There is convincing evidence for galactic dark matter
There is no convincing evidence at all for 'dark matter', which has become the running joke of the cosmological world. It is evoked wherever and whenever measurements don't match the expectations of physical laws. What is worse, it is invoked in whatever quantities it is imagined will 'balance' the equations.
Hartnett: Carmelli Metric...(above) wrote:
In fact, astronomers have traditionally resorted to ‘dark matter’ whenever known laws of physics were unable to explain the observed dynamics.
"However, the Sphere Theorem fails due to discrete localization of mass,"
It doesn't fail at all. It's a theorem and can be proven with math. There's no such thing as a perfect sphere in reality, but this is irrelevant.
The Sphere Theorem is a Physcial theorem, not just a mathematical construction. It is a statement about gravitational forces in physical situations (and applies to Electrostatics as well). The assumption in the 'proof' of the Sphere Theorem is that the mass (or charge) is continuously distributed. This is known to be false. As an approximation for large numbers of closely packed particles it works reasonably well, but not absolutely, or at molecular distances.
Since its a physical theorem, a purely 'mathematical' proof is not relevant. The question of the scope and applicability of the theorem is the whole point.
It can also be mathematically shown that the Sphere Theorem must fail when the sources of mass or charge are quantized. The 'math' is just as 'mathematical' and valid a tool for the disproof as for the proof.
I'll start a thread showing failure of the Sphere Theorem if you like.
There's no need. First of all, there's no such thing as a "Physical Theorem." A theorem is a mathmeatical statement that has been proven mathematically. Physics has theories, not theorems. Theories are physical hypotheses that have been tested so well to be accurate that the majority of physicists believes them to be true.
The physical analog of the spere theorem would be a sphere theory. I.e. that real physical spherical shells have no net force on the inside and behave as a point particle at its center on the outside. What you're essentially saying is that the sphere theory has limited applicability since matter is discretized and there is no such thing as a perfect sphere anyway. This is nothing new. And it does not shatter the mathematics behind the sphere theorem, which is unquestionably true.
As an analogy here, consider the Pythagorean theorem. This is not applicable to real triangles because of issues like sharpness of corners, and no object can be perfectly flat, and the geometry of space time is curved anyway. This doesn't negate the Pythagorean theorem as a mathematical statement.
There is convincing evidence for galactic dark matter
There is no convincing evidence at all for 'dark matter', which has become the running joke of the cosmological world. It is evoked wherever and whenever measurements don't match the expectations of physical laws. What is worse, it is invoked in whatever quantities it is imagined will 'balance' the equations.
Hartnett: Carmelli Metric...(above) wrote:
In fact, astronomers have traditionally resorted to ‘dark matter’ whenever known laws of physics were unable to explain the observed dynamics.
A lot of theories predict, in fact NEED, the existence of dark matter and dark energy. And it's not a joke at all. Most cosmologists believe in it.
"And of course no one has offered *any* coherent explanation at all for Newton's bucket experiment, which is crucial to any plausible version of gravity."
Newton's Laws predict the bucket to behave the way it does. Newton's Laws work in the realm in which this experiment has been performed. The issue of inertia and Mach's principle is really more of a philosophical question at this point.
By Newton's 'laws' I suppose you mean his discussions of circular motion and inertia. No educated person can be unaware at this point that Newton had to propose the artificial construct of 'Absolute Space' as an axiom in order to achieve his efficient version of the laws of motion. Newton never 'proved' anything about 'Absolute Space', which was rejected by the majority of physicists ever since as a kludge.
Even Einstein's General Relativity does not support the idea of 'Absolute Space', but rather a gravitational 'field' which moves along with the mass that generates it.
The point is, Newton describes the mechanism of the forces for the bucket experiment, and Einstein also conceives an explanation in terms of the gravitational field. But to say that there is 'Absolute Space' in Newton's sense is considered nonsense or 'useful fiction'.
When we turn to Newton's Gravity theory, there is *nothing* in it that can account for the bucket experiment. Even Mach acknowledged that the backdrop of the fixed stars had no known mechanism by which the bucket experiment could be explained.
