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26th May 2023, 11:16 AM  #41 
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"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

26th May 2023, 12:42 PM  #42 
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26th May 2023, 02:39 PM  #43 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

28th May 2023, 08:26 PM  #44 
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So what kind of geometry can time have?
We can say , What else is possible? Let's take , and make a circle, . Can we make the 1dimensional "surface" of the circle a dimension of time? If we place an event and an observer on that circle, separated by angle θ, the distance between the observer and an event along the circle will be rθ (assuming θ is in radians). But the distance in the ambient space (ambient time?) will be the pythagorean theorem between the x,y coordinates, so: This is the distance shown below the circle in the image. This would mean that time is circular, events that travel far enough in the past would also show up in the future. This would also "time contract" the past, and cause blueshifts to be observed. You shouldn't even need dimensions of space to reach that conclusion. So, I think you could say , and then we can induce a metric for it? Does that work for 1 dimension? A one element metric? The idea is the distances in the ambient space should carry over. https://en.wikipedia.org/wiki/Induced_metric
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So what's needed is X^{μ} and X^{ν}. In other words, an f(d)=x, and g(d)=y? Assuming the d is actually the distance along the curve, and we want to map that to the 2d plane, then f(d) = cos(d) and g(d) = sin(d). So I'm going to try to put that into the formula, I think you get this: Which is: Or: But this is a time contracting, blueshifting universe. How about the opposite. In 2d space, instead of a circle, draw a hyperbola, . Pretty much everything else applies, except that you end up with: How cool is that? For this to work, you'd have to consider where , so this would be on the "closed lower halfplane". So it describes a universe with a present and a past. ETA: That's not quite right. The derivative of cosh is just sinh, and cosh x + sinh x = e^{x}. So... I think that resolves that quite nicely. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

28th May 2023, 10:32 PM  #45 
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ackamarackus

28th May 2023, 10:57 PM  #46 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th May 2023, 07:19 AM  #47 
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That is the second of the two mistakes he made when calculating the induced g_{tt} for the embedded circle satisfying x^{2} + y^{2} = r^{2}.
g_{tt} = r^{2}His third mistake lay in failing to check his work by calculating a distance Δt along the circle from angles t_{1} to t_{2}. When done correctly: ds^{2} = g_{tt} dt^{2} = r^{2} dt^{2}so ds = r dtand Δt = ∫_{t1}^{t2} r dt = r (t_{2} − t_{1})That arc length is the correct answer. It is not the answer you get when you calculate using an incorrect value for g_{tt}. He repeated his g_{μν} mistake with the unit hyperbola x^{2} − y^{2} = 1, but did not give himself an opportunity to repeat the mistake of dropping r because he used the unit hyperbola. Parameterizing that hyperbola by x = cosh t and y = sinh t, the correct value of g_{tt} is g_{tt} = ∂_{t}X^{μ} ∂_{t}X^{ν} g_{μν}Unless you're selling rubbish, which is what the author and sole proponent of Helland physics has been doing throughout this thread and its predecessor, incorrect calculations of g_{tt} are not cool. 
29th May 2023, 07:50 AM  #48 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th May 2023, 08:03 AM  #49 
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29th May 2023, 08:17 AM  #50 
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29th May 2023, 08:42 AM  #51 
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29th May 2023, 09:04 AM  #52 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th May 2023, 09:38 AM  #53 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th May 2023, 01:11 PM  #54 
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In a nutshell...
The most direct evidence for the expanding universe is stretched wavelengths, and time dilated supernovae. When the electromagnetic wave's period to be stretched instead, well, that's redshift too. So maybe its like this: Which means they are basically the same phenomena, and it's based on time, not space. In that case, a time coordinate transformation would account for both. I say, transforming the map so it accurately represents reality is a good thing. The criticism is that changing coordinates isn't good enough. There should be some underlying geometrical reason for that. The solution is to give time some curvature, as a hyperbolic surface. That does the trick. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th May 2023, 02:00 PM  #55 
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Still confusing the map for the territory. I wonder how many years that will continue for.
Quote:
Quote:
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"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

