[Merged] Why the James Webb Telescope rewrites/doesn't the laws of Physics/Redshifts - Page 36

Mike Helland · 29th March 2023, 06:19 PM

Originally Posted by W.D.Clinger

Helland physics has given us an entirely new way to misunderstand the universe.

I'm ok with that.

If it's perfectly reasonable to adjust the space coefficients based on the time coordinate:

$g_{\mu\nu}=\begin{pmatrix} -1&0&0&0\\ 0&\frac{a^2}{1-kr^2}&0&0\\ 0&0&a^2r^2&0\\ 0&0&0&a^2r^2\sin^2\theta \end{pmatrix}$

Then it should be acceptable to make the time coefficient based on the space coordinates.

W.D.Clinger · 29th March 2023, 06:56 PM

Details matter.

Tom Knight was one of the lead designers of the MIT Lisp Machines. This story says a lot about the previous post.

A novice was trying to fix a broken Lisp machine by turning the power off and on.

Knight, seeing what the student was doing, spoke sternly: “You cannot fix a machine by just power-cycling it with no understanding of what is going wrong.”

Knight turned the machine off and on.

The machine worked.

Mashuna · 30th March 2023, 06:19 AM

Originally Posted by hecd2

You replied to me in three minutes. You're not stopping to think. No-one apart from you believes that the paradox is anything other than irresolvable. The only thing you have to measure time on is your clock at A, and the round trips of two pulses are different according to that clock. There is no way round that. I'm not starting this again. You can carry on thinking you've resolved it and everyone who knows what they're talking about, including the referee when you submit the embarassing "paper" that you will no doubt write, will tell you the same thing, and you still won't believe them, like you didn't believe the referee on your last "paper". It's a waste of everyone's time.

Originally Posted by Mike Helland

Sure. And in my model, photon 2 arrives late and photon 1 takes off early.

Changing where you start to count does not fix the paradox. It's like adding an extra flywheel to your perpetual motion machine.

Ziggurat · 30th March 2023, 08:57 AM

Originally Posted by Mike Helland

You said "you" thirteen times in seven sentences.

To paraphrase from here:
https://despair.com/products/dysfunction
The only consistent feature in all your failed theories is you. That's why I'm emphasizing you. The details of an individual failure are pretty secondary, far more significant is the consistent cause of those failures, and that's you. So you deserve attention, because that's the only possible source for a fix to any of this. Not tweaking your theory with yet another revision, but a fundamental change in how you approach everything. You need to start by learning, and not in this half-assed way you're currently doing it.

Quote:

I've always done calculus problems with a computer program and a lot of trial and error. I know that's severely limiting. (No pun intended.) But it usually gets the right enough answers.

I just don't understand why it won't fly.

Quote:

And based on your feedback over the last couple years, I have revisited calculus, to try to express it in the calculus way, but obviously not well enough. I went over linear algebra too, and a couple other things.

Indeed, it's not enough. Not close to enough. There's a reason people spend year and years just learning this stuff, before they even try to do something new.

Quote:

You were also the one that said photons can't lose frequency without clocks desynchronizing, which is why we're talking about dynamic time in the first place.

I did indeed say that, and it is indeed true. But you seem to think that desynchronizing clocks is some trivial thing. It's not. It is no small feat to develop a new theory of desynchronization in a manner that is self-consistent, let alone in a manner that is consistent with observations. The parts need to connect to make a self-consistent whole, and you're not doing that. It is beyond you. Hell, it's beyond me too. The difference is that I know I'm not up to the task, despite knowing far more math and physics than you. For some reason, and despite all evidence to the contrary, you think you are. You are not.

Quote:

Regarding the first, one example was the flight time paradox, I think that's resolved:

No, it isn't resolved. You've got hand waving nonsense about dynamic time that doesn't actually make any sense. You have no coherent picture of what your dynamic time actually is, or what it actually does.

Quote:

As far as expressing it in the framework of relativity, I don't think I'm that far off in thinking that could be in the form of a metric tensor that reduces to the Minkowski metric at less than cosmological scales. And that it makes a "v" look like a "u".

You seem to think that means something. It doesn't.

hecd2 · 30th March 2023, 09:07 AM

Originally Posted by Mike Helland

I'm ok with that.

If it's perfectly reasonable to adjust the space coefficients based on the time coordinate:

https://math-demo.abitti.fi/math.svg...d%7Bpmatrix%7D

Then it should be acceptable to make the time coefficient based on the space coordinates.

The Robertson-Walker metric is for an isotropic homogeneous Universe. In such a Universe, time passes at the same rate at all locations. You can write a 3 dimensional spatial metric for a given time which describes the intrinsic curvature and other properties, such as distances between points and angles between lines which are invariant under coordinate transformations.

If the rate of time is a function of location then the Universe is no longer homogeneous. But the Universe appears to us to be the same in all directions. The only way that can be is if the non-homogeneous Universe is spherically symmetric with us at its centre. That would make you a geocentrist. Is that what you arguing for?

Mike Helland · 30th March 2023, 09:54 AM

Originally Posted by Mashuna

Changing where you start to count does not fix the paradox.

That's not quite what I'm suggesting.

Time dilation makes durations longer. Whether that duration extends to the future, or the past, shouldn't make a difference.

Mike Helland · 1st April 2023, 01:28 PM

Originally Posted by W.D.Clinger

\
\According to the theory of relativity, light follows null geodesics. Analyzing Mike Helland's two guesses at a metric, that means light travels slower (according to his first guess) as x approaches the coordinate singularity than at x = 0 or negative values of x, or light travels faster (according to his second guess) as x approaches the coordinate singularity.

If dynamic time is something like:

$\begin{bmatrix} f(L)& 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\\end{bmatrix}$

Why do you say that changes the speed of light?

More importantly, why doesn't something similar happen when you stretch space:

$g_{\mu\nu}=\begin{pmatrix} -1&0&0&0\\ 0&\frac{a^2}{1-kr^2}&0&0\\ 0&0&a^2r^2&0\\ 0&0&0&a^2r^2\sin^2\theta \end{pmatrix}$

Mike Helland · 2nd April 2023, 12:16 AM

Originally Posted by Mike Helland

If dynamic time is something like:

https://latex.codecogs.com/png.image...\\end{bmatrix}

Why do you say that changes the speed of light?

More importantly, why doesn't something similar happen when you stretch space:

https://math-demo.abitti.fi/math.svg...A\end{pmatrix}

https://arxiv.org/abs/1804.10047

"At redshift z, the vacuum speed of light in comoving coordinates is a⁻¹c = (1 + z)c"

W.D.Clinger · 2nd April 2023, 01:39 AM

So I call these things Cargo Cult Science, because they follow all the apparent precepts and forms of scientific investigation, but they're missing something essential, because the planes don't land.

—Richard Feynman (1974 commencement address at Caltech)

Today is 2 April.

On 20 March, apropos of nothing, Mike Helland quoted the Minkowski metric he found online, and asked what happens to spacetime when g₀₀ (which he called the "t coordinate") isn't -1.
On 21 March, Mike Helland asked whether it was possible to put a variable in the g₀₀ component (which he called the "time coordinate") of the metric form. He asked this immediately after I had cited the Rindler metric form as an example of doing precisely that.
Later that day, he wrote "So in the manifold I'm thinking of, the spatial coordinates show up in the time coefficient. And so does the Hubble parameter."
On 23 March, Mike Helland explained why he had quoted the Minkowski metric form: Ziggurat and hecd2 had pointed out that his derivations violated relativity, and he thought he could fix that problem by quoting something he had found online that had something to do with relativity.
Later that day, he confirmed his cargo cult approach to science: "If the problem is that the model is not relativistic, then the solution is to make it relativistic....In a relativistic Helland physics, there is no scale factor for the size of space, but there is a time scale factor for the rate of clocks."
An hour later, he expressed his surprise upon being told there are non-FLRW models that define the Hubble parameter using the same scale factor that appears in FLRW models.
That afternoon, he described his idea as "you take a normal light cone, and warp the coordinates until it points straight up."
That bad idea came from his guess that Rindler coordinates had changed the spacetime manifold by doing something similar to the coordinates. He made that wrong guess even though I had explained to him that a mere change of coordinates has no effect upon the spacetime manifold. So I said the same thing again, in much greater detail.
But Mike Helland continued to conflate the map with the territory. The very next day, he posted a graph of t(x) = |x|. He had distorted that graph by using a non-linear vertical scale for no reason at all, as though he thought his ability to draw that distorted picture had any implications for science.
No one paid any immediate attention to that foolishness, so on the following day, 25 March, he asked me what I thought of his spacetime diagram. He went on to write: "It starts off with two lines that are perpendicular and end up nearing parallel. I suppose that means the manifold is the surface of a sphere (inside or outside)?"
I told him it just means "the buffoon who drew that picture used a nonlinear vertical scale for no good reason."
Mike Helland ignored that substantive response to his picture, but attempted a Gish Gallop involving the definition of "Gish Gallop".
On 27 March, Mike Helland announced the following principle of Helland physics: "Clocks always get faster in the direction the photon is traveling."
I asked him to clarify whether that means (1) clocks everywhere are always getting faster, or (2) clocks get faster only when a photon is traveling toward them.
It took only one day for Mike Helland to understand the question. He said it was (1).
hecd2 asked how you could tell clocks everywhere are continually running faster.
Mike Helland responded to that question by saying "Time dilation happens twice." As though to prove that nonsense, he again posted a variation of his distorted graph of t(x) = |x|.
Less than an hour later, he guessed that the spacetime shown in his distorted graph corresponds to a metric form with g₀₀ = – (1 – 0.0000756 * x).
Within half an hour of that hilarious wrong guess, he wrote "Or maybe that should -1 / (1 - 0.0000756 * x)." He went on to describe rolling a piece of paper into a tube, saying "This is "temporal curvature" rather than "spatial curvature", because the space dimension isn't curved, just the time dimension."
Apparently Mike Helland was unaware that rolling a piece of paper into a tube does not change its intrinsic curvature (so its metric form remains the same as for a flat piece of paper), and was also unaware that the mainstream concordance model also describes essentially flat space, with temporal curvature.
A mere 12 minutes later, Mike Helland responded to that fact by quoting the components of a metric form he found online, and asked whether the k that appears within that metric form is zero for a flat universe. (Odd that he had to ask. For several months now, he has been citing papers that explain that. I guess he doesn't actually read the papers he cites.)
Ziggurat reminded Mike Helland that his distorted graph is nothing more than a foolishly distorted picture of flat Minkowski spacetime. "This error has been pointed out to you before. There is no justifiable reason for you to continue to make it."
Less than half an hour later, Mike Helland responded to Ziggurat's reminder with this non-sequitur: "Take a 2d graph of y = abs(x), and project it onto a cylinder." He had to ask "Is that still Minkowski spacetime?"
When Mike Helland continued to post ignorant guesses about metric forms, several people pointed out that he simply does not know enough mathematics to discuss metric forms.
When Ziggurat pointed out that Mike Helland didn't know the difference between a coordinate singularity and a real singularity, Mike Helland said he had never heard of a coordinate singularity.
On 29 March, saying "Helland physics is cargo cult science," I supported that assertion by analyzing several recent examples.
Which brings us to this most recent example, quoted below.

