Markus Hanke

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.

No - but it’s a reasonably good analogy to demonstrate the basic principle. Where the analogy fails though is that metric expansion has nothing to do with any “stretching”. That’s why it’s just an analogy.

Because there is a difference between what we visually observe from a distance, and what actually happens locally where the galaxy is. The first is called coordinate acceleration, the latter is called proper acceleration. The difference between these is crucial. To see why, turn things on their head - from the perspective of a very far away galaxy, our own galaxy where Earth is located is moving away at a very high and accelerating rate. Yet if you stand up right now and look at an accelerometer, you won’t actually detect any massive acceleration acting on you (hence on the Earth, and our galaxy). There is coordinate acceleration (what you measure from a distance), but no proper acceleration (what an accelerometer physically measures). The same is true for forces of course.

I think it is important that you actually read the replies you get on here, because otherwise you will just keep going in circles. As already explained, there is no force acting on the galaxies. There are no forces involved in any of this at all. Gravity is not a force - it’s a geometric property of spacetime. If you drop an accelerometer, it will read exactly zero at all times (you can try that out yourself at home), so as per F=ma, with a=0, there is no force. Yet it will still fall under the influence of gravity, and according to its rules. Also, the weak/strong/EM interactions are not forces in the Newtonian sense either - they are interacting quantum fields. There are no mechanical forces involved anywhere in this. I think your basic problem is that you assume the universe and everything that is in it to be Newtonian (essentially the kind of physics you learn in high school) - but in reality it isn’t. Newtonian mechanics is just a highly simplified approximation that applies only under very limited circumstances. Even on comparatively small scales such as the solar system, Newtonian physics already fails miserably. Cosmology then is very far outside its domain of applicability. Trying to ask about what forces act on galaxies etc is hence largely meaningless, because the very concepts are essentially meaningless in the context of cosmology. There are other things at play here. All of this can very easily be understood in the framework of spacetime geometry - but if you do not acknowledge that as a valid concept (your own prerogative, of course), then there will be little point in this discussion.

This does not make any sense, I’m afraid.

Again, you need to remember that space is not any kind of mechanical medium, and that there is no motion involved, in the sense that no forces act on anything. If you were to attach an accelerometer to any of these galaxies, it would read exactly zero at all times, so there is no acceleration and hence no forces that act on anything. All that happens is that the distance between galaxies increases, because space there expands - so there is relative/apparent motion due to the increase in distances, but no local motion that involves forces or the transfer of energy. It’s purely a geometric phenomenon.

I don’t understand this question; can you explain a bit more? No, gravity is distinct from the weak, strong and EM interactions. They are not the same thing, and function in very different ways. Again, I am unsure what you mean by this. Space is not a separate entity in and of itself, and hence it does not “interact” with anything. It’s best understood as a background, a “stage” of you so will. I think a good way to look at space(time) is as a collection of events, and the relationships between these events are the geometry of spacetime. On very small scales, as on atomic and subatomic levels, gravity plays almost no role at all under normal circumstances, since its coupling strength is very much weaker than any of the other interactions by many, many orders of magnitude. There are, however, scenarios where gravity becomes so strong that it cannot be neglected even on small scales (e.g. the interior region of black holes, or the very earliest times in the evolution of the universe) - but we are not currently able to describe such domains, because unlike the other three fundamental interactions, gravity cannot be straightforwardly quantised, since its nature is very different from the one of the other interactions. This is currently an area of very active and ongoing research.

The mechanism would be the law of gravity itself. The macroscopic behaviour of galaxies etc across very large scales is taken to conform to the same law of gravity that also governs small scales, such as the motion of bodies in our solar system. We know from experiment and observation that this law (being the Einstein equations) is valid to a very high degree of accuracy on scales on the order of the solar system - from this, we extrapolate to larger scales, and the tendency to expand naturally emerges. So in essence, this tendency happens for the same reason why a rock falls towards the surface of the earth, when released somewhere high above. It’s a manifestation of gravity. It’s not so much an assumption as an extrapolation - it being that gravity works the same way on large scales as it does on small scales. If that extrapolation is accurate, then metric expansion naturally happens. Why is this a problem? We have no real reason to believe - as of yet - that gravity works differently on large scales than it does here in our neighbourhood. Of course, it is possible that gravity is scale-dependent - in fact, many alternative models of gravity have been developed over the past several decades that are based on precisely that possibility, so modern physics is definitely open to this idea. But the fact is also that none of these models have been able to match experiment and observation with the same degree of accuracy as General Relativity does. As “illogical” as standard cosmology may appear to the untrained eye (and I do grant you that it can appear that way), it is actually the simplest possible model to explain what we can observe. Most alternative models are very much more complicated, and require even more illogical assumptions.