Merged Relativity+ / Farsight

[lpetrich]

Note what Farsight seems to imagine space-time to be.

He seems to think that a universe with it would be absolutely frozen with no change in it. But we don't at it look from outside, we inhabit it, and we perceive it as changing over time.

He also seems to think that if time was a fundamental physical feature, then it would flow through clocks is if they were gas meters, as if it was some fluid.

But clocks work by their operation being a function of time, and marking out changes of state as functions of time. We have a sense of time, and it works in the same way (Time perception^WP).

Perceptions of objects works in the same way, but with space instead of time. We don't directly see objects. Instead, we notice gradients of incoming light as functions of direction, and we interpret the presence of objects from those gradients. Likewise, we don't directly feel objects by touch. We notice gradients of touch strength as a function of skin-relative position. So by Farsight's argument, gradients exist but space doesn't.

In fact, we don't directly perceive 3-space. Here is the spatial information that our senses return:

• Proprioceptive: joint angles (discrete)
• Skin senses: skin-relative positions (2D)
• Vision: directions (2D)
• Inner ear: acceleration and rotation

So by Farsight's argument, 3-space does not exist, because we do not directly perceive 3D information.

One can go even further and note that we do not directly perceive objects. Instead, we get ideas in our consciousnesses, which we interpret as having external causes. So by Farsight's argument, we end up with solipsism.

 

[lpetrich]

Another troublesome aspect of Farsight physics is its inability to accept space-time symmetries.

Three-space translation and rotation symmetries were more-or-less taken for granted for a long time. Consider Euclid's axiomatic foundation of geometry. He included his fifth postulate, which is far from obvious, but he took superposition for granted and he did not include it in his axioms, despite using it in some of his constructions. More recent geometry axioms have included superposition as the SAS postulate, that if one knows two side lengths and the size of the angle between them, one can deduce the rest of the triangle's features no matter where the triangle is or how it is oriented. Superposition implies maximal symmetry, symmetry under all possible translations, rotations, and reflections, something that implies constant curvature. Euclid's fifth postulate, however, turned out to be equivalent to zero curvature.

Time translation and reflection symmetry was also likely taken for granted for a long time.

But how might space and time be related?

Late in his life, Galileo published a thought experiment where he imagined being below decks in a ship, trying to tell what the ship's motion is. If it is moving at a constant rate, then there would be no way to tell that it was moving.

Newtonian mechanics involves the aforementioned space and time symmetries and also symmetry under what are called Galilean boosts, in honor of that thought experiment.
x' = x + v*t, y' = y, z' = z, t' = t

Newtonian mechanics was enormously successful, but it was inconsistent with Maxwell's equations. From those equations, speed of electromagnetic waves in a vacuum is a constant, while a Galilean boost can change its speed.

A popular solution was the "ether" or "aether", a reference frame where Maxwell's equations would be true without needing correction terms. Michelson and Morley famously tried to find the Earth's ether-relative velocity, and found that if it has one, then it is less than the Earth's orbital velocity.

Is the Earth cosmically stationary? That would violate Newtonian mechanics big time.

Does the Earth drag the ether near it? Other experiments showed no sign of ether drag.

Various physicists proposed that moving through the ether alters space and time in ways that make those experiments give negative results. Hendrik Antoon Lorentz came up with the most successful one, a Lorentz boost:
x' = γ*(x - v*t), y' = y, z' = z, t' = γ*(t - v*x/c²)
γ = (1 - v²/c²)^-1/2
Subjecting Maxwell's equations to a Lorentz boost gives Maxwell's equations again, with appropriate transformations of the electric and magnetic fields, and also the charge and current densities. Thus, Maxwell's equations are symmetric under Lorentz boosts.

Einstein recognized that Lorentz-boost symmetry make it impossible to find the ether, and he thus concluded that it is an unnecessary hypothesis, just like in Newtonian mechanics.

Enter Hermann Minkowski.

He took Lorentz boosts one step further, by considering what happens to an appropriately-defined line element under them. He found that
S = x² + y² + z² - c²*t²
is preserved by both rotations and Lorentz boosts. Thus, Lorentz boosts are a sort of rotation in space-time. This makes time much like space, something that Minkowski himself recognized:

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

("Space and Time")

General relativity further blurs the distinction between space and time, since space-time curvature is arbitrary in it to within satisfying Einstein's equations.

