If we place an analog clock with hands next to the lower bar that clock will appear to tick less than 1 time unit by the time the pulse has moved to the tips of the bar (assuming that local observer would think that it was covered in exactly 1 time unit). I am not sure you are using light as ruler in a correct way.
That’s what I mean by the observers measuring different times for light crossing the different points; the major thing is that A is longer than B, because I’m trying (possibly failing) to suggest that the difference in distance arises from the fact that an observer in A is measuring some distance that an observer in B would call time, instead.
The “boost to infinity” is just that energy requirements for high speeds seem to grow without bound. One way to measure change is one measure changing per change in another measure for example x per t. If a draw a curly line that has an U-turn in it I could get into trouble that at some point in the U turn the “next instantenous moment in coordinate time” could get a bit ambigious. Another concept could be the “next dot of the curve” and for curves that go relatively straight that next blob is likely to be in the “global forward” direction. So thinking in terms of max displacement per global forward tick vs maximum curl between adjacent blobs that the swiggle can have don’t neccesarily meet.
I think I see, yes. I think it’s correct to say that energy requirements grow without bound—but I also think that that is a Newtonian framing of the question, in which “velocity” is a property of matter, which has an inexplicable maximum value.
...but I’m failing utterly to come up with an explanation that I think conveys that velocity isn’t just a scalar property of matter. I think it’s all going to sound like nonsense. I’ll think about this and return to it.
Sorry, the signature is of the squares. The fuller equation is x^2+y^2+z^2-t^2=s^2. Increasing spatial separation gets you more of the measure, increasing time separation gets you less of the measure. If you take it in a certain way the underlaying number go complex but because people are allergic to the imaginary numbers people stay on the square level where it is just positive and negative reals.
If it helps—it probably won’t—I think time is distance projected onto (desuspending into?) an imaginary plane. Specifically I think time is probably a spiral, in which distance is the arc length, and my unified field theory is one of the two complex dimensions.
The minus sign doesn’t get you “anti-directionality”, (which would be parallel but opposite). You took my prompt in a somewhat consistent direction but I was misleading in making you head that way. Riemanninan rotations are weird and I can’t tell whether you are working with euclidean rotations, whether you have yet to incorporate the riemannian weirdness or you have another take on the weirdness. I don’t example know whether it makes sense to use 360 degrees when talking about boosts. If you do 36 10 degree rotations and get back to where you started. But you can take a small/moderate boost and you can keep doing it for a very long time without it “wrapping around”.
So this is where the “We need to consider rotation as hyperbolic” approach comes in. A ten degree rotation from one frame of reference is not a ten degree rotation from another frame of reference; frames of reference won’t agree on how far a given rotation is. From the perspective of an object inside space-time, I think you have to think of rotation as hyperbolic. When I think about these things, however, I’m usually thinking about them from a perspective I can only describe as outside all frames of reference.
That said, the space-time relationship I am attempting to describe is definitely not Euclidean.
I mention Matryoshka dolls; my view of time is something like nesting Matryoshka dolls. Consider the event horizon of a black hole, notice that it is the surface of a 3-sphere (two dimension making the obvious surface of a sphere, plus a distance dimension); now “unroll” the event horizon’s distance dimension along the dimension that is directional with the distance dimension of the event horizon. The other two dimensions remain closed—you have three dimensions, made up of one “linear” dimension and two closed dimensions. However, we didn’t actually unroll that third dimension, we more … mapped it onto a linear dimension, so it still has curvature (also it wasn’t precisely a closed dimension like the other two in the first place, it was more like the desuspension of a closed dimension). As we move away from the black hole, our mapping moves in a loop. Relative to our linear direction we have mapped onto, curvature is positive for part of the loop, and negative for part of the loop; this curvature is “impressed” upon space-time itself. So the “structure” of the black hole is, through this mapping, infinitely superimposing itself on spacetime as we move away. (But I think that maybe thinking of the black hole as the “real” structure, which is duplicated/imprinted outward from itself, is wrong; the black hole is this repeated structure in its entirety).
Time, then, is sometimes anti-directional, and sometimes directional, with respect to distance, as a function of distance. When it’s anti-directional, time is bent towards the object; with it’s directional, time is bent away from the object.
Or we could express all that as rotation-of-rotation; the rotation of space-time itself is rotating, as we move away from the black hole.
If any of that makes sense, which I kind of doubt.
If you are working from an euclidean standpoint then it will surprise you that taking all the events that are equidistant from a central event do not form a sphere. Your current language suggests that you use terminology with that kind of assumtion.
