Strange Dark Matter Theory

[YellowSubmarine]

General Relativity, like Special Relativity, is extremely well-tested and understood. Eddington's experiments, modern GPS satellites...

Urban legend.

Without relativity, GPS positions would be 65 ns off in only 2 minutes, which would put you dozens of meters away from your real position. Ten kilometres off in a day. Urban legend indeed.

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

 

[FlyingLemons]

This bit of Wikipedia pisses off one of my colleagues who teaches the Gen Rel class at my university as before said Wikipedia page it was a good question to set.

He will, no doubt, breath a sigh of relief at it being an urban legend. If it's physicsmyths.org.uk that's the source of this, I'm going to have to go and roll up a big one or bake some brownies to continue. I wonder if the board software supports LaTeX?

There ARE several holes in GR. A dizzying number of them,

And what are the holes that there are "a dizzying number of", anyway?

 

[bryce]

Space station detector gives first clues to 'dark matter'

http://www.cnn.com/2013/04/04/world/europe/space-dark-matter/index.html?iid=article_sidebar

 

[Crazy Eddie]

Urban legend.

Your source for this?

Dean of the physics department at the University of Pennsylvania in 2004, after running the numbers myself and finding out that the statistical error resulting from uncorrected relativistic effects was actually an order of magnitude smaller than was suggested in the textbook (it worked out to ten meters, NOT ten kilometers, and my professor couldn't figure out what I'd done wrong so we went to the dean on sort of a bar bet). His reply was exactly this: GPS satellites do not really account for relativistic effects because they don't have to: their onboard clocks re-synch periodically through ground stations to keep them coordinated with both the Earth clocks and one another. Meaning that, to the extent relativistic effects are relevant at all, the satellite's onboard clocks are updated via ground stations anyway and regular compensation is not necessary or indeed even implemented.

He expressed to me his belief that the idea that GPS satellites accounted for relativistic effects actually originated from physics textbooks that used the GPS satellites as real-world scenario for relativistic calculations and that the eventual graduates of those classes went on to write articles about GPS satellites accounting for relativistic effects without actually knowing whether or not this was the case.

Without relativity, GPS positions would be 65 ns off in only 2 minutes

Which might be a problem except that most GPS receivers are only accurate to at most about 100ns -- some up to a microsecond -- which in your interpretation would mean an error of not less than 100 meters. Either my math is off (a distinct possibility) or an error of 65ns would add up to pseudorange of between 20 and 70 centimeters, which becomes considerably less if the receiver is using more than three satellites.

GPS satellites re-synch their atomic clocks via ground stations multiple times a day -- I had heard every ten to 20 minutes, but can't find a source for this now. Either way, they apparently do this more often than they upgrade their ephemeris data, which I know for a fact is done every two hours.

Urban legend indeed.

Well, really a scientific legend. It's similar to some of the weird and exotic things scientists claim about human beings exposed to the vacuum of space. Actually, it seems to be the case that ALOT of what scientists understand about "Things that happen in space" contains a lot more speculation than fact and not everyone is careful to separate the two.

 

[Crazy Eddie]

Space station detector gives first clues to 'dark matter'

http://www.cnn.com/2013/04/04/world/europe/space-dark-matter/index.html?iid=article_sidebar

That's exactly what I'm on about:

According to a CERN statement, the results announced Wednesday "are consistent with the positrons originating from the annihilation of dark matter particles in space, but not yet sufficiently conclusive to rule out other explanations."

For one thing, this basically refers to the WIMPs -- specifically, to neutralino -- model of Dark Matter. The reason they think this is related to dark matter is because it is theorized that large objects (the sun, for example) would possess enough gravity to capture dark matter particles; those particles would accumulate in sufficient density to interact with the material of those stars via the weak force; that interaction would produce a neutrino, which in turn would react with other particles to produce a high-energy positron.

