Markus Hanke

The question is meaningless, because spacetime is not embedded into any higher dimensional manifold, so there simply is no “beyond”. Asking what is beyond is like asking what is north of the North Pole - it does not make any physical or mathematical sense. The existence of a boundary can also be ruled out via other, somewhat more technical arguments. First of all, it is not consistent with the laws of gravity - the Einstein equations have solutions that describe point singularities and ring singularities, but not sheet singularities, being singularities that are spread out like a 2D surface. Your hypothetical boundary would need to be of this kind, since it is by definition a region of geodesic incompleteness. The other main argument here is that, if there is a boundary in all spatial directions, we would essentially have to exist within the interior cavity of an energy-momentum shell of some kind (whether that is massive or not is irrelevant). Now, I do not have a solution to the Einstein equations to hand that describes a dust-filled cavity, but just by briefly thinking about it, and bearing in mind that spacetime in a vacuum cavity is everywhere Minkowski, I can pretty much guarantee that such a spacetime would be very different from the FLRW spacetime which we actually observe around us. In fact, given that ordinary matter density is actually very small over vast distances, I think such a spacetime could reasonably well be modelled by a linearly perturbed Minkowski metric - which is not what we observe. In other words, the FLRW metric that is the best fit for all the experimental data is simply incompatible with the notion of any kind of boundary. And these are only two arguments that immediately come to mind, I could probably come up with many more if I thought about this hard enough.

Spacetime is not the same as ether; it is not a medium with mechanical properties. Of course not, because this falls outside the domain of a classical theory such as General Relativity. You need quantum field theory - specifically, quantum electrodynamics - for a full understanding of this, but that was not developed until well after Einstein’s theory of relativity.

It’s more than just that. Gravity is defined as being geodesic deviation, i.e. a geometric property of spacetime. There is no meaningful distinction between the two. Gravity and electromagnetism are completely different - both in terms of their dynamics, and in terms of their underlying mechanism. There are links between the two, but they are nonetheless distinct phenomena.

Ok, the old German text is “Die neuen Inseln / so hinder Hispanien gegen Orient bey dem Land Indie ligen” I am actually unsure just what it is that they are trying to say here (German is my mother tongue, so I should know lol). I’d translate it something like “The new islands, which lie beyond Spain, in the region of the Orient towards India”. But it’s genuinely not easy to understand, not even for a native speaker.

It’s a very old form of German, written in a cursive script used at that time. The first three words mean “The new islands”, but I have difficulty deciphering the rest - is there no higher resolution image available anywhere?

The gravitational field is spacetime.

Any genuine physicist would be excited to discover evidence of new physics - that myths of “desperately trying to maintain the status quo” that is often bandied about does not make any sense at all. So yes, there are no such forces, nor will there ever be. There is only a healthy scepticism of extraordinary claims, which is how it should be.

Strictly speaking I think one might be able to make that argument. But then the same could be said for any QG model, since technologically speaking we are very far away from being able to experimentally test such models, so even a fully worked out and understood QG model is likely to remain speculation for some time to come. But it should be pointed out that not all speculations are created equal - some are speculative extensions or generalisations of already established models, while others are not rooted in established physics at all.

Indeed - that’s pretty much the point I am trying to make. Yes, I do not deny the importance of physical reasoning. What I am attempting to say is that this will be very difficult in the case of QG, because there is no direct observational data available (just yet), and we also do not know what such a model is even supposed to look like, so physical reasoning is hard. In the case of M-Theory the situation is worse still, because we don’t even have a complete formalism yet, let alone a physical interpretation of it.

There is much tit-for-tat going on with regards to this. Here’s another paper that makes the exact opposite claim, i.e. that observations of this event actually rule out a large number of GR alternatives, including TeVeS: https://arxiv.org/abs/1710.06168 ArXiv is in fact pretty much awash with papers on both sides of the divide. It is difficult for an amateur such as myself to really arrive at a conclusion, but I tend forwards GR as the model that best fits all our data about how gravity behaves. It is also the simplest possible model, and can be constructed more or less from first principles. TeVeS for example would require an extra vector field, two extra scalar fields, and an arbitrary function; that seems very ad-hoc to me, and does not easily relate back to any of our other physics models.