Originally Posted by Mike Helland

If dynamic time is something like:

https://latex.codecogs.com/png.image...\\end{bmatrix}

Details matter.

That's why I analyzed two of Mike Helland's specific wrong guesses about a metric form for Helland physics, relying on Mike Helland's explicit description of his coordinates: His unit for the time coordinate is a million years, and his unit for spatial coordinates is a million light years.

My specific analyses of Mike Helland's two specific wrong guesses do not generalize to "something like" the highly abstracted metric form he wrote above.

Originally Posted by Mike Helland

Why do you say that changes the speed of light?

Because, knowing his specified coordinates, I know how to analyze Mike Helland's specific wrong guesses.

Originally Posted by Mike Helland

More importantly, why doesn't something similar happen when you stretch space:

https://math-demo.abitti.fi/math.svg...A\end{pmatrix}

Something does happen, but it would be a stretch to say it's something similar.

I'll be happy to explain this stuff to Mike Helland, after he learns the relevant mathematics.

For most people, it takes several years to learn enough calculus, linear algebra, topology, and differential geometry to understand general relativity and the variety of metric forms that describe various spacetime manifolds. Truth be told, most people never learn enough math to understand general relativity, so his own failure to understand doesn't make him special.

The first principle is that you must not fool yourself—and you are the easiest person to fool.

—Richard Feynman (1974 commencement address at Caltech)

Mike Helland · 2nd April 2023, 01:56 AM

Originally Posted by W.D.Clinger

Something does happen, but it would be a stretch to say it's something similar.

If the speed of light in comoving coordinates is c(1+z):

c < f_emit * w_emit * (1+z)

c < f_emit * w_obs

W.D.Clinger · 2nd April 2023, 02:34 AM

Originally Posted by Mike Helland

https://arxiv.org/abs/1804.10047

"At redshift z, the vacuum speed of light in comoving coordinates is a⁻¹c = (1 + z)c"

From that very same paper:

Quote:

The vacuum speed of light c is invariant...

To reconcile those two statements, Mike Helland will have to learn that the map is not the territory.

By the way, the equation

a⁻¹c = (1 + z)c

is an immediate consequence of the equation

a⁻¹ = (1 + z)

which is an immediate consequence of the mainstream equation

1 + z = a(t₀) / a(t₁)

(where t₁ is the time at which the redshifted photon was emitted, and t₀ is the present time) because a(t₀) = 1 by convention.

Originally Posted by Wojtak and Prada

The canonical redshift–scale factor relation, 1/a = 1 + z, is a key element in the standard Λ cold dark matter (ΛCDM) model of the big bang cosmology.

As that paper points out, 1/a = 1 + z is a consequence of FLRW models that describe an expanding universe, and does not necessarily hold in non-FLRW models.

In particular, Helland physics insists the universe is not expanding, which implies a(t₁) = 1, from which the equation quoted by Mike Helland implies z = 0. Helland physics is not based on an FLRW model, however, so Helland physics is not constrained by the equation Mike Helland quoted. It is of course completely unclear why Mike Helland quoted that equation, apart from his habit of randomly quoting things he finds online in the hope some readers will make the mistake of assuming his random quotations of real science somehow transform the cargo cult we refer to as Helland physics into real science.

For an example of that behavior, see what Mike Helland wrote a little more than half an hour ago.

Mike Helland · 2nd April 2023, 02:50 AM

Originally Posted by W.D.Clinger

It is of course completely unclear why Mike Helland quoted that equation

Seems pretty clear to me.

I asked if the FLRW metric meant that stretching space resulted in a faster speed of light.

Seems like it does.

v = c(1+z)

1+z = v / c

We also know v > c, so v = c + v₂, where v₂ > 0.

That seems to be copacetic with relativity, so my derivation should be ok with it too.

The metric I'm suggesting simply changes the rubber ruler for a lazy clock.

W.D.Clinger · 2nd April 2023, 03:01 AM

Quoting here for the record, to protect against the possibility of subsequent edits:

Originally Posted by Mike Helland

https://arxiv.org/abs/1804.10047

"At redshift z, the vacuum speed of light in comoving coordinates is a⁻¹c = (1 + z)c"

Originally Posted by Mike Helland

If the speed of light in comoving coordinates is c(1+z):

c < f_emit * w_emit * (1+z)

c < f_emit * w_obs

Assuming z > 0, that first inequality doesn't have anything to do with comoving coordinates because it is equivalent to

c < c * (1 + z)

The second inequality also doesn't have anything to do with the speed of light in comoving coordinates.

The two posts quoted above tell us Mike Helland doesn't have a clue about comoving coordinates. But we could have guessed that.

ETA: I'm going to let others respond to the nonsense Mike Helland wrote immediately above. Why should I have all the fun?

Mike Helland · 2nd April 2023, 03:49 AM

Originally Posted by W.D.Clinger

Assuming z > 0, that first inequality doesn't have anything to do with comoving coordinates because it is equivalent to

c < c * (1 + z)

The second inequality also doesn't have anything to do with the speed of light in comoving coordinates.

The two posts quoted above tell us Mike Helland doesn't have a clue about comoving coordinates. But we could have guessed that.

This first link in your chronology is:

http://www.internationalskeptics.com...6#post14033386

Originally Posted by hecd2

Therefore Helland physics violates SR.

Originally Posted by Mike Helland

If you say so.

The first model is the expanding universe, which isn't Helland physics. The second model is the decelerating photon, which isn't Helland physics.

The third model is the one I find most interesting, where distant clocks run slower.

The Minkowski metric is:

Code:

https://mathworld.wolfram.com/MinkowskiMetric.html

The -1 is the t coordinate. What happens to spacetime when that isn't 1?

So, my derivation included the line:

1+z = (c + v) / c

Does that violate special relativity?

Let's say it does.

But in an expanding universe according to general relativity, that the speed of light is greater than c when z>0 seems to be a given.

We wouldn't say that general relativity violates special relativity.

So it seems the dynamic time conjecture can still operate in the framework of relativity as an alternative to the FLRW metric.

hecd2 · 2nd April 2023, 05:39 AM

Originally Posted by Mike Helland

So it seems the dynamic time conjecture can still operate in the framework of relativity as an alternative to the FLRW metric.

Leaving aside all the misunderstandings about tensor algebra that you demonstrate so clearly in your cargo cult posts, I pointed out to you that a metric in which the rate of time is a function of location (unlike FLRW which is based on a homogeneous, isotropic Universe where the gravitational potential, the mass-energy density and the pressure are uniform) would demand that we live in the centre of the Universe - and you ignored me. Are you a geocentrist?

Mike Helland · 2nd April 2023, 09:26 AM

Originally Posted by hecd2

Leaving aside all the misunderstandings about tensor algebra that you demonstrate so clearly in your cargo cult posts, I pointed out to you that a metric in which the rate of time is a function of location (unlike FLRW which is based on a homogeneous, isotropic Universe where the gravitational potential, the mass-energy density and the pressure are uniform) would demand that we live in the centre of the Universe - and you ignored me. Are you a geocentrist?

I did notice your attempt to change the subject.

"If the rate of time is a function of location then the Universe is no longer homogeneous."

Is it?

The rate at which galaxies move apart is a function of distance, and causes clocks to move slower. That's homogeneous? Seems like your definition is pretty arbitrary.

You say the universe is observed to homogeneous. Is it?

https://en.wikipedia.org/wiki/Lambda...of_homogeneity

Quote:

Based on N-body simulations in ΛCDM, Yadav and his colleagues showed that the spatial distribution of galaxies is statistically homogeneous if averaged over scales 260/h Mpc or more.[44] However, many large-scale structures have been discovered, and some authors have reported some of the structures to be in conflict with the predicted scale of homogeneity for ΛCDM, including

The Clowes–Campusano LQG, discovered in 1991, which has a length of 580 Mpc
The Sloan Great Wall, discovered in 2003, which has a length of 423 Mpc,[45]
U1.11, a large quasar group discovered in 2011, which has a length of 780 Mpc
The Huge-LQG, discovered in 2012, which is three times longer than and twice as wide as is predicted possible according to ΛCDM
The Hercules–Corona Borealis Great Wall, discovered in November 2013, which has a length of 2000–3000 Mpc (more than seven times that of the SGW)[46]
The Giant Arc, discovered in June 2021, which has a length of 1000 Mpc[47]

Other authors claim that the existence of structures larger than the scale of homogeneity in the ΛCDM model does not necessarily violate the cosmological principle in the ΛCDM model.[48][13]

Our latest assumption is that the universe is homogeneous at scales beyond which we actually observe.

That's the direction you want to go with this?

I take it you realized it's not internally inconsistent, and that it can be relativistic (and I take it you'll deny that up and down) hence resorting to a more dubious argument involving the cosmological principle.

W.D.Clinger · 2nd April 2023, 10:15 AM

Someone who doesn't know the difference between a map and the territory might look at a Mercator projection and conclude Greenland is the same size as Africa.

People who know enough to distinguish the map from the territory will say instead that the Mercator projection gives Greenland as much space on the map as it gives to Africa, but in reality Africa is about 14 times as large as Greenland.

The Mercator projection is great when you want to keep track of true north and south, and when you want the mapped shapes of land masses to approximate their real shapes, but it's quite misleading when what you care about is the areas of those land masses.

Mike Helland has consistently failed to distinguish maps from territories. The two quotations below are just the most recent examples of his confusion.

As background, consider this metric form for isotropic flat space in Cartesian coordinates:

ds² = – c² dt² + a(t)² dx² + a(t)² dy² + a(t)² dz²

Although that metric form is often called the FLRW metric, it is considerably more general; it expresses the metric of any isotropic flat spacetime. (To obtain an FLRW model, you combine that metric form with assumptions about the cosmological constant and the tensor on the right hand side of the Einstein field equations.)