Which is to say the conclusion "Evidence of dark matter" is based on a mathematical model, which is based on an assumption about the behavior of a hypothetical particle whose existence -- let alone behavior -- has never been demonstrated.

The search for dark matter has all the dynamics of an episode of Ghost Hunters. The only difference is the microphone that picks up the "strange noises that probably indicate a ghost" is a million times more expensive.

 

[Edit_XYZ]

Space station detector gives first clues to 'dark matter'

http://www.cnn.com/2013/04/04/world/europe/space-dark-matter/index.html?iid=article_sidebar

Here's the story - with less spin-doctoring:
http://arstechnica.com/science/2013/04/particle-detector-in-space-has-mixed-news-on-dark-matter/

Negative result for dark matter - but the tell-tale signs of dark matter (abrupt cutoff in positrons above a certain energy) may be beyond the range of the detector, the story goes, as always.

 

[FlyingLemons]

His reply was exactly this: GPS satellites do not really account for relativistic effects because they don't have to: their onboard clocks re-synch periodically through ground stations to keep them coordinated with both the Earth clocks and one another.

That's the GPS system recalibrating the satellite clock from the ground station to take into account the time dilation that would occur if the satellite clock were left to its own devices. It suppresses the time dilation effect by design - but without this built in would have problems as is well documented in the literature. Plenty of experiments have been done using the GPS system to examine the time dilation effect in general relativity, and thus we regard it as generally uncontroversial.

But I digress. I didn't read the rest of the thread...

Theoretical physicists have become so enamored by the possibilities of dark matter that derivative theories about what it could be and what it could DO extend far beyond any logical connection to the data that suggests its existence...

Uh... not really. The media would like to portray it that way, but in actual fact there are quite a few interesting debates going on surrounding that area.

If a highly respected physicist hacks together a bullshit mathematical equation that no one understands, who exactly is going to call him on it? Not his peers, who don't understand the equation and can't explain why it's bullshit.

Have you ever tried submitting a paper to Nature, PRD or JHEP? The reviewers there tend to be absolutely merciless if they find a mistake in your math - in my experience papers need to be mathematically watertight to get through at least for those journals. As iguana pointed out, physicists are pretty cut-throat and don't shy away from criticizing each other's work.

The only reason scientists question modified gravity is because they're uncomfortable with the idea that general relativity may be at least partially incorrect and/or inapplicable.

Theoretical physicist perfectly comfortable with the idea of modified gravity here...

Relativity itself has become a kind of academic sacred cow that scientists and engineers are reluctant to give the appearance of questioning, even when the theory itself is legitimately inapplicable.

Uh, what? Where'd you pick this up? There's plenty of us thinking about modifications and extensions to the theory of relativity because of the wealth of observational data in particle physics and cosmology telling us that something's not quite right with regards to the cosmological constant and high-energy behavior of gravity.

I'm a particle physicist so my interests lie towards the smaller areas of physics rather than the large, but off the top of my head:

There's the idea of inhomogeneous cosmologies that's been knocking about for ages and still generates papers. If the universe is not homogeneous and isotropic, perhaps dark matter doesn't exist after all and is instead an observational consequence of inhomogeneity.

Modified gravity, often involving scalar fields. Up until recently, I might have said "where's your scalar field?". There's now something vaguely Higgs-like floating around in LHC results... possibly we've found the first instance of a scalar field in nature.

Then there's one area I've worked in: that of the application of renormalization group. RG allows the constants of a quantum field theory to become subject to an energy scale, and allows us to vary said constants and study how the phenomenology of the system is affected by this.

Applying it to gravity, you can treat the theory of general relativity as an effective field theory and allow G and lambda to vary from the Planck era. This is quite interesting as some work by Percacci indicates that we could get inflation, reheating and the cosmological constant for "free" rather than through the introduction of new, unknown scalar fields.

Some also think that this idea could again be responsible for dark matter as well, meaning that it's down to a quantum gravity effect rather than any kind of new particle out there.

