What's the matter with mass?

I need to keep this going, had some interesting thoughts (oh yes!) but forgot to blog about them.

Mass appears to us in three forms.  The first is fixed to matter, giving matter its inertia and its weight in a gravitational field.  The second is dark matter, which is not matter at all because after decades of searching for it there is nothing there but mass, like the grin on a Cheshire cat.  This is Detached Mass (DM, conveniently).  The third is the mass in black holes, where any matter attached to it is unlikely to survice in a form we recognise, although obviously mass is retained when its matter enters a black hole.

I just want cosmologists to let their minds separate matter from mass and to detach the idea that everything has a particle associated.  At some point the null result of the dark matter particle search should be taken as an outcome, and a new approach tried.

Mass distinct from matter, and rotating galaxies rotate . .

Having gained my third degree, BSc Hons 2:1 in Nat Sci (Phys, Astro) am no longer thinking this subject so much.  I have learned something, but as expected the main lesson is how little I know. Main stimulus is New Scientist articles, with ever-more-esoteric explanations and 'discoveries' featuring the sentiment "might". Two things recently occurred to me out of this blue:

1) I have long held that it is not obvious that the content of black holes, matter, has the same form as its familiar form outside the black hole.  It is obvious that its mass is retained otherwise black holes could never happen or be sustained, and anyway, where would the mass go?  But no-one knows what form the matter can take after entering the event horizon, though surely is is very different even from its form in elementary particles, its most dense.

A way to look at it is not that mass is a property of matter, but rather that mass is a fundamental, and it may occupy matter as an essential constituent, but is not exclusive to matter.  By this view matter may be destroyed or completely transformed in a black hole, separated from its mass, while the mass exists in its basic or raw form taking up no space.

The only property of mass is its bending of spacetime to cause the effect of gravity, the intensity of the bending being directly related to the density of mass, and the amount of bend in a region relating to the totality of mass in that region.  (Whether the binding of mass with matter (optional to mass) is a property of mass or matter is moot.)  Mass exists in black holes, it exists in matter to give it inertia/weight, and it can also exist outside either black holes or matter in the form of - dark matter (DM).  Which hereby has a new and apposite name - unattached mass (UM).

2) This turns on its head my scepticism about so-called DM, as I have intuitively favoured MOND/TeVeS approaches, while seeking a way in which this conflict can instead be a duality.  MOND works very well in rotating galaxies but does not extend to larger-scale cosmology.  The increasingly detailed maps of DM as evidenced by gravitational lensing, the prime test for mass, are not helping the case for MOND, and it must be accepted that DM is ubiquitous and not necessarily related to the MOND acceleration a₀.

Yet the success of MOND to explain flat rotation curves without DM begs the question 'what is special about rotating galaxies that lets MOND work?'.  The answer may be that they are rotating.  I have argued at length about the special nature of rotation, causing an acceleration which once at steady rotational speed is constant and indefinite with no further energy requirement, also a description of gravity itself.  Rotation also has the property of existing in just two dimensions in terms of its plane, with the axis orthogonal and hence virtually defining an additional dimension.

So this conjecture is that mass is a fundamental and independent occupier and interactor of spacetime with no properties other than to bend spacetime, and (where required) to stiffen and weight matter.  It appears not to interact with itself, and cannot be expected to interact with matter (except as a constituent) or with the electromagnetic spectrum.  UM can be mapped in the cosmos by its gravitational effects but there are no particles of it.  Stop looking for Dark Matter, it does not exist.  But UM does link closely with rotational cosmology as evidenced in galaxy rotation curves, and points to a relationship between mass and a model for the universe as a whole involving rotational acceleration as an analogue for gravity.

The downgrading of matter from a fundamental to a derivative gives more options for the nature of matter and antimatter, ie less reason why there should be (or have been) the same amount of both.  Assume however that there is no such thing as anti or negative mass, but connect the fact that when antimatter and matter particles collide they disappear and release their mass in the form of energy.

What's the (dark) matter

These posts have been very sparse, as I expected, formal study of the subject stifles free thinking.  I tackled my tutors on my 2015 cosmology module on how a 3-d shape (a sphere) can be used to explain that 2-d space (its surface) can have curvature without invoking the third dimension, is fair to show that 3-d space can still have curvature without a 4th dimension, but hit a brick wall.  Unless time is sufficient alone to be that 4th dimension.

But as time goes on I am more confident to gloat, with gravitational waves now being clearly found in LIGO (Sept 2015), the seekers of dark matter particles must be getting increasingly desperate. With all their candidates, and all the possibilities of sensitive measurements, there must come a point soon where they admit that if dark matter is real, it must have been discovered by now.

I find it incredible that a phenomenon discovered by measurements of gravitational effects, and with no physical evidence, is taken as something with a physical explanation and not a gravitational one!  Just as Newton's relativity was upgraded by Einstein's, so can Einstein's relativity be upgraded to account for dark matter.  It seems to be apparent independence of DM that is holding us back, especially in cases like the bullet cluster where colliding gas slows down but the non-self-interacting DM does not, and separates out.  Well I would be more inclined to question these measurements or inferences than to search for the elusive lumps of non-interacting stuff.

The rotating analogy

Big gap while studying a serious cosmology module, and still (near the end of it) trying to understand how the surface of a solid object, even a simple one like a sphere, can be described in only two dimensions.  It just means the third dimension is implied in the frame of reference used, and it still (one way or another) needs coordinates in three orthogonal senses to define any point on it.  Tensors are all smoke and mirrors, a bit worrying just a couple of weeks from the exam!

