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.