Relativity isn't "sacred". Any of these three ideas being experimentally proved would cause the textbooks to be rewritten. However, there's definitely a lot of general relativity that is well-tested, and what some call "gaping holes" for some reason most of us who work in physics call research areas to be explored rather than things that have us "worried".

 

[Crazy Eddie]

His reply was exactly this: GPS satellites do not really account for relativistic effects because they don't have to: their onboard clocks re-synch periodically through ground stations to keep them coordinated with both the Earth clocks and one another.

That's the GPS system recalibrating the satellite clock from the ground station to take into account the time dilation that would occur if the satellite clock were left to its own devices.

That's kinda what I mean. The satellites aren't programmed to account for relativistic distortions; they re-synch manually via ground stations. The claim that the satellites have a corrective subroutine that accounts for relativistic effects is more legend than fact. Besides which, the accrued error due to time dilation alone would be relatively small even if it wasn't corrected.

Theoretical physicists have become so enamored by the possibilities of dark matter that derivative theories about what it could be and what it could DO extend far beyond any logical connection to the data that suggests its existence...

Uh... not really. The media would like to portray it that way, but in actual fact there are quite a few interesting debates going on surrounding that area.

And I've been following enough of those debates to know that several of them are debates between theorists over the nature of the derivative theories and their broader implications in cosmology. Always in such cases I get the sense that theorists are getting way ahead of themselves, debating the properties of something that has not yet been proven to exist in the first place, which explains why alot of those debates bear a rather disturbing resemblance to arguments between Trek fans over the nature of warp drive. In the complete absence of data, otherwise rational scientists begin to substitute personal bias and unsupported assumption in its place. When their peers blow those assumptions out of the water, suddenly it gets personal.

Have you ever tried submitting a paper to Nature, PRD or JHEP? The reviewers there tend to be absolutely merciless if they find a mistake in your math - in my experience papers need to be mathematically watertight to get through at least for those journals. As iguana pointed out, physicists are pretty cut-throat and don't shy away from criticizing each other's work.

I know that, but at the same time it goes both ways. If you construct an equation of great enough sophistication that nobody can actually tell what you did wrong, it becomes easier to attack the credibility of people who disagree with you. Which, again, is pretty much what happened with Reinhart and Rogoff's austerity study until somebody actually dug into the numbers and found them to be bullshit after all.

Uh, what? Where'd you pick this up?

From conversations with a friend of mine working in Fermilab, although I should clarify that this is less a problem with the theorists and more a problem with institutions that fund them (universities and government agencies, for example). This is where politics and the scientific method begins to clash, which is DEFINITELY a relationship that scientists are understandably uncomfortable talking about.

There's plenty of us thinking about modifications and extensions to the theory of relativity because of the wealth of observational data in particle physics and cosmology telling us that something's not quite right with regards to the cosmological constant and high-energy behavior of gravity.

I know, and I'm familiar with a lot of them too. MY personal bias (call it a pet theory) is that Einstein's interpretation of the implications of Lorentz contractions introduced some potentially unwarranted conclusions and there is actually no need to extend the theory beyond Minkowski spacetime. I think that General Relativity would work a lot better if a way could be found to systematically apply Lortentz transformations to a curved spacetime -- say, Minkowsky spacetime with a noticeable curve -- at which point the distinction between special and general relativity disappears.

I'm a particle physicist

I'm a skeptical asshat who reads too much. Pleased to meet you!

Then there's one area I've worked in: that of the application of renormalization group. RG allows the constants of a quantum field theory to become subject to an energy scale, and allows us to vary said constants and study how the phenomenology of the system is affected by this.

Applying it to gravity, you can treat the theory of general relativity as an effective field theory and allow G and lambda to vary from the Planck era. This is quite interesting as some work by Percacci indicates that we could get inflation, reheating and the cosmological constant for "free" rather than through the introduction of new, unknown scalar fields.

