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Old 26th May 2023, 11:16 AM   #41
Ziggurat
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Originally Posted by Mike Helland View Post
And the clock next to the prism clicks slower too.
I'm reminded of a line from Professor Farnsworth about the density of dark matter: "each pound of it weighs over ten thousand pounds."

Evidently one second can take longer than one second.
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Old 26th May 2023, 12:42 PM   #42
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Originally Posted by Mike Helland View Post
Let's say we have an RGB LED, and a prism, and a detector calibrated to detect a yellow photon.

When the RGB's light goes through the prism, it will only be broken into red, blue, and green, because that's all that's going on. Let's consider one photon of each. The red photon will be photon 1, green is 2 and blue is 3.

When the detector is close by, it won't go off. There are no yellow photons.

If you move the detector father and farther away, eventually it will go off, because photon 2 (green) will have redshifted to yellow.

The prism hasn't done anything different though.

I'm not sure where the inconsistency is.
Will the angle of refraction observed be consistent with the prism's refractive index for green light, or for yellow light?
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Old 26th May 2023, 02:39 PM   #43
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Originally Posted by Reformed Offlian View Post
Will the angle of refraction observed be consistent with the prism's refractive index for green light, or for yellow light?
Green.
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Old 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 1-dimensional "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 (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

Quote:


Here a, b describe the indices of coordinates ξa of the submanifold while the functions Xμ ( ξ a ) encode the embedding into the higher-dimensional manifold whose tangent indices are denoted μ , ν .
Well, the metric at the end is the Euclidean metric, so that's simple. a and b will both be 0, since we only have a g00.

So what's needed is Xμ and Xν. 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 half-plane". 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 = ex. So... I think that resolves that quite nicely.
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Last edited by Mike Helland; 28th May 2023 at 09:40 PM.
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Old 28th May 2023, 10:32 PM   #45
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ackamarackus

Originally Posted by Mike Helland View Post
https://en.wikipedia.org/wiki/Induced_metric

Quote:


Here a, b describe the indices of coordinates ξa of the submanifold while the functions Xμ ( ξ a ) encode the embedding into the higher-dimensional manifold whose tangent indices are denoted μ , ν .
Well, the metric at the end is the Euclidean metric, so that's simple. a and b will both be 0, since we only have a g00.

So what's needed is Xμ and Xν. 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:
No.
Evidently the author and sole proponent of Helland physics doesn't understand the equation he copy-pasted from Wikipedia. Or maybe he just has no clue as to what the gμν are.

Originally Posted by Mike Helland View Post
Which is:
Or:
No. No.
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Old 28th May 2023, 10:57 PM   #46
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Originally Posted by W.D.Clinger View Post
No.
Evidently the author and sole proponent of Helland physics doesn't understand the equation he copy-pasted from Wikipedia. Or maybe he just has no clue as to what the gμν are.
It's the Euclidean metric. So I forgot to cancel out those off diagonal terms.
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Old 29th May 2023, 07:19 AM   #47
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Originally Posted by Mike Helland View Post
It's the Euclidean metric. So I forgot to cancel out those off diagonal terms.
That is the second of the two mistakes he made when calculating the induced gtt for the embedded circle satisfying x2 + y2 = r2.
His first mistake was forgetting about r here:
Originally Posted by Mike Helland View Post
So what's needed is Xμ and Xν. In other words, an f(d)=x, and g(d)=y?
When the equation he copied from Wikipedia is applied correctly, you get the right answer:
gtt = r2
His third mistake lay in failing to check his work by calculating a distance Δt along the circle from angles t1 to t2. When done correctly:
ds2 = gtt dt2 = r2 dt2
so
ds = r dt
and
Δt = ∫t1t2 r dt = r (t2 − t1)
That arc length is the correct answer. It is not the answer you get when you calculate using an incorrect value for gtt.

He repeated his gμν mistake with the unit hyperbola x2 − y2 = 1, but did not give himself an opportunity to repeat the mistake of dropping r because he used the unit hyperbola.

Originally Posted by Mike Helland View Post
How about the opposite.