 

[Farsight]

Unlike you I'm a qualified physicist. I just pulled off my shelf one of my first year undergraduate texts, turned to the page where fields are first discussed, and temperature and water velocity are both amongst the first examples of fields given, along with electric and gravitational fields.

Then your textbook is wrong.

The mathematics is the precise and unambiguous statement of the physical theory. Noone is hiding behind it - exactly the opposite as it is the one case where everything is laid completely bare.

Edd, when people tell you to ignore what Einstein said because his mathematics allegedly says the opposite, run a mile.

Now do you want to talk physics, or are you with the naysayers and hyperskeptics who are determined to turn JREF into a physics-free zone?

It seems very strange to cling to scientific statements of a century ago and ignore all possibility of improvement. Given that Einstein himself recognized that he had made mistakes, it seems unwise to take everything Einstein says as gospel.

It's not like that. Instead we have a bunch of naysayer hyperskeptics here with a cargo-cult popscience misunderstanding of relativity that contradicts Einstein, contemporary authors such as Ned Wright and John Baez, and the hard scientific evidence.

You make me curious: it has been pointed out several times that Einstein's equations show something completely different from what you claims he said. Do you claim that Einstein's equations are wrong? Or can you show that there is no contradiction?

It hasn't been pointed out that Einstein's equations show something different, it's been alleged. Try linking to an instance, and you'll appreciate what I mean. No, I don't claim Einstein's equations were wrong. I claim they're right, along with what Einstein actually said, and I point to Magueijo and Moffat and Baez and Wright to back up what I'm saying. However there are quacks out there who know you don't understand the equations, they'll tell you they mean something different and they'll tell you to ignore Einstein. Don't.

Do you believe being able to understand these discussions is good for a person?

You can understand relativity and gravity, it's amazingly simple. But there are "high priests of science" who don't want you to. If there's anything you'd like to talk about, including dark matter and dark energy and cosmology, please do, and I'll tell you what I can. But do note that there are people on this thread who want to stifle all physics discussion. Be aware of that.

 

[edd]

Then your textbook is wrong.

Huh. Ok, what would it take to convince you that it and I are not wrong?

 

[edd]

Conclusive proof that Einstein was wrong. In this article you can read this:

In that article Einstein is clearly referring to certain fundamental physical fields (gravitational and electromagnetic). That doesn't mean he's supplying the textbook definition for all physics. You have to read it in context. And even when you do it is clear from your own quotation:

It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric.

that he is hypothesising at that point and obviously doesn't have a theory that lets him unify gravity and electromagnetism as he'd like to (which is a fine aim). People did indeed try to do that with moderate but incomplete success with the Kaluza-Klein models, but it isn't clear right now that every fundamental physical field arises in such a manner (or even any, beyond gravity). It absolutely isn't a definition of 'field', and absolutely doesn't mean that every time the word 'field' is used in physics it is referring to a fundamental field either.

 

[steenkh]

It hasn't been pointed out that Einstein's equations show something different, it's been alleged.

Actually, it has been more than alleged, and you have done absolutely nothing to dispel the allegation, just like you have done absolutely nothing to show that you understand Einstein's math. On the contrary, you have studiously ignored, or fopped off the problems. You even try to persuade us that the imprecise words are more important than the precise equations.

I could understand it if you were one like me who does not understand math, but for a self-declared math genius like you, it sounds suspicious.

Try linking to an instance, and you'll appreciate what I mean.

What about explaining that Clinger is wrong when he says that gστ is a symbol for spacetime?

No, I don't claim Einstein's equations were wrong. I claim they're right, along with what Einstein actually said, and I point to Magueijo and Moffat and Baez and Wright to back up what I'm saying.

Look at Clinger's latest post, and you will see that you have scored an own goal here. Prove him wrong. Show by actual math that Einstein did not combine space and time.

 

[edd]

Edd, the whole point of this thread is that definitions and interpretations have changed, and some aspects of contemporary textbooks are now flat out wrong. Defining a field to accommodate "height fields" or "pressure fields" or "wind speed fields" or "ocean salinity fields" is an example of this. And if you can't accept that, persuade yourself that we are discussing "fundamental physics fields", and move on.

