The future of the universe

All of the complexity and structure we see in the world around us will ultimately be degraded and eradicated.

Consider first the fate of gravitationally bound systems, such as galaxies and galaxy clusters. Let us first recall some concepts from Newtonian gravity. Because gravitation is an attractive force, the potential energy U of a system of gravitating objects is negative; the kinetic energy K of the system, the energy of motion of the objects, is positive; and the total energy is E = U + K. A gravitating system is said to be bound if the total energy E is negative. In other words, if the magnitude of the potential energy exceeds the magnitude of the kinetic energy, the system is bound. The more negative the total energy, the more tightly bound the system is.

Each gravitating system has associated with it an escape velocity, which is the speed a constituent object must attain if the distance between it and the other objects in the system is to become unbounded. A bound system is such that the average velocity of the objects in the system is less than the escape velocity. However, after the objects in the system have interacted for a period of time, there will be a distribution of velocities, and some will exceed the escape velocity. These objects will thence depart the system, never to return. This evaporation of objects from the system will remove positive kinetic energy from the system, hence the total energy of the system will become more negative, making the system more tightly bound. Nevertheless, the system will continue to evaporate.

Contemporary spiral galaxies are bright and vibrant star cities, evolving through multiple generations of star formation, and possessing an ecological structure in which material is cycled between the population of stars, and the gas and dust of the interstellar medium. Eventually, however, star formation will cease, all the stars in a galaxy will expend their nuclear fuel, and galaxies will be populated by black holes and the dead cinders of stars. These cold, dark galaxies will then evaporate, as Iain Nicolson explains:

"Although close encounters between stars are extremely rare, given sufficient time, many encounters between dead stars will take place. In each encounter, one star will gain energy and the other will lose energy. Even without any encounters of this kind, an orbiting star will gradually lose energy by radiating gravitational waves and so, very slowly, will migrate closer to the centre of its galaxy. Close encounters will accelerate this process. Over extremely long periods of time, most dead stars will evaporate from their host galaxies and the remainder will coalesce into gigantic 'galactic' black holes at their centres. A similar process is likely to happen to clusters and superclusters of galaxies, with dead galaxies merging at their centres to form 'supergalactic' black holes, and others being ejected into intercluster space." (The End of the Universe, 1998 Yearbook of Astronomy, pp220-232).

Smaller bound systems, such as molecules and atoms will also evaporate, but the reason for this is quite subtle. As John C.Baez explains, any system in thermal equilibrium will minimise its so-called free energy, the amount of energy which is available to perform work. The free energy can be defined to be E - TS, where E is the total (internal) energy, T is the temperature of the system, and S is the entropy of the system. The restriction to internal energy here simply means that one ignores the potential energy a system might possess in an external field, and one ignores any bulk energy of motion; internal energy includes the internal potential energy of the system, and its internal kinetic energy. The entropy S of a system can be seen in this context as the amount of unusable energy in the system, per unit of system temperature; hence, multiply the entropy by the temperature, and one obtains the total amount of unusable energy in the system. Subtract the amount of unusable energy from the total energy, and one obtains the free energy.

The free energy of a system E - TS can clearly be reduced either by reducing E, or by increasing TS. As Baez points out, an ionised gas (a so-called plasma) has more energy than a gas made from atoms or molecules of the same substance. When those atoms or molecules form, electromagnetic radiation is released, decreasing the total energy of the matter in the system. However, the atoms or molecules have less entropy than the ionised system. At high temperatures, the free energy is minimised by the high entropy plasma state. However, at lower temperatures, the free energy of a matter system can be minimised by reducing the total internal energy of the system. (Note, however, that although the atomic or molecular state is a lower entropy state for the matter, the total entropy still increases because of the entropy of the electromagnetic radiation released when the atomic or molecular state is formed).

