The Schwarzschild solution (Schwarzschild, 1915/16) to Einstein’s General Theory of Relativity (GTR) is accepted in theoretical physics as the unique solution to GTR for a central-mass system. In this paper I propose an alternative solution to GTR, and argue it is both logically consistent and empirically realistic as a theory of gravity. This solution is here called K-gravity. The introduction explains the basic concept. The central sections go through the technical detail, defining the basic solution for the geometric tensor, the (...) Christoffel symbols, Ricci tensor, Ricci scalar, Einstein tensor, stress-energy tensor and density-pressure for the system. The density is integrated, and some consistency properties are demonstrated. A notable feature is the disappearance of the event horizon singularity, i.e. there are no black holes. So far this is for a single central mass. A generalization of the solution for multiple masses is then proposed. This is required to support K-gravity as a viable general interpretation of gravity. Then the question of empirical tests is discussed. It is argued that current observational data is almost but not quite sufficient to verify or falsify K-gravity. The Pioneer spacecraft trajectory data is of particular interest, as this is capable of providing a test; but the data (which originally showed anomalies that match K-gravity) is now uncertain. A new and very practical experiment is proposed to settle the matter. This would provide a novel test of GTR, and a novel test of the cause of the Pioneer anomalies. In conclusion, K-gravity has extensive ramifications for gravitational physics and for the philosophy of GTR and space-time. (shrink)

This study analyses the predictions of the General Theory of Relativity (GTR) against a slightly modified version of the standard central mass solution (Schwarzschild solution). It is applied to central gravity in the solar system, the Pioneer spacecraft anomalies (which GTR fails to predict correctly), and planetary orbit distances and times, etc (where GTR is thought consistent.) -/- The modified gravity equation was motivated by a theory originally called ‘TFP’ (Time Flow Physics, 2004). This is now replaced by the ‘Geometric (...) Model’, 2014 [20], which retains the same theory of gravity. This analysis is offered partially as supporting detail for the claim in [20] that the theory is realistic in the solar system and explains the Pioneer anomalies. The overall conclusion is that the model can claim to explain the Pioneer anomalies, contingent on the analysis being independently verified and duplicated of course. -/- However the interest lies beyond testing this theory. To start with, it gives us a realistic scale on which gravity might vary from the accepted theory, remain consistent with most solar-scale astronomical observations. It is found here that the modified gravity equation would appear consistent with GTR for most phenomena, but it would retard the Pioneer spacecraft by about the observed amount (15 seconds or so at time). Hence it is a possible explanation of this anomaly, which as far as I know remains unexplained now for 20 years. -/- It also shows what many philosophers of science have emphasized: the pivotal role of counterfactual reasoning. By putting forward an exact alternative solution, and working through the full explanation, we discover a surprising ‘counterfactual paradox’: the modified theory slightly weakens GTR gravity – and yet the effect is to slow down the Pioneer trajectory, making it appear as if gravity is stronger than GTR. The inference that “there must be some tiny extra force…” (Musser, 1998 [1]) is wrong: there is a second option: “…or there may be a slightly weaker form of gravity than GTR.” . (shrink)

In our initial paper discussing plausible steps toward workable warp drive machines. The following article express our view on this debate. While there are still objections toward existing warp drive proposals, such as by G. Landis, Harold White etc., because they are all based on GTR, nonetheless we think it is possible by starting to see if it is possible to deviate from Newton's third law. And we discuss possible a propulsion method based on negative masses, and discuss how optical (...) diameter drive can be first step for realistic lab-scale version of negative mass propulsion. (shrink)

I argue that the best interpretation of the general theory of relativity has need of a causal entity, and causal structure that is not reducible to light cone structure. I suggest that this causal interpretation of GTR helps defeat a key premise in one of the most popular arguments for causal reductionism, viz., the argument from physics.