While I understand what you are saying, in terms of logic it is not a valid argument. Just because we do not yet know the full picture of what went on at the time of the Big Bang (but we know some parts of it), does not imply that there must be an outside agent acting on it. For example, in the old days people would get cholera, and put it down to an act of God punishing them for their sins, because they did not know any better. Nowadays of course we know that they got cholera because the water they drank was contaminated. Note though that this does not allow any truth statements either way - the Big Bang (or any other part of science) does not imply a personal God exists, but neither can it definitively rule out that notion. So there is still room for a concept of God, if you so choose. Essentially it always comes down to a personal choice of how you wish to understand the world you live in.

I would disagree with this. Science is an epistemological endeavour, not an ontological one - it is a system to organise knowledge. As such, I would argue that it seeks only to accumulate knowledge about our existence, not an understand of it. This might seem like nitpicking, but it’s actually very important. Especially on science forums such as this one, I very often see people who seem to think that physics (e.g.) is there to seek fundamental truths of the universe - as such, viewpoints can become deeply entrenched, because they are mistaken for absolute truths or falsehoods. But it’s not like that. What we do in physics is make models of the universe, or aspects of it - it’s more like drawing a map of the territory. But such a map is true only insofar as it is a faithful representation of the territory; one can examine how well the map represents the territory, and what limitations the map has. Strictly speaking, saying a map is “true” or “false” does not make much sense, rather, it is a question of the degree of accuracy. For example, Newton is a less accurate representation of gravity than Einsteinian, but it is meaningless to say that either one is true or false.

The former means that the divergence of the gradient of your function vanishes everywhere, so there are no sources or sinks of any gradient (not field) flow. In physical terms, this means that, if you consider a small region centered around some point, the average value of your function in that region must be equal to the value of your function at that point. If the relationship holds everywhere, then you are dealing with a harmonic function, which is physically often a wave field of some sort. Your latter example is a particular form of the Cauchy-Schwarz inequality - it physically means that the inner product of f and g can never be larger than either of these taken in isolation. So in other words, a projection is never larger than either of the vectors/states/functions that are involved in the projection. Both of the above are just common sense, and really quite simple - but you are absolutely right, actually extracting this information from the formalism is a non-trivial task. And that was precisely my point - we can have models of QG that give us a more or less straightforward mathematical statement, and yet we may be unable to physically interpret it. For example, without the entire theory of differential equations, you could not easily extract any physics out of Laplace’s equation, because you would have no way of solving them.

The problem is akin to having a mathematical formalism, but not being able to extract specific predictions from it, because the mathematical tools are missing to work with that formalism. For example, you can know the Einstein field equations, but if you haven’t got a clue how to go about solving them, then you can’t extract any of the physics. So it’s a matter of developing mathematical tools as you go along, and that takes time - which is why String theory appears to have stagnated of late. Actually there is continuous progress, but it’s mostly very technical stuff, and the progress is slow. This issue partly persists even with well-studied models. For example, a complete classification of all possible solutions of the Einstein equations is (to the best of my limited knowledge) still an outstanding problem. Another example is QCD (the strong force) - the field equations are so complex that no closed analytical treatment is possible; we largely rely on numerical simulations as well as simplified approximations. I don’t think there is an alternative to maths when it comes to QG. Of course, it all starts with ideas and approaches, but then these need to be fleshed out with a proper formalism, or else no one will ever know what these models actually say, in physical terms.

There is a substantial number of what I would consider promising approaches, though it is not yet obvious whether a fully self-consistent model of QG is among them - there is always a chance that there isn’t. The trouble is that we have not got the mathematical abilities to fully work out and understand many of these candidate theories, so it is difficult to evaluate their actual value to us. What’s more, we don’t even know what a fully consistent model of QG should look like, and what features it would have. At present the best candidate models would remain Loop Quantum Gravity, Non-Commutative Geometry, Causal Sets, Causal Dynamical Triangulations, Asymptotically Safe Gravity, and M-Theory. This is not a complete list though. M-Theory actually goes a step beyond QG, in that it is a candidate for a “theory of everything” that could model not just gravity, but the entire particle zoo through a unification of all fundamental interactions. There is a candidate theory of QG called Group Field Theory. I can’t really comment on it though, since I am largely unfamiliar with this particular model, except in the broadest of terms. Yes, because before you can even begin to worry about gravity on small scales, you need to first understand the other fundamental interactions, which are orders of magnitude stronger. Doing this leads to quantum field theory, which is the unification of quantum mechanics and special relativity.