I'll update my reading list for the weekend. Thanks for the tip!

 

[FlyingLemons]

That's kinda what I mean. The satellites aren't programmed to account for relativistic distortions; they re-synch manually via ground stations. The claim that the satellites have a corrective subroutine that accounts for relativistic effects is more legend than fact. Besides which, the accrued error due to time dilation alone would be relatively small even if it wasn't corrected.

I assume that most people reading when I mentioned GPS satellites would have understood about the clock problem. That's pretty much what most of everyone thinks of.

And I've been following enough of those debates to know that several of them are debates between theorists over the nature of the derivative theories and their broader implications in cosmology. Always in such cases I get the sense that theorists are getting way ahead of themselves...

We aren't "getting ahead of ourselves" when we've had pretty conclusive proof from observation and experiment that the basics of general relativity work. Some people get excited over more exotic theories, but until something to support them comes up we generally treat them as being theory only.

From conversations with a friend of mine working in Fermilab, although I should clarify that this is less a problem with the theorists and more a problem with institutions that fund them (universities and government agencies, for example).

Having been involved in reviewing several grant applications for the UK's STFC, I can officially say that "questioning relativity" will not get you in trouble career-wise. Among other things that have been approved are proposals to study Lorentz violation, which at least to me pretty much counts as "questioning relativity".

MY personal bias (call it a pet theory) is that Einstein's interpretation of the implications of Lorentz contractions introduced some potentially unwarranted conclusions and there is actually no need to extend the theory beyond Minkowski spacetime. I think that General Relativity would work a lot better if way could be found to systematically apply Lortentz transformations to a curved spacetime -- say, Minkowsky spacetime with a noticeable curve -- which which point the distinction between special and general relativity disappears.

Well, good luck with that but you've got a fair amount of observational evidence separating special and general relativity to overturn from cosmology, as well as finding a way of making transformations valid only in weak gravity work in a strong gravitational environment with non-vanishing curvature.

It would be an interesting paper to read, to say the least...

 

[Crazy Eddie]

And I've been following enough of those debates to know that several of them are debates between theorists over the nature of the derivative theories and their broader implications in cosmology. Always in such cases I get the sense that theorists are getting way ahead of themselves...

We aren't "getting ahead of ourselves" when we've had pretty conclusive proof from observation and experiment that the basics of general relativity work.

But not dark matter, which is what that paragraph was referring to.

From conversations with a friend of mine working in Fermilab, although I should clarify that this is less a problem with the theorists and more a problem with institutions that fund them (universities and government agencies, for example).

Having been involved in reviewing several grant applications for the UK's STFC, I can officially say that "questioning relativity" will not get you in trouble career-wise. Among other things that have been approved are proposals to study Lorentz violation, which at least to me pretty much counts as "questioning relativity".

But are actually related to quantum gravity and m-theory, and -- again, only going by what I hear from gripes -- is a delicate balance of proposing the new theory without offending the biases of establishmentarians.

OTOH, you work in the UK? It could just be cultural.

MY personal bias (call it a pet theory) is that Einstein's interpretation of the implications of Lorentz contractions introduced some potentially unwarranted conclusions and there is actually no need to extend the theory beyond Minkowski spacetime. I think that General Relativity would work a lot better if way could be found to systematically apply Lortentz transformations to a curved spacetime -- say, Minkowsky spacetime with a noticeable curve -- which which point the distinction between special and general relativity disappears.

Well, good luck with that but you've got a fair amount of observational evidence separating special and general relativity to overturn from cosmology, as well as finding a way of making transformations valid only in weak gravity work in a strong gravitational (highly curved, that is) environment.

If I ever did get around to I'd start from the latter -- getting the transformations work in a high curvature -- and then work backwards to the observational evidence to see if the numbers are (or could be made) consistent with it.

 

[FlyingLemons]

But not dark matter, which is what that paragraph was referring to.