But I come back to the rotation analogy.  The hammer-thrower, once he has got his hammer rotating, exerts an original force on the handle.  It does not come and hit him in the face (as it would if not rotating) because the moving mass has to continue moving.  Its inertia in the tangential direction makes it produce an equal and opposite force along the wire, putting the system in equilibrium.  This is an example (are there any others?) of how a force can be exerted on a free body, causing a constant acceleration, yet with no movement in the rotating frame of reference.

For a ball sitting on the ground there is an original force pushing it upwards, but it does not shoot up into the air, why?  Like the hammer, the ball is in equilibrium, and its inertia in some tangential direction makes it produce an equal and opposite force pushing it downwards.

A similar ball falling to Earth is not being 'pulled by the force of gravity', it is just sitting in spacetime with no forces acting on it, though it is accelerating.  The direction of acceleration is towards the Earth's centre, but this is not the tangential inertial direction as it is local to this system, and opposite to a similar experiment in Australia.

Setting the hammer system rotating gives it potential energy, equivalent to gravitational potential energy.  The difference in the analogies is that the forces on the hammer act in only two dimensions around an axis in the third.  It rotates with a certain period, so time is already involved.  For the ball on Earth neither the centre of rotation nor the axis can be readily identified.  But what other mechanism involves a force and an acceleration with no motion in the system frame of reference, and no energy expended?

How can it be infinite? What nonsense . .

The subject of a flat infinite universe came up again, on the physics forum.  For the first time I expressed my frustration at the claims that the universe might be infinite, and explained that infinity is just a mathematical term that does not have to be realisable.  The discussion highlighted the standard theory that the Big Bang is the point from which everything exists.  The universe does not seem to have been infinite then, so why should it be now?

I made the point that a mass is attributed (around 10^57 kg I believe).  Yes, this is understood to be of the visible universe.  A lot of stuff we can't see due to expansion in the last 13.5Ga, but it all still stems from the Big Bang.  So why do physicists like Brian Cox say, as he did again on TV last night, that the bit we can't see might be infinite?

All it takes is for the boundary to be defined.  The surface of a sphere defines the boundary of the sphere, but the surface itself has no boundary, you could walk round it for ever.  Extend by one dimension, so the volume of the universe has no boundary, but it has to form the boundary of a 4-dimensional entity.  This is the big conundrum, because GR has been defined to work in three spatial dimensions, and a fourth would mean that gravitation would not work as it does.  The inverse square law would be an inverse cube law, and that is not what we see.  Or is it?

There are some problems with GR.  It does not reconcile with quantum, with gravitation being the odd one out in the unification of primary forces.  It should be explaining Dark Matter, instead there are teams of scientists and engineers trying to detect matter that is only detectable through its gravitational effects!  It offers as an option the prospect of the universe being infinite, a nonsense to cover the fact that they don't know the shape of the thing they are talking about.

There is clearly a sense in which GR needs modifying to account for these well-known observations.  Start with an assumption that reality is finite, and that Dark Matter is an artifact of gravitation at the cosmological scale.

Dark Matter soon to be found !

The BBC has just reported that the search for dark matter is reaching a crux http://www.bbc.co.uk/news/science-environment-24733131 as measurements are now sensitive enough to have a high chance of finding it, if it exists.  I don't think it will be found, and now that a result is expected, it should start to change the direction of big physics when it is not.

As the article says "Dark matter is thought to make up 27% of the Universe. But astronomers have only been able to infer its existence through the gravitational effects it has on visible matter in the Universe". Surely it is much more reasonable to look for a gravitational explanation for the phenomenon, than to seek stuff that does not absorb, emit, have temperature or any other detectable characteristics.

We know that gravitational mass and inertial mass are the same thing.  I am also hanging my hat on the assumption that gravity is not a real force, but a fictitious force like centrifugal force.  If so it means that another set of physicists trying to reconcile gravity with the three fundamental forces are sort of wasting their time.  So if we have a system comprising a horizontal perfectly smooth table with a hole in the centre, a string through it holding a mass underneath connecting to a mass on the table, when the upper mass orbits the hole at a speed giving equilibrium, we have tension on the string caused by two fictitious forces balancing each other.  Tension in the upper part is centripetal force causing the upper mass to change its direction twice every revolution.  The equal and opposite lower-string tension is what is traditionally called the reaction force of the Earth opposing gravity's force, but is in fact the string accelerating the lower mass (F = m a) (though it appears stationary) at a rate of 9.81m/s^2 upwards.  Everything sitting on the surface of the Earth is experiencing a push upwards which amounts to the same thing.

This means, as I understand it from L2 Physics, that we are in a rotating (non-inertial) frame of reference (not the Earth rotating, that is irrelevant, I mean the whole of spacetime).  I expect that general relativists know this very well.  The quandary is that our environment is shaped such that the distance between ourselves and any recumbent antipodeans is not changing even though our relative acceleration is -19.62m/s^2.

The reference point is the centre of the Earth, the thing that is bending spacetime locally to result in this behaviour.  So the question is either (a) are three spatial + one time (3S+T) dimensions enough, and time is real enough to enable gravity, or (b) is a fourth spatial dimension (4S+T) required, as I have been arguing for a while now.  My reading of the subject so far tells me (a) that there cannot be a fourth large spatial dimension, or the inverse square law would have to be inverse-cube law, which it isn't, and (b) that physics doesn't need time, except to deal with entropy.  Well I'm sorry but you can't have it both ways.