Neither Newtonian Gravity nor Gen Rel properly accounts for Newton's bucket experiment. It remains one of the most difficult mysteries of gravitational theory. No known gravitational theory plausibly explains how and where the forces could come from to cause the experimental results of the bucket experiment.
If anything, modern particle theories make the problem more intractible than ever.
Newton erected the artificial axiom of 'Absolute Space' by fiat, and Einstein rewrote gravity as a field theory. Neither offered cogent cause and effect explanations for the bucket.
A gravitational theory that could explain the bucket would require more than simple 'unorientable' point-masses exerting simple direct attraction upon one another. Each particle would have to have orientation, chirality, and a way of distinguishing individual units not currently available.
(i.e. each electron would have to have a unique 'serial number').
First of all, absolute space was accepted up until Einstein. Some people (including Newton) were a little uneasy about it, but they still accepted it.
The bucket experiment can be explained very simply with Newton's Laws. The bucket spins. The water doesn't spin at first because it was at rest before. But eventually friction with the walls gets it going. It then takes a concave shape because of the centripetal force necessary to keep the water going around. When the bucket stops, the water keeps spinning due to inertia. It thus maintains its shape for the same reason, centripetal force. As it slows (because of friction with the walls) down it becomes ordinary, non-spinning water and thus loses this shape. In an empty universe, Newton's laws imply the water would take a concave shape. Whether or not this is correct, of course, remains to be see. But Newton's Laws handle the known experimental data just fine.
there's no such thing as a "Physical Theorem." A theorem is a mathmeatical statement that has been proven mathematically. Physics has theories, not theorems. Theories are physical hypotheses
What time-wasting nonsense. The last time I got into a discussion with someone about the Centre of Mass theorem, he insisted it not be called a 'theorem' but a 'method'. It has nothing to do with the issue at hand. It's just childish hairsplitting over words. The theory/theorem/method/hypothesis cannot be corrected with wordplay. It's physically incorrect.
Quote:
A lot of theories predict, in fact NEED, the existence of dark matter and dark energy. And it's not a joke at all.
I have to agree with you on this: if 'a lot of theories' depend upon 'dark matter', its not a joke, its just a comedy of errors, or rather a Greek tragedy.
Quote:
The bucket ...takes a concave shape because of the centripetal force necessary to keep the water going around. ...It thus maintains its shape for the same reason, centripetal force. As it slows ...down it becomes ordinary, non-spinning water and thus loses this shape.
What gobbledygook. Spinning relative to what? Absolute Space? which we know is a fraud? Even if the water was spinning relative to *something*, like say the collective mass of the universe = the backdrop of stars and galaxies (ala Machian relativity) there is no known force or method (certainly not gravity) that could connect the distant stars to the bucket and cause a physical action, like the water rising. The only known plausible force or field that could have done the job would have been gravity, but no known formulation or theory of gravity offers a mechanism to move the water up the sides of the bucket.
Quote:
and the geometry of space time is curved anyway.
Only if you believe in SRT or Gen Rel.
I prefer Weber's Electrodynamics. It is cogent, accurate, and makes verifiable predictions that neither SRT or GRT can.
Good luck with that.
"What time-wasting nonsense. The last time I got into a discussion with someone about the Centre of Mass theorem, he insisted it not be called a 'theorem' but a 'method'. It has nothing to do with the issue at hand. It's just childish hairsplitting over words. The theory/theorem/method/hypothesis cannot be corrected with wordplay. It's physically incorrect. "
It's not non-sense at all. It's an important point.
here's what you originally said: "However, the Sphere Theorem fails due to discrete localization of mass." This is simply false. And since you stated it from nowhere, how am i supposed to no what your issue was or what you were getting at?
"Spinning relative to what? Absolute Space?"
YES!! I've said several times I'm talking within the framework of Newton's Laws, which include Absolute Space.
"which we know is a fraud?"
Doesn't matter. It works well as an assumption if all you're doing is spinning a bucket around with water in it at moderate speeds.