29th May 2023, 03:16 PM  #56 
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I'm not saying it does.
We could say that , but we could also say , or , which gives us flat time, positively curved time, or negatively curved time. So I think what I'm looking for is this: Where , or something like that. Still working on that. Given the arc length on the hyperbola, we want to know the distance of events in the ambient space (or more accurately ambient time). To do that we would want to identify its first fundamental form: " It permits the calculation of curvature and metric properties of a surface such as length and area in a manner consistent with the ambient space. " https://en.wikipedia.org/wiki/First_fundamental_form Am I entirely sure what I'm talking about? No. But it is interesting stuff. And some pieces seem click into place occasionally. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th May 2023, 04:42 PM  #57 
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"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

29th May 2023, 05:41 PM  #58 
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Here are the premises:
* Time can be flat, positively curved, or negatively curved * Negatively curved time can be represented as the 1d surface of a hyperbola in 2d space * Given a set of events with a consistent interval between them when given by rθ, is an interval that increases as distance from the origin grows in the 2d space (). Are these a problem? 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th May 2023, 06:44 PM  #59 
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It seems Helland physics is vying to replace Time Cube.
Yes. Even more importantly, Mike Helland is mistaking his own incompetence for evidence. Look at the words I highlighted above. His assertion "that these geometries of time seem to cause blueshift and redshift" was never a fact, remains a nonfact, and will forever remain a nonfact. The stupidity of a claim does not count as evidence for the claim. A stunningly stupid claim does not become a fact by reason of the claim's stunning stupidity. All three of the sentences I highlighted are ignorant. The second sentence above, highlighted in pink, is stunningly ignorant. The induced metric on an embedded curve does not define the distance between two points of the curve as the distance between them in the embedding manifold. It defines the distance between two points of the curve in terms of both (1) the curve's parameter (which is where the subscripts on ∂_{a} and ∂_{b} come from) and (2) the integral along the curve of the embedding manifold's metric (which is where the g_{μν} comes from). The stupidity of the pink sentence is illustrated by this Fermat's spiral, in Cartesian coordinates parameterized by the angle φ ≥ 0: x = φ^{½} cos φFor each natural number n, let p_{n} be the point on that spiral with Cartesian coordinates ((2π n)^{½}, 0). As n increases without bound, the R^{2} distance between p_{n} and p_{n+1} converges to 0, but the distance along the spiral between those two points increases without bound. As for the two sentences highlighted in blue: There are infinitely many ways to parameterize a curve. Each parameterization amounts to a choice of coordinate (singular!) for the curve.As with any other choice of coordinate system, each choice of parameterization will have advantages and disadvantages. Mike Helland started out by parameterizing his circle by "angle θ":
Originally Posted by Mike Helland
Correcting those definitions, and assuming his parameter t was just a renaming of the angle θ, a correct calculation of the induced metric form yields g_{tt} = r^{2}. If he intended for t to be the arc length instead of the angle, and just forgot to tell us, then a correct calculation of the induced metric yields g_{tt} = 1. With that metric form, the sentences I highlighted in blue would be true. But those sentences are clearly false for g_{tt} = r^{2}, and that was the metric form he thought he was talking about. He was, as usual, quite confused. But the fact that both of the metric forms g_{tt} = 1 and g_{tt} = r^{2} are correct (ETA: and define exactly the same metric, albeit using different parameterizations, i.e. coordinates) does emphasize that we're talking about maps here, not territory, and Mike Helland is once again confusing the two. That is an outstandingly stupid claim. Its outstanding stupidity has already been explained time and again within this thread, but that claim climbs to new heights of stupidity when made about time in isolation, as a 1dimensional curve. Such curves can have extrinsic curvature when embedded within some manifold of higher dimension, but 1dimensional curves never have any intrinsic curvature. Furthermore their extrinsic curvature depends upon how they are embedded. The author and sole proponent of Helland physics has been basing his recent discussion of such curves on embeddings that are completely arbitrary. Different and equally valid choices of arbitrary embeddings would yield different extrinsic curvatures. We now turn to a spectacular example of Mike Helland's cargo cult approach to math and physics. The reason mathematicians use different notations for the 1sphere S^{1} and for the real line R^{1} is that those 1dimensional topological manifolds are not homeomorphic to each other. Mike Helland, mindlessly aping notation he doesn't understand, is trying to look smart by inventing a notation H^{1} for a topological space that is homeomorphic to R^{1}. To emphasize the stupidity of that cargo cult notation, he makes the stupid claim I highlighted below. What he wrote after that is even more stupid than the cargo cultism I quoted above. In particular, his yakking about the first fundamental form is stupid because his embeddings into R^{2} are arbitrary, with no motivation apart from his twin goals of (1) fooling himself and (2) thinking he can look smart by yakking about things he doesn't understand—which is of course just a special case of (1). 
Last edited by W.D.Clinger; 29th May 2023 at 07:48 PM. Reason: corrected the quotation to which Ziggurat was responding, etc 