If GR already explains how masses accelerating away from each other can also not be changing their distance apart, then surely the role of time is fundamental, and surely the shape of the Universe should be something that can be described in some way.  I look forward to seeing it.

Meantime I wait for the news that dark matter is made of cheese . . .

Silver Hammer Man

Inflation is an important topic to address.  Any model needs to include it, as the evidence from the CMB makes the fact of it generally accepted, yet it requires several leaps of faith to do so.  For that very short period of time everything exceeded the speed of light, and then it ceased abruptly.  I’ve not studied it very deeply at all yet but am still intrigued by how such a force or impulse could exist and then cease so momentarily, and even when the force subsided the speed thus imparted to all masses should surely have made the whole lot explode.

The obvious retort is that as everything was so close, gravity was very strong and reined in a runaway expansion.  But this was before the laws had settled down: and anyway I can’t use gravity to explain itself.  Fortunately.

The quick answer is that during inflation the shape of the universe was unfolding.  I would rather call it a deployment, like the unfurling of solar panels, antenna arrays and instruments on a newly-launched spacecraft.  Pre-deployment, it fits into its launch shroud and has been given spin of about 1Hz for stability, and post-deployment is 3-axis stabilised, often around a gyro system using magnetic bearings for contact-free rotation, the flywheels spinning at around 20k rpm I seem to recall.  But for the 4-D toroidal universe the idea of an inflating flotation ring is also apt.

Sam has already dubbed the Big Bang the ‘Big Spin’.  Well first came the release of the enormous bubble of energy in an unstable form, and immediately after, its inflation to a form which gave the universe its shape and stability, which included conversion of most of the energy into rotational potential energy.  This model requires mass to carry moment of inertia, so would have to include that mass condensed by this stage.  So in a flash we have a 4-D flywheel of rotating spacetime with which masses engage to store energy losslessly.  Masses can’t exceed the speed of light, and electromagnetic radiation flies around at the speed of light (or would if the medium wan’t still opaque).  What is the nature of the engagement of spacetime with EM energy and mass?

Maxwell’s equations are cited as the four most significant ever.  He also determined that visible light is EM radiation because his speed calculation matched its measured speed, and thereby predicted other forms of EM energy, verified soon after by Helmholtz and Hertz.  ε₀ and μ₀ define the spacetime engagement relationship of the electric and magnetic components respectively, and in EM radiation these components can’t exist separately.  But how does mass engage with spacetime?  It has to be fundamental, and we can recall Maxwell found that 1/c² = ε₀μ₀.  Sure thing, mass can’t go faster than c.  The harder it is pushed, the more its inertia increases to oppose further acceleration.  Spacetime has a grip on all masses, noticeable only as their speed becomes relativistic.

At first I thought c was a barrier to the rotating universe idea, as a radius would be reached where v = c, and spoil the party. However it is clearly central to it.  This is a big relief, to consider c as a central property of the rotation rather than a barrier to it.  c is central to everything.

There are other fundamental properties of spacetime.  It is elastic, so the elasticity will have a definable value.  Yet it is also apparently unbreakable.  This links to another mystery I need an answer to – how is it that mass, which so readily converts to energy in an ordinary star (OK very slowly) or in the accretion disc around a black hole (up to 10% conversion I believe) becomes so stable once it has entered the event horizon?  The simple answer is that whether it is in mass or energy form it is still equivalent stuff that contributes to the black hole effective mass.  But energy doesn’t show properties of mass elsewhere.  Interesting things, black holes.

Words coming together

It has been difficult to discuss gravity without everyday things like rubber sheets, whirling objects on strings etc, and previous attempts to summarise used too many of these.  But I've been inspired to try again by articles in New Scientist discussing progress, or lack of it, in big physics.  This time it worked, and I am submitting an essay on the subject to the Gravity Research Foundation, March 2013. This way, it will be published only if it does well, and can be safely ignored otherwise.  At least it's a stake in the ground for me, and a reference point if I dare to request serious comments.
Just an "as if" model, but offering a way of thinking about the fundamental cause of gravity, the requirement for the fourth spatial dimension and a bit of justification for this, the expansion of the universe, dark energy, dark matter, a potential prediction for the reduction of G with time, and the reason that gravity has never been related to the three fundamental forces of nature.
But I think we can leave inflation for another time . . .

Gravity is so weak because . . ?

Having been immersed in the last few months in the complexities of quantum mechanics, and other reading including about the quantisation of space itself, it has been too easy to park the subject of gravitation.  But it has emerged in two places recently, the Horizon programme and an article of the IoP.  Apparently the reason the 4th fundamental force, Gravity, is so weak is that the world we (and the other three Forces) inhabit has only three spatial dimensions and act entirely within them, whereas gravity exists mainly in a 4th spatial dimension.  Not a macro dimension (which would contradict GR) but a micro one, too small for us to observe.  A neat analogy is that a tightrope can only be walked on in one dimension, but ants can also walk all around it.

But the line defining the x dimension is just a mathematical construct, it has no thickness or circumference.  Put an ant on a spider thread, it can rotate around it (as a man on a tightrope could), but not walk around it.