"The only known plausible force or field that could have done the job would have been gravity, but no known formulation or theory of gravity offers a mechanism to move the water up the sides of the bucket. "
The water moves up the sides of the bucket because it is pushed up by the lower water. Think about the spinning swing ride at an amusement park. What is it that actually raises the swings and pushes them out? the ropes they're connected to. Then equilibirum is reached and all the ropes need to do is provide the necessary entripetal force to keep them going in a circle (and tension top keep them from falling). An anlogous thing happens with the water in the bucket. Only the ropes in this case is actually more water.
"Only if you believe in SRT or Gen Rel. "
As any reasonable physicist does.
"I prefer Weber's Electrodynamics. It is cogent, accurate, and makes verifiable predictions that neither SRT or GRT can.
Good luck with that."
Give me a link or something. My guess is it's probably nonsense but I'll take a look.
Perhaps you aren't thinking it through clearly:
If Absolute Space is a fiction, how is it supposed to create a force strong enough to move water upward? If it is a fiction, how do we know when something is 'rotating' and how fast it is rotating?
And even if Absolute Space were real, what possible mechanism can be postulated that could cause movement relative to it to generate a force? What do you push against in a vacuum? The aether?
According to Newton (Absolute Space + Vacuum!) there is no mechanism or means to exert a force, or even any method to know whether you are rotating or not relative to Absolute Space.
According to Einstein, (Gravitational Tensor Field Theory) you are being bent by and bending 'space' (!!), so that like storing energy in a flywheel, you are storing energy in a 'field'. But this field is not anchored to anything but other mass. So it is really an attempt at Mach's idea that you could somehow explain absolute rotation by reference to the fixed background of stars. Only Mach didn't know about Big Bangs, and didn't even believe in electrons in 1924.
Einstein failed to carry out Mach's plan, because even in an empty universe, there is absolute rotation according to Gen Rel, which bends space and radiates gravitational waves.
There is nothing really in either theory that can explain how the background of stars (through a field or not) can cause the rotating bucket experiment to work out.
Gravity as explained and defined by Newton himself does not and cannot include the action of the bucket experiment.
Quote:
Give me a link or something. My guess is it's probably nonsense but I'll take a look.
The unit of the magnetic field is the Weber. Its named obviously after one of the most brilliant and famous scientists of the age of electromagnetism. Assis published an updated and complete version of Weber's great work. A physicist who hasn't heard of Weber is like an electrical engineer who hasn't heard of Maxwell.
I think you've been sold a lot of worthless philosophy. There is an obvious physical difference between rotating frames of reference and inertial frames of reference. Would you like a mathematical proof? Try to extend my very general 1+1 dimensional universe to an extra spatial dimension and try to conceive of consistent laws of physics in that universe where it's impossible to distinguish between rotating and non-rotating frames of reference. What would the simplest equations of motion be?
Remember the first law of Shubertian physics: Nothing inconceivable exists.
"If Absolute Space is a fiction, how is it supposed to create a force strong enough to move water upward? "
It doesn't. Space doesn't create any force. The water itself pushes itself upward and provides this rather non-mysterious force that you are so puzzled about. See my previous post.
"The unit of the magnetic field is the Weber. Its named obviously after one of the most brilliant and famous scientists of the age of electromagnetism. Assis published an updated and complete version of Weber's great work. A physicist who hasn't heard of Weber is like an electrical engineer who hasn't heard of Maxwell."
Of course I've "heard" of Weber. I haven't seen this theory of Electrodynamics that you allege he conceeived. Sicne you won't post a link I will conclude I was correct in assuming it's nonsense. Also, I wouldn't be surprised if a lot of EEs haven't heard of maxwell. I taught 3rd semester engineering and we never even covered Maxwell's equations (although it was in the book). It's totally not relevant for the kinds of stuff they do.
Since you won't post a link I will conclude I was correct in assuming it's nonsense.
The new standard of scientific validity and orthodoxy is 'internet validation'. It works like parking validation at the mall. If you can prove you were in the internet store by an electronic receipt, you are not charged the parking fee for posting your scientific reference.