In 2d space, instead of a circle, draw a hyperbola, .
https://mikehelland.github.io/hubble...ehyperbola.png
Pretty much everything else applies, except that you end up with:

Parameterizing that hyperbola by x = cosh t and y = sinh t, the correct value of gtt is
gtt = ∂tXμtXν gμν
= (∂t (cosh t))2 + (∂t (sinh t))2
= (sinh t)2 + (cosh t)2
= cosh (2t)
= (e2t + e−2t) / 2
Originally Posted by Mike Helland View Post
How cool is that?
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 gtt are not cool.
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Old 29th May 2023, 07:50 AM   #48
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Originally Posted by W.D.Clinger View Post
That is the second of the two mistakes he made when calculating the induced gtt for the embedded circle satisfying x2 + y2 = r2.
His first mistake was forgetting about r here:
When the equation he copied from Wikipedia is applied correctly, you get the right answer:
gtt = r2
His third mistake lay in failing to check his work by calculating a distance Δt along the circle from angles t1 to t2. When done correctly:
ds2 = gtt dt2 = r2 dt2
so
ds = r dt
and
Δt = ∫t1t2 r dt = r (t2 − t1)
That arc length is the correct answer. It is not the answer you get when you calculate using an incorrect value for gtt.

He repeated his gμν mistake with the unit hyperbola x2 − y2 = 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 gtt is
gtt = ∂tXμtXν gμν
= (∂t (cosh t))2 + (∂t (sinh t))2
= (sinh t)2 + (cosh t)2
= cosh (2t)
= (e2t + e−2t) / 2

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 gtt are not cool.
Thanks for the corrections.

The fact remains that these geometries of time seem to cause blueshift and redshift. So that's progress.
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Old 29th May 2023, 08:03 AM   #49
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Originally Posted by Mike Helland View Post
Thanks for the corrections.

The fact remains that these geometries of time seem to cause blueshift and redshift. So that's progress.
Could you just recap on what it is you think it is progress towards?
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Old 29th May 2023, 08:17 AM   #50
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Originally Posted by zooterkin View Post
Could you just recap on what it is you think it is progress towards?
Keeping the thread going?
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Old 29th May 2023, 08:42 AM   #51
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Originally Posted by Mike Helland View Post
The fact remains that these geometries of time seem to cause blueshift and redshift.
No.

Originally Posted by Mike Helland View Post
So that's progress.
No.
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Old 29th May 2023, 09:04 AM   #52
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Originally Posted by W.D.Clinger View Post
No.
Why is that now? Am I confusing the territory for the map now?
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Old 29th May 2023, 09:38 AM   #53
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Originally Posted by W.D.Clinger View Post
That arc length is the correct answer. It is not the answer you get when you calculate using an incorrect value for gtt.
The arc length is what you started with though.

If you input the arc length, and get out the arc length, then what happened to the distance in (x, y)?

Your answer seems to just map arc length to arc length.
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Old 29th May 2023, 01:11 PM   #54
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Originally Posted by zooterkin View Post
Could you just recap on what it is you think it is progress towards?
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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Old 29th May 2023, 02:00 PM   #55
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Originally Posted by Mike Helland View Post
In that case, a time coordinate transformation would account for both.
Still confusing the map for the territory. I wonder how many years that will continue for.

Quote:
I say, transforming the map so it accurately represents reality is a good thing.
That's not how it works. If the map is a map of reality, then it's accurate. Transforming it will not change its accuracy. Conversely, if it's not a map of reality, it's not accurate, and transforming it cannot make it accurate.

Quote:
The criticism is that changing coordinates isn't good enough. There should be some underlying geometrical reason for that.
Yes. And it's a very simple and obvious reason: transformations change the map, not the territory. Geometry is a property of the territory, not of the map.

Quote:
The solution is to give time some curvature, as a hyperbolic surface. That does the trick.
Coordinate transformations cannot create curvature. You're just spewing words hoping something will stick. You have no idea what any of this actually means.
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Old 29th May 2023, 03:16 PM   #56
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Originally Posted by Ziggurat View Post
Coordinate transformations cannot create curvature.
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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Old 29th May 2023, 04:42 PM   #57
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Originally Posted by Mike Helland View Post
Am I entirely sure what I'm talking about? No.
That's an understatement. You're talking complete nonsense.
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Old 29th May 2023, 05:41 PM   #58
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Originally Posted by Ziggurat View Post
That's an understatement. You're talking complete nonsense.
Here are the premises:

* Time can be flat, positively curved, or negatively curved

* Negatively curved time can be represented as the 1-d surface of a hyperbola in 2-d 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 2-d space ().

Are these a problem?
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Old 29th May 2023, 06:44 PM   #59
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It seems Helland physics is vying to replace Time Cube.