And you're arguing that usage over time changes and that a quote from Einstein in 1929 supercedes my book first published in 1966 (repub 1983, and probably since then) means this definition is wrong? Just searching the arxiv for 'velocity field' this last year produces 186 results. I think if the usage has changed (and I'd argue it actually hasn't significantly - I'd bet Einstein would be quite happy to talk of a velocity or pressure field in relation to his own fluid dynamics work) then it's not gone the way you think.

If you want to go on and just stick to a certain subset of fields then fine, but I think you should also clarify exactly what you think a "state of space" is, because you clearly seem to think that those fields are all somehow geometric distortions in space. It may be the case that this is true in higher dimensions, but this has never been demonstrated, and I don't think you should be stating it as fact. Einstein in your own quotation of him only 'suspected' it.

 

[Farsight]

And you're arguing that usage over time changes and that a quote from Einstein in 1929 supercedes my book first published in 1966 (repub 1983, and probably since then) means this definition is wrong? Just searching the arxiv for 'velocity field' this last year produces 186 results. I think if the usage has changed (and I'd argue it actually hasn't significantly - I'd bet Einstein would be quite happy to talk of a velocity or pressure field in relation to his own fluid dynamics work) then it's not gone the way you think. If you want to go on and just stick to a certain subset of fields then fine

Move on, edd.

but I think you should also clarify exactly what you think a "state of space" is, because you clearly seem to think that those fields are all somehow geometric distortions in space.

Actually, I don't. I've referred to the gravitational field as inhomogeneous space. Think of this as space being "denser" lower down. A gravitational field is not curved space.

It may be the case that this is true in higher dimensions

What higher dimensions? There is no evidence of any higher dimensions.

but this has never been demonstrated

Oh, OK.

and I don't think you should be stating it as fact. Einstein in your own quotation of him only 'suspected' it.

OK, I'll qualify such statements. But do google electromagnetic geometry. I'm not some "my theory" guy, it isn't something I've made up.

 

[Kwalish Kid]

Then your textbook is wrong.

While there are mistakes that creep into textbooks, it seems more than a little paranoid to claim that a physics textbook is wrong when it writes about the definition of a field and about the idea of a temperature field, especially when it is not alone in these.

Edd, when people tell you to ignore what Einstein said because his mathematics allegedly says the opposite, run a mile.

That also seems very paranoid: all of contemporary physics is built upon the ability to precisely match theory to observations using mathematics and to deny the mathematics is to claim a vast conspiracy.

Now do you want to talk physics, or are you with the naysayers and hyperskeptics who are determined to turn JREF into a physics-free zone?

This is a strange question from a poster who has never produced an accurate description of a single physical system.

It's not like that. Instead we have a bunch of naysayer hyperskeptics here with a cargo-cult popscience misunderstanding of relativity that contradicts Einstein, contemporary authors such as Ned Wright and John Baez, and the hard scientific evidence.

The evidence from the scientific publications of Wright and Baez indicates that they disagree with your ideas. If you are attempting to pick statements outside of this context to claim that they side with your beliefs, this is tantamount to lying.

It hasn't been pointed out that Einstein's equations show something different, it's been alleged. Try linking to an instance, and you'll appreciate what I mean. No, I don't claim Einstein's equations were wrong. I claim they're right, along with what Einstein actually said, and I point to Magueijo and Moffat and Baez and Wright to back up what I'm saying. However there are quacks out there who know you don't understand the equations, they'll tell you they mean something different and they'll tell you to ignore Einstein. Don't.

Could you show us where in Einstein's equations we find your specific claims? For example, could you show us where Einstein uses the slowing of the speed of light to govern the behaviour of a system? This seems to be where any physicist or philosopher of physics would begin in their analysis.

You can understand relativity and gravity, it's amazingly simple. But there are "high priests of science" who don't want you to. If there's anything you'd like to talk about, including dark matter and dark energy and cosmology, please do, and I'll tell you what I can. But do note that there are people on this thread who want to stifle all physics discussion. Be aware of that.

You claim that dark matter and dark energy are merely part of the operation of Einstein's equations. This claim means that Einstein was grossly wrong about his own theory. Can you provide evidence for your claim that corresponds to measurements of galaxies or structures at the cosmological scale?