Good point...but then, you wouldn’t be looking directly at the mirror either, you’d be looking through an eye piece, which presumably is an arrangement of lenses. Or not? I never owned one of these things.

You are right that under most normal circumstances, gravity plays no role on very small scales, because the other fundamental forces (weak, strong, and electromagnetism) are very much stronger on those scales by many, many orders of magnitude. However, there are situations when gravity becomes substantial enough that it can no longer be ignored, not even on small scales - for example in the region behind event horizons of black holes, or at the very earliest moments after the Big Bang. So in order to understand those scenarios, we need to find ways to bring together gravity and quantum physics, which is not at all a trivial task (for mostly technical reasons). This is currently an area of intensive and very active research, and has been for some time.

I presume it would be more beautiful (it needs an astronaut who has been to space to authoritatively answer this) - but if you are looking at the mirror through a telescope, then you are also going through a lense.

Sure it is possible. Whether it is practical is another question, though. Depending on how high you are planning to go, you’d need a fairly sizeable mirror, and/or a good sized telescope, in order to get a clear image. There is also the issue of the mirror moving around with the winds, so it would be hard to really see anything much. What is the purpose of this? Why not just use a remote camera that transmits back in real time? Has this anything to do with “flat earth”?

Yes, the tendency to expand is already intrinsic in the FLRW solution to the Einstein equations. This is simply a natural consequence of laws of gravity. You would need to introduce a counter-mechanism to stop this from happening, such as an appropriate chosen cosmological constant. It is not completely unfeasible - you can construct a “steady state” type of model by balancing out the observed average energy density of universe with an appropriately chosen cosmological constant. The trouble with this (apart from it not being what we actually observe) is that it is an extremely unstable configuration, like balancing a mountain on a needle - the cosmological constant would have to have an extraordinarily precise value, and even the slightest perturbation of that numerical value would destroy the balance. There is no known physical mechanism that could guarantee the stability of such a configuration, not even in principle; on the other hand, there are plenty of physical mechanisms that would introduce fluctuations in the value of that constant over time and space. So all considered, the “steady state” concept is not very physically feasible.

As already explained in considerable detail - there is no proper acceleration. So you are not asked to buy into anything more than the validity of the law of gravity.

Indeed - some of the roads are shocking here. I know this better than most, because I’ve been a full-time van-lifer for a while, so these roads are my home. A healthy dose of respect is needed. Thank you Oftentimes, explaining things to others is the best way to deepen your own understanding of it. The challenging bit is always to figure out whether the other party is actually receptive, or whether you are talking to a wall.

...until you meet you meet a 10t cement truck head-on at the other side of the crest. All of a sudden acceleration becomes very real again Lol, I like this

It doesn’t need to “make sense” (a purely subjective perception!), it just needs to fulfil the requirements of a scientific model. Which the laws of gravity demonstrably do very well. The situation is the exact same as when you jump off a board into a swimming pool - a stationary bystander can measure your motion from afar, and will argue that you undergo acceleration, based on what he measures (9.81m/s2). But if you yourself carry an accelerometer with you as you jump off, you will find that it reads exactly zero at all times during your free fall. This is not just some theoretical speculation, but something you can actually try out yourself. In fact, I would encourage you to go ahead and do this experiment, if you are really in doubt over the differences between coordinate and proper measurements. Just make sure your accelerometer is waterproof Alternatively, you can just recognise that this funny feeling you get in your tummy while you are in free fall is just precisely this - the absence of any acceleration (i.e. force) acting on you. And yet you fall under the influence of gravity.

It’s useful so long as you bear in mind the difference between “analogy” and “model” - they have different aims and goals.