29th May 2023, 08:51 PM  #60 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th May 2023, 09:41 PM  #61 
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H^{1} isn't just homeomorphic to R^{1}. It's diffeomorphic.
Which means the relationship between H^{1} and R^{1} is essentially the same as the relationship between R^{1} and R^{1}. Which means it is outstandingly stupid to pretend H^{1} differs from R^{1} in any way that could possibly be meaningful for physics. ETA:
Originally Posted by Wikipedia

29th May 2023, 10:14 PM  #62 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th May 2023, 11:38 PM  #63 
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More wrong guesses...but who can pass up an opportunity to talk about the philosophy of Friedrich Nietzsche?
That is not why S^{1} isn't homeomorphic to R^{1}. As you have been told, repeatedly, S^{1} has no intrinsic curvature. That's why a cylinder has no intrinsic curvature. One can, for example, construct a perfectly flat spacetime manifold homeomorphic to S^{1} × R^{3} whose metric tensor field is the Minkowski metric. That spacetime is cylindrical. The fact that its curvature is zero follows immediately from the fact that its metric tensor is the Minkowski metric. Unlike Minkowski spacetime, which can be covered by a single chart (e.g. the standard Minkowski coordinates), every atlas for that cylindrical manifold will have at least two charts. The reason for that twochart minimum is essentially the same reason that S^{1} is not homeomorphic to R^{1}. That particular cylindrical manifold is probably the simplest spacetime manifold one can use to prove that time travel is compatible with relativity. Nietzsche would have hated it. 
30th May 2023, 06:31 AM  #64 
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Ok, Mike, so here's another way to think about how completely wrong you are here. Let's suppose that there's some sort of "true" time that our universe is embedded in, and our experienced time speeds up relative to this "true" time.
Would that produce red shifts? No, it would obviously not. Why not? Because that wouldn't change wavelengths. Let's take a snapshot of our universe just after our photon is emitted from point A to later be received at point B. That photon is not a point particle. It is spread out over space. It has a wavelength that can be determined by examining how the electric field at that moment in time varies with position. Let's call that wavelength x. OK, now let's play this scenario forward in time. We can track the peak of one crest and the peak of the next crest, which start out at a distance of x from each other. As time advances, what happens to those two peaks? Well, if space is homogeneous and unchanging, then it doesn't matter what happens to time: they're going to travel the same distance, so they will remain separated by the same distance x. The wavelength cannot change. What you do to time has no effect on wavelength. And if it has no effect on wavelength, how can it change frequency? It can't, unless the speed of light is varying too. But you haven't made the claim that the speed of light changes. So no matter what you do to your time coordinate, you can't get a red shift. 
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30th May 2023, 06:48 AM  #65 
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Ok. It seemed relevant.
Just so I understand... on a circle 0, 2pi, 4pi... map to (1,0). That does exclude it from being homeomorphic, correct? Is there a more significant criteria you have in mind?
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But even with one point of curvature, it will still circle back on itself. (ETA, "point" being a poor choice of words here. Plane? )
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