The comoving coordinates that appear within that metric form are <t, x, y, z>.

In what follows, keep in mind that although the actual speed of light in vacuo is invariant, the coordinate-dependent speed of light depends upon the coordinates you're using.

To calculate the coordinate-dependent speed of light in those comoving coordinates, consider a photon moving through a vacuum along the x axis at some time t. Photons follow null geodesics, so

0 = – c² dt² + a(t)² dx²

High school algebra then tells us

c² dt² = a(t)² dx²
c² / a(t)² = dx² / dt²
dx/dt = c / a(t)

That is the comoving coordinate velocity of the photon. We can rewrite that equation as

c = a(t) dx / dt

which says the true velocity of light is obtained by multiplying the coordinate-dependent velocity by the scale factor.

Which makes perfect sense if you understand comoving coordinates. A comoving object is an object following a geodesic that preserves its view of the universe as isotropic. In an expanding universe, the distance between comoving objects increases as the universe expands. The comoving coordinates x, y, and z ignore that. By ignoring the time-dependent scale factor a(t), the comoving coordinates essentially pretend a comoving object has always had and always will have the same coordinates x, y, and z that place it at a distance (as of today!) of sqrt(x² + y² + z²) from the (arbitrary) origin of the spatial coordinates.

So comoving coordinates are convenient for calculations that need to keep track of the spatial coordinates of comoving objects, because their comoving spatial coordinates don't change over time. When you need to calculate actual distances and velocities, however, you have to take the scale factor into account.

Assuming the coordinate-dependent speed of light in comoving coordinates is the actual speed of light is like assuming the area of a Mercator projection devoted to land masses such as Greenland and Africa accurately quantifies the relative areas of those land masses. It's a novice's mistake.

So Mike Helland made that mistake, and based everything he wrote in the quotations below upon that error.

Originally Posted by Mike Helland

Seems pretty clear to me.

I asked if the FLRW metric meant that stretching space resulted in a faster speed of light.

Seems like it does.

v = c(1+z)

1+z = v / c

We also know v > c, so v = c + v₂, where v₂ > 0.

That seems to be copacetic with relativity, so my derivation should be ok with it too.

The metric I'm suggesting simply changes the rubber ruler for a lazy clock.

Originally Posted by Mike Helland

This first link in your chronology is:

http://www.internationalskeptics.com...6#post14033386

So, my derivation included the line:

1+z = (c + v) / c

Does that violate special relativity?

Let's say it does.

But in an expanding universe according to general relativity, that the speed of light is greater than c when z>0 seems to be a given.

We wouldn't say that general relativity violates special relativity.

So it seems the dynamic time conjecture can still operate in the framework of relativity as an alternative to the FLRW metric.

Mike Helland · 2nd April 2023, 10:42 AM

Originally Posted by W.D.Clinger

Someone who doesn't know the difference between a map and the territory might look at a Mercator projection and conclude Greenland is the same size as Africa.

This is pretty unrelated, but I always like to point out that Greenland is closer in size to Mexico, and then show people this website:

https://thetruesize.com/

Quote:

Mike Helland has consistently failed to distinguish maps from territories. The two quotations below are just the most recent examples of his confusion.

As background, consider this metric form for isotropic flat space in Cartesian coordinates:

ds² = – c² dt² + a(t)² dx² + a(t)² dy² + a(t)² dz²

Although that metric form is often called the FLRW metric, it is considerably more general; it expresses the metric of any isotropic flat spacetime. (To obtain an FLRW model, you combine that metric form with assumptions about the cosmological constant and the tensor on the right hand side of the Einstein field equations.)

The comoving coordinates that appear within that metric form are <t, x, y, z>.

In what follows, keep in mind that although the actual speed of light in vacuo is invariant, the coordinate-dependent speed of light depends upon the coordinates you're using.

To calculate the coordinate-dependent speed of light in those comoving coordinates, consider a photon moving through a vacuum along the x axis at some time t. Photons follow null geodesics, so

0 = – c² dt² + a(t)² dx²

High school algebra then tells us

c² dt² = a(t)² dx²
c² / a(t)² = dx² / dt²
dx/dt = c / a(t)

That is the comoving coordinate velocity of the photon. We can rewrite that equation as

c = a(t) dx / dt

which says the true velocity of light is obtained by multiplying the coordinate-dependent velocity by the scale factor.

Ok. So are you saying:

$\begin{bmatrix} f(L)& 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\\end{bmatrix}$

Where f(L) = -(1 - HL²), makes the speed of light slower in that coordinate system?

W.D.Clinger · 2nd April 2023, 11:08 AM

Originally Posted by Mike Helland

Ok. So are you saying:

https://latex.codecogs.com/png.image...\\end{bmatrix}

Where f(L) = -(1 - HL²), makes the speed of light slower in that coordinate system?

I have never said that. Until now, you have never even hinted at what f(L) might be in that matrix. Even now, you have not even hinted at what L might be.

And while I would ordinarily assume H is the Hubble parameter, which changes over time, you have insisted that the Hubble parameter does not change over time, and you have responded to irrefutable proofs that Helland physics requires the Hubble parameter to be zero by saying those proofs depend upon the Hubble parameter having the meaning it has in mainstream science. In Helland physics, you are using H to stand for something altogether different, something we might call the Helland parameter. And you have never given us any quantifiable indication of what the Helland parameter might be.

So I'd be a fool to take your f(L) = -(1 - HL²) seriously, inasmuch as it contains two distinct letters whose meaning you have left completely undefined.

Mike Helland · 2nd April 2023, 11:34 AM

Originally Posted by W.D.Clinger

I have never said that. Until now, you have never even hinted at what f(L) might be in that matrix. Even now, you have not even hinted at what L might be.

And while I would ordinarily assume H is the Hubble parameter, which changes over time, you have insisted that the Hubble parameter does not change over time, and you have responded to irrefutable proofs that Helland physics requires the Hubble parameter to be zero by saying those proofs depend upon the Hubble parameter having the meaning it has in mainstream science. In Helland physics, you are using H to stand for something altogether different, something we might call the Helland parameter. And you have never given us any quantifiable indication of what the Helland parameter might be.

So I'd be a fool to take your f(L) = -(1 - HL²) seriously, inasmuch as it contains two distinct letters whose meaning you have left completely undefined.

Fair enough.

I usually write H₀ instead of just H but that was a slip.

L should be:

L² = dx² + dy² + dz²

I guess the desired effect is:

c² = L² / (f(L)² * dt²)

f(L)² c² dt² = L²

0 = - f(L)² c² dt² + dx² + dy² + dz²

Ziggurat · 2nd April 2023, 11:39 AM

Originally Posted by Mike Helland

Ok. So are you saying:

https://latex.codecogs.com/png.image...\\end{bmatrix}

Where f(L) = -(1 - HL²), makes the speed of light slower in that coordinate system?

How do you think you determine the speed of light from a metric tensor? This is actually a non-trivial question. You probably think you know the answer, but you probably do not actually know it.

Mike Helland · 2nd April 2023, 12:27 PM

Originally Posted by Ziggurat

How do you think you determine the speed of light from a metric tensor? This is actually a non-trivial question. You probably think you know the answer, but you probably do not actually know it.

Is it what W.D.Clinger wrote today, that culminates with: c = a(t) dx / dt ?

$c = \frac{a(t)dx }{dt}$

That's for dynamic space. So the dynamic time analog would be:

$c = \frac{ dx }{f(L) dt}$

Or is it something else?

W.D.Clinger · 2nd April 2023, 12:36 PM

Originally Posted by Mike Helland

$\begin{bmatrix} f(L)& 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\\end{bmatrix}$

Where f(L) = -(1 - HL²), makes the speed of light slower in that coordinate system?

Originally Posted by Mike Helland

I usually write H₀ instead of just H but that was a slip.

L should be:

L² = dx² + dy² + dz²

Then you are posting gibberish. You haven't said anything about the units you're using now, but H₀ has units of inverse time and L² has units of area (i.e. length squared), so your f(L) = -(1 - HL²) subtracts something with units area/time from the dimensionless constant 1, which probably yields a negative number, which you negate, thereby most likely yielding a non-Lorentzian metric form.

You really and truly have absolutely no idea of what you're doing.

Originally Posted by Mike Helland

I guess the desired effect is:

c² = L² / (f(L)² * dt²)

f(L)² c² dt² = L²

0 = - f(L)² c² dt² + dx² + dy² + dz²

Oh dear. Oh dear.

Your

f(L)² c² dt² = L²

can be rewritten as

dt² = L² / (f(L)² c²)

which says dt is a pure function of the location (via L and f(L)) independently of dx, dy, or dz.

That's a truly impressive pile of ackamarackus you dumped there.

Mike Helland · 2nd April 2023, 12:52 PM

Originally Posted by W.D.Clinger

Then you are posting gibberish. You haven't said anything about the units you're using now, but H₀ has units of inverse time and L² has units of area (i.e. length squared), so your f(L) = -(1 - HL²) subtracts something with units area/time from the dimensionless constant 1, which probably yields a negative number, which you negate, thereby most likely yielding a non-Lorentzian metric form.

H₀ has units of distance / time / distance.

L² is a mistake. The ² should be outside the parenthesis. And that too might be a mistake. Because:

Quote:

You really and truly have absolutely no idea of what you're doing.

To be fair, I think I have 0.0000756% of a clue. It ain't much, I'll give you that.

Quote:

Oh dear. Oh dear.

Your

f(L)² c² dt² = L²

can be rewritten as

dt² = L² / (f(L)² c²)

which says dt is a pure function of the location (via L and f(L)) independently of dx, dy, or dz.

Hmmm. Is that because I used L instead of dL? Should it be:

dL² = dx² + dy² + dz²

Mike Helland · 2nd April 2023, 01:14 PM

Originally Posted by W.D.Clinger

which says dt is a pure function of the location (via L and f(L)) independently of dx, dy, or dz.

Not sure what you mean.

L is just short hand for:

$\sqrt{dx^2 + dy^2 + dz^2}$

If what you said before:

$c^2 dt^2 = a(t)^2 dx^2$

Then:

$dx^2 = \frac{c^2 dt^2}{a(t)^2}$

Isn't that analogous?

W.D.Clinger · 2nd April 2023, 01:31 PM

Originally Posted by Mike Helland

Originally Posted by W.D.Clinger

Then you are posting gibberish. You haven't said anything about the units you're using now, but H₀ has units of inverse time and L² has units of area (i.e. length squared), so your f(L) = -(1 - HL²) subtracts something with units area/time from the dimensionless constant 1, which probably yields a negative number, which you negate, thereby most likely yielding a non-Lorentzian metric form.