This assumes, however, that the system occupies a fixed volume. If the volume available to the constituents of the system is constantly increasing, as is the case in an expanding universe, then the maximum available entropy S of the system will be constantly increasing, and eventually, even at very low temperatures, the free energy of a gas will be minimised in the ionised, plasma state, the state which maximizes the entropy of the system.

Black holes, of course, are also capable of evaporating into radiation, but only do so if their temperature is lower than that of their surroundings. Crucially, some theorists currently argue that the presence of the dark energy, responsible for the acceleratory expansion of the universe, equips the universe with a minimum temperature. The temperature of a black hole is inversely proportional to its size, hence if sufficiently large black holes form from the merger of smaller black holes (and they would have to be as large as the currently observable universe), then such black holes would never evaporate.

Thus, (neglecting some questions over the fate of protons) the future of the universe is a future in which all galaxies, stars, planets, complex molecules and atoms eventually evaporate, and all that remains will be gravitational radiation, electromagnetic radiation, black holes, and isolated elementary particles.

Lewis Hamilton and instability

The Eurofighter-Typhoon jet aircraft is so unstable, that it cannot be controlled by a pilot alone, and requires the intervention of electronic control systems to prevent it from stalling in flight. Hold that thought in your head as you read the description of Lewis Hamilton's raw driving ability, which McLaren director of engineering, Paddy Lowe, gave to Autosport's Mark Hughes in 2008:

"He's tremendously good at controlling a car in oversteer. We saw that from the first moment he got in our car. We saw the data, and on every entry we could see there was a massive correction on the steering, and our normal drivers would have been bitching like hell that the car was undriveable, yet he didn't even pass comment. So with a driver like that, you're better equipped to push the boundaries to new levels. Speaking generically of that characteristic, a lot of the performance limit of a car is set by stability; if you can't hang on to it, you will have to introduce understeer in that zone. But if you have a driver better able to deal with oversteer in those zones that induce it, then you will have a less-understeery car elsewhere and therefore more total grip over the lap. The great drivers over the years - Senna, Schumacher, Mansell - have all had that ability. Like for like compared to other drivers, they want more front end."

There are two particular concepts in Lowe's analysis which need to be distinguished: corner entry oversteer, and entry instability. To understand Hamilton's unique capabilities, we therefore need to briefly introduce some definitions from stability theory.

If a car (or aircraft) is initially in an equilibrium state, and there is a transitory control input (or external disturbance), a stable vehicle will return towards its initial equilibrium state of its own accord, whilst an unstable vehicle, in the absence of any further control inputs, will diverge even further from the initial state. To be precise, the first condition is sometimes called static stability, and the latter condition is called static instability. Whether a vehicle is stable or not can be speed dependent. For example, a bicycle is stable at higher speeds, but is unstable at low speed, requiring continuous corrective inputs from the rider to remain vertical.

In the case of an F1 car, an initial steering input induces an initial slip-angle in the front tyres, which induces an initial direction change (a rotation about the vertical axis, called a yaw motion). If an F1 car is statically stable, the car will then return towards a state of zero yaw. If an F1 car is statically unstable, an initial steering input would not just induce an initial slip-angle and change of direction, but an ever greater change of direction (in the absence of corrective action from the driver), giving the vehicle a tendency to spin on entry to every corner. In particular, if an initial steering input provokes the car into oversteer, then that oversteer will increase the initial direction-change. Hence, the driver must supply opposite-lock steering corrections to reduce the direction-change. Oversteer and instability are therefore related. To be precise, turn-in oversteer is a statically unstable handling characteristic, albeit one which Lewis Hamilton is clearly capable of dealing with.

There is a further nuance here, however, because even statically stable vehicles can be either dynamically stable or dynamically unstable. After an initial input, the attitude of a dynamically stable vehicle will oscillate with simple harmonic motion of decreasing amplitude about the initial attitude. In contrast, in the case of a dynamically unstable vehicle, whilst its attitude will at first return towards the initial state, it will then oscillate with increasing amplitude about that initial attitude, leading to a loss of control (in the absence of corrective inputs). These two behavioural characteristics are also sometimes dubbed positive stability, and relaxed stability, respectively. The Eurofighter Typhoon possesses dynamic instability (relaxed stability).

