Markus Hanke

Actually, it is based on the principle that the spacetime interval between two events is invariant (as others here have already pointed out). The invariance of SOL is a consequence of that. Because the spacetime interval is an invariant. Because the spacetime interval is invariant. All observers agree on the same reality - being the invariant spacetime interval. I don’t know what number five was meant to be, but it’s almost certainly addressed by the fact that - you guessed it - the spacetime interval is invariant. One twin is inertial, the other one isn’t, so obviously there is no symmetry, because the frames aren’t related by a Lorentz transformation, but by something a little more complicated. The one who physically measures a non-zero value on his accelerometer at some point on his journey. So you would accept a model that precludes elementary particles from having the property of spin, and where the strong, weak, and EM interactions do not exist? Because all of these things are intrinsically relativistic phenomena. I presume you hold this view because you are not aware of the crucial role relativity plays for the dynamics - and even mere existence - of the particles we observe, never even mind how those particles move under the influence of gravity. There is no ‘space being created’, not sure where you got that from. Apart from that, intelligent people use relativity because they are intelligent enough to realise that it works very well within its domain of applicability. But intelligence isn’t the problem, because you are evidently very intelligent as well, in your own way. The problem is that you equate it (the model) not making sense to you with it having to be wrong. But that’s just a common logical fallacy. Relativity is very much “true”, in the sense that it is a model that works extremely well; whether it makes “sense” (what does that even mean?) to you as an individual person or not is entirely irrelevant to this. Quantum field theory (e.g.) makes little sense to me, it feels like an odd jumble of ad-hoc made-up bits, which are made to fit using even more ad-hoc made-up bits. Nonetheless, I acknowledge that it works really well within its domain, and right now it is the best description of the microscopic world that we have, so I choose to accept it for what it is and study it to the best of my ability. But let’s just say you won’t see me loosing any sleep should it one day be augmented/replaced by something different. This is why we have the scientific method - to minimise subjective measures such as “making sense”. “It doesn’t make sense to me” is simply not a scientific argument. The other problem I see on this thread is that you are rejecting something that you evidently don’t understand very well, judging by some of the statements you have made here. That would be like me fighting tooth and nail against some particular design for a building, even though I know absolutely nothing about design principles, very little about structural mechanics, and even less about how it all fits into the surrounding cityscape. My arguments would thus just be personal opinions without any objective basis, and thus pretty much meaningless to any architect worth their salt. Long story short - if your opinion about relativity is not based on thorough and intensive study of the model itself (which it isn’t - no offence intended at all), and how it fits into the overall framework of physics, then it is scientifically unreliable and you need to question it. This is the core issue that you haven’t grasped in all this - relativistic effects are relationships between frames/observers in spacetime, not things that happen “to” or “in” a single frame. So there is no force contracting anything, and nothing slowing down any clocks. It is only when you take two clocks or two rulers from different frames, and compare them in some suitable manner, that you find that the relationship between them is such that one is dilated/contracted with respect to the other. So for example, when we collide heavy gold ions in the RHIC, then the resulting shower of particles after the collision as seen in the lab frame is consistent only with the gold ions having the shape of flattened disks (due to length contraction in the direction of motion only), not with them being spherical - we can easily tell, because the transition amplitudes of the various scattering and decay processes seen in the lab frame explicitly depend on the spatial distribution of the original ensemble (the ion). The necessary calculations are complicated, but the result is not only consistent with, but mandated by relativity. The same is true in the ion frame (in the sense that the exact same outcome is predicted) - now the ion itself is seen as spherical, but distances in the accelerator are length-contracted, and the oncoming ion is more heavily time-dilated and contracted. But the eventual outcome is the same, so there is perfect symmetry (at the time of collision, i.e. after the acceleration phase). This is a real-world experiment, so we know experimentally that it all checks out.

Lorentz invariance isn't a problem, it's a solution to an awful lot of issues that plagued physics before relativity. Without Lorentz invariance, you wouldn't be here right now. You are free to choose a distance standard in any way you want, so long as it is consistent. All laws of physics are invariant (i.e. make the same predictions) under consistent changes of units. I highlighted the operative word for you. These quantities not being constants in vacuum is inconsistent with both Maxwell's laws, as well as quantum field theory.