H₀ has units of distance / time / distance.

FYI: "units of distance / time / distance" is just a complicated way to say units of inverse time.

Originally Posted by Mike Helland

L² is a mistake. The ² should be outside the parenthesis.

Moving the exponent outside the parenthesis doesn't fix anything. In one important sense that I explained to you a couple of weeks ago, it actually makes things worse. But you ignored me then, because you don't know enough high school algebra and calculus to understand even the simplest explanations of what you're doing wrong.

Originally Posted by Mike Helland

Hmmm. Is that because I used L instead of dL? Should it be:

dL² = dx² + dy² + dz²

Actually, I misread your definition of L as L² = x² + y² + z². You are correct, however, that writing L instead of dL led me to jump to the conclusion that there were no differentials on the right hand side either.

Originally Posted by Mike Helland

Not sure what you mean.

L is just short hand for:

$\sqrt{dx^2 + dy^2 + dz^2}$

If what you said before:

$c^2 dt^2 = a(t)^2 dx^2$

Then:

$dx^2 = \frac{c^2 dt^2}{a(t)^2}$

Isn't that analogous?

See above.

Please take note, however, that your gibberish has quite a few other obvious problems that I haven't mentioned and probably won't ever bother to mention. There's no use.

Mike Helland · 2nd April 2023, 01:42 PM

Originally Posted by W.D.Clinger

FYI: "units of distance / time / distance" is just a complicated way to say units of inverse time.

Yes, very true.

It's just a different way to follow the units.

distance/time/distance = velocity / distance

So in Hubble's law, v = H₀d, you get

velocity = velocity / distance * distance

Rather than using natural units (c=1), the coefficient for the time coordinate should be:

$\frac{c-H_0 L}{c} c^2$

Ziggurat · 2nd April 2023, 02:59 PM

Originally Posted by Mike Helland

Is it what W.D.Clinger wrote today, that culminates with: c = a(t) dx / dt ?

$c = \frac{a(t)dx }{dt}$

That's for dynamic space. So the dynamic time analog would be:

$c = \frac{ dx }{f(L) dt}$

Or is it something else?

I was asking how to do it in general, given a metric tensor. If you are asking if that's the right answer, then you don't know, and if you don't know, you don't understand any of what you're talking about. This isn't news, but you're acting like you think you are on the cusp of understanding and you aren't. You don't have the foundation necessary to understand any of the answers you are being given.

W.D.Clinger · 2nd April 2023, 03:13 PM

This is what cargo cult physics looks like. Just within the past day or so, Mike Helland has made at least five different wild guesses (in the spoiler) concerning what he guesses he hopes to be a plausible metric form for Helland physics.

What a mess.

I sincerely hope Mike Helland will clean up that mess by giving us just one last guess at a metric form, complete with a description of its coordinates and units, so we can have one last laugh before turning to the next chapter of this cargo cult physics.

Mike Helland · 2nd April 2023, 03:30 PM

Originally Posted by W.D.Clinger

I sincerely hope Mike Helland will clean up that mess by giving us just one last guess at a metric form, complete with a description of its coordinates and units, so we can have one last laugh before turning to the next chapter of this cargo cult physics.

Ok. Well, the lookback time for an FLRW universe with Ω_Λ=1 is:

$t = \frac{1}{H_0}\int\frac{1}{1+z}dz$

It gives the right graph when I plot this:

https://www.wolframalpha.com/input?i...%2Bx%5D%2Cx%5D

So that should give the coordinate time.

Whereas the "true" or "actual" time as you put it is L/c.

W.D.Clinger · 2nd April 2023, 03:57 PM

Originally Posted by Mike Helland

Originally Posted by W.D.Clinger

I sincerely hope Mike Helland will clean up that mess by giving us just one last guess at a metric form, complete with a description of its coordinates and units, so we can have one last laugh before turning to the next chapter of this cargo cult physics.

Ok. Well, the lookback time for an FLRW universe with Ω_Λ=1 is:

$t = \frac{1}{H_0}\int\frac{1}{1+z}dz$

It gives the right graph when I plot this:

https://www.wolframalpha.com/input?i...%2Bx%5D%2Cx%5D

So that should give the coordinate time.

Whereas the "true" or "actual" time as you put it is L/c.

So that is Mike Helland's very best guess at what the metric form for Helland physics should look like.

Mike Helland's very best guess at the metric form for Helland physics does not resemble a metric form in any way.

But that's the very best he can do: quoting some random thing he found on the World-Wide Web, hoping it will fool some readers into thinking it has some remote relevance to the issue at hand.

hecd2 · 2nd April 2023, 05:27 PM

Originally Posted by Mike Helland

I did notice your attempt to change the subject.

How on earth is it a change of subject to point out to you that your silly attempts to write down a metric tensor with a function of location in g₀₀ results in a description of a non-homogeneous Universe. We observe the Universe to be isotropic. The only way that we can combine observed isotropy with inhomogeneity is if the Universe is spherically symmetric with us at its centre. (For example the Schwarzschild solution is spherically symmetric but not homogeneous).

Quote:

"If the rate of time is a function of location then the Universe is no longer homogeneous."

Is it?

Absolutely. The Robertson-Walker metric describes a homogeneous isotropic Universe (and is provably the only metric for a homogeneous isotropic Universe). In the FLRW solution the proper time is the same at all locations for comoving observers (so, for example, things which are functions of time, for example the scale factor, are universal and do not vary by location)

Quote:

The rate at which galaxies move apart is a function of distance, and causes clocks to move slower. That's homogeneous? Seems like your definition is pretty arbitrary.

You are confusing proper time with coordinate time.

Quote:

You say the universe is observed to homogeneous. Is it?

https://en.wikipedia.org/wiki/Lambda...of_homogeneity

I said the Universe appears to be the same in all directions - ie we observe it to be isotropic. For example the CMB is uniform to one part in 100,000. If the Universe is isotropic but inhomogeneous it must be spherically symmetric with us at the centre.

Quote:

I take it you realized it's not internally inconsistent, .

Your utterly daft idea that light pulses travelling the same distance at the same speed can have a different round trip flight time is totally inconsistent and FUBAR. You have been told that over and over again, but you are too ignorant and arrogant to accept it.

Mike Helland · 2nd April 2023, 05:58 PM

Originally Posted by hecd2

How on earth is it a change of subject to point out to you that your silly attempts to write down a metric tensor with a function of location in g₀₀ results in a description of a non-homogeneous Universe.

Let's say you have a fish pond. In the middle the fish are relatively still. But as you increase toward the edges, the fish are progressively more active and swimming faster.

Is the pond homogeneous?

Mike Helland · 2nd April 2023, 06:16 PM

Originally Posted by W.D.Clinger

So that is Mike Helland's very best guess at what the metric form for Helland physics should look like.

Well it would be (and point out any mistakes, cause I'm sure there are some):

$\begin{bmatrix}f(L)^2c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1 \end{bmatrix}$

So:

$0 = - f(L)^2 c^2 dt^2 + dx^2 + dy^2 + dz^2$

Earlier I said:

$t = \frac{1}{H_0}\int\frac{1}{1+z}dz$

But that's in terms of z, and probably needs to be in terms of L.

This also calculates lookback time:

$f(L) = \int\frac{c}{c-H_0L}dL$

So that's what should be in place of f(L).

hecd2 · 3rd April 2023, 02:23 AM

Originally Posted by Mike Helland

Let's say you have a fish pond. In the middle the fish are relatively still. But as you increase toward the edges, the fish are progressively more active and swimming faster.

Is the pond homogeneous?

No, it would be inhomogeneous and isotropic about the centre. And your point is?

ETA: for a fish living in such a pond, the only way that things would appear to be the same in all directions (isotropic) is if it was at the centre.

hecd2 · 3rd April 2023, 02:44 AM

Originally Posted by Mike Helland

Well it would be (and point out any mistakes, cause I'm sure there are some):

$\begin{bmatrix}f(L)^2c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1 \end{bmatrix}$

So:

$0 = - f(L)^2 c^2 dt^2 + dx^2 + dy^2 + dz^2$

Earlier I said:

$t = \frac{1}{H_0}\int\frac{1}{1+z}dz$

But that's in terms of z, and probably needs to be in terms of L.

This also calculates lookback time:

$f(L) = \int\frac{c}{c-H_0L}dL$

So that's what should be in place of f(L).

Others have already pointed out that in Helland physics H0 = H(t) = 0 (that's precisely what a static Universe means). So your integral $f(L) = \int\frac{c}{c-H_0L}dL = L+b$ where $b$ is a constant of integration.

Mike Helland · 3rd April 2023, 05:40 AM

Originally Posted by hecd2

Others have already pointed out that in Helland physics H0 = H(t) = 0 (that's precisely what a static Universe means). So your integral $f(L) = \int\frac{c}{c-H_0L}dL = L+b$ where $b$ is a constant of integration.

That ol' strawman.

H₀ is a measured constant in Helland physics.

The FLRW model to which it is analogous is Ω_Λ=1.

H(t) / H₀ = E(z)

Which is 1 for the Ω_Λ plus 0 for Ω_M and Ω_R.

H₀ = H_t

Because the constant doesn't change in that model, that's why its d_obs exactly matches d=zc/H₀ and d_emit exactly matches d=z/(1+z) * c/H₀.

FWIW, it should be:

$f(L) = \int_{0}^{L}\frac{c}{c-H_0L'}dL'$

W.D.Clinger · 3rd April 2023, 06:12 AM

Originally Posted by Mike Helland

That ol' strawman.

H₀ is a measured constant in Helland physics.

The FLRW model to which it is analogous is Ω_Λ=1.

H(t) / H₀ = E(z)

Which is 1 for the Ω_Λ plus 0 for Ω_M and Ω_R.

H₀ = H_t

Because the constant doesn't change in that model, that's why its d_obs exactly matches d=zc/H₀ and d_emit exactly matches d=z/(1+z) * c/H₀.

What Mike Helland wrote above implies

a(t) = e^H₀t

In other words, Mike Helland is saying that, in Helland physics, the size of the universe increases exponentially with time.

But Mike Helland doesn't know enough mathematics to realize he's saying that, and will undoubtedly respond to the facts stated above with more ackamarackus.

Mike Helland · 3rd April 2023, 06:17 AM

Originally Posted by W.D.Clinger

What Mike Helland wrote above implies

a(t) = e^H₀t

In other words, Mike Helland is saying that, in Helland physics, the size of the universe increases exponentially with time.