Centrifugal force is not a force, unlike the centripital force (which is a true force) required to balance it in a stable, whirling (can on a string) system.  Centrifugal force is known as a virtual or "imaginary" force, a consequence of an object with mass and hence inertia being constantly accelerated in a circular path.  Gravity is the same kind of imaginary force, such that in the case of an orbiting planet, the two imaginary forces, centrifugal and gravity, balance each other.  The object is being acted upon in two ways (a) by the elastic space it and its massive partner are being accelerated by, thereby sharing a dent in the space, and (b) by the inertia of the orbiting masses resisting the dent pulling them together.  Gravity replaces the centripetal force applied by the string.  Hence gravity and centrifugal are equivalent, the mass and its inertia affecting them both identically, but the difference is a two-dimensional shape, the circle (more generally the ellipse).  Gravity has an extra dimension S4, and it is one that we all experience.

Maybe that extra dimension is just time T, but I would rather use S4 and then determine if S4 = T.  But no need for gravity to be locked into "micro-S4" - it is not a force at all (let alone a fundamental force).

Everyone is hung up about dark matter being needed to explain why galaxies clump together as they do, and dark energy to explain why dark matter is not causing the expansion of the universe to slow down, but accelerate.  The higgson explains why matter has mass, but I wonder if it can explain how nothing can also have mass?  It is clear that dark matter can be mapped by the observation of distant objects through gravitational lensing.  But can't the lumpy shape of dark matter be modelled instead by clumpiness of space itself?  Not easy, I know.  I need dark energy, not to expand the Universe, but as the rotational potential energy in S4 with which space is whirling all the mass within it.  If I had my way, the zero of potential energy would be the bottom of the largest possible black hole, and the value at "infinity" would equal the total DE.  Though that might not be very convenient.

I am worried by the finding that the Universe is flat, and therefore infinite, as infinity is just another mathematical construct, 1/0, impossible in reality.  Seems to me they are asking the wrong question, and just ending up with the number they first thought of.  Naive, maybe, but interesting . .

Take a fresh look . .

I posted something profound the other day.  Richard Feynmann is quoted by John Gribbin as saying that if each point in space takes a huge (infinite?) amount of computing effort to describe what it is and does, then something is wrong with our understanding.  It has to be fundamentally simple.  And in a whimsical post on a forum I asked (independently) how did all those electrons learn all that maths? We do seem to be a pre-Copernican maelstrom, like  trying to make sense of planets in curly orbits around the Earth.  Whatever happened to Occam's razor?

I still wonder why physicists hope or expect to reconcile the three main forces with gravitation.  They do so because they are part of the same universe, and clearly all involved in the processes we observe, like star evolution.  But it does not follow that the container should be directly related to the contents, even in this context.

Gravitation is a feature of the shape and (I contend) motion of spacetime, whereas the strong, weak and electromagnetic forces are properties of the 'medium' of spacetime and the particles in it.  Mass is a property of some particles, and masses interact with spacetime as they resist being pulled along by it, but that does not mean that gravitation is related.  The same can be argued for radiation, that it follows the shortest path through spacetime even though it is bent by the interaction with large masses.  It doesn't "know" it is being bent.

This separation approach seems to me to be the only way to progress the explanation for dark energy and dark matter, since otherwise it makes no sense that with all our detection means and theories there is no direct evidence for either.  They have to be results of the interaction between masses and the motion of spacetime, clearly measurable only on the same large scale as relativistic effects.

I think a good new approach will be for experts to define contrary projects and spend at least 10% of their time on them.  In other words, take some of their pet theories or dogma or "facts" and try to show they are not true.  Peers will then check how honest and diligent they have been, the payoff being that a thorough honest contradiction by an expert, which fails, will properly enhance their orignal premise.  But there are bound to be some successes in the contradiction, or new ambiguities, or new pathways discovered, leading to some answers.

This may be a way for amateurs or undergrads to contribute, because they can come up with contradictory project ideas without necessarily understanding the subject to the detail of the expert.  In fact it is an area where naivity may allow a question to be asked, that an expert (or his expert rivals) would not.

Well it worked for Galileo, Copernicus, Newton, Maxwell, Schrodinger et al.  Maybe time to study alchemy . .

Not a game for amateurs

Studying physics is a broad process - as well as formal study, questions arise which lead to reading recommended material, which shows that the experts are scratching their heads.  The fact that some physicists are almost in despair that their quest for the truth appears further, not closer, indicates a huge challenge ahead.

Richard Feynmann said that if you watch a safecracker trying to crack a combination, there is no point in asking "Have you tried 10-20-30?".  Of course he has, and many others besides.  Yet it is as if science is taking a blind turn, and could be relaxing its rules of evidence to accept bizarre theories while curtailing its ability to question some of its fundamentals.

Reading of Lee Smolin and John Gribbin (I have Penrose but no time yet to read) indicates that space itself is quantised, but with enormous problems of scale; that string theory proceeds with no predictions or evidence in a closed shop; that our view of reality is subjective no matter how objective we try to be, as we use our photons and electrons to observe - photons and electrons.  SR limits to light speed, yet wave functions collapse everywhere at the same instant.

However, as I continue to have assessments to submit and exams to take, there are plenty of my original questions still to tackle.  There is no real progress on dark matter or dark energy; the subject of the number of dimensions is still apparently open, despite GR appearing to stick with 3s+t; he distinction between gravity and the other three main forces is very confused.

No answers here, but it is fun trying to understand the questions.  What a subject to be working in!

I often muse how fortunate we are to be living at a time when most of us live comfortably, have all this information and IT at our disposal, and can can probe to the smallest and largest scales in the universe.  We should be walking around in wonder at it all.  Well in a sense we are, even as we take it in our stride and press on . . .

A path well-trod . . ?