The "dark matter problem" is not a consensus, even in theoretical physics. Some physicists don't even accept the existence of dark matter and believe it's just weird gravity effects... cosmologists haven't just decided "dark matter exists" without proving it and if the LCDM model was violated it'd be chucked out along with the steady-state universe and others that proceeded it.

But are actually related to quantum gravity and m-theory, and -- again, only going by what I hear from gripes -- is a delicate balance of proposing the new theory without offending the biases of establishmentarians.

What "establishment" do you speak of? If you present a coherent case for a program of study to most funding councils, generally you'll get a fair hearing and most of the time funding is turned down because there just isn't enough.

Many who rail against "the establishment" not listening to them aren't maverick geniuses that threaten "the consensus", whatever that is, but often people who lack the personal skills to be able to be in a room with others.

There are "independent researchers" outside the physics community, who often have the above problems but also generally tend to tie their "research" in with unscientific New Age ideas or who have theories that are mathematically unsound. Appointing any of these individuals to an academic position would be a waste of public money, as aside from anything the return on their "research" would be non-existent.

Before anyone mentions it, the idea that funding particle physics and astrophysics research that is seemingly esoteric to the layman is a waste is a lie. In particular, the study of computational quantum field theory is a key driver of the development of massively parallel computer architectures such as QCDOC which have commercial applications. Many of these things would be horrendously difficult to develop on the timescales demanded by the free market.

If I ever did get around to I'd start from the latter -- getting the transformations work in a high curvature -- and then work backwards to the observational evidence to see if the numbers are (or could be made) consistent with it.

In order to do that, you'd have to first to start reinventing what we know about differential geometry in order to get it to work before even starting to think about applications to physics.

I think proving that highly curved spaces are in fact flat would raise eyebrows among geometers and topologists, let along theoretical physicists.

 

[Crazy Eddie]

The "dark matter problem" is not a consensus, even in theoretical physics.

It is according to proponents of dark matter theory. But if you're right that reports of a consensus are exaggerated, then I stand properly corrected.

If I ever did get around to I'd start from the latter -- getting the transformations work in a high curvature -- and then work backwards to the observational evidence to see if the numbers are (or could be made) consistent with it.

In order to do that, you'd have to first to start reinventing what we know about differential geometry in order to get it to work before even starting to think about applications to physics.

I don't think so, actually. My sense is that this would involve one of those horrendously complicated recursive processes like third or fourth derivative calculus (which I fucking HATE doing, by the way). You wouldn't need to treat a curved space as if it was flat, you'd just need a mathematically consistent way to account for that curvature itself. Which is, like, stupefyingly difficult, but hardly impossible.

As an extreme oversimplification: you have a formula to calculate the surface area of a sphere (general relativity) and to calculate the surface area of a cube (special relativity). The basic problem is that there's no elegant way to calculate the surface area of an irregularly shaped object like, say, a rock or an oddly-shaped peanut. Locally-flat spacetime is a mathematical conceit that doesn't actually exist in reality and so special relativity itself is just an approximation (like using the ideal gas model to calculate drag coefficients on a spacecraft; you can get away with it under some circumstances, but not all).

I'm not, IOW, saying it would be simple or formulaic as such. Really, I'm saying that Einstein's relativity is a paradigm that obfuscates the fact that Minkowski spacetime IS applicable to curved (or rather BUMPY) spacetime and we simply lack an efficient way to calculate those spacetimes much the way we lack an efficient way to calculate the surface area of a oddly-shaped peanut.

 

[FlyingLemons]

You wouldn't need to treat a curved space as if it was flat, you'd just need a mathematically consistent way to account for that curvature itself. Which is, like, stupefyingly difficult, but hardly impossible

The Minkowski metric is the very definition of flat. It's simple: (-1, 1, 1, 1) - apart from the minus sign, it's pretty much a straight map from number to space, no transformation, so if I feed x = 2, y = 3 and z = 3 into it it gives me back x = 2, y = 2 and z= 3.