I said that expanding model is analogous to my model, in the sense that the same z, lookback time, and d_emit values are predicted identically by both models.

There is no big bang in a "pure" expanding universe, Ω_Λ=1, Ω_M=0. Lookback time grows and grows. Not that I'm advocating that. But it is analogous to what I am suggesting for said values.

W.D.Clinger · 3rd April 2023, 06:23 AM

Originally Posted by Mike Helland

There is no big bang in a "pure" expanding universe, Ω_Λ=1, Ω_M=0. Lookback time grows and grows.

That's because, looking backwards in time, the size of the universe shrinks exponentially.

Exponential decay converges toward zero, but never actually reaches zero. Mike Helland didn't know that either.

Which is why we're seeing more of the old ackamarackus.

29th March 2023, 06:56 PM	#1402
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Details matter. Tom Knight was one of the lead designers of the MIT Lisp Machines. This story says a lot about the previous post. A novice was trying to fix a broken Lisp machine by turning the power off and on. Knight, seeing what the student was doing, spoke sternly: “You cannot fix a machine by just power-cycling it with no understanding of what is going wrong.” Knight turned the machine off and on. The machine worked.
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047

30th March 2023, 06:19 AM	#1403
Mashuna Ovis ex Machina Join Date: Jan 2006 Location: Sir Ddinbych Posts: 6,963	Originally Posted by hecd2 You replied to me in three minutes. You're not stopping to think. No-one apart from you believes that the paradox is anything other than irresolvable. The only thing you have to measure time on is your clock at A, and the round trips of two pulses are different according to that clock. There is no way round that. I'm not starting this again. You can carry on thinking you've resolved it and everyone who knows what they're talking about, including the referee when you submit the embarassing "paper" that you will no doubt write, will tell you the same thing, and you still won't believe them, like you didn't believe the referee on your last "paper". It's a waste of everyone's time. Originally Posted by Mike Helland Sure. And in my model, photon 2 arrives late and photon 1 takes off early. Changing where you start to count does not fix the paradox. It's like adding an extra flywheel to your perpetual motion machine.
	__________________ I’d rather be a rising ape than a falling angel. - Sir Terry Pratchett

30th March 2023, 08:57 AM	#1404
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 53,938	Originally Posted by Mike Helland You said "you" thirteen times in seven sentences. To paraphrase from here: https://despair.com/products/dysfunction The only consistent feature in all your failed theories is you. That's why I'm emphasizing you. The details of an individual failure are pretty secondary, far more significant is the consistent cause of those failures, and that's you. So you deserve attention, because that's the only possible source for a fix to any of this. Not tweaking your theory with yet another revision, but a fundamental change in how you approach everything. You need to start by learning, and not in this half-assed way you're currently doing it. Quote: I've always done calculus problems with a computer program and a lot of trial and error. I know that's severely limiting. (No pun intended.) But it usually gets the right enough answers. I just don't understand why it won't fly. Quote: And based on your feedback over the last couple years, I have revisited calculus, to try to express it in the calculus way, but obviously not well enough. I went over linear algebra too, and a couple other things. Indeed, it's not enough. Not close to enough. There's a reason people spend year and years just learning this stuff, before they even try to do something new. Quote: You were also the one that said photons can't lose frequency without clocks desynchronizing, which is why we're talking about dynamic time in the first place. I did indeed say that, and it is indeed true. But you seem to think that desynchronizing clocks is some trivial thing. It's not. It is no small feat to develop a new theory of desynchronization in a manner that is self-consistent, let alone in a manner that is consistent with observations. The parts need to connect to make a self-consistent whole, and you're not doing that. It is beyond you. Hell, it's beyond me too. The difference is that I know I'm not up to the task, despite knowing far more math and physics than you. For some reason, and despite all evidence to the contrary, you think you are. You are not. Quote: Regarding the first, one example was the flight time paradox, I think that's resolved: No, it isn't resolved. You've got hand waving nonsense about dynamic time that doesn't actually make any sense. You have no coherent picture of what your dynamic time actually is, or what it actually does. Quote: As far as expressing it in the framework of relativity, I don't think I'm that far off in thinking that could be in the form of a metric tensor that reduces to the Minkowski metric at less than cosmological scales. And that it makes a "v" look like a "u". You seem to think that means something. It doesn't.
	__________________ "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 all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law

30th March 2023, 09:07 AM	#1405
hecd2 Graduate Poster Join Date: Oct 2013 Posts: 1,609	Originally Posted by Mike Helland I'm ok with that. If it's perfectly reasonable to adjust the space coefficients based on the time coordinate: https://math-demo.abitti.fi/math.svg...d%7Bpmatrix%7D Then it should be acceptable to make the time coefficient based on the space coordinates. The Robertson-Walker metric is for an isotropic homogeneous Universe. In such a Universe, time passes at the same rate at all locations. You can write a 3 dimensional spatial metric for a given time which describes the intrinsic curvature and other properties, such as distances between points and angles between lines which are invariant under coordinate transformations. If the rate of time is a function of location then the Universe is no longer homogeneous. But the Universe appears to us to be the same in all directions. The only way that can be is if the non-homogeneous Universe is spherically symmetric with us at its centre. That would make you a geocentrist. Is that what you arguing for?
hecd2 Graduate Poster Join Date: Oct 2013 Posts: 1,609	__________________ Gulielmus Princeps Haroldum Principem in catino canino impulit

2nd April 2023, 01:39 AM	#1409
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	time line of another bad idea So I call these things Cargo Cult Science, because they follow all the apparent precepts and forms of scientific investigation, but they're missing something essential, because the planes don't land. —Richard Feynman (1974 commencement address at Caltech) Today is 2 April. On 20 March, apropos of nothing, Mike Helland quoted the Minkowski metric he found online, and asked what happens to spacetime when g₀₀ (which he called the "t coordinate") isn't -1. On 21 March, Mike Helland asked whether it was possible to put a variable in the g₀₀ component (which he called the "time coordinate") of the metric form. He asked this immediately after I had cited the Rindler metric form as an example of doing precisely that. Later that day, he wrote "So in the manifold I'm thinking of, the spatial coordinates show up in the time coefficient. And so does the Hubble parameter." On 23 March, Mike Helland explained why he had quoted the Minkowski metric form: Ziggurat and hecd2 had pointed out that his derivations violated relativity, and he thought he could fix that problem by quoting something he had found online that had something to do with relativity. Later that day, he confirmed his cargo cult approach to science: "If the problem is that the model is not relativistic, then the solution is to make it relativistic....In a relativistic Helland physics, there is no scale factor for the size of space, but there is a time scale factor for the rate of clocks." An hour later, he expressed his surprise upon being told there are non-FLRW models that define the Hubble parameter using the same scale factor that appears in FLRW models. That afternoon, he described his idea as "you take a normal light cone, and warp the coordinates until it points straight up." That bad idea came from his guess that Rindler coordinates had changed the spacetime manifold by doing something similar to the coordinates. He made that wrong guess even though I had explained to him that a mere change of coordinates has no effect upon the spacetime manifold. So I said the same thing again, in much greater detail. But Mike Helland continued to conflate the map with the territory. The very next day, he posted a graph of t(x) = \|x\|. He had distorted that graph by using a non-linear vertical scale for no reason at all, as though he thought his ability to draw that distorted picture had any implications for science. No one paid any immediate attention to that foolishness, so on the following day, 25 March, he asked me what I thought of his spacetime diagram. He went on to write: "It starts off with two lines that are perpendicular and end up nearing parallel. I suppose that means the manifold is the surface of a sphere (inside or outside)?" I told him it just means "the buffoon who drew that picture used a nonlinear vertical scale for no good reason." Mike Helland ignored that substantive response to his picture, but attempted a Gish Gallop involving the definition of "Gish Gallop". On 27 March, Mike Helland announced the following principle of Helland physics: "Clocks always get faster in the direction the photon is traveling." I asked him to clarify whether that means (1) clocks everywhere are always getting faster, or (2) clocks get faster only when a photon is traveling toward them. It took only one day for Mike Helland to understand the question. He said it was (1). hecd2 asked how you could tell clocks everywhere are continually running faster. Mike Helland responded to that question by saying "Time dilation happens twice." As though to prove that nonsense, he again posted a variation of his distorted graph of t(x) = \|x\|. Less than an hour later, he guessed that the spacetime shown in his distorted graph corresponds to a metric form with g₀₀ = – (1 – 0.0000756 * x). Within half an hour of that hilarious wrong guess, he wrote "Or maybe that should -1 / (1 - 0.0000756 * x)." He went on to describe rolling a piece of paper into a tube, saying "This is "temporal curvature" rather than "spatial curvature", because the space dimension isn't curved, just the time dimension." Apparently Mike Helland was unaware that rolling a piece of paper into a tube does not change its intrinsic curvature (so its metric form remains the same as for a flat piece of paper), and was also unaware that the mainstream concordance model also describes essentially flat space, with temporal curvature. A mere 12 minutes later, Mike Helland responded to that fact by quoting the components of a metric form he found online, and asked whether the k that appears within that metric form is zero for a flat universe. (Odd that he had to ask. For several months now, he has been citing papers that explain that. I guess he doesn't actually read the papers he cites.) Ziggurat reminded Mike Helland that his distorted graph is nothing more than a foolishly distorted picture of flat Minkowski spacetime. "This error has been pointed out to you before. There is no justifiable reason for you to continue to make it." Less than half an hour later, Mike Helland responded to Ziggurat's reminder with this non-sequitur: "Take a 2d graph of y = abs(x), and project it onto a cylinder." He had to ask "Is that still Minkowski spacetime?" When Mike Helland continued to post ignorant guesses about metric forms, several people pointed out that he simply does not know enough mathematics to discuss metric forms. When Ziggurat pointed out that Mike Helland didn't know the difference between a coordinate singularity and a real singularity, Mike Helland said he had never heard of a coordinate singularity. On 29 March, saying "Helland physics is cargo cult science," I supported that assertion by analyzing several recent examples. Which brings us to this most recent example, quoted below. Originally Posted by Mike Helland If dynamic time is something like: https://latex.codecogs.com/png.image...\\end{bmatrix} Details matter. That's why I analyzed two of Mike Helland's specific wrong guesses about a metric form for Helland physics, relying on Mike Helland's explicit description of his coordinates: His unit for the time coordinate is a million years, and his unit for spatial coordinates is a million light years. My specific analyses of Mike Helland's two specific wrong guesses do not generalize to "something like" the highly abstracted metric form he wrote above. Originally Posted by Mike Helland Why do you say that changes the speed of light? Because, knowing his specified coordinates, I know how to analyze Mike Helland's specific wrong guesses. Originally Posted by Mike Helland More importantly, why doesn't something similar happen when you stretch space: https://math-demo.abitti.fi/math.svg...A\end{pmatrix} *Something* does happen, but it would be a stretch to say it's something *similar. I'll be happy to explain this stuff to Mike Helland, after* he learns the relevant mathematics. For most people, it takes several years to learn enough calculus, linear algebra, topology, and differential geometry to understand general relativity and the variety of metric forms that describe various spacetime manifolds. Truth be told, most people never learn enough math to understand general relativity, so his own failure to understand doesn't make him special. The first principle is that you must not fool yourself—and you are the easiest person to fool. —Richard Feynman (1974 commencement address at Caltech)
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047

29th March 2023, 06:19 PM	#1401
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger Helland physics has given us an entirely new way to misunderstand the universe. I'm ok with that. If it's perfectly reasonable to adjust the space coefficients based on the time coordinate: $g_{\mu\nu}=\begin{pmatrix} -1&0&0&0\\ 0&\frac{a^2}{1-kr^2}&0&0\\ 0&0&a^2r^2&0\\ 0&0&0&a^2r^2\sin^2\theta \end{pmatrix}$ Then it should be acceptable to make the time coefficient based on the space coordinates.