 

[Kwalish Kid]

I'm not a liar. And I responded in full with references to your points.

It is odd that you respond that you are not a liar and then immediately lie. This seems to be your main method of argument.

 

[Kwalish Kid]

...when a few second's worth of do your own research will come up § 2. The Fundamental Equations for Æther by Hermann Minkowski. Note that lpetrich knows about this but he didn't chip in to correct you. And note that you're a naysayer. A hyperskeptic. You're just like a creationist. You are prey to conviction, and nothing I show you will persuade you that you're wrong.

That Minkowski worked out the physics for a contemporary physical theory does not mean that he endorsed the theory. Can you show us that that section of that piece plays a role in all of Minkowski's work on relativity theory? Otherwise there seems to be no basis for your claim that Minkowski believed in the ether.

Fair enough. And one depicts the path of an object through space as a world line in spacetime. But note that the river is frozen. The object doesn't move around in this frozen river. But objects do move around in space. So when you see a shooting star, remind yourself that it's moving through space, not spacetime.

Any description of motion through space requires a time coordinate. Thus it too is using spacetime. Until you produce some means of describing motion without time, you are forced to do physics with the same "block universe" as anyone who uses GR. (Note that this is not the same "block universe" as those who argue for a block universe interpretation of time.)

I'm not confused, you are. Spacetime is curved, not inhomogeneous. And space is inhomogeneous, not curved. See this Baez article where you can read this: "Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial".

It would be a lie to say that article says anything about inhomogeneity. If you want to link the two, you need to show a general means of using inhomogeneity to account for gravity.

And don't be fooled into dismissing Einstein because some ignorant quack is telling you something different.

You are claiming that we should ignore Einstein's mathematics (something you do not know).

All: this is straw-man trash that's best ignored. Also note that lpetrich is being less than honest about aether. he knows about Einstein's Leyden Address. He says Enter Hermann Minkowski but he didn't tell you about § 2. The Fundamental Equations for Æther .

lpetrich seems to be scrupulously honest here: he is not ignoring Einstein's reference to his own mathematics in that address as you seem to be doing and he is not elevating a passing reference by Minkowski into an endorsement of traditional aether theories.

 

[lpetrich]

(a textbook that refers to "velocity fields")

Then your textbook is wrong.

Farsight, I found numerous references to "velocity fields", and I thought of posting some, but I don't want to drown this post in links.

Edd, when people tell you to ignore what Einstein said because his mathematics allegedly says the opposite, run a mile.

Emphasis mine. Note the style of argument, treating Einstein's statements as revealed truth that it would be wrong to reject. I sometimes feel like I'm reading some scriptural percussionist's writings.

...when a few second's worth of do your own research will come up § 2. The Fundamental Equations for Æther by Hermann Minkowski.

I read it. He gives some equations for electromagnetism in their traditional 3+1 form, and he constructs a full-4D version of them.

So when you see a shooting star, remind yourself that it's moving through space, not spacetime.

Since it advances in time, it moves through spacetime. Denying spacetime is denying Minkowski and Einstein and Feynman and John Baez and Ned Wright and ... to use one of your favorite arguments.

Spacetime is curved, not inhomogeneous. And space is inhomogeneous, not curved.

Both can be any selection of {homogeneous, inhomogeneous} and {not curved, curved}. In fact, 3-space is a slicing of space-time where all the directions in each slice are spacelike. The slices are usually chosen to make the slice-to-slice directions all timelike.

... and of course Einstein's Leyden Address.

What makes that document an inspired text?

So according to Einstein, a field is a state of space.

He was speculating about a unified field theory.

That's good enough for me.

In other words,

Give me that old-time religion.
It was good enough for Einstein,
It was good enough for Maxwell,
It was good enough for Minkowski,
It was good enough for Newton,
It was good enough for Feynman,
And it's good enough for me.

We wouldn't want anybody getting sceptical about the multiverse or the holographic universe or WIMPs, now would we?

Whatever makes those theories heretical.

But do google electromagnetic geometry. I'm not some "my theory" guy, it isn't something I've made up.

Search-engine result page again. Farsight, did you *read* any of that page's links?

