Markus Hanke

There is no “discrepancy”, so the point is moot. Non-sequitur. If you arrive at some kind of “discrepancy”, then that means you did something wrong, plain and simple. Tensor calculus is not a “theory”, it’s a mathematical framework that has been extensively developed, and is fully self-consistent.

This is not what I said - you need to go back and look at what I actually said, and you will also find the maths there. Photons have no rest mass, so according to your expression, the inner product of photon momentum with itself is zero. Since the inner product can vanish only if the two vectors are either perpendicular, or one of the vectors has zero magnitude, that means that according to you the photon has no net momentum. Just repeating the same thing again does not make it any less wrong.

As joigus said, there are no conflicts or discrepancies at all. As you correctly say, the covariant derivative yields a tensor, so it automatically has the correct transformation properties. This is so pretty much by definition, because otherwise it wouldn’t be a covariant derivative at all!

\[x^2\]

This is meaningless. If you are projecting a shorter 4-vector onto a longer one, the result can never exceed the length of the longer vector, that’s just basic geometry. In other words, the longest a projection can ever be is that of a 4-vector onto itself, which, in Minkowski spacetime, is thus -1. Since the inner product is invariant, this is true for all 4-vectors in all frames. Consider a general 4-velocity of the type \[u^{\mu } =( \gamma ,\gamma v_{x} ,\gamma v_{y} ,\gamma v_{z})\] The inner product with itself is \[u^{\mu } u_{\mu } =-\gamma ^{2}\left( 1-v^{2}\right) =-\gamma ^{2} /\gamma ^{2} =-1\] as expected. So your claim is wrong. If this were true, the momentum of a photon would be zero. This is evidently false, as we know already from experiment and observation. Mathematically, you can show this in a similar manner as above. So again, you are wrong. I’ve already shown above that the inner product of a 4-velocity with itself is -1, so the magnitude of a 4-velocity in spacetime is always exactly c. Since the inner product is invariant, this is true in all frames, so it can’t be a function of the gamma factor. Also, if you look at this expression, you should notice immediately that the resultant magnitude of v does not correspond to the gamma factor you are inputting, so the expression is meaningless. You are wrong on this one, too. Yes, because all three points you have presented contradict both basic maths, as well as observation in the real world. It’s simply wrong.

Peer review is not meant to be “fair” (what does that even mean?) - on the contrary, it is designed to be as critical as possible, so as to really put the ideas within the publication to a rigorous test. It is the most effective way to tease out any problems; remember, you want to end up with something that actually works, in the sense of the scientific method. You are missing the salient point. Science has nothing at all to say as to the existence or supposed characteristics of anything that isn’t part of nature, including any and all notions of deities. This is quite simply outside the domain of applicability of science, because the very notion of “God” is not amenable to the scientific method. So science neither rejects nor endorses the Christian faith, because it deals with a different domain of enquiry. However - and this is the important point - if someone proclaims an element of their faith as being objective truth, then this claim will of course be challenged by science. Some such claims may turn out to be compatible with scientific evidence, so they are fine; others may not be, and those will be rejected. To give a simple example - if someone claims, based on certain readings of the Bible, that the Earth is ~6000 years old, then science will certainly reject this, because that claim is evidently false based on all available scientific data. So the issue isn’t faith and belief - the issue is only when people try to misrepresent their beliefs as objective, scientific facts. That’s what’s called a category mistake, and it will always be challenged.

No, a flat manifold without boundary is simply one of the topologies that naturally arise from the mathematics of the Lambda-CDM model, when certain observational parameters take on specific values. It’s just one among several possible options. It can be closed on itself - so there can be a largest possible separation between two suitably chosen points, without there being any kind of boundary. Much like (to pick a lower-dimensional analogy) a spherical surface. A manifold being finite in extent does not imply the presence of a boundary.

The mechanism is one of spontaneous symmetry breaking, so it would depend on whatever parameters appear in the Lagrangian. In this specific case it would be the speed of light, Planck’s constant, as well as the coupling constants between the various fields. The Higgs mechanism has no effect on the value of fundamental constants (other than ones related to the masses of particles of cause, which aren’t really ‘fundamental’). It only gives rise to some new coupling constants within the Lagrangian, since after the event you end up with more fields than you started off with.

This is evidently not true, since the very mechanism that creates the property of mass (the Higgs mechanism and spontaneous symmetry breaking) already presupposes the existence of at least a Minkowski background spacetime prior to said process; without this, there would be no universe as we know it today.

We are not really in a position to give any kind of medical advice or diagnosis here, especially not based on very non-specific symptoms such as the ones you describe; if you are concerned about your friend, you need to urge them to go and see a medical professional.

