Markus Hanke

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.

Space is a 3D hypersurface of simultaneity, for some fixed instant in time. Spacetime is the collection of all such hypersurfaces. This question does not make sense, because there is no acceleration involved, so the galaxies do not “move” as a result of metric expansion. It’s only the empty space between the galaxies that expands. This phenomenon has to do with the geometry of spacetime, not with any mechanical forces. I don’t know what you mean by this - space is not a medium, it doesn’t “flow”. That’s because the question does not make any sense in the context of physics.

It’s space that expands, not spacetime. This is an important distinction in this context. The tendency for the spatial part of it to expand is intrinsic in this type of spacetime geometry; this means it’s a natural feature of this particular type of geometry. It requires no further cause or agent, other than the nonlinear law of gravity itself. This is somewhat analogous to shaving foam - once released from its spray can, it will have a natural tendency to expand, without the need for any external catalyst; this tendency is already intrinsic in its chemical composition and their physical properties. The function of dark energy is only to regulate the rate at which the expansion happens - you can accelerate or decelerate the expansion over time, or - if its distribution is chosen in just the right manner - bring it to a halt. You can again liken that to shaving foam - its rate of expansion depends (assuming normal atmospheric pressure) on ambient temperature, just as the rate of metric expansion depends on the distribution of dark energy. They aren’t. What is expanding is only the space between them, so it’s the distance between galaxies that increases over time. In general, expansion happens only in regions that are not (or only very weakly) gravitationally bound; also, this expansion is noticeable only across very large scales, on the order of dozens of MPc and above.

GR is not intended as a complete description of the universe, it’s specifically a model for gravity (which is what this thread is about), that is all. And as such, it does a remarkably good job.

That means the OP is approaching this subject from the wrong angle, because GR is the proper description of gravity; Newtonian physics are only the weak field limit. And issues about who observes what don’t arise if the proper formalism is used right from the start. Let’s think about this for a minute. First of all, “energy” - when taken in isolation - is an observer-dependent concept, so observers will in general not agree on its conservation, or lack thereof. It’s therefore unsuitable as the source of gravity. So before we can do anything else, we need to ask ourselves just what it is that is actually conserved. To answer this, we consider a small patch of spacetime, and apply Noether’s theorem - out of all the possible symmetries, we find that it is time translation invariance that gives us a conserved quantity related to energy; that is the stress-energy-momentum tensor. It is locally (!) conserved in the sense that [math]\displaystyle{\triangledown_{\mu}T^{\mu \nu}=0}[/math] Two things need to be noted here: first of all, the fundamental concept here is not energy-momentum, but spacetime. It’s from spacetime and its local symmetries that, via Noether’s theorem, the notion of energy-momentum arises. Therefore, saying that gravity is the result of the conservation of energy-momentum is missing the point - gravity is the result of the geometry of spacetime. Energy-momentum just forms the source term in the dynamical laws; that’s not the same thing. Secondly, energy-momentum is a purely local concept, and as a tensor it is a purely local mathematical object. Its conservation cannot be easily extended across regions of curved spacetime, because if you integrate the above expression across some volume of curved spacetime, you are left with non-covariant curvature terms that do not identically vanish. So physically, energy-momentum is conserved everywhere locally, but in general no conservation law exists for global regions. Since gravity is clearly a global concept, this will again not get us very far. This being said, the above expression is one of the constraints that must hold when we construct the field equations from the source term. If the energy-momentum tensor is conserved in the above manner, then so must be the entire other side of the field equation. When we bring together the entire list of mathematical and physical requirements needed to make everything self-consistent, we find that the only object that fulfills them all is a tensor constructed from the Ricci tensor, less its trace; this is called the Einstein tensor. Up to a proportionality constant (and a term of the form const*metric, which we ignore here), this fixes the field equations: [math]\displaystyle{G^{\mu \nu}=\kappa T^{\mu \nu}}[/math] And we find that the Einstein tensor is conserved just in the same way as the energy-momentum tensor: [math]\displaystyle{\triangledown_{\mu}G^{\mu \nu}=0}[/math] To summarise: the conservation of energy-momentum plays a role in determining the form of the field equations, but it isn’t in itself where gravity comes from. This should be rather obvious, because in vacuum the above equations (after trace-reversal) reduce to [math]\displaystyle{R^{\mu \nu}=0}[/math] There is no energy-momentum, but we still get non-trivial solutions (i.e. gravity) to these equations.

There is one fundamental issue in this thread that hasn’t even been acknowledged - “gravity” cannot be described as a scalar field; it can’t even consistently be modelled as a vector field. It’s a rank-2 tensor - and it has to be, in order to capture all relevant degrees of freedom. What’s more, real-world gravity is self-coupling, and hence non-linear, unlike any of the concepts bandied about in this discussion. It is therefore futile to play around with notions of acceleration and energy, since at the very best this would produce something akin to linear Newtonian gravity, which is not a complete description of what we see in the real world. So what is the point in all of this?