Around here, we don't rely upon the internet. It just isn't there yet. 80% of scientific publications are still not available on the net. Try a library for Weber. *Every* university library will have Assis' book on Weber's Electrodynamics.
Dogpile gave me 19 references however, on the first try:
[url=http://www.ifi.unicamp.br/~assis/Revista-Facultad-Ingenieria-(Chile)-V9-p29-34(2001).pdf]EM field & Bohm Effect[/url]
[url=http://www.ifi.unicamp.br/~assis/Phys-Lett-A-V268-p274-278(2000).pdf]Weber vs Maxwell (again)[/url] - note: Phys-Lett-A.
A small list of Assis on Weber Assis' work is found in almost every respectable Physics journal known.
Assis is one of the most respected physicists in the field of Electrodynamics today, internationally.
Also, I wouldn't be surprised if a lot of EEs haven't heard of maxwell. I taught 3rd semester engineering and we never even covered Maxwell's equations (although it was in the book). It's totally not relevant for the kinds of stuff they do.
I'd be greatly surprised!
The 'Maxwell' equations you refer to aren't Maxwells: His confused set of 12 to 20 equations are a mess. Heaviside singlehandedly sorted it all out, reduced the 'Maxwell' equations to four, invented vector calculus, named 9 out of 10 electrical quantities, and virtually created all of Electrical Engineering and the age of Electronics. I'd be surprised if some EE somewhere hadn't heard of Maxwell, but I demand every EE know who Heaviside is.
"It's totally not relevant for the kinds of stuff they do." !!?!?!
What can I say? 90% of EE is vector algebra, vector calculus, and vector analysis. Try doing Fourier Analysis without vectors (or matices, their mathematical equivalent). Better yet, try to unpack quaternions without the mathematical apparatus of vectors.
Tait promoted quaternions, but (Gibbs & especially) Heaviside took us from the dark ages of horse and buggy to harnessing Niagara Falls.
Try doing that without Heaviside's 'Maxwell Equations'.
But my original point was, 'Maxwells Equations' are primitive approximations compared to Weber's Electrodynamics. And Einstein blew it by choosing 'Maxwell' as the basis for modern physics instead of Weber.
Ok, well, don't have time to look it up in the library. Maybe when I return my transcendental number theory books in a few months I'll check it out.
"The 'Maxwell' equations you refer to aren't Maxwells: His confused set of 12 to 20 equations are a mess. Heaviside singlehandedly sorted it all out, reduced the 'Maxwell' equations to four, invented vector calculus, named 9 out of 10 electrical quantities, and virtually created all of Electrical Engineering and the age of Electronics. "
They're still called Maxwell's Equations. That's what everyone calls them, whether it's justified or not.
"What can I say? 90% of EE is vector algebra, vector calculus, and vector analysis. Try doing Fourier Analysis without vectors (or matices, their mathematical equivalent). Better yet, try to unpack quaternions without the mathematical apparatus of vectors."
You don't need to understand Maxwell's equations to do all of that.
"But my original point was, 'Maxwells Equations' are primitive approximations compared to Weber's Electrodynamics. And Einstein blew it by choosing 'Maxwell' as the basis for modern physics instead of Weber."
But not so right that Einstein didn't have to point out the ridiculous contradiction in the equations for a stationary vs moving coil, and rewrite everything covariantly, and propose a whole new theory (SRT).
And not so right that Weber's equations turn out less accurate. In fact rather, there is serious physical evidence that Weber, not Maxwell, is more accurate where they differ (see links above), and predicts new phenomenae.
Teachers and University apologists defend old theories like SRT. Physicists prefer the cutting edge, looking for the undiscovered.
But not so right that Einstein didn't have to point out the ridiculous contradiction in the equations for a stationary vs moving coil, and rewrite everything covariantly, and propose a whole new theory (SRT).
What's so ridiculous about it? Relativity hadn't been discovered yet. That was part of Einstein's genius, that he just new the answer couldn't depend on some kind of absolute motion. But other people did.
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