Now I've started some serious reading in parallel with undergrad study, it is a relief to find that Gunnar Nordstrom came this way back in 1914.  With the big 5th dimension, out popped gravity, and it even unified with electromagnetism.  His work is being continued today.  It seems that it stands up well against Einstein's GR except (among other things) the prediction of light being bent around masses.  There are only a couple of bits of independent recent work on the web, neither refereed or developed, which also involve rotation. Just as Einstein was stopped in his search for GU by difficult maths, so it is probably the maths that defeats most people's progress.
What Einstein achieved was a solution for a number of key observations which makes it best, nay the only, viable theory.  To me in my naivity it looks like his maths has succeeded in flattening the universe into 3sd+t.  Those who understand it have no choice but to pursue it, and the rest of us can go and puzzle and dream.  Many attempts have been made to explain GR to the layman, including by Einstein himself and Eddington.
Although GR purports to be dynamic, I have not found it involving a rotation, and neither (I believe) did Nordstrom.  And GR is still 'king', even though dark energy and dark matter are known only through their gravitational effects, yet our best theory of gravity does not explain them.
Back to my own experience, I am aware of gravity not through skydiving etc but the mundane activity of barrowing piles of earth from A to B, every Thursday.  Now I know that if I lie on a fast-turning roundabout with my feet braced against a panel on the circumference, I will be restrained from being flung off it by a force through the soles of my feet.  And if I try to move a mass by my feet towards my head it will require work to do so.  If I look at the sky I realise I am being whirled.  And that force is no different from pulling down on me and the rocks as I go about my earth-moving activities.  Except that gravity is being focussed through the mass of the Earth.  The Earth, me and my rocks are all being whirled in space, causing it to be dented, and our sharing of the Earth's large dent causes us to be attracted together.  Simple.
There are some fundamental effects or values that the rotational 4sd+t model will predict, including dark energy, dark matter, and an absolute value for gravitational potential energy at infinity (which nonsensically is presently taken as 0).  This value will set a finite maximum on the gravity inside black holes, presently taken to be infinite at the singularity.  Why do physicists cling on to the idea that infinity is a real value, when it is obvious it is just a mathematical construct?  Finite gravity links with a finite radius of a black hole, within the Schwatzchild radius, helping to explain how its mass is somehow retained despite being "crushed into nothing".  Funny how the most efficient conversion of mass into energy occurs in the accretion disc aound a black hole (about 10% efficient), yet it does not in the even more extreme conditions inside the horizon.
My main realistic expectation is not that this model will survive scrutiny, but that it offers an "as if" explanation to the layman of how gravity works.
Mass couples to the 'medium' of spacetime just as electromagnetic charges, poles and waves couple to spacetime.  They have permittivity and permeability constants, mass will have a prehensibility constant.  It should not be too difficult to identify or find it.  But the model does require that extra big dimension.

What is the problem with rotation?

After further reading of my own books by communicators of the subject, and web sites, I am more intrigued by the lack of reference to the possibility that gravitation is connected to a grand rotation, and that GR defines four spatial and one time dimanesion, total five dimensions.  A lot of maths is being done to limit the number of big dimensions to four, eg the path integral, using complex numbers to convert 3s+t into 4s.

The nature of gravitation does not appear to be one of the outstanding mysteries, yet if this is the case there should be a popularly-understood model of it.  Instead we are being told that it just is.

The conundrum to me is, how are things which are so obviously apparent from our observations and accepted therories not clearly acknowledged?  Specifically:

• just as the bobbles on the surface of an orange indicate the existence of the 3rd dimension (up-down) to a 2-d being, the bending of spacetime by masses shows the existence of the 4th spatial dimension to our 3s+t classical world
• the idea that inertial mass and gravitational mass might be different, and their equivalance to very fine experimental accuracy may still be a coincidence, may be good scientific practice.  But in reality they are clearly the same thing
• a can whirling around on a string experiences fictional centrifugal force, and a body in orbit round a planet is subject to two fictional forces - centrifugal, and the centripetal force produced by gravity.  It orbits forever, with no new energy, and feels nothing!  The two forces are one and the same, and their common cause is - rotation.
• the differences between linear acceleration and constant-ω rotation are that (a) in rotation the acceleration is achieved with no work being done, and (b) an additional dimension is required, namely the axis of rotation
• I have seen it stated that masses bend spacetime, it is implied "just by being there".  But this only makes sense if there is interaction.  You don't dent a mattress standing against a wall just by standing next to it.  You have to push against it for the denting to happen - or it has to push against you.

I suppose the answer to the conundrum is that if time is sufficient as the fourth dimension, there is no need to invent a fourth spatial dimension.  But G appears to have been constant for the last 12 billion years or more, so the shape of time in terms of the radius of curvature characteristic of the whole universe is already fixed.

Maybe easier to assume s4, find its properties, then try to equate s4 with t.  But I do need to find how this has been written up already, in an understandable way.

The energy in rotation

A straightforward mechanics problem: a mass whirling round a central point in a frictionless environment, set in motion and restrained by a string providing centripetal force to counter the tendency (as Newton's 2nd law) for the mass to fly off at a tangent in a straight line.  So the string is imparting a force to the mass, accelerating across the diameter from 0 to V and back to zero, twice each revolution.  The mass is moving, so we have a force and a distance moved, so work is being done and energy is being expended.  Yet we know that once rotating, it will continue to do so indefinitely with no further energy after the start.

