But it wouldn’t in any real sense be the magnetism that bends spacetime, but the contribution of the magnetic field to the stress-energy; you’d be better off just using something really massive. In fact, it would probably be the mass of the magnet that yields the bigger contribution.
Stress-energy induces a non-vanishing spacetime curvature, so in that sense, it does bend spacetime (which is a dynamical quantity in general relativity, so not something that ‘just is’).
Penrose diagrams have nothing to do with singularities, but rather, represent the conformal structure and the causal relations between spacetime points of a given spacetime.
Exactly what I was going to say. In principle, there are ways to contrive it so that the magnetic energy is the dominant energy source present, but even so, it’s a gravitational effect that warps spacetime, not a magnetic one.
And one of the things that happens at the event horizon of a black hole is that r becomes a timelike coordinate and t becomes a spacelike coordinate, but that really says more about the particular coordinate system we’re in the habit of using than it does about the black hole itself. There are other coordinate systems that don’t have that particular bit of weirdness (though they’re inconvenient for some other purposes), and in fact the first step in constructing a Penrose diagram is to convert to one of those other coordinate systems.
A couple of nitpicks, here. First, I’m not clear on what distinction you’re drawing between a representation and a description. Second, it’s not really the singularity itself you’re representing (they be whacked out, man), but the spacetime around it. Third, you can draw Penrose diagrams of spacetimes without singularities, too; they just look rather boring (basically just a square tilted to stand on one corner)
OK, I’m over my head and I admit it. I was trying to suggest something like the difference between a Mercator projection and a globe, in which lines of constant course are curved in one and straight in the other, but are the same path regardless.
Clear up one more point of my confusion. Is the “non-vanishing spacetime curvature” a constant curvature or a variable one? If constant doesn’t that imply that spacetime cannot be bent, and if variable how does that differ from the overall curvature or flatness of the universe?
A Penrose diagram is really just a way of drawing a picture of the whole of the spacetime whilst still preserving certain relationships between spacetime events/spacetime curves. The equivalent of a 2-D map of a 2-D surface would be to take the map of an infinite 2-D surface and map it onto a finite 2-D surface, whilst still preserving the angles between curves.
Spacetimes with constant curvature are essentially devoid of matter and radiation, but have a positive negative or zero cosmological constant. Their lack of matter and radiation precludes them from being realistic models of our Universe.
I think though what you actually mean to ask are all spacetimes stationary (a stationary spacetime is one in which the metric can be written in a way that is independent of the time coordinate). The answer to that is that some are and some aren’t. The Kerr-Newman solutions for black holes are example of a stationary spacetime, though the ‘stationariness’ is unphysical as for example real black holes are dynamic (i.e. the form, they accrete matter, they evaporate, etc) which isn’t represented in the Kerr-Newman solution. All cosmological solutions representing Universe filled with matter and/or radiation are non-stationary for example, except the unstable Einstein static Universe.
The curvature of spacetime is different from the spatial curvature in cosmological models. For example the Universe is believed to be spatially flat or very close to it, but the spacetime modelling such a Universe is definitely not flat.
You can also have a constant-curvature universe containing matter, as long as the matter distribution is perfectly uniform. In our Universe of course we know it’s not, but it can still be a reasonable approximation on sufficiently large scales.
Actually just another matter of scale. It’s flat on large scales, but non-flat on small scales. Think of one of those sheets of egg-crate foam.
I’m talking specifically about spacetime curvature, rather than spatial curvature. A universe containing matter cannot have constant spacetime curvature. This is a direct result of Einstein’s field equations.
Again I’m trying to distinguish between spacetime and spatial curvature. We usually model space as flat, but, even ignoring the local bumps due to the fact that the distribution of matter is not 100% homogeneous, the corresponding model of spacetime for our Universe is not flat.
That’s a bit of an overstatement. Sending a message forward in time at different rates is completely possible, just requires relativity. Put a message in a capsule that can circle the sun at thousands of miles per second, that message can land back on earth a few minutes later (relative to the message’s time frame) and the future people will have gotten a message from the past. Sending the message back is a bit of a problem though. Guess that’s where magnets come into play?
If I could save time in a bottle,
The first thing that I’d like to do,
Is put a supermagnet up next to it and fuck that shit all up.
Get bent, yo. Jim Croce
Ah, I see the problem, Asymptotically Fat. I, too, was referring to spacetime curvature as a whole… but I was taking “constant” as meaning “constant in space”, not including changes with time, since you mentioned that separately as “stationary”.
Since super-model is not explained (or even used) anywhere in the article itself, I have to assume that Super-Model Graphene is skinnier but bustier than normal model graphene.
In a very rough sense, the configuration and flow of matter and energy determine the spacetime metrc, which is what determines the notion of spatiotemporal distance, and hence, also the curvature. This then determines how matter and energy move around. If you’ve got no gravitational field, i.e. no metric, then in a sense you have no geometry, thus it’s often said that spacetime is the gravitational field. Any solution to Einstein’s field equations is then a complete spacetime, a universe if you will, in which (spatial) curvature varies with time according to the way matter moves around.
Penrose diagrams are a representation of this in the following sense: if the spacetime has rotational symmetry, you can get rid of two (spatial) dimensions, leaving you with a sheet having one spatial and one temporal dimension in which every point corresponds to a sphere in the real space. Penrose diagrams now arrange things such that the metric of the diagram is equivalent to that of the spacetime by a so-called conformal, i.e. angle-preserving, transformation; thus, the diagram carries all the relevant information about the original spacetime and its causal structure (i.e. which points can be reached from which other points by a light ray, or something going slower).
Yep I realize it wasn’t that clear, I meant that the spacetime manifold had constant sectional curvature. As this requires that the spacetime is everywhere a locally maximally symmetric vacuum (I think that’s the right way to say it) there can’t be any matter. The simplest examples would be Minkowski, de Sitter and anti-de Sitter spaces and all other constant sectional curvature spacetimes would have the same local geometry as one of these 3.
The important thing about Penrose diagrams is that they are pretty much bog standard spacetime diagrams of what are sometimes called “unphysical spacetimes”, which are the conformal compactifcations of the spacetimes used to describe physics in general relativity. A conformal compactification of a spacetime essentially means to take a spacetime and make all the distances (distances in time, distances in space and even ‘lightlike distances’) such that there is a maximum distance of any type, whilst preserving the spacetime angles.
This is why you’re analogy isn’t very complete Exapno Mapcase, because for example the Mercator projection is a picture of a space that is already compact.
But the Mercator projection itself is not compact, being infinitely tall (classroom maps usually cut off somewhere around the Arctic Circle or so, but they can be extended indefinitely).
And Exapno, that article has nothing to do with space or time per se. It’s just saying that they’ve found a new technique for making graphene that’s quicker and easier than before. The graphene itself doesn’t do anything weird to spacetime.
Of course, if you have a supermagnet big enough to send signals backward in time, this would mean that the rate at which the signal occilates (or is otherwise modulated) would become inverted as it crossed the spacetime threshold into “timespace” (i.e. Brownian Space).
So inversion of the signals is a requirement. You’d have to also make sure the energy you’re using to power such a Brownian device has its polarity reversed, as well as any signal or message. This would mean you’d need to acquire supermagnets with inverted poles, and any anodes within the device’s circuit be created out of positronic matter.
Of course, the above also assumes the reader knows what fiction means and that all of the above is, in fact, fiction. Including the OP.
