energy flow. Therefore it is natural to expect that information transfer should endorse the same constraints that apply on energy transfer, for example the light speed limit and the principle of causality. But is that so obvious? For example can we imagine information faster than light? This paper will show that surprisingly energy causality does not imply information causality. But this in fact comes from an incompleteness of Shannon theory that lead to a misinterpretation of quantum entanglement in information theory. But it is known that quantum entanglement cannot carry "useful" information random entropy. Nevertheless we can break this apparent paradox by introducing the concept of space-time relaying which restore a kinf of information causality. Interesting enough the information causality is not directly dependent on energy causality but is rather a consequence of a much weaker axiom in physics, namely the principle of unitarity in quantum mechanics.

To the author best knowledge it is the first time such issue is addressed (following [START_REF] Jacquet | Capacity of retro-information channels[END_REF]). It outlines the unexpected result that indeed information transfers and energy transfers don't play in the same arena and need definitely to be treated differently. The paper is organized as follows: the next section reviews closely the notion of causality. Section III addresses the concept of causality with information and shows how a basic reading of this concept is broken by the concept of quantum information entanglement. Section IV introduces the concept of space relaying that restore the principle of causality in information theory as a consequence of unitarity principle.

The principle of causality 2.1 Philosophical Causality

The popular acception of causality is that "the cause precedes the effects", this means that if an event X has an effect on another event Y , then X precedes Y . But imagining "cause" and "effect" is difficult without an implicit time reference. One could try to express "X has effect on Y " by the fact that the mutual information I(X, Y ) is non zero, transposing causality into an information transfer. But this viewside does not distinguish at all between emitter and receiver. In fact, by virtue of the identity I(X, Y ) = h(X) + h(Y ) -h(X, Y ), h(•) being the entropy, we have the symmetry I(X, Y ) = I(Y, X).

Restricting causality to non zero mutual information may lead to absurb situations. For example let imagine the mother of two twin traveler salesmen who travel to two different locations the same day. Before they leave their house their mother leave the same amount of money in their luggage. In the evening in their respective hotel each twin discovers its money, respectively X and Y . Since X = Y then the mutual information is non zero. But none of the twins is the emitter nor the receiver. This example illustrates the paradox known as the Einstein-Podolski-Rosen (EPR) paradox where a correlation occurs between two particles at a speed that can exceed the speed of light but which does not result from any information transfer.

There is no proper definition of emitter and transmitter, excepted that the emitter contains the information to be transmitted just before the emission, and the receiver contains the information just after the reception. Notice that these definitions require a temporal order related to time. Also notice that if time were to be reversed, then the emitter and receiver would switch their status.

Physical causality

The present acception of causality involves the concept of causality lines (or causal lines). A causality line is an ordered sequence of events such that event i is a cause to event i + 1. For example the space-time trajectory of a particle from the past to the future is a causality line. In this perspective the physical principle of causality is the following: two causality lines that have in common two events X and Y must contains these events in the same order, i.e. if event X precedes event Y in one causality line, then event X precedes event Y in all causality lines that contains both events. Of course by event we mean local event such as collision of particles and not a remote consequence of this event (which will be a separate event, created by the flow of photons generated by the first event for example).

As we can see this physical definition of causality does not bring any insight on how to distinguish between cause events and effect events, but at least it states the rules that makes all causal lines consistent. Two consecutive events in a causality line can be separated by a flow of energy or matter, for example the trajectory of a particle. Therefore causality line slopes must satisfy the light speed limit. In other words, the effect events must always stand in the light cone of a cause event.

If we apply the concept of causality lines to particle trajectory, then it turns out that two particles A and B that meet twice, respectively on event X and Y , must experience these events in the same sequence in their respective history. In other words, if X precedes Y in A's history, then X must precedes Y in B's history. This rule directly derived from causality lines property actually excludes the concept of time warp derived via unclassical solution of general relativity. Indeed if particle B after event X travels backward in time through a black hole, or what so ever, and loops back with particle A on event Y before event X there is a causality loop failure.

In the following we denote P(X) the set of events that belongs to the past of X, i.e. the set of events that precede X in any causality line that contains X. By convention the event X itself is excluded from P(X). Indeed P(X) is included in the past light cone of X. But it does not necessarily contain all events in the light cone since some causal lines that intersects the light cone may not contain X, because the particle are refrained interfering (because of an opaque screen for example).

Using this terminology the causality principles becomes X / ∈ P(X); ∀Y ∈ P(X): P(Y ) ⊂ P(X).