Stay with the diameter, and imagine instead the mass not orbiting the centre point, but being pulled to the centre with an impulse, travelling through the centre to the other side and being restrained and re-accelerated inwards again to the other side.  In this case work is being done, as energy lost in the sudden braking and pulling is replenished.  But if the string and pulling effort is replaced by an ideal spring, the system exhibits simple harmonic motion (SHM) and the energy is exchanged periodically with no loss, between the accelerating mass and the expanding spring.

An orbiting mass is just doing SHM in two orthogonal axes, so that the spring is being replaced by the motion in the second axis, there is a constant exchange of energy between the x and y axes, and no new energy is needed to sustain the orbit.  An orbit (this would extend to any ellipse) is SHM where the energy storage is provided not by a physical storage entity, but just by virtue of the mass moving also in the second dimension.

There is an interesting limiting case.  For increasing ellipticity the finite length of the minor axis allows the energy storage to sustain the high-amplitude oscillation of the major axis.  But as the minor axis length tends to zero this storage disappears, and SHM ceases.  The practical limit is the strength of the centripetal force.  In orbital mechanics the natural tendency is for ellipticity to reduce, ie the orbit to become more circular.

So gravity provides the centripetal force to enable bodies to orbit each other.  What provides the centripetal force to enable the rotating engine of gravity?  Whatever it is, it is fundamental.

The properties that rotation shares with gravity seem to be:
- once the system is started, masses are constantly accelerated yet with no energy input required
- unlike SHM (eg with a mass and a spring), for rotation there is a constant force, ie always positive in the direction towards the centre
- rotation involves angular momentum, which is (a) a conserved quantity and (b) has an additional dimension, the axis of rotation, at right angles to the plane of the rotating mass.  It is clear that gravity acts in not two but three dimensions, so the question of the 4th spatial dimension in which its "axis" exists is begged, since it can't be found in the first three spatial dimensions, and time is common to both rotation and gravity.

It is difficult to visualise a 4th spatial dimension and this axis (which is still linear, but in 2-d!)  I think back to earlier posts, postulating a circular axis (to 4d+t toroidal space-time) to avoid it having ends, to avoid needing further dimensions just for the purpose of accommodating it, and to enable the toroidal volume (4d+t equivalent to a 3d+t toroidal surface).  Amongst the properties of a toroid are:
- it has both positve and negative curvature, and can expand in either or both its two radii r and R
- potentially it has net zero angular momentum of rotation "through the hole"
- its shape suggests a time before the hole was created and a time since - the hole creation could be part of the process of inflation, one of the ongoing mysteries.

Yes it seems odd if the universe is just a gigantic smoke ring - yet surprisingly, I have not found anything in study over the last two years to put me off the idea.  And scope is still there to help explain dark energy (the net angular momentum), dark matter (an artifact of GR or 4d+t curvature on the largest scale), and potential shortcut paths for speeding neutrinos.

Use it to help explain (or describe) it . .

For the first time I have posted a view on a web forum that the force of masses attracted to each other by gravity is just a symptom or artifact (due to the elastic nature of space-time) of a much larger force acting on all masses.  I posted in response to two interesting discussions (a) that gravitational mass (=) inertial mass, and (b) that two masses of 1kg each, separated by 1m, experience a force towards each other of 6.67 x 10^-11 Newton, ie the gravitational constant G.

But it has led me to a step I have avoided so far, to use gravity to help describe gravity.  We have a video of Aristotle telling the young Alexander that gravitational attraction is a property of nature not to be tested. The stone falls to the ground and remains stuck there.  But if they had lain on a rubber sheet stretched on a frame, they would have noticed a tendency to roll towards each other.  Experiments could have measured the force involved, and its dependence on their masses, the distance, and the thickness and stretchiness of the sheet.  The body indentations would also have been apparent.  All their weight is supported by the sheet.

If the frame is now stood vertically and they stand against it, there is no indentation and no tendency to move together.  But now mount the vertical frame jusr within the wall of a cylinder (say 20m diameter) which is able to rotate freely about its vertical axis, and closed so the occupants can't see anything outside.  An air cushion horizontal bearing would be good, like those linear tracks used for mechanics experiments, and a nice firm smooth axis bearing.  The subjects standing with their backs to the rubber sheet may experience a tendency for more and more of their weight to be borne by the sheet, and there could be a point where there are indentations in the sheet, and an attractive force between each other equal to that experienced when flat on their backs.  The only difference is that now they have 2^0.5 ("root 2") times their weight, and it acts at 45 degrees in the direction down and behind them.  Two equal components of weight, one acting downwards as usual, and the other through the sheet at their backs.  Coincidence, or perhaps the same cause?  The cylinder is rotating at a rate which accelerates them at 9.8ms^-2.  (We used to have a fairground ride which did this, but stuck people to the wall - if your clothes had sufficient friction . .)

And yet if the rotation is increased from zero very gently, and those bearings are smooth, there is no way the standing subjects would know that they were rotating, except for the increasing pressure on their backs.  How to explain it - Aristotle would have been stumped.

To cause the rotation would require work, and an exchange of angular momentum with the Earth in order to conserve it.  But once rotation is up to speed, and ignoring the friction in those bearings, no further energy is required, indefinitely, even though masses are continously being accelerated.  The only other problem with this model is that in four dimensions (3s+t) it acts only in the plane of the local cyclinder wall, whereas gravity acts in the volume of local space.  Implying that the real universe has 4s+t, ie 5 major dimensions.

Question for today - does General Relativity allow the rotation model?  If it does, how?  And if not, why not?