30th March 2023, 09:54 AM	#1406
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by Mashuna Changing where you start to count does not fix the paradox. That's not quite what I'm suggesting. Time dilation makes durations longer. Whether that duration extends to the future, or the past, shouldn't make a difference.

1st April 2023, 01:28 PM	#1407
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger \ \According to the theory of relativity, light follows null geodesics. Analyzing Mike Helland's two guesses at a metric, that means light travels slower (according to his first guess) as x approaches the coordinate singularity than at x = 0 or negative values of x, or light travels faster (according to his second guess) as x approaches the coordinate singularity. If dynamic time is something like: $\begin{bmatrix} f(L)& 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\\end{bmatrix}$ Why do you say that changes the speed of light? More importantly, why doesn't something similar happen when you stretch space: $g_{\mu\nu}=\begin{pmatrix} -1&0&0&0\\ 0&\frac{a^2}{1-kr^2}&0&0\\ 0&0&a^2r^2&0\\ 0&0&0&a^2r^2\sin^2\theta \end{pmatrix}$

2nd April 2023, 12:16 AM	#1408
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by Mike Helland If dynamic time is something like: https://latex.codecogs.com/png.image...\\end{bmatrix} Why do you say that changes the speed of light? More importantly, why doesn't something similar happen when you stretch space: https://math-demo.abitti.fi/math.svg...A\end{pmatrix} https://arxiv.org/abs/1804.10047 "At redshift z, the vacuum speed of light in comoving coordinates is a⁻¹c = (1 + z)c"

2nd April 2023, 01:56 AM	#1410
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger *Something* does happen, but it would be a stretch to say it's something *similar. If the speed of light in comoving coordinates is c(1+z): c < f_emit w_emit * (1+z) c < f_emit * w_obs

2nd April 2023, 02:34 AM	#1411
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	yet another example of the cargo cult Originally Posted by Mike Helland https://arxiv.org/abs/1804.10047 "At redshift z, the vacuum speed of light in comoving coordinates is a⁻¹c = (1 + z)c" From that very same paper: Quote: The vacuum speed of light c is invariant... To reconcile those two statements, Mike Helland will have to learn that the map is not the territory. By the way, the equation a⁻¹c = (1 + z)c is an immediate consequence of the equation a⁻¹ = (1 + z) which is an immediate consequence of the mainstream equation 1 + z = a(t₀) / a(t₁) (where t₁ is the time at which the redshifted photon was emitted, and t₀ is the present time) because a(t₀) = 1 by convention. Originally Posted by Wojtak and Prada The canonical redshift–scale factor relation, 1/a = 1 + z, is a key element in the standard Λ cold dark matter (ΛCDM) model of the big bang cosmology. As that paper points out, 1/a = 1 + z is a consequence of FLRW models that describe an expanding universe, and does not necessarily hold in non-FLRW models. In particular, Helland physics insists the universe is not expanding, which implies a(t₁) = 1, from which the equation quoted by Mike Helland implies z = 0. Helland physics is not based on an FLRW model, however, so Helland physics is not constrained by the equation Mike Helland quoted. It is of course completely unclear why Mike Helland quoted that equation, apart from his habit of randomly quoting things he finds online in the hope some readers will make the mistake of assuming his random quotations of real science somehow transform the cargo cult we refer to as Helland physics into real science. For an example of that behavior, see what Mike Helland wrote a little more than half an hour ago.
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Last edited by W.D.Clinger; 2nd April 2023 at 03:52 AM. Reason: added link to final sentence; corrected a subscript

2nd April 2023, 02:50 AM	#1412
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger It is of course completely unclear why Mike Helland quoted that equation Seems pretty clear to me. I asked if the FLRW metric meant that stretching space resulted in a faster speed of light. Seems like it does. v = c(1+z) 1+z = v / c We also know v > c, so v = c + v₂, where v₂ > 0. That seems to be copacetic with relativity, so my derivation should be ok with it too. The metric I'm suggesting simply changes the rubber ruler for a lazy clock.

2nd April 2023, 03:01 AM	#1413
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Quoting here for the record, to protect against the possibility of subsequent edits: Originally Posted by Mike Helland https://arxiv.org/abs/1804.10047 "At redshift z, the vacuum speed of light in comoving coordinates is a⁻¹c = (1 + z)c" Originally Posted by Mike Helland If the speed of light in comoving coordinates is c(1+z): c < f_emit * w_emit * (1+z) c < f_emit * w_obs Assuming z > 0, that first inequality doesn't have anything to do with comoving coordinates because it is equivalent to c < c * (1 + z) The second inequality also doesn't have anything to do with the speed of light in comoving coordinates. The two posts quoted above tell us Mike Helland doesn't have a clue about comoving coordinates. But we could have guessed that. ETA: I'm going to let others respond to the nonsense Mike Helland wrote immediately above. Why should I have all the fun?
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Last edited by W.D.Clinger; 2nd April 2023 at 03:14 AM. Reason: added ETA

2nd April 2023, 03:49 AM	#1414
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger Assuming z > 0, that first inequality doesn't have anything to do with comoving coordinates because it is equivalent to c < c * (1 + z) The second inequality also doesn't have anything to do with the speed of light in comoving coordinates. The two posts quoted above tell us Mike Helland doesn't have a clue about comoving coordinates. But we could have guessed that. This first link in your chronology is: http://www.internationalskeptics.com...6#post14033386 Originally Posted by hecd2 Therefore Helland physics violates SR. Originally Posted by Mike Helland If you say so. The first model is the expanding universe, which isn't Helland physics. The second model is the decelerating photon, which isn't Helland physics. The third model is the one I find most interesting, where distant clocks run slower. The Minkowski metric is: Code: -1000 0100 0010 0001 https://mathworld.wolfram.com/MinkowskiMetric.html The -1 is the t coordinate. What happens to spacetime when that isn't 1? So, my derivation included the line: 1+z = (c + v) / c Does that violate special relativity? Let's say it does. But in an expanding universe according to general relativity, that the speed of light is greater than c when z>0 seems to be a given. We wouldn't say that general relativity violates special relativity. So it seems the dynamic time conjecture can still operate in the framework of relativity as an alternative to the FLRW metric.

2nd April 2023, 05:39 AM	#1415
hecd2 Graduate Poster Join Date: Oct 2013 Posts: 1,609	Originally Posted by Mike Helland So it seems the dynamic time conjecture can still operate in the framework of relativity as an alternative to the FLRW metric. Leaving aside all the misunderstandings about tensor algebra that you demonstrate so clearly in your cargo cult posts, I pointed out to you that a metric in which the rate of time is a function of location (unlike FLRW which is based on a homogeneous, isotropic Universe where the gravitational potential, the mass-energy density and the pressure are uniform) would demand that we live in the centre of the Universe - and you ignored me. Are you a geocentrist?
hecd2 Graduate Poster Join Date: Oct 2013 Posts: 1,609	__________________ Gulielmus Princeps Haroldum Principem in catino canino impulit

2nd April 2023, 09:26 AM	#1416
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by hecd2 Leaving aside all the misunderstandings about tensor algebra that you demonstrate so clearly in your cargo cult posts, I pointed out to you that a metric in which the rate of time is a function of location (unlike FLRW which is based on a homogeneous, isotropic Universe where the gravitational potential, the mass-energy density and the pressure are uniform) would demand that we live in the centre of the Universe - and you ignored me. Are you a geocentrist? I did notice your attempt to change the subject. "If the rate of time is a function of location then the Universe is no longer homogeneous." Is it? The rate at which galaxies move apart is a function of distance, and causes clocks to move slower. That's homogeneous? Seems like your definition is pretty arbitrary. You say the universe is observed to homogeneous. Is it? https://en.wikipedia.org/wiki/Lambda...of_homogeneity Quote: Based on N-body simulations in ΛCDM, Yadav and his colleagues showed that the spatial distribution of galaxies is statistically homogeneous if averaged over scales 260/h Mpc or more.[44] However, many large-scale structures have been discovered, and some authors have reported some of the structures to be in conflict with the predicted scale of homogeneity for ΛCDM, including The Clowes–Campusano LQG, discovered in 1991, which has a length of 580 Mpc The Sloan Great Wall, discovered in 2003, which has a length of 423 Mpc,[45] U1.11, a large quasar group discovered in 2011, which has a length of 780 Mpc The Huge-LQG, discovered in 2012, which is three times longer than and twice as wide as is predicted possible according to ΛCDM The Hercules–Corona Borealis Great Wall, discovered in November 2013, which has a length of 2000–3000 Mpc (more than seven times that of the SGW)[46] The Giant Arc, discovered in June 2021, which has a length of 1000 Mpc[47] Other authors claim that the existence of structures larger than the scale of homogeneity in the ΛCDM model does not necessarily violate the cosmological principle in the ΛCDM model.[48][13] Our latest assumption is that the universe is homogeneous at scales beyond which we actually observe. That's the direction you want to go with this? I take it you realized it's not internally inconsistent, and that it can be relativistic (and I take it you'll deny that up and down) hence resorting to a more dubious argument involving the cosmological principle.