INRIA 3 Information causality

Admitting the acception of physical causality, the definition of information causality comes as follow:

The receiver must be on a causal line of the emitter.

Or in other words, to take the classic characters of information theory, Bob must stand on a causal line of Alice. When information transfer are made via energy-matter flows, then the information causality is simply implied by physical causality. But information theory foundations are not based on the concept of physical flows, and only deal with the correlation between the event X (the emission) and the event Y (the reception).

More generally we can generalize to the assertion that if none of events X and Y are not in a causal line of the other (i.e. X / ∈ P(Y ) and Y / ∈ P(X)) then

I(X, Y | P(X) ∩ P(Y )) = 0 . (1)
It means that if we fix the common past history of two events, then the latter become independent because the only events that may make them correlated should be in their common history which is fixed. With this definition we immediately eliminate the pseudo information transfer between the twin traveler salesmen. Indeed their mother is in their common history. Fixing the latter means that X and Y are fixed then no mutual information is exchanged.

In this section we closely investigate the concept of information causality in the framework of modern physics. Quantum physics revolutionized physics during the twenties. Having less famous fathers than relativity it less known by the public, but its consequence are far more astounding. It introduced the concept of incertainty, the concept of of vector state. Its first victim was determinism. Its second victim was information causality.

Quantum non causal information transfers

A source of information is deterministic X when h(X|P(X)) = 0. Conversely a source is non deterministic, or is "purely random", when h(X|P(X)) > 0. Or equivalently h({X} ∪ P(X)) > h(P(X)).

Quantum mechanics enables the existence of non deterministic sources. The result X of the measurement of the spin of a particle is non deterministic. X ∈ {-1, 1} (spin 1 2 ) and can take any value independently of its past history. The key concept of quantum mechanics is that the state of a particle parameter, for example its spin, is given by a complex state vector ψ. The spin can have two pure states |s u for spin value +1 (up), and |s d for spin value -1

(down). ψ = α u |s u + α d |s d
The vector is assumed to be unitary, i.e. |α u | 2 + |α d | 2 = 1 and indicates the probability distribution of the spin measurement outcome X:

P (X = +1) = |α u | 2 and P (X = -1) = |α d | 2 .
A spin is measured via a polarizer and the result X(θ) depends on the angle θ of the polarizer.

The first known of information causality failure, due to quantum physic is a consequence of this simple measurement on entangled particles. Two particles with a common past are entangled: they have a quantum state in common. For example their spin may be exactly inversed. If one measures the spin X(θ) of the first particle on a given angle θ and if another operator measures the spin of the other particle Y (θ) on the same angle then

X(θ) + Y (θ) = 0 (2)
In other words the quantities (X(θ), Y (θ)) are strongly correlated.

Theorem 1. The spin measurement on entangled particles are correlated source of information that breaks the information causality.

Proof If the spins are measured according to different angle θ 1 and θ 2 then we have

P (X(θ 1 ) = -Y (θ 2 )) = cos 2 θ1-θ2 2 P (X(θ 1 ) = Y (θ 2 )) = sin 2 θ1-θ2 2 or E(X(θ 1 )Y (θ 2 )) = -cos(θ 1 -θ 2 ).
The above result does not depend on the relative position of the measures in the space-time. The measures can be done when the particle are very far apart. One measure can be far in the future. it will not change the correlation equation. This is a non local phenomenon. In particular the measure X(θ 1 ) and Y (θ 2 ) can done such that the events cannot be linked by a causal line, for example such that none is in the light cone of the other. Therefore one should have correlated information sources that are not causal. Since the source are not deterministic

I(X(θ 1 ), Y ((θ 2 ) | P(X) ∩ P(Y )) = I(X(θ 1 ), Y (θ 2 )) = 1 + (cos 2 θ1-θ2
2 ) with (x) = -x log 2 x -(1 -x) log 2 (1 -x). We have I(X(θ 1 ), Y (θ 2 )) > 0 as long as θ 1 and θ 2 are not orthogonal. Therefore the entangled particles contradicts the information causality principle.

Remark In fact the proof is more complicated and is due to Bell that succeeded in eliminating so-called hidden variables, i.e. hypothetical variables that were supposed to complete any quatum system to make it determinist.

However this dependence between sources does not allow to transmit any other information than the one created by the source themselves: this cannot be used to move information faster than light. Indeed since E(X(θ 1 )Y (θ 2 ) does not vary whatever which measure occurs the first, the entanglement phenomenon is just a non local correlation between sources of information. However this a very clear blow against information causality.