30th May 2023, 07:34 AM  #66 
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What you do to time effects period, which is the inverse of frequency, so that all seems alright to me.
The energy of a photon is E=hf. The photon's frequency is f=1/t. According to an observer, that's the frequency and energy. Since it's speed is c(1+z)^{1}, and every observer is at z=0, light will always be observed at c, with a frequency determined by a local clock, and a wavelength of w = c / f. That's the hypothesis anyways. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

30th May 2023, 11:03 AM  #67 
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Not in the way you assume.
Quote:
How are you changing the wavelength? You aren't. It can't change. It's conserved. 
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"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

30th May 2023, 12:33 PM  #68 
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We've talked about this before. Are wavelength and frequency "equally real", to use an unfortunate choice of words, so take that loosely.
Frequency is directly related to energy. If you had a laser beam with variable energy, ideally continuous down to zero, as you turn it off, you would be producing photon's whose calculated wavelength would eventually be larger than the observable universe. The "ground" floor of frequency and energy is zero. For wavelength it is infinity big. It would be reasonable to conclude (out of ignorance and of convenience to the hypothesis) frequency and energy are "closer" to the physical reality than wavelength. But let's forget that, and try for less of a copout answer. I've referenced this before, Edwin Hubble in 1937:
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What I'm describing is I think a third option, revealing such concerns to be a false dilemma. Here is the fundamental physical assumption challenged by the hypothesis. Let's imagine a Mario Kart driver traveling in straight line at a constant speed laying down green turtle shells at a consistent interval. From the frame of reference of the kart, it will be at reset, and it will look like it is shooting the shells backwards at a consistent rate, and the shells will move at a constant speed away from the kart. Assumption: that's how time works. A stationary clock in spacetime will tick away, and each event will flow neatly into the past. The evidence suggests that's not how time works. Hypothesis: that's not how time works. Place our gokart driver on a circular track. As it starts shooting shells out its back (from its frame of reference) eventually those shells come back to it. Were we standing at the middle of the track, we would see the kart dropping shells and them circling around back to them. The hypothesis says it works something more like the following. You are an observer standing at 0,0, and along the path of x^{2}  y^{2} = 1 is a conveyor belt, moving opposite of the yaxis. Our gokart driver as at (1, 0), facing the same direction as the yaxis. The gokart driver starts dropping shells, and they beginning moving away, along the hyperbola conveyor belt. Back at the origin we determine the position to each shell relative to us is cosh(t) in the xdirection, and sinh(t) in the ydirection. That's the hypothesis, and we've found that we could debate that on and on. Let's just use that for context. So, frequency, speed, wavelength, period, energy, what does the hypothesis actually say is changing and where. Expanding space and tired light have one thing in common, the photon either gets an elongated wavelength during its journey because space expands then, or some thing else lowers its frequency (energy) on the journey. In both cases, it's all in the journey from the past to the present. To a look at this again: An important thing to note is that all the photons on the right still encounter the present (t=0) at a 45 degree angle. And all the photons in the past that leave the yaxis in a timelike path, well, back if you reverse time to back to closer to when they were emitted, they are at a 45 degree angle. This is all a round about way of saing, the photon never loses energy during its journey from the past to the present. It is always in the present, at t=0, moving horizontally along the xaxis. Due to its hyperbolic journey from the present to the past, it loses frequency, and thus energy. The light cone of an observer, say at x=7 billion light years away in that diagram intersects the yaxis at 10 billion years. That's when the the photon emitted at x=0 will reach the observer at x=7 Gly. Within the light cone of the observer, the photon never actually loses energy or frequency. This hypothesis is like an "antitired light" model. You see, according to the distant observer, the light actually starts out moving slowly (timelike), because it's now being measured by a clock from its future. The light gains speed and reaches c just before it hits the present. Assuming energy is conserved through the photon's existence in the observer's light cone, that means its wavelength must have started out small and grew until being observed. So where does the energy go? It is lost in the journey from the present to the past, where it intercepts an observer's light cone. The journey from the present to the past is uneven because time is "hyperbolic". That's what the hypothesis seems to suggest, anyways. See signature. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

30th May 2023, 01:10 PM  #69 
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Keep it going at any cost. When shown to be talking arrant nonsense, wait 48 hours and just repeat the gibberish. Not worth a substantive reply anymore.