"Minkowski space with curvature" isn't Minkowski space but something else. Once you introduce a set of co-ordinates with anything other than -1 and 1 as the metric, you're back in curved space. And special relativity comes out of pretty much all spaces, but only in locally flat co-ordinates and linearized gravity in that space thus making it a sub-case of GR.

Locally-flat spacetime is a mathematical conceit that doesn't actually exist in reality and so special relativity itself is just an approximation (like using the ideal gas model to calculate drag coefficients on a spacecraft; you can get away with it under some circumstances, but not all).

"Special relativity is just an approximation" - where's your experimental evidence for this? Hundreds of experiments have been done which have verified special relativity, taking place in locally flat spacetime. You've said dark matter theorists are getting ahead of themselves, but here you mention something which flies in the face of modern quantum field theory and astrophysics without anything to back that up.

"Dark matter", whatever it is, isn't just a mathematical invention done for shits and giggles. We have CMB observations from Planck, and observations of gravitational lensing which tells us that there's something going on there. It could be an undiscovered form of matter, it could be quantum gravity effects... but apart from the "dark matter" problem we know the rest of relativity is pretty much right.

This isn't "the establishment" talking, but rather experimental data. Special relativity has been verified time and again by RHIC, LEP, LHC and many other experiments. If an unusual gravitational effect had popped up at any of these that indicated something was wrong with basic special relativity, it would have been noticed and studied.

Nothing so far, and unless a spectacular deviation from special relativity at the colliders no reason to doubt relativity. Physicists don't just "accept" relativity - if, say, we discovered Lorentz violations at a collider we'd go and start reworking what we know about it.

Really, I'm saying that Einstein's relativity is a paradigm that obfuscates the fact that Minkowski spacetime IS applicable to curved (or rather BUMPY) spacetime

This is a speculation on your part, not a fact. I'm a theoretical physicist: what I do is theory, and fact only if it pops up in an experiment. If I say something is a fact in a paper, then I've got to back it up. I can say many aspects of the Standard Model are a fact: they've been measured. Relativistic time dilation: a fact, it has been measured.

Academic language is full of disclaimers when applied to theoretical physics - fact is a very loaded term to use, and here you're saying that a flat space metric is applicable to curved spaces which kind of flies in the face of geometry. The distance measures of Minkowski space when applied to curved space will not give correct results as they would fail to take into account the properties of that space - (-1,1,1,1) would give wrong answers when mapping numbers to the manifold surrounding, say, a star or other spherically symmetric body.

If you can put forth a substantial body of experimental data to show that equations of motion in curved spaces can be found using the Minkowski metric, I'd accept that as a fact. I accept that there is something we call "dark matter" out there because of experimental evidence, although what the specifics of it are I would say are unknown.

When it comes to "the Minkowski metric can be applied to a curved space" I generally tend to trust my differential geometry books which define it as a flat space and only a flat space, rather than your statement that this isn't true.

 

[JarodRussell]

Could Dark Matter be the result of a gross underestimation of the masses of black holes, planets, asteroids, dust and shit? Especially the shit?

 

[Asbo Zaprudder]

As I said, cosmic squirrels -- they must surely defecate...

But no, the numbers don't appear to add up if you assume dark matter is baryonic.

http://en.wikipedia.org/wiki/Baryonic_dark_matter

Re Crazy Eddie's curved spacetime, which appears to be envisaged as being a patchwork of Minkowski spacetimes, although I might be wrong. Perhaps it might have difficulty explaining effects such as frame dragging, although the experimental results for that are somewhat inconclusive.

http://en.wikipedia.org/wiki/Frame_dragging

Certainly, a new theory would have to be consistent with the large amount of experimental evidence already collected.