Space time relaying and Anti-causal information transfers

We have seen that information can actually break causality if we are not careful with the concept of information transfer. Entangled sources leads to information transfers on random bits created by the measurement themselves which is not "useful" information.

In order to get further we need to define what we would like to exactly mean by useful information. But this is a very difficult question. Instead we will use a side concept we call space-time relaying.

INRIA

Definition 1. A space-time relay emitter is an event X that transmits information that can come from any source in the past of X. A space-time relay receiver is an event Y which receives information which can be delivred to any point in its future.

Internet is based on space time: a web page on a server can contain any kind of information obtained from the past and the internet can transfer this information to another machine that can deliver the information to any receiver in its future. Conversely, in the example of the twin salersmen, none of the twin can play the role of the relay emitter of the information contained in his luggage, since in order to the other twin to receive the information the source of information shall exclusively be his mother in the common past of X and Y . Similarly, in the example of entangled pairs, none is relay emitter, since they are the source of information and cannot relay any information coming from their past.

Faster than light information

We will show that faster than light information transfer leads to anticausal information. As a direct application of theorem 2 that will be developped in the next section, anticausal information implies unitarity violation. Therefore it would be impossible to develop a faster than light information system in an unitary model. Lemma 1. Faster than light information makes anticausal information possible.

Proof The special relativity theory states the invariance of light speed with respect to moving coordinate systems thanks to the Lorentz transform for spacetime coordinate systems. When a coordinate system leaves at time t = 0 the origin at a constant speed v (oriented on x axis), then the ccordinate of a point (x, y, z, t) becomes (x , y , z , t ) = (x, y, z, t)

1 1 -v 2 /c 2     1 0 0 -v c 2 0 1 0 0 0 0 1 0 -v 0 0 1    
Consequently if a node moves at light speed c then it also moves at speed c in the new coordinate system: the light speed is invariant. If a node moves at a speed V < c then it will move at a speed still smaller than c in the new coordinate system: the light cones are invariant. The rule of relativistic speed composition makes the mobile trajectoryin space time is oriented with (V -v, 1 -vV c 2 ) in the new coordinate reference, therefore the new speed is V -v 1-vV /c 2 . This is an old and well known property of Lorentz transform: when a mobile moves at a speed V , faster than light, then there exists a coordinate system moving at a speed c 2 V < v < c where the mobile moves backward in time. Therefore faster than light moving physical object should not be allowed. Since 1 -vV c 2 < 0 the mobile moves backward in time. In other words, in hyper-relativistic ping-pong, a ball moving at speed V received on a racket moving at speed v makes the ball back to the past of the sender. Indeed the ball leaves the racket with relative speed RR n°0123456789 (-V + v, 1 -vV c 2 ) which lead to a trajectory back to the sender in the past of the incoming trajectory.

The only thing we need to show is that we can apply this property to superluminal information transfer. We take the assumption that information delivery at speed V > c is possible. To this end we consider a superluminal trajectory as above with point A on the first end point such the vector AB is colinear to speed V . The vector BC is colinear to the speed (-V, 1) in the referential of the racket and C is in the past of point A. Without lost of generality we can assume a small translation of point B in its future, called point B , and a similar translation of C, called C such that B C remains colinear to BC and C is still in the past of A.

At point A we assume a relay emitter, Alice, immobile, in other words her space-time trajectory is oriented with vector (0, 1), and a relay receiver on point B, Bob. Information is transmitted from Alice to Bob. Now assume a relay emitter, Bob Prime moving at speed v on B . Assume that Bob relays its information to Bob prime via a classical channel. Now put a relay receiver, Carol Prime on C also moving at speed v. Since B C is colinear to speed (-V, 1) in the referential moving at speed v, then the same system of information transfer between Alice and Bob, can be applied between Bob Prime and Carol Prime. Therefore the information can be transmitted from Alice to Carol Prime in the Alice's past.

Anti-causal information

We will show that non causal information transfer between a relay emitter and a relay receiver is equivalent into breaking the principle in physics called unitarity.