2nd April 2023, 10:15 AM	#1417
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Seven hours ago, I wrote: Originally Posted by W.D.Clinger ETA: I'm going to let others respond to the nonsense Mike Helland wrote immediately above. Why should I have all the fun? But I'm going to have a little fun here because Mike Helland's subsequent post made his obvious confusion even clearer. Someone who doesn't know the difference between a map and the territory might look at a Mercator projection and conclude Greenland is the same size as Africa. People who know enough to distinguish the map from the territory will say instead that the Mercator projection gives Greenland *as much space on the map* as it gives to Africa, but in reality Africa is about 14 times as large as Greenland. The Mercator projection is great when you want to keep track of true north and south, and when you want the mapped shapes of land masses to approximate their real shapes, but it's quite misleading when what you care about is the areas of those land masses. Mike Helland has consistently failed to distinguish maps from territories. The two quotations below are just the most recent examples of his confusion. As background, consider this metric form for isotropic flat space in Cartesian coordinates: ds² = – c² dt² + a(t)² dx² + a(t)² dy² + a(t)² dz² Although that metric form is often called the FLRW metric, it is considerably more general; it expresses the metric of any isotropic flat spacetime. (To obtain an FLRW model, you combine that metric form with assumptions about the cosmological constant and the tensor on the right hand side of the Einstein field equations.) The comoving coordinates that appear within that metric form are <t, x, y, z>. In what follows, keep in mind that although the actual speed of light in vacuo is invariant, the coordinate-dependent speed of light depends upon the coordinates you're using. To calculate the coordinate-dependent speed of light in those comoving coordinates, consider a photon moving through a vacuum along the x axis at some time t. Photons follow null geodesics, so 0 = – c² dt² + a(t)² dx² High school algebra then tells us c² dt² = a(t)² dx² c² / a(t)² = dx² / dt² dx/dt = c / a(t) That is the comoving coordinate velocity of the photon. We can rewrite that equation as c = a(t) dx / dt which says the true velocity of light is obtained by multiplying the coordinate-dependent velocity by the scale factor. Which makes perfect sense if you understand comoving coordinates. A comoving object is an object following a geodesic that preserves its view of the universe as isotropic. In an expanding universe, the distance between comoving objects increases as the universe expands. The comoving coordinates x, y, and z ignore that. By ignoring the time-dependent scale factor a(t), the comoving coordinates essentially pretend a comoving object has always had and always will have the same coordinates x, y, and z that place it at a distance (as of today!) of sqrt(x² + y² + z²) from the (arbitrary) origin of the spatial coordinates. So comoving coordinates are convenient for calculations that need to keep track of the spatial coordinates of comoving objects, because their comoving spatial coordinates don't change over time. When you need to calculate actual distances and velocities, however, you have to take the scale factor into account. Assuming the coordinate-dependent speed of light in comoving coordinates is the actual speed of light is like assuming the area of a Mercator projection devoted to land masses such as Greenland and Africa accurately quantifies the relative areas of those land masses. It's a novice's mistake. So Mike Helland made that mistake, and based everything he wrote in the quotations below upon that error. Originally Posted by Mike Helland Seems pretty clear to me. I asked if the FLRW metric meant that stretching space resulted in a faster speed of light. Seems like it does. v = c(1+z) 1+z = v / c We also know v > c, so v = c + v₂, where v₂ > 0. That seems to be copacetic with relativity, so my derivation should be ok with it too. The metric I'm suggesting simply changes the rubber ruler for a lazy clock. Originally Posted by Mike Helland This first link in your chronology is: http://www.internationalskeptics.com...6#post14033386 So, my derivation included the line: 1+z = (c + v) / c Does that violate special relativity? Let's say it does. But in an expanding universe according to general relativity, that the speed of light is greater than c when z>0 seems to be a given. We wouldn't say that general relativity violates special relativity. So it seems the dynamic time conjecture can still operate in the framework of relativity as an alternative to the FLRW metric.
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Last edited by W.D.Clinger; 2nd April 2023 at 10:23 AM. Reason: minor corrections

2nd April 2023, 10:42 AM	#1418
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger Someone who doesn't know the difference between a map and the territory might look at a Mercator projection and conclude Greenland is the same size as Africa. This is pretty unrelated, but I always like to point out that Greenland is closer in size to Mexico, and then show people this website: https://thetruesize.com/ Quote: Mike Helland has consistently failed to distinguish maps from territories. The two quotations below are just the most recent examples of his confusion. As background, consider this metric form for isotropic flat space in Cartesian coordinates: ds² = – c² dt² + a(t)² dx² + a(t)² dy² + a(t)² dz² Although that metric form is often called the FLRW metric, it is considerably more general; it expresses the metric of any isotropic flat spacetime. (To obtain an FLRW model, you combine that metric form with assumptions about the cosmological constant and the tensor on the right hand side of the Einstein field equations.) The comoving coordinates that appear within that metric form are <t, x, y, z>. In what follows, keep in mind that although the actual speed of light in vacuo is invariant, the coordinate-dependent speed of light depends upon the coordinates you're using. To calculate the coordinate-dependent speed of light in those comoving coordinates, consider a photon moving through a vacuum along the x axis at some time t. Photons follow null geodesics, so 0 = – c² dt² + a(t)² dx² High school algebra then tells us c² dt² = a(t)² dx² c² / a(t)² = dx² / dt² dx/dt = c / a(t) That is the comoving coordinate velocity of the photon. We can rewrite that equation as c = a(t) dx / dt which says the true velocity of light is obtained by multiplying the coordinate-dependent velocity by the scale factor. Ok. So are you saying: $\begin{bmatrix} f(L)& 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\\end{bmatrix}$ Where f(L) = -(1 - HL²), makes the speed of light slower in that coordinate system?

2nd April 2023, 11:08 AM	#1419
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Originally Posted by Mike Helland Ok. So are you saying: https://latex.codecogs.com/png.image...\\end{bmatrix} Where f(L) = -(1 - HL²), makes the speed of light slower in that coordinate system? I have never said that. Until now, you have never even hinted at what f(L) might be in that matrix. Even now, you have not even hinted at what L might be. And while I would ordinarily assume H is the Hubble parameter, which changes over time, you have insisted that the Hubble parameter does not change over time, and you have responded to irrefutable proofs that Helland physics requires the Hubble parameter to be zero by saying those proofs depend upon the Hubble parameter having the meaning it has in mainstream science. In Helland physics, you are using H to stand for something altogether different, something we might call the Helland parameter. And you have never given us any quantifiable indication of what the Helland parameter might be. So I'd be a fool to take your f(L) = -(1 - HL²) seriously, inasmuch as it contains two distinct letters whose meaning you have left completely undefined.
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Last edited by W.D.Clinger; 2nd April 2023 at 11:17 AM. Reason: added link

2nd April 2023, 11:34 AM	#1420
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger I have never said that. Until now, you have never even hinted at what f(L) might be in that matrix. Even now, you have not even hinted at what L might be. And while I would ordinarily assume H is the Hubble parameter, which changes over time, you have insisted that the Hubble parameter does not change over time, and you have responded to irrefutable proofs that Helland physics requires the Hubble parameter to be zero by saying those proofs depend upon the Hubble parameter having the meaning it has in mainstream science. In Helland physics, you are using H to stand for something altogether different, something we might call the Helland parameter. And you have never given us any quantifiable indication of what the Helland parameter might be. So I'd be a fool to take your f(L) = -(1 - HL²) seriously, inasmuch as it contains two distinct letters whose meaning you have left completely undefined. Fair enough. I usually write H₀ instead of just H but that was a slip. L should be: L² = dx² + dy² + dz² I guess the desired effect is: c² = L² / (f(L)² * dt²) f(L)² c² dt² = L² 0 = - f(L)² c² dt² + dx² + dy² + dz²

2nd April 2023, 11:39 AM	#1421
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 53,938	Originally Posted by Mike Helland Ok. So are you saying: https://latex.codecogs.com/png.image...\\end{bmatrix} Where f(L) = -(1 - HL²), makes the speed of light slower in that coordinate system? How do you think you determine the speed of light from a metric tensor? This is actually a non-trivial question. You probably think you know the answer, but you probably do not actually know it.
	__________________ "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 all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law

2nd April 2023, 12:27 PM	#1422
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by Ziggurat How do you think you determine the speed of light from a metric tensor? This is actually a non-trivial question. You probably think you know the answer, but you probably do not actually know it. Is it what W.D.Clinger wrote today, that culminates with: c = a(t) dx / dt ? $c = \frac{a(t)dx }{dt}$ That's for dynamic space. So the dynamic time analog would be: $c = \frac{ dx }{f(L) dt}$ Or is it something else?

2nd April 2023, 12:36 PM	#1423
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	more cargo cultism Originally Posted by Mike Helland $\begin{bmatrix} f(L)& 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\\end{bmatrix}$ Where f(L) = -(1 - HL²), makes the speed of light slower in that coordinate system? Originally Posted by Mike Helland I usually write H₀ instead of just H but that was a slip. L should be: L² = dx² + dy² + dz² Then you are posting gibberish. You haven't said anything about the units you're using now, but H₀ has units of inverse time and L² has units of area (i.e. length squared), so your f(L) = -(1 - HL²) subtracts something with units area/time from the dimensionless constant 1, which probably yields a negative number, which you negate, thereby most likely yielding a non-Lorentzian metric form. You really and truly have absolutely no idea of what you're doing. Originally Posted by Mike Helland I guess the desired effect is: c² = L² / (f(L)² * dt²) f(L)² c² dt² = L² 0 = - f(L)² c² dt² + dx² + dy² + dz² Oh dear. Oh dear. Your f(L)² c² dt² = L² can be rewritten as dt² = L² / (f(L)² c²) which says dt is a pure function of the location (via L and f(L)) independently of dx, dy, or dz. That's a truly impressive pile of ackamarackus you dumped there.
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Last edited by W.D.Clinger; 2nd April 2023 at 12:38 PM. Reason: parentheses

2nd April 2023, 12:52 PM	#1424
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger Then you are posting gibberish. You haven't said anything about the units you're using now, but H₀ has units of inverse time and L² has units of area (i.e. length squared), so your f(L) = -(1 - HL²) subtracts something with units area/time from the dimensionless constant 1, which probably yields a negative number, which you negate, thereby most likely yielding a non-Lorentzian metric form. H₀ has units of distance / time / distance. L² is a mistake. The ² should be outside the parenthesis. And that too might be a mistake. Because: Quote: You really and truly have absolutely no idea of what you're doing. To be fair, I think I have 0.0000756% of a clue. It ain't much, I'll give you that. Quote: Oh dear. Oh dear. Your f(L)² c² dt² = L² can be rewritten as dt² = L² / (f(L)² c²) which says dt is a pure function of the location (via L and f(L)) independently of dx, dy, or dz. Hmmm. Is that because I used L instead of dL? Should it be: dL² = dx² + dy² + dz²

2nd April 2023, 01:14 PM	#1425
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger which says dt is a pure function of the location (via L and f(L)) independently of dx, dy, or dz. Not sure what you mean. L is just short hand for: $\sqrt{dx^2 + dy^2 + dz^2}$ If what you said before: $c^2 dt^2 = a(t)^2 dx^2$ Then: $dx^2 = \frac{c^2 dt^2}{a(t)^2}$ Isn't that analogous?