The appearance of a singularity in a model of physics generally means that the model has broken down because it has been extend beyond its domain of applicability. It does not mean that the model actually predicts a physical singularity to occur. In that sense, singularities - whether gravitational or at the BB - (almost) certainly are not actual, physical objects; they are more like flags saying “we don’t know yet what happens here”. Mass as a property of elementary particles only appeared at and after electroweak symmetry breaking (~10^-35s) when the Higgs mechanism kicks in; prior to that, all particles would have been massless. So yes, the very early universe contained only various forms of energy - which, however, still has a gravitational effect of course.

This seems like an awfully complicated way to do this. Why not just use Helmholtz’s Theorem? We know that the curl of the potential field gives the magnetic field (by definition!), so this is already fixed. The potential field is also invariant under certain gauge transformations (I think it’s the addition of a scalar field gradient, but I’d have to check that), hence we will always be free to make the divergence vanish, simply be choosing a suitable gauge, without affecting the curl. So in essence, under Helmholtz’s Theorem, the divergence has no physical relevance at all in this.

! Moderator Note Moved to Speculations.

I would just like to add a remark here, perhaps some readers may find it helpful. I am a regular and committed meditator - I practice several hours of formal meditation every day, and have done so for some years. Many of the perceptions described here are common and well known phenomena that naturally arise when the mind settles and becomes concentrated; in the Pāli language they are called nimittā. This can be anything from a slight tickling sensation somewhere, to pins and needles, to a sensation of something moving as a current through the body, to various pains, to full blown auditory and/or visual hallucinations, among other things. A sensation of electrical currents in parts of the body is especially common, from what I have seen. A had a period a few years back when I used to get this regularly, and the sensation of electricity sometimes got strong enough to cause me considerable discomfort, and gave me twitches and involuntary muscle spams during meditation sits. I have heard of people for whom this becomes so strong that they suffer intense pain, muscle cramps, and involuntary movements - they literally “jump” on their meditation cushions. Some people need to temporarily stop sitting because of this. As described here, with a little practice it is easy to induce these sensation at will, and control them to some extent - one can move them around the body, make them stronger or weaker, change their qualities etc etc. I cannot speculate what the underlying mechanisms are, as the human body is not my area of scientific expertise. What is clear though is that body and mind are not separate things, they are intimately connected, so it isn’t surprising that such things may occur. These phenomena are quite natural, and very common among meditators; there are specific ways and methods to address these things, in the context of an ongoing meditation practice. The general advice is to not pay too much attention to them, since directing the focus of attention towards these phenomena will strengthen them and make them occur over and over again. In many specific practice frameworks the occurrence of such phenomena is in fact taken as a sign of progress, since they naturally develop when concentration and single-pointedness become stronger. They can also become a hindrance though, because they can distract from practicing the main technique, and some people become infatuated with these sensations, as they also can feel very pleasant at times. So most of what has been described here is natural and quite well known, and not a cause for concern. This, however, is not: As someone with experience as a volunteer in the emergency services, this would have me concerned; anisocoria isn’t normal (unless you were born with it, which does happen), so I would strongly advise a precautionary trip to your doctor, to rule out other underlying issues.

There are no guarantees here. The best we can do is make the assumption that whatever finds the message has a roughly similar sensory apparatus as we do, and that their mental processes are roughly similar to our own; we can then attempt to construct a pictorial or auditory message in the most general and (to us) universal of forms, and hope for the best. Over and above that, all bets are off. The thing is that all languages are social constructs - words, sounds and pictograms mean to us what we take them to mean because everyone within our social context agrees that they do mean that, and we have been taught those particular conventions in early childhood. Even amongst us humans it can sometimes be very difficult to communicate certain ideas and concepts outside of a given social context, and our attempts at communication with other species in the animal kingdom have met with at best limited success. Communicating to an alien species that may share few or even none of our cultural and social conventions could be exponentially harder still - and potentially disastrous, should we get it wrong. In the worst case, the alien race may be sufficiently different in terms of sensory apparatus and mental processes that there isn’t even a common channel for communication, never even mind a common language. I don’t know how such an encounter would pan out.

Presumably an omnipotent being would have no need to observe the quantum system, he could have knowledge of its entire history without having to collapse it first. Since that knowledge is not accessible to us, this case would be indistinguishable from God not existing.

