Markus Hanke

I may be wrong on this (someone correct me, if so), but I think there has not actually been any observations of electrically charged black holes (or any other body with substantial net charge, for that matter). It may still be possible for this to happen during short periods of time, but I think such net charge would be neutralised fairly quickly. Actually, the Schwarzschild solution is just a 1-parameter family of metrics that arises from the field equations for a certain set of boundary conditions - one amongst which is asymptotical flatness. It is also a vacuum solution, so the energy-momentum tensor vanishes everywhere in this spacetime. We identify the one free parameter that appears as “mass”, but that is not a source that is part of the manifold, and that identification with mass arises from boundary conditions (specifically, from the demand that Newtonian gravity is reproduced at infinity). As such, the mass is actually a global property of the entire spacetime, not of any body within it.

I honestly don’t understand what it actually is you are asking - could you reformulate your question in a different way? At the moment you are bringing up many different concepts which are not really related, for example SR mixed with wave-particle duality, or the evolution of the universe.

I wouldn’t think so, since all objects we observe around us carry some form of angular momentum. It doesn’t seem as if such a cancelling out is happening. The thing is that the Schwarzschild solution requires spacetime to be empty and asymptotically flat, neither of which is a situation we actually find in the real world (except as an approximation). It is also stationary, which excludes any evaporation processes, or any changes at all to the black hole over time. I think in terms of real-world finding, a Vaidya-type spacetime is far more realistic - specifically, the Vaidya-Bonnor-Kerr metric could be a good model of the natural end state of a black hole.

Actually, this is not correct. The charge that is associated with the weak interaction is a quantum number called “weak isospin”. All particles possess this, and it is conserved in all types of interactions - unlike flavour, which is carried only be quarks, and is not conserved anyway. Thus, the weak interaction concerns more (elementary) particles than just quarks. To be honest, I don’t think there is an intuitive way to really understand the weak interaction. It’s really quite a complicated mechanism, and requires quite a bit of background knowledge in quantum field theory to fully understand.

I think what you are asking is whether solutions to the gravitational field equations linearly superimpose (like EM waves do). The answer is no, unfortunately. Unlike electromagnetism, gravity is a non-linear affair - this means that the effects of the rotating bodies will combine in some way to yield an overall metric of spacetime, but this combination is not a linear superposition, but something much more complicated. Having four charged, rotating bodies in General Relativity is a scenario so complex that it could only be solved numerically (and would require substantial computing power to do so). Yes, it generally would. I’m not so sure about this one. But what mechanism would it get neutralised? In either case, this does not appear to be what we observe around us. The Schwarzschild solution requires spacetime to be everywhere empty and asymptotically flat. This is not a situation that we will ever find in the real world, except as an approximation. No black hole can ever be perfectly Schwarzschild.

No, but you are tacitly assuming it in the way you are thinking about the situation. For example in your next sentence: Different times according to who? Since time in relativity is a purely local concept, simultaneity becomes relative too. The same is true for “always” - it’s an observer-dependent concept. Actually, it isn’t. The metric is a tensorial quantity, so the relationship between events in spacetime does not depend on your choice of coordinates. In the specific case of Special Relativity, you don’t even need to pick any coordinate system at all - you need to know only that the metric is constant. This is a valid question, but it is not how I understood your OP. So I may have misunderstood you. Perhaps you can clarify again exactly what it is that you are asking, maybe in more general terms? In relativity there is a causal order to things, but not a chronological one (i.e. one that is based on clock readings), because time is a relative concept that not all observers agree on. The notion of “at the same time” is thus not shared by all observers. What is shared between all observers is the spacetime interval between events, specifically whether it is a timelike, spacelike, or null interval. This imposes a causal structure on spacetime, which everyone agrees on.

This is true, but it is not what the OP has asked. The original question was why the electron does not fall into the nucleus, i.e. how is an atom different from a purely classical system of a charge in free fall towards another (opposite) charge, which of course is not a stable situation in the classical domain. So the OP wanted to know how this is possible, so I have attempted to answer the question. The spontaneous tunnelling through the nucleus - or any other classically forbidden region - is not the same as the electron “falling in”.

I’m having trouble understanding your point, I’m afraid. There is no absolute time nor is there absolute space, so it is irrelevant just where you place your point of origin. Either observer can choose any suitable coordinate system he/she likes, as this makes no difference to the physics. What is important is only the relationship between the observers, and this is something they both agree on. Specifically, and assuming they are inertial observers in flat spacetime, their two reference frames are related by a simple hyperbolic rotation about some angle, and the spacetime interval AB is the same as the spacetime interval BA. So there are no contradictions. More generally, you can actually prove that no matter how you set up your observers, there are never any inconsistencies. It should be mentioned also that spacetime is the collection of all events, i.e. of all points in space at all instances in time; there is not actually any concept of “flow of time”, there are only geometric relationships between events in spacetime. The theory of relativity cannot answer the question as to why we experience a “flow” from past to the future, as this is outside its scope.