Originally Posted by W.D.Clinger View Post
Originally Posted by Mike Helland View Post
The fact remains that these geometries of time seem to cause blueshift and redshift.
No.
Originally Posted by Mike Helland View Post
Why is that now? Am I confusing the territory for the map now?
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 non-fact, and will forever remain a non-fact.

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.

Originally Posted by W.D.Clinger View Post
When the equation he copied from Wikipedia is applied correctly, you get the right answer:
gtt = r2
His third mistake lay in failing to check his work by calculating a distance Δt along the circle from angles t1 to t2. When done correctly:
ds2 = gtt dt2 = r2 dt2
so
ds = r dt
and
Δt = ∫t1t2 r dt = r (t2 − t1)
That arc length is the correct answer. It is not the answer you get when you calculate using an incorrect value for gtt.
Originally Posted by Mike Helland View Post
The arc length is what you started with though.

If you input the arc length, and get out the arc length, then what happened to the distance in (x, y)?

Your answer seems to just map arc length to arc length.
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 gμν 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 cos φ
y = φ sin φ
For each natural number n, let pn be the point on that spiral with Cartesian coordinates ((2π n), 0). As n increases without bound, the R2 distance between pn and pn+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
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).
With his customary sloppiness, he defined Xx (which he renamed to f(d)) to be x, and he defined Xy (which he renamed to g(d)) to be y. The only way to reconcile his definitions of Xx and Xy with his equation for the circle was to assume he dropped the r from his definitions of Xx and Xy.

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 gtt = r2.

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 gtt = 1. With that metric form, the sentences I highlighted in blue would be true.

But those sentences are clearly false for gtt = r2, 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 gtt = 1 and gtt = r2 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.

Originally Posted by Mike Helland View Post
The solution is to give time some curvature, as a hyperbolic surface. That does the trick.
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 1-dimensional curve. Such curves can have extrinsic curvature when embedded within some manifold of higher dimension, but 1-dimensional 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 1-sphere S1 and for the real line R1 is that those 1-dimensional 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 H1 for a topological space that is homeomorphic to R1. To emphasize the stupidity of that cargo cult notation, he makes the stupid claim I highlighted below.

Originally Posted by Mike Helland View Post
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.

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 R2 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).

Originally Posted by Mike Helland View Post
Am I entirely sure what I'm talking about? No.
Originally Posted by Ziggurat View Post
That's an understatement. You're talking complete nonsense.

Last edited by W.D.Clinger; 29th May 2023 at 07:48 PM. Reason: corrected the quotation to which Ziggurat was responding, etc
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Old 29th May 2023, 08:51 PM   #60
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Originally Posted by W.D.Clinger View Post
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 gtt = 1.
"the distance between the observer and an event along the circle will be rθ", "Assuming the d is actually the distance along the curve"...

Quote:
Mike Helland, mindlessly aping notation he doesn't understand, is trying to look smart by inventing a notation H1 for a topological space that is homeomorphic to R1. To emphasize the stupidity of that cargo cult notation, he makes the stupid claim I highlighted below.
So 2 or 3, or 10 or 20 dimensions can be curved, but not 1?

Why would it matter?
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Old 29th May 2023, 09:41 PM   #61
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Originally Posted by Mike Helland View Post
Quote:
Mike Helland, mindlessly aping notation he doesn't understand, is trying to look smart by inventing a notation H1 for a topological space that is homeomorphic to R1. To emphasize the stupidity of that cargo cult notation, he makes the stupid claim I highlighted below.
So 2 or 3, or 10 or 20 dimensions can be curved, but not 1?

Why would it matter?
H1 isn't just homeomorphic to R1. It's diffeomorphic.

Which means the relationship between H1 and R1 is essentially the same as the relationship between R1 and R1.

Which means it is outstandingly stupid to pretend H1 differs from R1 in any way that could possibly be meaningful for physics.
Which explains, in a way, why Mike Helland is pretending H1 differs from R1 in a way that has implications for physics.

ETA:
Originally Posted by Wikipedia
In dimensions 1, 2 and 3, any pair of homeomorphic smooth manifolds are diffeomorphic.

Last edited by W.D.Clinger; 29th May 2023 at 09:48 PM. Reason: added ETA
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Old 29th May 2023, 10:14 PM   #62
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Originally Posted by W.D.Clinger View Post
H1 isn't just homeomorphic to R1. It's diffeomorphic.

Which means the relationship between H1 and R1 is essentially the same as the relationship between R1 and R1.

Which means it is outstandingly stupid to pretend H1 differs from R1 in any way that could possibly be meaningful for physics.
Which explains, in a way, why Mike Helland is pretending H1 differs from R1 in a way that has implications for physics.