 

[Crazy Eddie]

You wouldn't need to treat a curved space as if it was flat, you'd just need a mathematically consistent way to account for that curvature itself. Which is, like, stupefyingly difficult, but hardly impossible

The Minkowski metric is the very definition of flat.

Yes, I know all that. All I've said is that the solutions for Lorentz transformations could be modified to account for anomalies in the actual coordinate system, provided you can quantify them in a mathematically consistent way.

A better way to conceptualize it would be, say, a superposition of two different transformations that treats the curvature of space as an inherent vector and thus becomes the coordinate system for for the observer's relative motion.

"Minkowski space with curvature" isn't Minkowski space but something else.

Minkowsky space assumes the flatness of space even when it demonstrably isn't. You could still account for that curvature even if the metric doesn't explicitly reflect its presence.

"Special relativity is just an approximation" - where's your experimental evidence for this?

The fact that Special Relativity assumes a locally flat spacetime even when when evaluating the behavior of objects moving within gravitational fields that are themselves non-uniform.

It's therefore an approximation, like Kepler's Laws or Newtonian gravity. It's a very good approximation, but it explicitly avoids dealing with gravitational effects by assuming their effect is negligible -- which is true on the small scale -- despite the fact that those effects are ubiquitous in the universe. It works well enough on the small scale, but that means we lack a way to apply special relativity to very large objects (galaxies and stars, for instance) whose relative velocity is very high and whose gravitational fields cannot be ignored.

here you're saying that a flat space metric is applicable to curved spaces which kind of flies in the face of geometry.

I don't see how. It's relatively simple, geometricaly, to project a curved surface onto a flat one. Why should Minkowski space be any different?

The distance measures of Minkowski space when applied to curved space will not give correct results as they would fail to take into account the properties of that space - (-1,1,1,1) would give wrong answers when mapping numbers to the manifold surrounding, say, a star or other spherically symmetric body.

And yet you say it gives correct answers when calculating transformations on GPS satellites in Earth orbit...

If you can put forth a substantial body of experimental data to show that equations of motion in curved spaces can be found using the Minkowski metric, I'd accept that as a fact.

If I could do that, we wouldn't be having this conversation, because you'd be reading about it in a newspaper and I'd be filthy rich.

 

[Asbo Zaprudder]

If you can put forth a substantial body of experimental data to show that equations of motion in curved spaces can be found using the Minkowski metric, I'd accept that as a fact.

If I could do that, we wouldn't be having this conversation, because you'd be reading about it in a newspaper and I'd be filthy rich.

I doubt that coming up with a replacement for GR would make anyone filthy rich. You might get tenure in a respectable university.

I'd suggest working on a way to make all the molecules in a hostess's undergarments leap simultaneously one foot to the left. You might even come up with the infinite improbability drive, but beware of the rampaging mob of respectable physicists who realize that the one thing they can't stand is a smart-ass.

ETA: Ripped off Douglas Adams, of course.

 

[JarodRussell]

As I said, cosmic squirrels -- they must surely defecate...

But no, the numbers don't appear to add up if you assume dark matter is baryonic.

http://en.wikipedia.org/wiki/Baryonic_dark_matter

Hm well, the theoretic amount of baryonic dark matter depends on the Big Bang nucleosynthesis theory. Another part of the puzzle that might be just wrong.

The possible margin of error there is extremely great. We don't really know what the hell happened at the beginning of the universe, so if that assumption is wrong, any explanation derived from it is wrong as well.

 

[iguana_tonante]

This thread is slowly turning into "will someone checkproof my cosmological pet theory". I'm more than willing to help. For a price. We've all got bills to pay, and this is how I pay mine.

Crazy Eddie, I appreciate your curiosity and enthusiasm for the topic, but the points you raise are either nonsensical (a curved Minkowski's space?), or already well-known. Still, if you think your hypothesis is robust, I urge you to submit it to the scientific community. One way or the other, you will have your answer.