 

[W.D.Clinger]

Edd, the whole point of this thread is that definitions and interpretations have changed, and some aspects of contemporary textbooks are now flat out wrong. Defining a field to accommodate "height fields" or "pressure fields" or "wind speed fields" or "ocean salinity fields" is an example of this. And if you can't accept that, persuade yourself that we are discussing "fundamental physics fields", and move on.

Einstein's doctoral dissertation (1905) involves pressure fields. Einstein's dissertation also uses stress and velocity fields.

Einstein's dissertation is in German, but see for example:

Dwight E. Neuenschwander. Albert Einstein's Dissertation
Norbert Straumann. On Einstein's Doctoral Thesis​

Pressure fields (of a different sort) are also present in Einstein's papers on general relativity, because three components of the stress-energy tensor field T_μν represent pressure. See, for example, equation (58) of Einstein's Die Grundlage der allgemeinen Relativitätstheorie.

I try to persuade you to go and read what Einstein said, and to be sceptical of the sophistry that tells you not to. Or tells you to ignore it, because the truth is in the math. Which you don't understand. Duh!

From Farsight's denial of pressure fields, I can only conclude that Farsight doesn't know enough math to realize notations such as ∇p imply p is a field.

In the quotation above, Farsight is saying his personal inability to understand Einstein's mathematics should lead others to ignore arguments based upon that math. That's a prescription for ignorance.

Because he wasn't wrong about that. He was wrong to claim that Einstein meant spacetime is inhomogeneous. See what I said to Perpetual Student in this post. We talk of curved spacetime and inhomogeneous space. Not inhomogeneous spacetime. Clinger knows he's wrong. He's being less than sincere, and he's carping to try to spoil the thread, because he can't stand the fact that when it comes to relativity and gravity, I'm the expert round here.

The highlighted text reveals that Farsight has no idea of what I've been saying. That's hardly surprising, because my argument has been based upon Einstein's math, which Farsight doesn't understand.

Clinger scored the own goal, and there is no way to "show by actual math" that Einstein meant spacetime when he said space. It's nonsense to think maths can be used for such a purpose. You wouldn't understand it anyway.

It's easy to "show by actual math" that Einstein's discussions of the relativistic "ether" refer to spacetime. That was in fact done in post #1960 and post #1965 of this thread.

When Farsight says "You wouldn't understand it anyway", he's projecting his own mathematical illiteracy onto others.

 

[steenkh]

No it hasn't. That's why you can't point to an instance.

But I can of course:

Farsight, of course, has only read about general relativity; he has never studied it. That's why he's been quoting Einstein's Leiden address for years without ever understanding what Einstein meant by the "ten functions (the gravitation potentials g_μν)" mentioned within the very sentence Farsight was quoting.


The ten functions g_μν are the components of what Einstein called the fundamental tensor. The subscripts range over the four indices of spacetime. The tensor is symmetric, meaning g_μν = g_νμ, which is why there are only ten different functions instead of sixteen.

If Farsight were right about Einstein's ether referring to space rather than spacetime, then the subscripts would range over only the three spatial indices, implying at most nine functions. Einstein said "ten" because he's referring to spacetime.

You followed this up in post #889 where you completely ignored the argument. And apparently you now admit that Clinger was right about g_μν.

I try to persuade you to go and read what Einstein said, and to be sceptical of the sophistry that tells you not to. Or tells you to ignore it, because the truth is in the math. Which you don't understand. Duh!

You have a point there. But I can see who ignores arguments and claims it is a virtue not to use equations, and I have got a strong feeling that you are almost as helpless with math as I am, but you just do not admit it as freely.

Because he wasn't wrong about that. He was wrong to claim that Einstein meant spacetime is inhomogeneous.

You could perhaps demonstrate this by pointing this out in Einstein's equations? Even if I cannot follow the argument, I can see the reaction to it by people who can.

Come on steenkh, make your mind up, what do you want to be, an Emperor's New Clothes sucker, or a sceptic?

You claim to be the emperor expert around here, so you should be very careful with your quips.

 

[Farsight]

While there are mistakes that creep into textbooks, it seems more than a little paranoid to claim that a physics textbook is wrong when it writes about the definition of a field and about the idea of a temperature field, especially when it is not alone in these.

It isn't paranoid, it's plain speaking. Everybody knows about electromagnetic fields and gravitational fields. To come on all high and mighty and sniffy about temperature fields and velocity fields is just erudite trash.