If an F1 car was statically stable, but dynamically stable on turn-in, an intial steering input would create an initial direction-change, and the direction-change would then oscillate with decreasing amplitude. If, however, an F1 car was dynamically unstable on entry to a corner, then the direction-change would oscillate with increasing amplitude, (in the absence of corrective action), giving the vehicle a tendency to spin.

Rear-end instability on corner entry is reportedly the handling characteristic which Jenson Button struggles most to deal with, but as his Brawn team-mate, Rubens Barrichello, demonstrated this year, it is a characteristic which different drivers can cope with to different degrees. Perhaps, then, the type of instability exhibited at times by the Brawn in the second half of the 2009 season, was merely the dynamic instability of a statically stable car.

Judging from Paddy Lowe's remarks, one can speculate that not only is Lewis Hamilton able to cope with such dynamic instability on corner entry, but to a degree unique amongst his peers, he is able to supply the corrective inputs necessary to prevent a statically unstable car from spinning on corner entry.

Why did Jenson Button leave Brawn?

On Friday, Eddie Jordan announced to the world that Michael Schumacher will be making a comeback with the Mercedes Formula 1 team. Generally speaking, Eddie Jordan is a reliable source of motorsport information in the same sense that Gillian McKeith is a qualified authority on diet and nutrition. In this case, however, Jordan's prediction makes a lot of sense, for Michael is clearly directionless without the opiate of Formula 1, and Mercedes have conspired to lose their World Champion driver, Jenson Button, to erstwhile partners McLaren.

And here's an interesting thing: Jordan claims that Mercedes's attempts to woo Michael "started with a meeting between Michael, Ross Brawn and Daimler chief executive officer Dieter Zetsche at the Abu Dhabi Grand Prix." This claim was corroborated on Sunday by Willi Weber, latterly Schumacher's manager, who said he was "sure that Schumacher had had talks with Dr Dieter Zetsche, head of Mercedes-Benz and Norbert Haug, who runs the company’s motor-sport division, at the Abu Dhabi Grand Prix."

At Abu Dhabi? Reports that Button could be lured to McLaren had surfaced in the week after he secured the World Championship in Brazil, but still it seemed that an agreement between Button and Brawn/Mercedes was a mere formality. As Ross Brawn commented at the time, "We are working with Jenson to find a balance between what we can afford and what he feels is fair for his status and what he can contribute in the future...You are never 100% but I would say 99% [certain it will happen]."

The possibility of Button switching to McLaren was interpreted as a mutually convenient negotiating ploy: it let Brawn/Mercedes know that Button had another option, and it let McLaren candidate Kimi Raikkonen know that McLaren too had other options. Mercedes motorsport boss Norbert Haug, for one, was rather dismissive of the possibility that Jenson Button and Lewis Hamilton could end up in the same team: "I do understand that people in England are dreaming of an English team with two world champions in the cockpits... However, dreams don't always come true."

By Abu Dhabi, however, Haug and Mercedes were apparently considering the loss of Button as a serious prospect, and began exploring the Schumacher option before Button put pen to paper with McLaren.

Both Mercedes and McLaren now claim that money was not an issue, that Mercedes offered Button the £8 million a year salary he was seeking, and that McLaren ultimately granted Jenson a deal worth less than Mercedes were offering. This, however, is not the point. Whilst Mercedes's final offer matched Button's salary requirements, the initial deal which Brawn/Mercedes offered to Jenson was only £4 million. This constituted little advance on the reduced salary which Jenson had voluntarily accepted to keep the team afloat when Honda pulled out at the end of 2008, and Jenson probably perceived this as something of a slight. By the time that Jenson was escorted on a tour of the Sir Norman Foster-designed McLaren Technology Centre (MTC) at Woking, the damage may already have been done.