ETA:
Well, I see your point.

isn't homeomorphic to , because it's many-to-one, for one thing. So the two are distinguishable.

So what about ? A time dimension with positive curvature? That'll work, right?
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Old 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?
Frankly, I'd rather talk about the philosophy of Ray Nitschke, but I must reluctantly admit that Nietzsche is more relevant to this thread.
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On the Packers' practice field on September 1 [1960], a 1,000-pound (450 kg) steel coaching tower was blown over by a strong gust of wind, on top of Nitschke. [Packers coach] Lombardi ran over to see what had happened, but when told it had fallen on Nitschke, said, "He'll be fine. Get back to work!" According to Nitschke's biography, a spike was driven into his helmet, but did not injure him. The helmet (with the hole) is currently on display in the Packer Hall of Fame in Green Bay.

Originally Posted by Mike Helland View Post
isn't homeomorphic to , because it's many-to-one, for one thing.
That is not why S1 isn't homeomorphic to R1.

Originally Posted by Mike Helland View Post
So what about ? A time dimension with positive curvature? That'll work, right?
As you have been told, repeatedly, S1 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 S1 R3 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 two-chart minimum is essentially the same reason that S1 is not homeomorphic to R1.

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.

Last edited by W.D.Clinger; 29th May 2023 at 11:42 PM. Reason: one misspelling of Nietzsche
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Old 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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Old 30th May 2023, 06:48 AM   #65
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Originally Posted by W.D.Clinger View Post
That is not why S1 isn't homeomorphic to R1.
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?

Quote:
As you have been told, repeatedly, S1 has no intrinsic curvature. That's why a cylinder has no intrinsic curvature.
I understand. I think.

Quote:
If both principal curvatures are of the same sign: κ1κ2 > 0, then the Gaussian curvature is positive and the surface is said to have an elliptic point. At such points, the surface will be dome like, locally lying on one side of its tangent plane. All sectional curvatures will have the same sign.

If the principal curvatures have different signs: κ1κ2 < 0, then the Gaussian curvature is negative and the surface is said to have a hyperbolic or saddle point.
Having only one point of curvature means there is no Gaussian curvature.

But even with one point of curvature, it will still circle back on itself.

(ETA, "point" being a poor choice of words here. Plane? )

Quote:
That particular cylindrical manifold is probably the simplest spacetime manifold one can use to prove that time travel is compatible with relativity.
Well, time dilation is an observed phenomena, so that's probably more important than time travel.
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Last edited by Mike Helland; 30th May 2023 at 07:56 AM.
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Old 30th May 2023, 07:34 AM   #66
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Originally Posted by Ziggurat View Post
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?
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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Old 30th May 2023, 11:03 AM   #67
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Originally Posted by Mike Helland View Post
What you do to time effects period
Not in the way you assume.

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light will always be observed at c, with a frequency determined by a local clock, and a wavelength of w = c / f.
The frequency is determined by the wavelength just as much as the wavelength is determined by the frequency. If the wavelength is conserved, then so is the frequency.

How are you changing the wavelength? You aren't. It can't change. It's conserved.
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Old 30th May 2023, 12:33 PM   #68
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Originally Posted by Ziggurat View Post
Not in the way you assume.

The frequency is determined by the wavelength just as much as the wavelength is determined by the frequency. If the wavelength is conserved, then so is the frequency.

How are you changing the wavelength? You aren't. It can't change. It's conserved.
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 cop-out answer.

I've referenced this before, Edwin Hubble in 1937:

Quote:
If the primary change is in the wave-length, then red-shifts are probably velocity-shifts. But the primary change might possibly be a loss of energy, which we would observe as a red-shift. In the latter case the law of red-shifts would be fully described by the simple statement that light loses energy in proportion to the distance it travels through space.
He seems to be weighing between expanding space and tired light.

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 go-kart 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 x2 - y2 = 1 is a conveyor belt, moving opposite of the y-axis.

Our go-kart driver as at (1, 0), facing the same direction as the y-axis.

The go-kart 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 x-direction, and sinh(t) in the y-direction.

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 y-axis in a time-like 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 x-axis.

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 y-axis 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 "anti-tired light" model. You see, according to the distant observer, the light actually starts out moving slowly (time-like), 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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Old 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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Old 30th May 2023, 01:27 PM   #70
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Originally Posted by Mike Helland View Post
He seems to be weighing between expanding space and tired light.