Measure permittivity and permeability of the vacuum, preferably many times over in a number of different ways so as to obtain a large sample size, to reduce the overall error margin. Once you know the values for these to the desired degree of accuracy, the speed of light follows directly, given the validity of Maxwell’s equations.

It isn't as simple as that, because intelligence (which I assume is the 'observable' you are quantifying here) isn't a linear thing, it is multi-dimensional. What I mean by that is that most people are differently abled in different areas of life. For example, I have a friend who is absolutely useless in maths and most other academic subjects, but a brilliant artist, and earns a decent living by producing art. I myself am very intellectual-minded, and thus perform well in academic subjects such as maths and physics, but I am useless when it comes to social skills, so I'd be a miserable failure if I were to go into (say e.g.) politics. So what does it mean for someone to be 'stupid' or 'intelligent'? These terms are meaningful only in a specific context. You don't need to have book smarts to be successful in life, and conversely plenty of book-smart people never do particularly well in the competitive world of business. So no, we shouldn't give money to people purely for lack of intelligence, unless of we are dealing with a recognised intellectual disability. What would be a far better thing to do is provide an unconditional universal basic income for everyone, because that would give people a better chance to develop their full potential in life without having to worry about their basic survival, even if that potential cannot be immediately quantified in terms of monetary value.

The direction of currents make no difference whatsoever to the physical nature of the surrounding field - in both cases they produce the same electromagnetic field, just oriented differently in space. So long as those are peer-reviewed publications, we shall be looking forward to it.

So you mean there would be dynamics of the mass distribution within such a universe, but not of the universe (i.e. spacetime) itself. That is indeed true, at least in principle - but it isn't what we observe in the real world.

Where is the difference, exactly? Both of these are electromagnetic fields, they are of the exact same nature.

Just to add to all the excellent points already made - the invariance of the speed of light, i.e. Lorentz invariance, is fundamental to the Standard Model of Particle Physics. If you take away Lorentz invariance, you 'break' all the fundamental interactions. You wouldn't even end up with the same elementary particles! In other words, we wouldn't be here to discuss this (let alone type on anything resembling a computer) if this symmetry didn't hold. And signal delays due to finite speed of light isn't the same as Lorentz invariance. In terms of the bigger picture, special relativistic effects (invariance of spacetime interval, time dilation, length contraction, relativity of simultaneity, Thomas rotation) arise from the geometry of spacetime, which now is no longer Euclidean. This goes far beyond signal delays (which isn't a relativistic effect btw).

A Newtonian universe would have a fixed spacetime background with Euclidean geometry - there is no basis there for any dynamics in the metric.

I would do two things: 1. Never use this ability, because I understand that even minute interventions (such as my mere presence in another time) can mushroom into unpredictable and undesirable consequences over time (ref the Butterfly effect). History is the mother of all complex and chaotic systems, so it wouldn't be wise to mess with it. 2. I would do everything in my power to ensure that no one else ever finds out that this ability exists, and that I have it. I am convinced that humanity has not reached the level of maturity required to responsibly wield this kind of power (we don't even seem to be handling far more mundane powers very well) - this could too easily be turned into a dangerous and unpredictable weapon, or at least cause havoc through unintentional misuse. So I would try to destroy all outwards traces of this knowledge, and never speak of it again. The question is of course if a single person should be able to make this kind of call on behalf of all humanity...but I know I would!

It's rather the other way around - relativity being valid is a prerequisite for the evolution of the universe to occur in the first place. If there were preferred frames, and relativity did not hold, then the universe would either not exist at all, or it would look very different. After all, the expanding universe is a consequence of the laws of gravity, which are intrinsically relativistic.

Maybe It has long ago become such an integral part of my world-view that I find it difficult to understand why anyone would question or doubt the concept. After all, the world would look very different if spacetime was Euclidean. My first contact with relativity was at a tender age of 11-12 years I think, in a (very well written) series of pop-sci books on modern physics. I distinctly remember it immediately making sense to me, though of course at that age - and lacking much of the physical and practically all of the mathematical background - I did not understand many of the finer details, and misunderstood some other aspects. Nonetheless, even then I was able to grasp the fundamental message - that space and time are local and depend on the observer. The whole thing made such an impression on me that it motivated me to teach myself calculus with books from my local library, so that I could understand more of it; so at the age of 13 or 14 I did differentials and integrals, and made my first clumsy attempts at messing about with tensors, much to the puzzlement of my classmates and astonishment of my teachers.