I do not really wish to get involved in this discussion, as I believe that understanding the human condition should not become a partisan issue. But I do wish to offer two observations: 1. It seems that almost everyone here equates religion with theism, or (even more narrowly) with Christianity. This is misguided - all theistic world views are to some degree religious, but not all religions are theistic, or even supernatural. There are religious systems that are expressly empirical, right here and now in this lifetime. I think it is important to clarify what you all actually mean by 'religion', in the context of this debate. 2. For those of you who know me from here and other forums, you will probably agree that I am all about science - it's a huge part of my life, and I spend a lot of time researching and teaching myself physics, and that's not likely to ever change. Nonetheless, there is also a religious dimension to me - in fact, I live full-time in a monastery, and have plans to ordain as a monk in a contemplative order next year. This dimension is equally as important to me as is science. For me personally, there has never been a conflict between the scientific and the religious/spiritual sides of me. I understand them as complementary domains of enquiry, that ask different questions about the same human condition. My scientific enquiries have helped me gain insights on my spiritual path, and the spiritual practice has helped me gain new angles on scientific issues. So, for both the religionists who reject science, and the scientists who reject anything religious, you need to ask yourselves the question - why does this need to become/continue to be a partisan issue? The "us vs you" mentality isn't helpful, and can - if taken to the extreme - frequently be dangerous. But when approached with wisdom, the two sides have the potential to coexist harmoniously, and inform each other constructively. Just my humble opinion and experience

Are all affluent people honest?

I think everyone is always responsible for their actions. Whether or not they should be answerable for them is another matter - it essentially boils down to the question of how much choice someone actually had in a given situation. Someone’s social environment, upbringing, mental disposition etc may place strong constraints on their behavioural patterns, so they may not have been as free to choose their actions as we’d think. But then again, this is very difficult to measure objectively, because on the flip side you have plenty of people from extremely difficult backgrounds who are not prone to criminal behaviour at all. So I don’t know what the answer is, but it can’t be a simple one.

I did not make any reference to Newtonian gravity or any particular form of potential, I am only using the fact that the energy-momentum tensor has to be locally conserved. The relation I gave follows from Noether’s theorem, and not any particular theory of physics. The point was simply that, if you allow c to vary, this conservation law no longer holds, because the underlying symmetry that gives rise to the conserved quantity is no longer there. If c is not constant, energy-momentum cannot be conserved, irrespective of what else you attempt to change.

Again, gravitational potential - if it can be meaningfully defined at all - is a gauge field with a gauge freedom to choose a zero point, whereas Planck’s constant obviously isn’t. It is not physically meaningful to relate the two in this manner.

Yes it will be. If you look at the above equation, if c is variable, the covariant derivative will contain extra terms including derivatives of c. These terms don’t cancel out, so there is no way to not violate the relation.

So does the idea that c is a variable. Consider the local conservation of the energy-momentum tensor in the presence of gravity: \[T{^{\mu}}{_{\nu ||\mu}}=0\] Since the covariant derivative depends on the metric, which explicitly contains c, and because in your idea c varies in a way that is not covariant, the above relationship ends up being no longer valid. This whole idea puts you in a situation where there is no longer any conservation of energy-momentum, not even locally. This is clearly in direct contradiction to experiment and observation.

Just to add to what has already been said by other contributors here: 1. First and foremost, the notion of "gravitational potential" can only be defined in spacetimes that are stationary (more precisely: those which admit a time-like Killing vector field) and asymptotically flat. It cannot be generalised to more general spacetimes, which makes it useless so far as a general model for gravity is concerned 2. Gravitational potential itself is not an observable, only differences in potential can be observed and measured. This is because the potential has a gauge freedom, in that one can freely choose where the zero point is, without affecting the physics. The same is not true for the speed of light, hence the relation above is trivially and obviously wrong, since it equates two quantities that cannot physically and numerically be equal, on fundamental grounds. 3. A varying speed of light would constitute a violation of Lorentz invariance. This symmetry has been experimentally and extensively tested with modern equipment to extremely high precision, both here on Earth and in the vacuum of space - needless to say, no such violations have ever been found. Given the degree of precision of these tests, any variability in the speed of light can effectively be ruled out far beyond the usual 5 sigma threshold. 4. A variable speed of light would also break CPT symmetry, which underlies the Standard Model of Particle Physics. Since we continue to successfully use and test this model in particle accelerators on pretty much a daily basis, any variability in c can also effectively be ruled out on that ground. 5. Neither classical Maxwellian electrodynamics nor quantum electrodynamics allow for varying values of permittivity and permeability (in the same medium of course). Hence the notion of a varying speed of light is actually in direct contradiction to what we know about electrodynamics. 6. As has been pointed out on another recent thread, a scalar field theory such as this one is fundamentally incapable of capturing all required degrees of freedom of gravity; there is more to gravity than just time dilation! I could probably go on, but these are the points that immediately come to mind without thinking about the issue too much. I'll leave it at this.

No, not including Russian.