...huh. No, I don’t mean a Euclidean sphere. Or, above, a Euclidean 3-sphere, although maybe the surface of a 3-sphere remains at least approximately correct, I’d have to think about that.
We can talk about delta-Vs ie changes in velocity but that doesn’t lend to rotation language. To the extent that we use a rotation understanding numbers don’t make sense.
True, I think. Well, they can make sense, but it’d probably require the hyperbolic version of rotation in order to make sensible use of numbers.
There is a thing where black holes make time and spcae reverse roles. I don’t know whether you diverge from that or have a unconvetional grab of it.
Maybe unconventional? Strictly speaking it doesn’t matter if you start with two space dimensions and one time dimension, or three space dimensions, but I think singularities bend time into space, or space into time, “creating” the fourth dimension, which is why it doesn’t act like a properly independent fourth dimension in some respects; it’s just a superimposition. (Also all particles in this are expected to be singularities, or possibly quasi-singularities in the case of neutrinos)
That’s what I mean by the observers measuring different times for light crossing the different points; the major thing is that A is longer than B, because I’m trying (possibly failing) to suggest that the difference in distance arises from the fact that an observer in A is measuring some distance that an observer in B would call time, instead.
I think I see, yes. I think it’s correct to say that energy requirements grow without bound—but I also think that that is a Newtonian framing of the question, in which “velocity” is a property of matter, which has an inexplicable maximum value.
...but I’m failing utterly to come up with an explanation that I think conveys that velocity isn’t just a scalar property of matter. I think it’s all going to sound like nonsense. I’ll think about this and return to it.
If it helps—it probably won’t—I think time is distance projected onto (desuspending into?) an imaginary plane. Specifically I think time is probably a spiral, in which distance is the arc length, and my unified field theory is one of the two complex dimensions.
So this is where the “We need to consider rotation as hyperbolic” approach comes in. A ten degree rotation from one frame of reference is not a ten degree rotation from another frame of reference; frames of reference won’t agree on how far a given rotation is. From the perspective of an object inside space-time, I think you have to think of rotation as hyperbolic. When I think about these things, however, I’m usually thinking about them from a perspective I can only describe as outside all frames of reference.
That said, the space-time relationship I am attempting to describe is definitely not Euclidean.
I mention Matryoshka dolls; my view of time is something like nesting Matryoshka dolls. Consider the event horizon of a black hole, notice that it is the surface of a 3-sphere (two dimension making the obvious surface of a sphere, plus a distance dimension); now “unroll” the event horizon’s distance dimension along the dimension that is directional with the distance dimension of the event horizon. The other two dimensions remain closed—you have three dimensions, made up of one “linear” dimension and two closed dimensions. However, we didn’t actually unroll that third dimension, we more … mapped it onto a linear dimension, so it still has curvature (also it wasn’t precisely a closed dimension like the other two in the first place, it was more like the desuspension of a closed dimension). As we move away from the black hole, our mapping moves in a loop. Relative to our linear direction we have mapped onto, curvature is positive for part of the loop, and negative for part of the loop; this curvature is “impressed” upon space-time itself. So the “structure” of the black hole is, through this mapping, infinitely superimposing itself on spacetime as we move away. (But I think that maybe thinking of the black hole as the “real” structure, which is duplicated/imprinted outward from itself, is wrong; the black hole is this repeated structure in its entirety).
Time, then, is sometimes anti-directional, and sometimes directional, with respect to distance, as a function of distance. When it’s anti-directional, time is bent towards the object; with it’s directional, time is bent away from the object.
Or we could express all that as rotation-of-rotation; the rotation of space-time itself is rotating, as we move away from the black hole.
If any of that makes sense, which I kind of doubt.
...huh. No, I don’t mean a Euclidean sphere. Or, above, a Euclidean 3-sphere, although maybe the surface of a 3-sphere remains at least approximately correct, I’d have to think about that.
True, I think. Well, they can make sense, but it’d probably require the hyperbolic version of rotation in order to make sensible use of numbers.
Maybe unconventional? Strictly speaking it doesn’t matter if you start with two space dimensions and one time dimension, or three space dimensions, but I think singularities bend time into space, or space into time, “creating” the fourth dimension, which is why it doesn’t act like a properly independent fourth dimension in some respects; it’s just a superimposition. (Also all particles in this are expected to be singularities, or possibly quasi-singularities in the case of neutrinos)