Yes, they would have to vary in some way between frames - in what sense could any one frame be considered 'preferred', otherwise? The lack of a preferred frame means that no law of physics can vary if you go from one frame to another ('preferred' would need to mean that something about it is different compared to other frames), and that includes Maxwell's equations.

I don’t think it is counterintuitive - on the contrary, I would struggle to imagine what a universe would look like where this isn’t true. Saying that c is invariant between inertial frames is saying that all inertial observers experience the same laws of physics - whether you turn on your laptop in your living room, or while travelling in a very fast rocket, it will function the same in both cases. Intuitively, this is exactly what I would expect to happen. But maybe that is just me again

It’s consistent with the numbers being essentially random.

No, there are other ways to avoid the singularity - namely by making adjustments to the laws of (classical) gravity. The most straightforward amendment would be to allow what is called torsion in your spacetime. GR is explicitly constructed to use only curvature to describe gravity, so torsion always vanishes. If one allows torsion (simply by choosing a different connection), then we end up with a model called Einstein-Cartan gravity (ECG). In this model, the singularity never happens, and the collapse actually turns into a bounce, so after a very long time everything that fell into the black hole will bounce back out (but in scrambled form). This would also be true for the Big Bang singularity, so the BB model is naturally replaced by a ‘Big Bounce’ scenario. The issue with this is that when you allow torsion on your spacetime, then this has consequences not just for gravity, but for some other laws of physics as well - specifically, it makes the Dirac equation for spin-½ particles non-linear, and also has other impacts on the Standard Model. The resulting effects would be too small to be detectable at currently available energies (at least as far as I know), so ECG remains a potentially viable model that can’t be ruled out (but also not confirmed) at present. Yes, this is what would happen if String Theory is physically viable - the interior of black holes would then simply be the highest form of degeneracy, being what is called a fuzzball (see link in previous post). The singularity is again avoided. Well, instead of having a model of gravity that accounts for quantum effects, you can of course look for an extension of the Standard Model that accounts for gravitational effects. The end result is the same

! Moderator Note Moved to ‘Puzzles’, pending further development. Not sure what to make of this thread just yet, but it most certainly has nothing to do with black holes.

Ok, I get you now. This is not a trivial question, and the short truth is that we do not really know the answer, based on currently known physics. The trouble is this - the established model currently available to describe gravity (General Relativity, or GR for short) is purely classical, meaning it does not and cannot account for quantum effects. When we describe the process of gravitational collapse, then in the beginning stages of that process quantum effects can be neglected, so up to a certain point GR does a really good job in describing things. We can even cheat a bit, and extend the range for which our description is valid by considering already known quantum effects simply as classical pressures that counteract gravity. For suitable initial conditions, this may yield an equilibrium state such as a dwarf star, or a neutron star, or something more exotic like quark stars. However, once the total mass of the collapsing object exceeds a certain limit, there is no known mechanism by which the collapse could be stopped - in these cases the object keeps collapsing under its own gravity, and eventually becomes so dense that quantum gravitational effects can no longer be ignored. At that point General Relativity quite simply stops being a valid model. And this is where we get stuck, because we do not yet have a model of quantum gravity, so we simply do not know what happens in the final stages of such a collapse, and what happens to the mass of the original object. There are a few speculations, hypotheses and candidate models, but none of them is sufficiently well understood, or tested in any way. If we naively consider GR on its own, the end result of this collapse is a singularity - all the mass of the collapsing object becomes concentrated in a single point of infinite density, and infinite spacetime curvature. The ‘size’ of that infinity is always zero, regardless of how much mass you start out with, and regardless of how much mass falls into it later on. However, this is not to be understood as a physical prediction - in physics, when a model becomes singular and infinite, then that simply means that we have wrongly extended that model beyond its domain of applicability. In this particular case, we have attempted to apply a purely classical model to a physical situation that is decidedly not classical, so obviously the answer we get is not physically meaningful. Note that the singularity itself, for mathematical reasons, wouldn’t be part of the spacetime manifold, so counterintuitively the entire spacetime in and around a black hole of this kind would be completely empty. The mass of such a black hole is actually a global property of the entire spacetime, and cannot be localised anywhere. The volume of a singularity - in so far as that concept makes sense (it doesn’t, really) is zero. This is true for both point singularities, and ring singularities. Yes, in the purely classical picture of GR it would be matter compressed to infinite density. But we know (see above) that this is not a physical meaningful concept, since it cannot happen in the real universe. Even the already known laws of quantum physics prohibit such a state (ref e.g. the Pauli exclusion principle). Again, in the classical picture of GR the answer is no - the singularity remains point-like or ring-like. What does change though is the radius of the event horizon. When we look at current attempts to write out a model of quantum gravity (a very difficult problem!), then three main themes emerge, depending on which model is used: 1. Below a certain length scale, a new symmetry emerges that turns the collapse into a rebound - so the collapsing matter will never become singular, but instead begins to ‘bounce’ back out while the event horizon shrinks. However, due to the extreme time dilation in that region, this process would take a very long time (~100s of billions of years) as seen by an outside observer, which is why it has never been observed. 2. You end up with some sort of exotic degeneracy state below the horizon, such as a fuzzball. 3. Spacetime itself becomes quantised below a certain length scale, so the question as to what happens to the matter or where it goes becomes meaningless There is no telling at present if any of these possibilities describes what actually happens in the real world. Yes, but at the same time it will also continue to evaporate via Hawking radiation.