To understand the effect this may have had on Jenson, it's worth recalling the words of Ron Dennis, speaking to Nigel Roebuck in late 2001 (Autosport, December 20-27, p23) before the opening of the MTC:

We were looking for perfection, so we didn't want [MTC] to look out over any buildings. When people are working there, all they'll see out of the windows is fields and trees...I believe that good technical resources attract the best people like a magnet...OK, they want money - and money becomes like a rate card...You measure yourself in financial terms - yes, it affects your lifestyle, but primarily it's a reflection of how good or bad you are. The best people get the most money - that should just be common sense. And once you've satisfied that desire, you've got to give them the best facilities.

So perhaps, then, the picture is as follows: Brawn/Mercedes made an offer which undervalued Button's services, at which point Jenson's management team made contact with McLaren to develop some negotiating leverage; in response, Brawn/Mercedes tried to cover the possibility of losing their new World Champion by developing an interest in Michael Schumacher; already offended by the comparatively low nature of the salary on offer, Button possibly became aware of Mercedes's apparent attempt to seduce Schumacher out of retirement, and decided to take the McLaren offer seriously; Jenson's eyes were then opened by the yin and the yang of the McLaren Technology Centre, and he reciprocated the interest of his new suitor, irrespective of salary.

Can Jenson beat Lewis?

It seems to be a week for unusual and inexplicable combinations. Erstwhile Toyota F1 driver Jarno Trulli revealed at the weekend that he was seriously considering an eventual move to NASCAR, the American stock-car racing series. On the face of it, this would be as appropriate as Brian Sewell playing centre-forward for Caledonian Thistle.

Jarno, of course, was so indignant at being hung out to dry by Adrian Sutil in the Brazilian Grand Prix, that he turned up at the next race in Abu Dhabi with a portfolio of photographs and video evidence to prosecute his case. Sadly, however, the driving tactics in NASCAR hardly constitute the Queensberry Rules either...

This is completely overshadowed, however, by Jenson Button's apparently counter-intuitive decision to join Lewis Hamilton at McLaren next year. Many pundits have advised Jenson against this because McLaren appears to be very much Lewis's team, and many have predicted that Lewis would blow Jenson away if the two were partnered in the same car.

There is, however, at least one factor in Jenson's favour. Next year's cars will have narrower front tyres, and the presence of larger fuel tanks will shift the centre of mass, and therefore the centre of aerodynamic pressure, further towards the rear of the car. This is potentially very much to the favour of Jenson, and to the detriment of Lewis. A centre of pressure further towards the rear potentially alleviates the possibility of rear instability under braking, a handling trait which Jenson struggles to deal with. Furthermore, Lewis notoriously favours a car with a strong front-end, and the narrowing of the front tyres and the shift in the centre of aerodynamic pressure will both contribute towards making next year's cars more liable to understeer. Perhaps Jenson, then, fancies his chances against Lewis...

Sebastian vettel tutup gelar juara GP 2009 Abu Dhabi

Sebastian Vettel mengakhiri musim dengan kemenangan di seri terakhir. Untuk pembalap Red Bull itu, inilah akhir yang sempurna untuk musim 2009. Balapan di Yas Marina, Minggu (1/11/2009), sukses dilalui Vettel sebagai pembalap yang paling pertama melewati garis finis. Itu dia capai dari posisi start dua.Di awal balapan, Vettel sebenarnya masih terpaku di belakang Lewis Hamilton yang start dari

Acura Integra with BMW 5-Series

Acura Integra GSR modified with a BMW 5 series headlight an taillight conversion.

Acura Integra BMW 5-Series


Acura Integra GSR


Acura Integra wheels


BMW Acura Integra rear


Acura Integra interior

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“Super Hybrid Sports” model that would be powered by a 450-hp 3.5L V6 engine mated to a hybrid system.

New Acura NSX

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