2nd April 2023, 01:31 PM	#1426
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	Originally Posted by Mike Helland Originally Posted by W.D.Clinger Then you are posting gibberish. You haven't said anything about the units you're using now, but H₀ has units of inverse time and L² has units of area (i.e. length squared), so your f(L) = -(1 - HL²) subtracts something with units area/time from the dimensionless constant 1, which probably yields a negative number, which you negate, thereby most likely yielding a non-Lorentzian metric form. H₀ has units of distance / time / distance. FYI: "units of distance / time / distance" is just a complicated way to say units of inverse time. Originally Posted by Mike Helland L² is a mistake. The ² should be outside the parenthesis. Moving the exponent outside the parenthesis doesn't fix anything. In one important sense that I explained to you a couple of weeks ago, it actually makes things worse. But you ignored me then, because you don't know enough high school algebra and calculus to understand even the simplest explanations of what you're doing wrong. Originally Posted by Mike Helland Hmmm. Is that because I used L instead of dL? Should it be: dL² = dx² + dy² + dz² Actually, I misread your definition of L as L² = x² + y² + z². You are correct, however, that writing L instead of dL led me to jump to the conclusion that there were no differentials on the right hand side either. Originally Posted by Mike Helland Not sure what you mean. L is just short hand for: $\sqrt{dx^2 + dy^2 + dz^2}$ If what you said before: $c^2 dt^2 = a(t)^2 dx^2$ Then: $dx^2 = \frac{c^2 dt^2}{a(t)^2}$ Isn't that analogous? See above. Please take note, however, that your gibberish has quite a few other obvious problems that I haven't mentioned and probably won't ever bother to mention. There's no use.
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047

2nd April 2023, 01:42 PM	#1427
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger FYI: "units of distance / time / distance" is just a complicated way to say units of inverse time. Yes, very true. It's just a different way to follow the units. distance/time/distance = velocity / distance So in Hubble's law, v = H₀d, you get velocity = velocity / distance * distance Rather than using natural units (c=1), the coefficient for the time coordinate should be: $\frac{c-H_0 L}{c} c^2$

2nd April 2023, 02:59 PM	#1428
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 53,938	Originally Posted by Mike Helland Is it what W.D.Clinger wrote today, that culminates with: c = a(t) dx / dt ? $c = \frac{a(t)dx }{dt}$ That's for dynamic space. So the dynamic time analog would be: $c = \frac{ dx }{f(L) dt}$ Or is it something else? I was asking how to do it in general, given a metric tensor. If you are asking if that's the right answer, then you don't know, and if you don't know, you don't understand any of what you're talking about. This isn't news, but you're acting like you think you are on the cusp of understanding and you aren't. You don't have the foundation necessary to understand any of the answers you are being given.
	__________________ "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 all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law

2nd April 2023, 03:13 PM	#1429
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	This is what cargo cult physics looks like. Just within the past day or so, Mike Helland has made at least five different wild guesses (in the spoiler) concerning what he guesses he hopes to be a plausible metric form for Helland physics. Originally Posted by Mike Helland Ok. So are you saying: $\begin{bmatrix} f(L)& 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\\end{bmatrix}$ Where f(L) = -(1 - HL²), makes the speed of light slower in that coordinate system? Originally Posted by Mike Helland I usually write H₀ instead of just H but that was a slip. L should be: L² = dx² + dy² + dz² I guess the desired effect is: c² = L² / (f(L)² * dt²) f(L)² c² dt² = L² 0 = - f(L)² c² dt² + dx² + dy² + dz² Originally Posted by Mike Helland $c = \frac{a(t)dx }{dt}$ That's for dynamic space. So the dynamic time analog would be: $c = \frac{ dx }{f(L) dt}$ Or is it something else? Originally Posted by Mike Helland L² is a mistake. The ² should be outside the parenthesis. Originally Posted by Mike Helland Rather than using natural units (c=1), the coefficient for the time coordinate should be: $\frac{c-H_0 L}{c} c^2$ What a mess. I sincerely hope Mike Helland will clean up that mess by giving us just one last guess at a metric form, complete with a description of its coordinates and units, so we can have one last laugh before turning to the next chapter of this cargo cult physics.
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047

2nd April 2023, 03:30 PM	#1430
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger I sincerely hope Mike Helland will clean up that mess by giving us just one last guess at a metric form, complete with a description of its coordinates and units, so we can have one last laugh before turning to the next chapter of this cargo cult physics. Ok. Well, the lookback time for an FLRW universe with Ω_Λ=1 is: $t = \frac{1}{H_0}\int\frac{1}{1+z}dz$ It gives the right graph when I plot this: https://www.wolframalpha.com/input?i...%2Bx%5D%2Cx%5D So that should give the coordinate time. Whereas the "true" or "actual" time as you put it is L/c.

2nd April 2023, 03:57 PM	#1431
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047	ackamarackus Originally Posted by Mike Helland Originally Posted by W.D.Clinger I sincerely hope Mike Helland will clean up that mess by giving us just one last guess at a metric form, complete with a description of its coordinates and units, so we can have one last laugh before turning to the next chapter of this cargo cult physics. Ok. Well, the lookback time for an FLRW universe with Ω_Λ=1 is: $t = \frac{1}{H_0}\int\frac{1}{1+z}dz$ It gives the right graph when I plot this: https://www.wolframalpha.com/input?i...%2Bx%5D%2Cx%5D So that should give the coordinate time. Whereas the "true" or "actual" time as you put it is L/c. So that is Mike Helland's very best guess at what the metric form for Helland physics should look like. Mike Helland's very best guess at the metric form for Helland physics does not resemble a metric form in any way. But that's the very best he can do: quoting some random thing he found on the World-Wide Web, hoping it will fool some readers into thinking it has some remote relevance to the issue at hand.
W.D.Clinger Philosopher Join Date: Oct 2009 Posts: 5,047

2nd April 2023, 05:27 PM	#1432
hecd2 Graduate Poster Join Date: Oct 2013 Posts: 1,609	Originally Posted by Mike Helland I did notice your attempt to change the subject. How on earth is it a change of subject to point out to you that your silly attempts to write down a metric tensor with a function of location in g₀₀ results in a description of a non-homogeneous Universe. We observe the Universe to be isotropic. The only way that we can combine observed isotropy with inhomogeneity is if the Universe is spherically symmetric with us at its centre. (For example the Schwarzschild solution is spherically symmetric but not homogeneous). Quote: "If the rate of time is a function of location then the Universe is no longer homogeneous." Is it? Absolutely. The Robertson-Walker metric describes a homogeneous isotropic Universe (and is provably the only metric for a homogeneous isotropic Universe). In the FLRW solution the proper time is the same at all locations for comoving observers (so, for example, things which are functions of time, for example the scale factor, are universal and do not vary by location) Quote: The rate at which galaxies move apart is a function of distance, and causes clocks to move slower. That's homogeneous? Seems like your definition is pretty arbitrary. You are confusing proper time with coordinate time. Quote: You say the universe is observed to homogeneous. Is it? https://en.wikipedia.org/wiki/Lambda...of_homogeneity I said the Universe appears to be the same in all directions - ie we observe it to be isotropic. For example the CMB is uniform to one part in 100,000. If the Universe is isotropic but inhomogeneous it must be spherically symmetric with us at the centre. Quote: I take it you realized it's not internally inconsistent, . Your utterly daft idea that light pulses travelling the same distance at the same speed can have a different round trip flight time is totally inconsistent and FUBAR. You have been told that over and over again, but you are too ignorant and arrogant to accept it.
hecd2 Graduate Poster Join Date: Oct 2013 Posts: 1,609	__________________ Gulielmus Princeps Haroldum Principem in catino canino impulit Last edited by hecd2; 2nd April 2023 at 05:41 PM.

2nd April 2023, 05:58 PM	#1433
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by hecd2 How on earth is it a change of subject to point out to you that your silly attempts to write down a metric tensor with a function of location in g₀₀ results in a description of a non-homogeneous Universe. Let's say you have a fish pond. In the middle the fish are relatively still. But as you increase toward the edges, the fish are progressively more active and swimming faster. Is the pond homogeneous?

2nd April 2023, 06:16 PM	#1434
Mike Helland Illuminator Join Date: Nov 2020 Posts: 3,643	Originally Posted by W.D.Clinger So that is Mike Helland's very best guess at what the metric form for Helland physics should look like. Well it would be (and point out any mistakes, cause I'm sure there are some): $\begin{bmatrix}f(L)^2c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1 \end{bmatrix}$ So: $0 = - f(L)^2 c^2 dt^2 + dx^2 + dy^2 + dz^2$ Earlier I said: $t = \frac{1}{H_0}\int\frac{1}{1+z}dz$ But that's in terms of z, and probably needs to be in terms of L. This also calculates lookback time: $f(L) = \int\frac{c}{c-H_0L}dL$ So that's what should be in place of f(L).
	Last edited by Mike Helland; 2nd April 2023 at 06:17 PM.

3rd April 2023, 02:23 AM	#1435
hecd2 Graduate Poster Join Date: Oct 2013 Posts: 1,609	Originally Posted by Mike Helland Let's say you have a fish pond. In the middle the fish are relatively still. But as you increase toward the edges, the fish are progressively more active and swimming faster. Is the pond homogeneous? No, it would be inhomogeneous and isotropic about the centre. And your point is? ETA: for a fish living in such a pond, the only way that things would appear to be the same in all directions (isotropic) is if it was at the centre.
hecd2 Graduate Poster Join Date: Oct 2013 Posts: 1,609	__________________ Gulielmus Princeps Haroldum Principem in catino canino impulit Last edited by hecd2; 3rd April 2023 at 02:25 AM.