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30th May 2023, 01:27 PM  #70 
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Hubble didn't consider your third option because your option is so stupid it's not worth considering. Seriously, your idea makes no sense, it doesn't work, it wouldn't produce red shifts.
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No, that's NOT how time works. Events are not objects. The analogy makes no sense.
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It should be obvious how expanding space can expand the wavelength without scattering. How does your model expand the wavelength?
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Oops.
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"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

30th May 2023, 01:55 PM  #71 
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I admit, it's pretty strange.
Instead of us moving into the future and encountering new things, this is more like new things happen, and it pushes the other things into the past. Could we tell by experiment whether we are moving into the future, or the past is moving away from us? Seems equivalent. Maybe if you were in a closed room, there would be no way of telling. Since we can look deep into the past, we see its dilated, so maybe we aren't moving into the future, the past is moving away from the present, and not linearly. In a sense, an event, of maybe just information about the event, has an "inertia" of its own, and follows a curved (not Gaussian) path. Can information have inertia? You wanna hear a really stupid idea? https://www.newscientist.com/article...offorgetting/
Quote:

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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

30th May 2023, 04:12 PM  #72 
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You don't learn anything, do you? You still confuse the map for the territory. A coordinate singularity is not a real singularity. It is an artifact of your choice of coordinates, nothing more. Pick different coordinates, and there is no singularity. The origin of the Euclidean plane is a coordinate singularity in polar coordinates, but not in Cartesian coordinates. Nothing special happens there.
So no, a coordinate singularity won't generate heat. That's just stupid. 
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30th May 2023, 06:53 PM  #73 
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In the expanding space model there is a big bang singularity at the same time, where the whole universe began.
You must be hard to buy presents for. In the expanding time model, that's just the limit of an observer's light cone. One tells the story of everything. The other tells the story of what can be observed. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

31st May 2023, 05:38 AM  #74 
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You still don't understand the difference between a coordinate singularity and a geometric singularity? After all this?
No, at this point it's my fault for expecting any better.
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"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

31st May 2023, 10:13 AM  #75 
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You said nothing special happened ~14 billion years ago.
It was a joke. Look, maybe the universe is expanding, maybe it started with a big bang, maybe at the beginning it hyperexpanded, and maybe we know how the universe actually began. Maybe that's all completely wrong. I'm keeping an open mind. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

31st May 2023, 10:16 AM  #76 
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"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

31st May 2023, 10:36 AM  #77 
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Well, the expanding model is the main model right now. And it tells us how everything began, which is among the oldest recorded questions humans ever asked. So that's cool.
If it's wrong, what then? Is there a backup? I've got a couple ideas. Strange, wild, nonsensical ideas. But it's an interesting question to me. Every culture devises a Genesis of sorts. The one I was taught as a child involves the Big Bang. Perhaps our version is the exception. Perhaps, we are actually right? Doesn't seem likely, when you look at it objectively.
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We can get that geometrically by replacing expanding space with expanding time. "Pure nonsense!" As you can tell, I'm not particularly daunted by insults. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

31st May 2023, 10:44 AM  #78 
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31st May 2023, 10:46 AM  #79 
Illuminator
Join Date: Nov 2020
Posts: 4,240


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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

31st May 2023, 10:55 AM  #80 
Ovis ex Machina
Join Date: Jan 2006
Location: Sir Ddinbych
Posts: 6,986


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I’d rather be a rising ape than a falling angel.  Sir Terry Pratchett 

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