Observations re OPERA at San Grasso

Responses to the OPERA results are interesting, and  a BBC TV documentary on Tuesday 18th Oct 2011 summarised that opinion is finely balanced between systematic errors and the results being correct.  My course leader however told me that errors is the very probable explanation - think this is too conservative an interim conclusion.  The doco said over 100 papers have been published to discuss/review, well I have no time to find or read them, but have seen some blogs which indicate that neutrinos have a licence to behave oddly, and we should keep an open mind. Hardly any mass, very weakly interacting with baryons, very limited info about them so far.
Views have been expressed that they could be taking shortcuts through a universe with more than 4 dimensions, however these seem to relate to string theory with its 6 miniature dimensions, and reference to a 5th large dimension is only vague.  Talk of violating Special Relativity, yet isn't General Relativity itself an extension (hence "violation") of SR?
Talk of crossing cause and effect relationship, and time travel - but we are talking neutrinos here, they have a free pass.  Most intriuging to me (in the doco) is the recognition that in the Big Bang there was no speed limit, the laws of physics had not settled, and there is a scenario for laws to be broken. And a plaintive question from a lone blog responder "the biggest question is the existence of existence".  Too right mate.
It is beginning to fit, not only that cause and effect may have been / are being confused, but that they have to be.  As I said months ago, existence is the result of the conflict between the impossibility of existence and the impossibility of non-existence.  Let us take as read that for the Big Bang to happen our known rules and frames of reference are suspended.  The timescale of the Big Bang is such that only a logarithmic scale makes sense (on a linear scale, too much is happening to too much material & energy in too short a time), the implication of this being that t=0 does not exist, the start is always further back.  More work needed on how logs and exponents relate to the real world (after my career with dBs!).
So there is credibility among some professionals for the idea of a 5th large dimension, though I have not yet seen anyone ascribe a "shape" to it.  Why are they not seeing the bendiness of spacetime found in GR as evidence for a full 5thD?
I did some calculations to see if the 60ns / 16m lead of the neutrinos could be explained by gravitational lensing by the earth's mass, and neutrinos taking the "straight line" across curved spacetime.  But this would only account for 8mm, much less than the experimental error (position accuracy 20cm over 733km, time accuracy 2ns over I think 2ms).  And leads nicely to the spacetime curve being much larger than the tiny bump caused by the earth.  My thoughts from Cuba were that the gravitional attraction between masses is but a symptom or artifact of the real force of gravity, which is many times larger.  Let's take another look at G.  Funny that the reciprocal of the Hubble Constant gives us an estimate of the age of the Universe, how elegant if 1/G had a comparable real result.
My limited or focussed reading/study has so far isolated me from other views confirming my suspicion of the toroidal 5th dimension, its properties including: all gravitational energy stored in its rotation, yet still powers the universe (formed in the Big Bang like a big smoke ring); it is expanding as cosmologists observe (but being a toroid can expand in its big R and its little r); in this model is the explanation for dark energy, and dark mass whereby galaxies stick together due to the spacetime curvature on the galactic scale; the toroid "surface" has both positive and negative curvature.  I am also thinking that the phenomenon of inflation (instantaneous expansion shortly after the BB) could relate to the formation of the shape of the toroid, ie the start of the "hole".  Study required of how doughnuts are made.

Negative progress?

I need to make an occasional progress report.  Near-completion of a tough Astrophysics module ought to qualify, but instead I feel less in touch with my thoughts from the start of this blog, and barely scratching the surface of the formal subject.
However, my course has now broadened to include more basics of physics, more formal maths, and so it is more realistic that I can take on the ability to understand, calculate and articulate the issues.  And though a Masters or higher is far too soon to contemplate, it is clearly the only route towards tackling my objectives.
I am still puzzled that the identification of space-time as a four-dimensional world defined by Special Relativity has not developed into the acceptance of perturbed/folded space-time as the five-dimensional world defined by General Relativity.  The evidence for this model is clear, taking the view of the ant walking the surface of an orange, that the surface indentations are the clue to the existence of the third dimension (up-down).
But in two years of formal study so far I am not yet in a position to ask the question of my peers or tutors.  I prefer first to have some answers, or further questions to follow-up initial answers.  Also of course I am concerned that the question may be ridiculous.  The answer of course is that I need to be able to understand the answers, and with several specific modules including maths, QP, EM to go, it will take some time yet.
Meanwhile all this formal study is squeezing the original naive ideas out, well maybe that is the "right thing", but I owe it to myself to maintain and develop them, if only to have something to identify and formally bury when the time comes.
Meantime I have just read some module material that is disturbing for physics, and encouraging for the side view, regarding the "end of physics".  The idea that a unified theory may not get us much further forward is very sad.  Having spent pages explaining the non-determinism of QP, it then rues the fact that a theory will not enable us to predict the exact starrting condition or eventual outcome of the world.  How banal!  The question of knowing the shape of the universe, and all relating to its existence, origin, insight into its raison d'etre appears irrelevant to teaching the formal subject.  We'll see about that . .

Slow but steady progress

Engaged now in 3rd-year undergraduate study of astrophysics, feeling daunted not by the concepts of high-energy large-scale or quantum physics, but by the complexity of the maths needed to explain observed phenomena and to predict scenarios.

Of course, to understand quantum physics it is essential to know the maths, as the subject is so counter-intuitive. As is gravitation. Ah, something these subjects have in common then . . .