I am not sure what you are asking here - what do you mean by black holes being ‘infinitely small’? Usually, the size of a (non-rotating, electrically neutral) black hole is given by the radius of its event horizon, which is finite and well defined. For example, if our sun was to undergo gravitational collapse, the resulting black hole would have a Schwarzschild radius on the order of ~3km.

The rotation isn’t in 3D Euclidean space, but in the 4D Minkowski spacetime of Special Relativity. The geometry of that spacetime is hyperbolic, so the situation is more complex than what can be easily visualised. Note also - and that is important - that spin is not a function of spacetime coordinates, so visualising it as some kind of rotation about itself is highly misleading. Rather, the rotation involved is one of the wavefunction about a hyperbolic angle in spacetime - in other words, a Lorentz transformation between inertial frames. I think a better way to understand spin is to take it to signify what kind of mathematical object the quantum mechanical wavefunction of the entity in question needs to be, in order for it to be compatible with both the laws of quantum mechanics and Special Relativity. Spin-0 means we are dealing with a scalar, spin-½ means it is a Dirac spinor (bispinor), spin-1 means it is a vector, and spin-2 means it is a rank-2 tensor. Of course all these object types are closely related, in that they are all representations of the Lorentz group - that group which captures the symmetries of spacetime. So spin is at its heart a relativistic phenomenon, and an expression of symmetry.

Having a geometric interpretation of the Dirac equation would certainly be a good start, since it is a special case of Bargmann-Wigner for spin-½. There has to be a way to do that, somehow.

Hi all, Consider the Bargmann-Wigner equation, which is the relativistic wave equation for particles of arbitrary spin (i.e. valid for both bosons and fermions). This is a set of coupled differential equations for the components of the wave function, which is an object the type of which is in turn a representation of the Lorentz group. So for example, this would be a bispinor for the Dirac field, or a Rarita-Schwinger spinor for spin-3/2 particles, and so on. This equation can be generalised to curved spacetime backgrounds. I’ve struggled for a long time with the attempt to come up with some kind of geometric interpretation for this equation (or even just for the Dirac equation), in the same way as one can find geometric interpretations for the GR equations. Thus far unsuccessfully. Does anyone here know if such a geometric interpretation exists? Of course I know that it does not necessarily need to exist, but it would be really helpful if it did. With wave equations being in some sense representations of the Lorentz group, it ought to be possible to somehow bring this back to rotations in spacetime, though I struggle to find an intuitive, visualisable interpretation.

This is a valid question in its own right, but it isn’t directly related to the topic of this discussion. It would be better to start a new thread on this.

Sorry, but...I had to laugh at this 😄

Interesting...I hadn’t heard of this one before