The indirect argument (IA) for incompatibilism is based on the principle that an action to which there is no alternative is unfree, which we shall call ‘PA’. According to PA, to freely perform an action A, it must not be the case that one has ‘no choice’ but to perform A. The libertarian and hard determinist advocates of PA must deny that free will would exist in a deterministic world, since no agent in such a world would perform an action (...) to which there were alternatives: an action there being the necessary consequence of preceding events and the laws of nature, it would not be possible for a person to perform actions besides those he actually performs. Determinism is seen here as “indirectly” ruling out free will by making the satisfaction of a necessary condition of free agency impossible, the former requiring, according to the leading proponent of libertarianism, Robert Kane, the performance of free actions. To have a free will, on his view, is to have committed “self-forming” actions, that is, to have done things to which there were alternatives the doing of which led to the development of the desires, preferences, and beliefs that make up one’s character. -/- The range of phenomena obeying probabilistic laws has yet to be ascertained. Under certain assumptions, both STR and GTR entail an indeterministic mechanics. But, contrary what is often claimed, quanta do not behave indeterministicly: the wave function/probabilistic laws being necessary only insofar as we wish to macroscopicly describe their behavior. It is far less clear, however, that the macro-events involved in human decision making and behavior, such as the releasing of neurotransmitters and the contracting of muscles, occur indeterministically. The ontological status of these events-whether or not they are the necessary effects of prior occurrences-is, of course, what matters in the free will debate. For present purposes, however, this question will be put aside. Instead, I will concentrate on buttressing the existing case against PA, aiming to show that even if deterministic laws hold at the level of macro-phenomena, free will remains a possibility. That is to say, I shall defend the thesis that so-called “Frankfurt cases” demonstrate that alternatives are not required to perform an action that is free in the sense of being something for which its agent is responsible. -/- My defense will be carried out in three stages. First, I must respond to those who maintain that a Frankfurt case is not a counterexample to PA because it is not an example of someone acting without alternatives. Here, I confront the question of how “robust” an alternative must bein order to provide an agent with a way of avoiding praise or blame for the action that she actually commits. Secondly, I must show that an agent may be praiseworthy or blameworthy despite lacking alternatives at the time at which she acts, i.e., an appropriate object of one of a Strawsonian “reactive attitude” sans what I shall call “local” alternatives. At this point, I must attend to David Widerker’s recent critique of the use of Frankfurt cases as counterexamples to PA. Finally, I set for myself what I take to be the most difficult task of a compatibilist: demonstrating that not even an “historical” alternative-the possibility of having chosen a different path in life than the one that one has actually taken-is needed to have a free will. In this connection, it will be incumbent upon me to explain why it would be fair to hold someone accountable for behavior issuing from a self she did not create, dispositions originating from natural conditions she did not establish. That is to say, in denying that a free will entails the ability to transcend oneself, I shall be faced with what Kane calls the “ultimacy” problem: how to explain away the incompatibilist’s intuition that it is senseless to adopt a reactive attitude towards someone incapable of self-transcendence, even if such a reaction is itself unavoidable. By showing that the desire for self-transcendence is itself irrational, I intend to solve this problem. I will, thus, be left defending a version of compatibilism according to which a free will is to be understood as a healthy faculty-the will-being exercised in an environment conducive to self-realization, which is its purpose. (shrink)

In this paper I argue that to understand minded agency – the capacity we typically find instantiated in instances of human behaviour that could sensibly be questioned by asking “What did you do?” – one needs to understand childhood, i.e. the trajectory of learning to act. I discuss two different types of trajectory, both of which seem to take place during childhood and both of which might be considered crucial to learning to act: a growth of bodily control (GBC) and (...) a growth in taking responsibility (GTR). The discussion of GTR takes up about half of the entire paper. In the final two sections I argue that GTR is the most promising trajectory in terms of which to understand a child’s process of learning to act. (shrink)

In his [1937, 1938], Paul Dirac proposed his “Large Number Hypothesis” (LNH), as a speculative law, based upon what we will call the “Large Number Coincidences” (LNC’s), which are essentially “coincidences” in the ratios of about six large dimensionless numbers in physics. Dirac’s LNH postulates that these numerical coincidences reflect a deeper set of law-like relations, pointing to a revolutionary theory of cosmology. This led to substantial work, including the development of Dirac’s later [1969/74] cosmology, and other alternative cosmologies, such (...) as the Brans-Dicke modification of GTR, and to extensive empirical tests. We may refer to the generic hypothesis of “Large Number Relations” (LNR’s), as the proposal that there are lawlike relations of some kind between the dimensionless numbers, not necessarily those proposed in Dirac’s early LNH. Such relations would have a profound effect on our concepts of physics, but they remain shrouded in mystery. Although Dirac’s specific proposals for LNR theories have been largely rejected, the subject retains interest, especially among cosmologists seeking to test possible variations in fundamental constants, and to explain dark energy or the cosmological constant. In the first two sections here we briefly summarize the basic concepts of LNR’s. We then introduce an alternative LNR theory, using a systematic formalism to express variable transformations between conventional measurement variables and the true variables of the theory. We demonstrate some consistency results and review the evidence for changes in the gravitational constant G. The theory adopted in the strongest tests of Ġ/G, by the Lunar Laser Ranging (LLR) experiments, assumes: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m, as a fundamental relationship. Experimental measurements show the RHS to be close to zero, so it is inferred that significant changes in G are ruled out. However when the relation is derived in our alternative theory it gives: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m – (dR/dt)/R. The extra final term (which is the Hubble constant) is not taken into account in conventional derivations. This means the LLR experiments are consistent with our LNR theory (and others), and they do not really test for a changing value of G at all. This failure to transform predictions of LNR theories correctly is a serious conceptual flaw in current experiment and theory. (shrink)