What I'm describing is I think a third option, revealing such concerns to be a false dilemma.
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.

Quote:
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.
God damn, but that's retarded.

No, that's NOT how time works. Events are not objects. The analogy makes no sense.

Quote:
The evidence suggests that's not how time works.
Of course time doesn't work that way. But what on God's green earth made you think that anyone else thought time works that way? What on God's green earth made you think that physics is modeled as if time worked that way?

Quote:
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.
Tired light can only expand the wavelength by scattering it, which we observe doesn't happen. Absent scattering, no expansion can happen because of self-interference.

It should be obvious how expanding space can expand the wavelength without scattering.

How does your model expand the wavelength?

Quote:
To a look at this again:
Huh. Your wavelength never changed. That means frequency didn't change either.

Oops.

Quote:
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.
Here's the kicker: energy conservation only applies when the laws of physics are time invariant. You're explicitly trying to make the laws of physics time-dependent. Energy conservation need not apply.

Quote:
That's what the hypothesis seems to suggest, anyways. See signature.
Except it doesn't. You're so bad at physics, you can't understand it even when you make it up yourself.
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Old 30th May 2023, 01:55 PM   #71
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Originally Posted by Ziggurat View Post
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.
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...of-forgetting/

Quote:
In 1961, Rolf Landauer proposed that the key to the conundrum was the demons memory. As the creature gathers information on the motion of molecules, it must erase a previous memory. Landauer suggested that the process of erasure dissipates heat. This expended heat could balance out the useful work gained by the demon and ensure it does not, in fact, get something for nothing.

Not everyone agreed with this explanation. Now Eric Lutz of the University of Augsburg in Germany and colleagues have shown that there is indeed a minimum amount of heat produced per bit of erased data.
In the TDP hypothesis, there's that coordinate singularly, where time gets forgotten. That should generate some heat, I would think...
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Old 30th May 2023, 04:12 PM   #72
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Originally Posted by Mike Helland View Post
In the TDP hypothesis, there's that coordinate singularly, where time gets forgotten. That should generate some heat, I would think...
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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Old 30th May 2023, 06:53 PM   #73
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Originally Posted by Ziggurat View Post
Nothing special happens there.
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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Old 31st May 2023, 05:38 AM   #74
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Originally Posted by Mike Helland View Post
In the expanding space model there is a big bang singularity at the same time, where the whole universe began.
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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You must be hard to buy presents for.
Not in the least. You're just wrapping up dog **** and calling it chocolate. Nobody likes that.
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Old 31st May 2023, 10:13 AM   #75
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Originally Posted by Ziggurat View Post
You still don't understand the difference between a coordinate singularity and a geometric singularity?
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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Old 31st May 2023, 10:16 AM   #76
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Originally Posted by Mike Helland View Post
You said nothing special happened ~14 billion years ago.
Nothing special happens in YOUR model where there's a coordinate singularity.

Quote:
I'm keeping an open mind.
That's not a virtue when you're dumping garbage into it.
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Old 31st May 2023, 10:36 AM   #77
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Originally Posted by Ziggurat View Post
Nothing special happens in YOUR model where there's a coordinate singularity.
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.



Quote:
That's not a virtue when you're dumping garbage into it.
Well, I started with a formula, and that made an algorithm, which made an integral, simplifies to a logarithm, and that predicts the data better than LCDM.

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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Old 31st May 2023, 10:44 AM   #78
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Originally Posted by Mike Helland View Post
Well, I started with a formula, and that made an algorithm, which made an integral, simplifies to a logarithm, and that predicts the data better than LCDM.
I find it interesting, from a psychological point of view, that you still consider this to be true.
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Old 31st May 2023, 10:46 AM   #79
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Originally Posted by Mashuna View Post
I find it interesting, from a psychological point of view, that you still consider this to be true.
It's what you get when you take the sum of squared errors, :



The lower the number, the better the fit. The hypothesis fits the data better than LCDM.

LCDM's own best fit misses its projected value of 67.5 km/s/Mpc by a good margin.
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Old 31st May 2023, 10:55 AM   #80
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Originally Posted by Mike Helland View Post
It's what you get when you take the sum of squared errors, :

https://mikehelland.github.io/hubbles-law/img/sse.png

The lower the number, the better the fit. The hypothesis fits the data better than LCDM.

LCDM's own best fit misses its projected value of 67.5 km/s/Mpc by a good margin.
Do you remember the previous sixteen hundred posts explaining in great detail where your misunderstandings are? I think youre going to have to change your sig at this point.
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