On the other hand, what I don't appreciate is the standard reply of "mean scientists are mean meanies" to cover one's shortcomings. What is see in your posts is a lot of "I have a feeling", "I believe", "my friend told me", "a professor once said to me", "what I hear from gripes". And I can tell you exactly what that is worth: Nada. Zero. Zilch. Nothing.

So, you can either support your pet theory, or you can't.

Dark matter is simply a mathematical placeholder; arguing that we even have a convincing - aka, in accord with all experimental evidence, with properly determined characteristics, etc - conjecture as to what it is says more about the arguer.

Please tell me. I'm quivering in anticipation. Especially since I never argued that we know what it is, only how it behaves.

If you can put forth a substantial body of experimental data to show that equations of motion in curved spaces can be found using the Minkowski metric, I'd accept that as a fact.

If I could do that, we wouldn't be having this conversation, because you'd be reading about it in a newspaper and I'd be filthy rich.

I doubt that coming up with a replacement for GR would make anyone filthy rich. You might get tenure in a respectable university.

I am especially intrigued when people say that I am paid good money by the CIA, the Mossad, the Illuminati, the Vatican, and the Mafia to suppress the truth. I wish. I wish.

 

[FlyingLemons]

Minkowsky space assumes the flatness of space even when it demonstrably isn't. You could still account for that curvature even if the metric doesn't explicitly reflect its presence.

No, you just use a metric more suited to the property of that space.

The fact that Special Relativity assumes a locally flat spacetime even when when evaluating the behavior of objects moving within gravitational fields that are themselves non-uniform.

You can create a tangent space which appears locally flat, but not globally in strong gravity. If the universe was a purely weak gravity environment then "Minkowski everywhere" works, otherwise no.

It's therefore an approximation, like Kepler's Laws or Newtonian gravity. It's a very good approximation, but it explicitly avoids dealing with gravitational effects by assuming their effect is negligible -- which is true on the small scale -- despite the fact that those effects are ubiquitous in the universe.

That's why it's special relativity - a special case for locally flat spacetimes.

It works well enough on the small scale, but that means we lack a way to apply special relativity to very large objects (galaxies and stars, for instance) whose relative velocity is very high and whose gravitational fields cannot be ignored.

That's when special relativity is generalized to general relativity and more complicated math becomes involved. When dealing with galaxies and cosmological scales, we use the FRW metric. When dealing with stars and other spherically symmetric bodies, we use the Schwarzchild metric. The cases you talk about have very well-known relativistic solutions backed up by experiment and observation.

We've got an entire mathematical apparatus to describe motion in curved spaces - Christoffel symbols, the Ricci tensor being two examples. They fit experimental data, and to boot you can retrieve the special relativistic and Newtonian cases from them. It's not "so mathematical it can't be checked", either. Many physics students, or indeed anyone, can develop a basic understanding with a little effort.

I don't see how. It's relatively simple, geometricaly, to project a curved surface onto a flat one. Why should Minkowski space be any different?

The Minkowski line element is x^2 + y^2 + z^2, and that's it. Try applying that metric to a strong gravitational field and your equations of motion will be nonsense because the geometry of space won't be described by it.

And yet you say it gives correct answers when calculating transformations on GPS satellites in Earth orbit...

That's because it's not applying the Minkowski metric but instead an approximation of the Schwarzchild metric, the one you use for a spherically symmetric body such as the Earth.

Did you actually take a class in general relativity and cosmology at college? It sounds as if you're sort of unaware of the existence of metrics which perfectly solve the problems (motion on a cosmological scale, gravity surrounding spherically symmetric objects) that Minkowski can't handle that you describe.

]I am especially intrigued when people say that I am paid good money by the CIA, the Mossad, the Illuminati, the Vatican, and the Mafia to suppress the truth. I wish. I wish.

Remember the song we sang at the last Physics Conspiracy Meeting? 'Twas glorious.

[yt]http://www.youtube.com/watch?v=_ZI_aEalijE[/yt]