The quantum unitarity

Unitarity is a property in quantum physics that makes the modulous of a quantum state ψ(t) invariant with time t. We have

ψ(t) = U(t)ψ(0) (3)
where U(t) is a linear unitary operator. By implication the trace of the derived density operator ρ(t) is invariant with time t. Unitarity makes universe time lines to diverge from pure state superposition to state mixture. How strong is the unitarity axiom? Certainly it is weaker than the causality principle. Early in 1976 Hawking [1] was the first to conjecture that black holes evaporation was violating unitary. Although recently Hawking has partially refuted his previous argumentation the question is still open. Wald has noticed [START_REF] Wald | Quantum field theory in Curved Spacetime and Black Hole Thermodynamics[END_REF] that some quantum fields in curved spacetime (as it is the case with general relativity) would necessarily be non unitary. More generally the extension of string theories rise the existence of ghost states for spin 0 and spin 2 fields which could be the first sign of non unitary effects [START_REF] Chiba | Generalized gravity and a ghost[END_REF].

These considerations have a considerable impact on grand unification and the problem is still widely open. We can be sure that there will be many exotic theories before getting the right one. However it must be noted and stressed that if non-unitary physics was a necessary amendment, then its effects would be only noticeable on very curved space-time, in conditions existing only on the edge to a black hole, or approachable in the very dense heart of stars. Of course INRIA the effects would be undistinguishable from unitary physics in conditions that physicists can reproduce in laboratories.

Information causality and unitarity

We show the following theorem. It is not a "standard" theorem since it is related to physical considerations, and the proof is not a standard proof but rather a hint.

Theorem 2. Anti-causal information between a relay emitter and a relay receiver implies unitarity violation Proof: Let consider two spacetime points A (Alice) and B (Bob) such that the vector (B, A) is time like and A in the future of B. We assume that Bob makes a physical measurement on B, for example a spin measurement, whose result is Y . We suppose that the measurement depends on the value of some setting X operated by Alice so that retro-information occurs between A and B. In other words, X and Y are not independent random variables.

Let an observer be on a point Q located in both futures of A and B. We assume a classical channel between B and Q. The channel has output Z and is correlated with Y : Z = Y (for example Z is the spin measurement on a particle that gave the same spin on the same angle on A).

Without loosing generality, we also suppose that Y and X both take binary values, 0 and 1. We denote e i the state corresponding measurement Z = i and P i the Hilbertian projection e i ⊗ e i . Since there is information transfer from A to B and to Q, P (Z = 0 | X = 0) = P (Z = 0 | X = 1). Let ρ j be the density operator of measurement Z when X = j. ρ j = ρ j (0)P 0 + ρ j (1)P 1 . We assume a contrario unitarity, thus Tr(ρ j ) does not depend on j: Tr(ρ 0 ) = Tr(ρ 1 ) = 1.

In order to show non-unitarity we imagine the same experimental system but now with a classical channel established from B to A that does not disturb the measurement on B and Q and such that setting X is the output of the channel. The channel depends on an operator Carol which can activate a switch C in the past of B. As usual Carol is in charge of disrupting the communication between Alice and Bob. Switch C has a binary setting σ. The switch operates to make setting X depending on measurement Y as follow: X = Y + σ modulo 2. For example X is the spin measurement on a particle that gave the same spin and on the same angle on B. When σ = 0, the angle is the same on A when σ = 1 the angle is reversed. Now the result Z depends on setting σ. Let ρ j be the density operator of measurement Z when σ = j. When σ = 0, (Z, X) attains only values (0, 0) and (1, 1) with respective weight given by Hilbertian projection (since we apply linear unitary evolution): ρ 0 = ρ 0 (0)P 0 + ρ 1 (1)P 1 . When σ = 1, only (1, 0) and (0, 1) are attainable: ρ 1 = ρ 1 (0)P 0 + ρ 0 (1)P 1 Since we have Tr(ρ 0 ) = Tr(ρ 1 ), there is an unitarity violation.

Reverse theorem

From now we handle non-unitary systems: we couple a particle in an non unitary environment (e.g. in a non unitary black hole) with a classical system in an unitary environment (e.g. outside the black hole). Depending on the outcome of the classical system we apply a different operator to the particle in the non unitary environment. For example we throw or we do not throw the particle in the black hole. The density operator of the non-unitary system is not unitary. Hartle [START_REF] Hartle | Unitarity and causality in generalized quantum mechanics for non-chronal spacetimes[END_REF] has proven the following lemma.

Lemma 2. Let ρ be the density operator of an non-unitary system. The probability P (φ) of a time line φ is given by

P (φ) = φ ρφ Tr(ρ) (4)
Remark: Notice that Hartle renormalization acts like a non-linear effect and justifies a link with non-linear quantum of Weinberg. Polchinsky [START_REF] Polchinski | Weinberg's nonlinear quantum mechanics and the EPR paradox[END_REF] in his discussion about Weinberg non-linear quantum mechanics, has acknowledged that certain non-linear effects can allow super-luminal transmissions via entanglement, that we have shown is a special case of anti-causal information.