The top-down approach (trying to police what appears in the media) is never going to work, in my opinion. The best chance we have on this issue is going bottom-up - education is the key. We need to teach people the critical thinking skills that will enable them to distinguish between what is real and what is fake, or at the very least to question suspicious claims. To some of us these skills come naturally, but to the vast majority of the populace they do not. However, at least to some degree, this is a skill that can be taught and learned - I think it is high time we make engagement with media a subject in our school curriculums, instead of taking it for granted that people somehow just have the necessary skills. Is education a magic bullet? Of course not, but it would at least alleviate the problem.

While that is indeed the basic idea, I should clarify that the notion of “event” in GR is not the same as the term “event” in everyday speech. A GR event is simply a point in space at an instant in time, meaning a point on a 4-dimensional manifold. When you describe a real-world object that persists over a period of time, then this becomes a collection of events, i.e. a world line in spacetime. But yes, in GR terms, the “universe” is the collection of all points in space at all instances of time. GR is a purely classical model, meaning it does not account for any quantum effects, such as uncertainties in measurement outcomes. That is what I meant when I mentioned that everything is deterministic in GR. You can try to interpret QM in the context of spacetime, which basically leads you to the “many worlds” interpretation. That is indeed a gigantic collection of events!

It’s like one of those old style film projectors - you project a rapid succession of frames onto a screen, and as a result you get the illusion of motion. But in reality, there is no motion, because the reel of film itself is a completely static construct. All frames are there already, eternalised on the reel, and never change; in fact, the very notion of “change” is meaningless here, except as a relationship between static frames. But neither the frames themselves, nor the collection of all frames (the film reel) ever changes in any way. In the context of GR, there is also not really any such thing as motion, or the passage of time; those are only auxiliary concepts that are “left-overs” (so to speak) from the old Newtonian paradigm. For example, we usually think of the moon revolving around Earth - a dynamic process, described by an elliptic orbit in space, that repeats in time. But in GR, we no longer separate space and time, so the moon becomes a bundle of world lines in spacetime, that looks like a helix winding around another bundle of world lines that is the Earth. This geometric structure encompasses both space and time, and is itself completely static (just like the film reel), because it encompasses all locations in space of these objects at all instances in time throughout their history. Any notion of “past”, “present”, “future” and “motion” is now completely arbitrary, and not fundamental to the universe. Everything that was, is and will be, is there - and that collection of all points in space at all instances in time is not embedded in anything else, and hence the notion of “change” is meaningless if applied to it. As such, GR is a completely deterministic view of the world (ref “block universe”). The same is true for the spacetime geometry that accompanies the world lines (or for gravitational waves) - they are just continuous deformations at all points in space and all instances in time, and themselves completely static. But of course, one can always recover the notion of dynamics, by “slicing up” spacetime into hypersurfaces of simultaneity. You then have slices of 3D space, which are ordered in an oriented way (i.e. from past to future), and which are causally linked to each other by dynamic laws. This is called the “ADM formalism”, and is analogous to the film reel being projected onto a screen. However, such a “slicing-up” of spacetime into hypersurfaces is a completely arbitrary procedure, and not in any way fundamental to nature. One must remember that - in the context of GR - the passage of time is merely an artefact of human perception of consciousness. There is no fundamental mechanism that picks out a particular hypersurface of simultaneity, and gives it any kind of physical property that somehow distinguishes it from any other hypersurface (“the present” as opposed to past and future), or “advances” that hypersurface selection in a linear manner. GR simply treats all points in space and all instances in time in the exact same way. One can impose other structures on top of that, but those will always be arbitrary, and have no real physical significance. To give a very practical example - the process of free fall is not described as a dynamic process. Instead, it becomes a purely geometric problem - we find that world line between two given events on a static manifold, which forms a geodesic of that manifold, given a connection and a metric. Mathematically this is done by finding that world line, which parallel-transports its own tangent vector at all points; so the “process” of free fall becomes a simple concept in static geometry. If you write this statement down in mathematical form, you end up with the geodesic equation. That’s all there is to it. As mentioned before, it can be a useful analogy to explain certain situations in a visually appealing manner. But that’s all it is - an analogy.

The gravity/fluid duality is not the same thing as the “flow of spacetime into the earth” comment I responded to. If you think about it carefully, you will realise quickly that spacetime is a completely static construct, in the sense that it is not embedded in any higher-dimensional manifold with additional dimensions of time. Spacetime is hence the totality of all events at all times, and therefore cannot in itself exhibit any dynamics. You can, however, use the idea of dynamics as an illustrative analogy in some situations, similar to the rubber sheet analogy - but it is always important to bear in mind that an analogy is not the same as the actual model. I should also mention that the gravity/fluid duality never really made it into the mainstream, because the expected experimental evidence of gravitational turbulence has not been observed.