That also seems very paranoid: all of contemporary physics is built upon the ability to precisely match theory to observations using mathematics and to deny the mathematics is to claim a vast conspiracy.

Huh? Nobody is denying the mathematics. Instead we've got naysayer quacks telling you to dismiss what Einstein or Minkowski or Maxwell actually said. Because what they really meant, dear boy, is contained in this here mathematics that you don't understand. I mean, here we are on a skeptic website, and people like you expect people will fall for that? LOL!

The evidence from the scientific publications of Wright and Baez indicates that they disagree with your ideas...

Are you for real? They aren't my ideas. I refer to Einstein and Minkowski and Maxwell, and I refer to Wright and the Baez website to back it up:

"Einstein talked about the speed of light changing in his new theory. In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers..."

Could you show us where in Einstein's equations we find your specific claims? For example, could you show us where Einstein uses the slowing of the speed of light to govern the behaviour of a system? This seems to be where any physicist or philosopher of physics would begin in their analysis.

No, because after 1911 he employed the locally-measured speed of light rather than the coordinate speed of light. And do note that the beginning of the analysis is what Einstein said, not dismissing what he said.

You claim that dark matter and dark energy are merely part of the operation of Einstein's equations. This claim means that Einstein was grossly wrong about his own theory.

I don't quite claim that, but don't forget that this area is where Einstein made his "greatest blunder".

Can you provide evidence for your claim that corresponds to measurements of galaxies or structures at the cosmological scale?

Huh? Does not parse. But I can refer to information about the cosmological constant:

"In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is the value of the energy density of the vacuum of space. It was originally introduced by Albert Einstein in 1917 as an addition to his theory of general relativity to "hold back gravity" and achieve a static universe, which was the accepted view at the time. Einstein abandoned the concept as his "greatest blunder" after Hubble's 1929 discovery that all galaxies outside our own Local Group are expanding away from each other, implying an overall expanding universe. From 1929 until the early 1990s, most cosmology researchers assumed the cosmological constant to be zero."

It's spatial energy. And in case you hadn't noticed, space is dark.

 

[Kwalish Kid]

It isn't paranoid, it's plain speaking. Everybody knows about electromagnetic fields and gravitational fields. To come on all high and mighty and sniffy about temperature fields and velocity fields is just erudite trash.

Given your history of insulting physicists, it is not surprising that you refer to the everyday practice of physicists as trash.

Huh? Nobody is denying the mathematics.

Effectively a lie: you are asking us all to ignore everything that we have learned about the mathematics of relativity theory in favour of your personal interpretation gained only from a selective reading of specific texts. This is denying the mathematics.

Are you for real? They aren't my ideas.

Also effectively a lie: you are presenting your ideas on how one should interpret or use relativity theory. You certainly know this, since you know that textbooks disagree with you. You also know that nobody, including John Baez, agrees with your interpretation of Baez' website.

No, because after 1911 he employed the locally-measured speed of light rather than the coordinate speed of light. And do note that the beginning of the analysis is what Einstein said, not dismissing what he said.

You are explicitly admitting that your ideas play no role in anything to do with the science of relativity theory.

I don't quite claim that, but don't forget that this area is where Einstein made his "greatest blunder".

You have made specific claims that you seem now to be trying to deny. You have yet to produce any observational evidence for your claims.

Huh? Does not parse.

It's actually a straightforward question: can you produce evidence for your claims about dark matter or dark energy from observations of galaxies or from structures of greater size?

You seemingly cannot even describe the rotation of a galaxy. This means that your only source of belief for your claims of dark matter are your own dogma.

But I can refer to information about the cosmological constant:

You can do this, but you can't demonstrate that your own special claims about gravity match observations at these scales or any scales.

It's spatial energy. And in case you hadn't noticed, space is dark.

That would be a lie you just wrote about the content of that article.

 

[Kwalish Kid]

You can't. Yes the gμν subscripts range over the four indices of spacetime, but it describes the state of space. You shine a light beam through it. If the light moves slow, space has one state, if it moves fast space has a different state. If it curves space has an inhomogeneity, and its state is not uniform.

Could you please show us how to decompose this spacetime mathematics into space and... well, space and whatever we are supposed to use since you don't believe in time. Then please show us where Einstein did this same thing.