No, not really. The Pauli principle states that no two fermions can share the same quantum state, but I assumed in my answer that there is only one electron anyway. I guess my answer comes down to the fact that the ground state (i.e. lowest possible excitation) of a single electron around a nucleus is non-trivial, meaning it is not just a point centered at the origin where the nucleus is; instead, it’s a spatially distributed probability cloud with corresponding non-vanishing energy. Note that we are talking bound states here - it is of course still possible to fire an electron at the nucleus, and hit it in the process, but that is not a stable bound state, and won’t happen spontaneously.

The answer is yes to both. Maxwell’s equations can very easily be generalised to curved spacetimes; in fact all you need to do here is write them in terms of the differential forms formalism, which is fully covariant. Likewise, EM fields function as sources of gravity - all you need to do here is insert the stress-energy tensor for the electromagnetic field into the Einstein equations. Ideally one of these (either a metric, or an EM field) will be given, and you can then calculate the other. If you know only a distribution of sources, but neither metric nor EM field, then you will need to solve a system of equations that comprises both the Maxwell and the Einstein equations. This is potentially very challenging, mathematically speaking. But yes, EM fields influence the geometry of spacetime, and the geometry of spacetime influences EM fields. It’s a pretty complex and non-linear “feedback system”.

Lorentz transformations are a relationship between inertial frames in flat spacetime; you cannot straightforwardly apply them when spacetime is not flat. Also “rate of change of spacetime” is not a meaningful concept. On a more general level, I think it would be helpful if you familiarise yourself with what we already know first, before starting to speculate about new theories. As it so happens, the existing theory of gravity we have at present (General Relativity) works very well within its domain of applicability.

Because the electron is not a classical particle (“little ball of mass and charge”), but a quantum object. As a first approximation, you can picture an electron as a 3D standing wave around the nucleus - you can only get standing waves of a given wavelength in specific places, which is why orbitals come in discrete levels. Crucially, there is a lowest energy level, which corresponds to the minimum distance an electron can be with respect to the nucleus (let’s assume here there is only one electron) - and that lowest energy level is not zero. Therefore the electron cannot fall all the way to the nucleus, it can only fall into its lowest energy level, which corresponds to an orbital that is still some distance outside the nucleus. This is a direct consequence of the laws of quantum mechanics, and coincidentally one of the questions that motivated the development of quantum mechanics in the first place.

When you have two rotating objects orbiting one another, then each of them will have an influence on the geometry of spacetime. But this combination will be a highly non-linear and complex affair, so it’s not possible for me to tell exactly how this would look like. The dynamo effect is a mechanism by which magnetic fields are generated in the interior of rotating bodies, such as planets. I do not see the connection to frame dragging.

There are three main concepts: 1. Granularity: physical observables can only take on discrete values 2. Indeterminacy: the outcome of measurements is stochastic in nature (unless of course the system has been prepared in a definite state) 3. Relationality: It is not meaningful to attribute properties to quantum systems, until such time when they are actually measured (lack of counterfactual definiteness)

Experiment, observation, and a mathematical framework to describe them.

Actually no, there doesn’t. The questions you pose tacitly assume that notions such as “before”, “after”, “here”, “there” etc are physically meaningful at and around the BB event; in other words, you assume that there was a well-ordered causal structure in place back then. The trouble is that there is nothing to suggest that this is actually the case - quite the contrary actually, because if we look at modern approaches to quantum gravity, then you will find that in many of these models there simply was no classical spacetime with a well-ordered set of events present back then. To put it differently - if you go back far enough to towards the BB, the concepts of a metric and causal structure increasingly begin to loose their meaning. Eventually, the question “what came before...” becomes simply meaningless, because there is no longer any ordering of events either in time nor in space. Going back even further then, the very notions of “time” and “space” as traditionally understood loose their meaning as well, so you end up with a scenario that may still exhibit dynamics, but in a background-independent manner without any classical spacetime. So I think the skill here is not so much to find answers, but to ask the right questions.

Yes, and that’s no problem, because KE is a quantity that signifies a relationship between observer and the object (i.e. it’s relative, and not invariant); it’s not intrinsic to the distant object itself. You don’t need to balance anything out, because there is no conservation law that needs to be satisfied in the first place.