We now turn to specific non-unitarity effects. If non-unitarity effect comes from space curvature as suggested by Wald, then one may expect that the trace of the density operator varies with the space curvature, i.e. with the density of matter. In other words, if an operator changes the density of matter it changes the trace of the density operator of the universe. Equivalently if matter or energy is thrown in a black-hole, then the trace of the density operator takes a value different of that it would have taken without thrown matter. In other words the trace value depends on history (past and future).

In the proof of theorem 2 setting σ affects the trace of the density operator. We will prove that if we have a non-unitary operator U (e.g.U = e iA for a **non-adjunt operator A) then can have retro-information. In fact we should need two operators U out and U in such that U out ψ = U in ψ, but we take U out unitary since we assume that we keep the particle outside on non unitary environmenet (the black hole). Imagine that point A is close to a black-hole about to fade. From point A there are particles or group of particles called probes. Alice has the choice to either throw a probe in the black-hole or to throw it away. Let ρ in be the trace of the density operator of the system probe plus black hole after black hole fading in the state "probe thrown-in". Let ρ out be the trace when the system is in the state "probe thrown-out". Since we assume directed unitarity violation between state "probe thrown-in" and state "probe thrown-out", there is a unitarity violation and ρ in = ρ out .

Assume that a spin measure on a particle decides on the state "thrown-in" and "thrown-out". If spin is 1, then the probe is thrown in, and if the spin is 0, then the probe is thrown out. The trace of the density operator of system made of the spin and the probe is Trρ = 1 2 ρ in + 1 2 ρ out and the probability to have the spin value equal to 1 is This discrepancy in unitary makes that the time lines containing the state "probe thrown-in" have a different weight than the time lines containing the state "probe thrown-out" and distorts the probability of the events attached to these time lines. This distorsion gives rise to retro-information as described below.

Theorem 3. Non-unitary operators can lead to retro-information.

INRIA

Proof: Let imagine, as in proof of theorem 1, that a quantum measurement with binary output occurs on point A. We assume that the density operator without non-unitary distorsion is ρ = 1 2 P 0 + 1 2 P 1 (for example a 1/2 spin measurement).

We imagine that there is a classical noiseless channel (figure 1) between point B and point A. We imagine the following algorithm: when the output measured by Bob on B is 0 then Alice on point A throws a probe inside the black hole, otherwise she throws the probe out. We also assume that the black hole is the only non-unitarity effect on the causality line of the output measurement (or more generally the other non-unitary effects on the causality line occur independently of the actual output measurement). We assume that the history of the system decoheres between state "throw-in" and state "thrown-out" (e.g. the support of the wave functions are non-overlapping).

In this case the density operator of the measurement on B becomes

ρ = ρ in 2 P 0 + ρ out 2 P 1 . (5)
This density operator, even when renormalized by its trace 1 2 ρ in + 1 2 ρ out , is different of ρ. Therefore there is an information transfer from Alice to Bob. This is retro-information since the transmitter is on the causality line of the receiver.

The determination of the channel capacity is a specific problem. If we tune the number of spins to be measured at B, i.e. namely the size of the message received by Bob, with Alice still holding a single probe and without changing the non unitary parameter of the system, then it turns out that the capacity of the channel is at least equal to | log ρ out ρ in | as proven in [START_REF] Jacquet | Capacity of retro-information channels[END_REF].

Conclusion and perspective

In this short paper we have addressed the unusual concept of causality in information. To the author best knowledge this simple question has not been addressed before. Surprisingly the physical causality does not imply information causality. In other words information transfers could travel backward in time without affecting the principle of causality. But this is merely due to some incompleteness in information theory since the information that can be transfered by this mean is not useful. We suggest to partially fill this gap by introducing the concept of space-time relaying. In this case we show that the principle of information causality is equivalent to the principle of unitarity, a weaker axiom in physics.

Assuming that unitarity holds, we prove that informations cannot travel faster than light.

Is unitarity an inalterable principle of physics is still an open question since unified theories such as strings and super-strings seem to have hard nuts to crack in this domain. But of course this far outside the scope of this paper.

More generally the results contained in this paper establish that energy and information don't necessary obey to the same rules, and finally bring an interesting new perspective on the intricate relations between information and space and time.

Figure 1 :

 1 Figure 1: Retro-information from A to B

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