Damn right I do. Who are you going to believe, Einstein and Newton and Minkowski and Maxwell and me, saying things you can understand? Or Clinger giving you maths you can't?

So far, you aren't giving us things we can understand. We understand the mathematics, we do not understand it when you claim that there is some sort of inhomogeneous space that Einstein talked about in one place but seemingly nowhere else. Showing us how to decompose gμν into space and whatever would go a long way to demonstrating that you are not simply spouting your own dogma.

I'm not hopeless at maths. You want some maths? Here you go:

[qimg]http://www.forkosh.com/mimetex.cgi?G_{\mu \nu} + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}.[/qimg]

Pasting this seems to indicate that you are hopeless at maths. Addressing the relevant questions mathematically, something you have never done, would indicate otherwise.

No I can't. Because Einstein's equations don't have "space is inhomogeneous" in them.

Ah, so you were lying to us all along and you plainly knew it.

 

[Farsight]

Einstein's doctoral dissertation (1905) involves pressure fields. Einstein's dissertation also uses stress and velocity fields.

Einstein's dissertation is in German, but see for example:

Dwight E. Neuenschwander. Albert Einstein's Dissertation
Norbert Straumann. On Einstein's Doctoral Thesis​

Unfortunately for you, Clinger there's no mention of "pressure field" in the latter. And we don't talk about "pressure fields" when we're discussing the weather, do we?

Pressure fields (of a different sort) are also present in Einstein's papers on general relativity, because three components of the stress-energy tensor field T_μν represent pressure. See, for example, equation (58) of Einstein's Die Grundlage der allgemeinen Relativitätstheorie.

From Farsight's denial of pressure fields, I can only conclude that Farsight doesn't know enough math to realize notations such as ∇p imply p is a field.

Again unfortunately for you Clinger, I'm on record as having described a gravitational field as a pressure gradient in space. Ah, here we go, see post #11

I should justify that I suppose. See the energy-pressure diagonal in Einstein's stress-energy-momentum tensor? Stress is directional pressure. A gravitational field is a "pressure gradient in space". It alters the motion of light and matter through space, but it doesn't suck space in. Think of space as something that has an innate pressure, like a squeezed-down stress-ball. Open your fist and watch it expand. It expands, it doesn't collapse. In similar vein the universe didn't collapse under its own gravity when it was very small and very dense. And it isn't going to collapse when it isn't.

In the quotation above, Farsight is saying his personal inability to understand Einstein's mathematics should lead others to ignore arguments based upon that math...

I'm telling others not to ignore what Einstein said. Especially when some guy is telling them something that totally contradicts Einstein, and trying to justify it by saying "Einstein's maths says it". Knowing full well that others don't understand that maths. That's sophistry, Clinger. As you know full well.

 

[Kwalish Kid]

Unfortunately for you, Clinger there's no mention of "pressure field" in the latter. And we don't talk about "pressure fields" when we're discussing the weather, do we?

They appear on the televisions screen with amazing regularity!

I'm telling others not to ignore what Einstein said.

But you are: you want us to ignore the entirety of the content of Einstein's work on actually applicable relativity theory in favour of one cherry-picked quotation that you admit plays no role in the work Einstein did. That is stunning.

 

[W.D.Clinger]

another example of Farsight's expertise

Earlier this morning, I wrote:

From Farsight's denial of pressure fields, I can only conclude that Farsight doesn't know enough math to realize notations such as ∇p imply p is a field.

In his response, Farsight confirmed that conclusion:

Einstein's doctoral dissertation (1905) involves pressure fields. Einstein's dissertation also uses stress and velocity fields.

Einstein's dissertation is in German, but see for example:

Dwight E. Neuenschwander. Albert Einstein's Dissertation
Norbert Straumann. On Einstein's Doctoral Thesis​

Unfortunately for you, Clinger there's no mention of "pressure field" in the latter.

Straumann's first numbered equation includes the ∇p that (as predicted) Farsight failed to recognize as a pressure field.

From page 5 of that paper:

...the basic equations become
∇p = − η ∆v, ∇∙v = 0. (1)
These imply that the pressure is harmonic: ∆p = 0.

Note also that v is the velocity field, and the words "velocity field" appear twice on page 6 alone.