It is going to take me some years to cover key material ie electromagnetism, quantum physics, cosmology, and the maths needed just to keep up. The idea of making a contribution to the subject of the number of dimensions seems completely unrealistic. Yet the intractable problems of dark energy, dark matter, inflation and the cause of gravitation will be unsolved for a while yet. An intuitive non-mathematical model works for me so far, I don’t see why study should reduce my ability to think that way, but it should let me narrow down options and find the relevant questions to ask.

My current thought is the corollary to M-theory. There is nothing elegant about 10^500 universes of which we happen to be in one where the physical constants are “just right”. Elegance is supposed to be an objective for scientific process, and to say “spontaneous creation is proven by the fact that we are here, so everything is possible and everything is true” is just a cop-out.

But the corollary is that we are in the only universe, its physical constants are “just right” for matter to coagulate, heat up and make energy and materials available for it for long enough to become alive and aware of itself. And to enable the question “Why?” to be asked. It obviously begs the question not just of a master designer, but an extremely accomplished one.

The more you learn, the less you know . .

Having recently completed a 2nd-year higher–ed module in astronomy and cosmology, awaiting my score with eagerness but little confidence, I have a much better understanding of the big things in the universe (from stars upwards) – how they are born, live and die, interact with each other, and are used to learn more about the big picture. I have also covered special and general relativity, scaling, the event history of the big bang and various models of the expansion and the likely outcome of the universe. But I can’t say I have yet understood much of that part. The algebra at this level is linear and straightforward – (1/Hubble constant) gives the age of the universe. The next level requires much more maths, so to me it means that the study is moving away from an intuitive understanding, and more an interpretation of the algebra.
It is as if some cosmologists live in the real world (the ones who don’t “do” dimensions) and others manipulate maths in an attempt to explain the so-far inexplicable.
The most interesting outcome of the module for me was the summary of ongoing mysteries. The nature of dark energy and dark matter; why, after the big bang and the annihilation of matter with antimatter, was some matter left over; the process of inflation in which the universe expanded many orders of magnitude in a minute space of time, in order to explain the horizon problem; and the failure to reconcile gravity with the other fundamental forces (there were more, I am writing this from memory). Another is the ‘pressure waves’ which cause galactic spiral arms to ‘orbit’ the centre in an unexplained way.
I have also read Prof Hawking’s book The Grand Design, very illuminating and from which I took two key points. The first is the credibility he gives to the possibility of 10^500 universes being created each with different laws, those that survive any length of time being the ones whose laws of physics are mutually sustainable. The figure of 10^500 is as near infinity without saying infinity. One feature of a good theory is elegance, but this is as elegant as a blunderbus (in my respectful opinion). Come back God, all is forgiven! (That will be a prayer, then . .)
The second is his sudden diversion to explain that there are only four big dimensions, three in space and one in time (3s+t) – there cannot be a fifth (4s+t), otherwise gravity would exert a smaller pull than it does (instead of the inverse square law, the inverse cube law would apply). This is where I feel that, in my present naivety, I can make a challenge. I think:
- General relatively says that there is a fifth large dimension (total 4s+t) in the observation of the curvature of space-time. Just like the bobbles on the surface of an orange may suggest to an ant walking on it that there may be an up-down dimension to add to forward back and left-right. And its infinite surface is not so infinite after all
- Dimensions can depend on scale. Not just their perception/measurement, but their existence, depends on size
- The discovery of dark matter on the galactic scale (some 90% of the mass of a large galaxy like our own as measured by its gravitational effects on its own stars and neighbouring galaxies is dark, ie unexplained, matter) suggests that, instead, there is a phenomenon that known matter on the galactic scale exerts less force than the 3s+t model allows
- The discovery of dark or “missing” energy looks to me like the kind of balanced rotation (in the 4s+t toroid concept) that is continuously accelerating all masses in the ‘medium’ of space, and giving the observed mutual attraction of gravity.
So I think I have made some progress in 2010, but have yet to find out how much.

As a matter of fact, it's all dark . . .

Just a fill-in update, I realise these posts are very idiosyncratic and apparently disjointed. As might be expected from an amateur's attempt to make sense of an apparently intractable problem.

In fact it is as if every attempt to find a simple core to the answer results in the exposure of another layer of complexity. Having got a good handle on the nature of matter, the normal or baryonic kind, it turns out that 90% of it, including our own Galaxy, comprises dark matter. It can't be detected directly at any wavelength, the only evidence for it is the gravitational effect it has on observed galactic dynamics.

As if the suspected black hole at the centre of each galaxy is a lot more massive than thought. But the unseen mass is distributed in an oblate (80%) spheroid encompassing the visible and detectable material. It "is" all around us.

Plenty of scope for surmising that the mystery of dark matter is a feature of gravitation. Just as a mass distorts local space causing other masses nearby moving or being moved through it to appear to attract each other, a large accumulation of mass (as a galaxy) further significantly distorts the space it occupies with the effect of making it seem 10 times more massive than its baryonic material.

My surmise is to do with the relationship between the size/dimension of galaxies compared with the universe as a whole - galaxies are macro scale. In what sense is the gravitational constant a variable after all?

I always had an intuitive problem with the big bang, preferring a continuum to be more elegant, but realise the evidence for the big bang is irrefutable. Well I am also sceptical about the existence of dark matter, and will be betting the solution lies in the measurement method and theory rather than in some new and totally undetectable form of matter.

Why does nature have to be so intractably complicated? At what point in human investigation will it start to become simpler? Answers on a postcard please . .