There is no global energy conservation law across regions were gravitational effects cannot be neglected. But energy-momentum (not just energy) continues to be conserved everywhere locally.

No combination of protons and neutrons can have overall spin 2. This is completely meaningless.

Yes it will indeed, and that is definitely a problem. To give you just one specific example of what would happen - without Lorentz invariance, particles will cease to have spin. Without spin and its relevant statistics (i.e. the Pauli exclusion principle), all atomic shells will collapse into just one single shell, which is then shared by all electrons. This will render the period table defunct, and will make it impossible for molecules to form. Macroscopic matter as we know it will cease to exist. This is evidently not what we observe in the real world.

Essentially yes. But you need to also remember that this is not really a physically valid question in the first place, because energy-momentum is a locally conserved quantity, so the sun cannot just disappear in the real world. But if it could, then this change would propagate at c, like all other information. A more meaningful scenario would be to ask what happens if the distribution of mass changed (in the right ways), without anything disappearing - how long would it take for us to notice that? The answer is 8+ minutes. This is just gravitational radiation. Note that the observations of gravitational waves we have made are consistent with them moving at c.

Except that it’s wrong, (mainly) for two reasons: 1. There is no such thing as a stationary photon in vacuum. They don’t exist, because no particle with vanishing rest mass can accelerate or decelerate. 2. Velocities do not add linearly, except as an approximation in the Newtonian case. It is important that you stay within the parameters of what we can actually observe in the real world. What we do observe is that photons always locally move at c, irrespective of the observer. What we don’t observe is stationary photons (or any other particle with vanishing rest mass). It’s all good and well if you can come up with some model in which photons can be stationary, but that model will evidently not correspond to the real world, so it will be meaningless. Also, if you break SR, you will also break the Standard Model, since Lorentz invariance implies CPT invariance, and vice versa. Since all of these work very well in the real world, this won’t go down very well.

I find it difficult to fathom how anyone could claim that SR is inconsistent; after all, the relationship between inertial frames is given by a simple hyperbolic rotation. That’s it, that’s all there is to it - a rotation about some angle. Claiming that SR (between inertial frames) is inconsistent amounts to claiming that there are rotations that are not reversible. Can anyone show us an example of a rotation about some point and angle that is not reversible by counterrotating about the same angle? I guess not. Taking it further, beyond purely inertial frames, the claim of inconsistency would amount to saying that Minkowski spacetime permits violations of causality. While the formal proof of this one is more tricky, it should nonetheless be intuitively obvious that - since this spacetime is everywhere flat, and has a constant metric - no such violations are possible. This kind of discussion is just a waste of time, since the internal consistency of SR is not under any kind of contention. The only point that one could possible argue about is the question of whether SR is a good and valid model of the real world. Given that no violations of Lorentz invariance have ever been observed, it stands to reason that it is indeed a good description, at the very least within the domain of applicability that we can currently probe. And that’s a pretty wide domain.

These links are examples of publications that either do not appear in peer-reviewed journals, have been falsified during peer review, or are based on erroneous assumptions & misunderstandings of what SR is actually about. To name just two examples - viXra is not a peer-reviewed journal (anyone can publish anything there, so it is of no scientific value), and Stephen Crothers is a known crank and crackpot, devoid of any scientific credibility. What I am trying to say is that you need to be more careful in choosing your sources. On the other hand, it is scientific fact that no violations of Lorentz invariance (the symmetry that underlies the theory of relativity) have ever been observed: https://en.m.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation Relativity is evidently valid within its domain of applicability. Obviously, that domain is limited, just like for any other model of physics. For example, Newtonian gravity is valid in the weak-field, low-velocity domain, but fails miserably outside of this. Likewise, we expect relativity to break down also at some point, presumably in the domain of quantum gravity. That does not make it wrong though, any more than relativity makes Newton wrong; it’s just a question of getting the domain of applicability right.

Not in mainstream physics, no. However, there are speculations and hypotheses - mostly in the realm of metaphysics and philosophy - which consider the question of whether our sensed “flow of time” is an artefact of our perception/brain, rather than a fundamental part of nature. I don’t think this type of speculation belongs into this thread, though. This is true, but there is a caveat - the notion of “gravitational potential” can only be meaningfully defined in spacetimes that admit a time-like Killing field, whereas time dilation arises directly from the metric. So I would argue that time dilation is a more general concept than gravitational potential. But of course, in Schwarzschild spacetime the two concepts are largely interchangeable, due to the symmetries present here.