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The fact that EM < 1 is what makes perturbation theory possible, since we can expand a quantity in powers of EM to obtain approximate answers. A similar procedure can be applied to gravity. We consider the gravitational force because it is the only force not described in a uni ed framework based on quantum theory. The other known forces, the electromagnetic, the weak, and the strong forces are described by the standard model, while gravity sits on the sidelines relegated to the second string classical team. The constants important in gravitational interactions include Newton s gravitational constant G, the speed of light c, and if we are talking about a quantum theory of gravity, then we need to include Planck s constant . Two fundamental quantities can be derived using these constants, a length and a mass. This tells us the distance and energy scales over which quantum gravity will start to become important. First let s consider the length, which is aptly called the Planck length. It is given by lp = G 10 35 m 3 c (1.14)

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These may include (and in some cases already do) Web access, IM, e-mail, collaborative gaming, location-based services, personalized event notification, content aggregation, and personal information portals In 2004 alone, more than 600 million mobile phones were sold Interestingly, 70 million of them had built-in cameras, adding some credence to the belief that the ability to transmit and receive digital photographs from one cell phone to another device is a desirable application (Although I have yet to meet anyone who regularly transmits photographs from their cell phone) Two-thirds of all cell phones shipped today have color screens, and multiple service providers have announced multimedia applications for their mobile users including downloadable games and music clips, as well as a wide variety of customizable ring tones Don t believe that these are desirable applications In 2004, mobile games generated $1.

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This is one very small distance. For comparison, the dimension of a typical atomic nucleus is lnucleus 10 15 m

1 billion in revenues, while downloadable ring tones generated an almost unbelievable $35 billion Even so, a study performed recently by Bear Stearns-Booz Allen & Hamilton predicted that wireless data services are unlikely to exceed ten percent of carrier revenues by 2007 But here s a question for readers: Should they.

which is bigger than the Planck length by a factor of 10 20! This means that quantum gravitational effects can (naively at least) be expected to take place over very small distance scales. To probe such small distance scales, you need very high energies. This is con rmed by computing the Planck mass, which turns out to be given by Mp = 10 8 kg (1.15)

Wow, that was easy. Let s see how this can affect the thruster particles:

3G, billed as the ideal mobile data solution, has failed to live up to expectations or to satisfy the promises its developers made. Frankly, it has been a poorly positioned solution a technology in search of a problem to solve. Originally positioned as the facilitator of the wireless Internet, customers have come to realize that the wireless Internet today is largely

While this is a small value to what might be measured when considering your waistline, it s pretty large compared to the masses of the fundamental particles. This tells us, again, that high energies are needed to probe the realm of quantum gravity. The Planck mass also turns out to be the mass of a black hole where its Schwarzschild radius is the same as its Compton wavelength, suggesting that this is a length scale at which quantum gravitational effects become signi cant. Next we can form a Planck time. This is given by tp = lp c 10 44 s (1.16)

particles.force = BBPointMake(0.0, -20.0, 0.0);

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This is a small time interval indeed. So if you think quantum gravity, think small distances, small time intervals, and large energies. At these high energies gravity becomes strong. To see how this works think about the following. In a freshman physics course you learn that the electromagnetic force is something like 10 40 times as strong as the gravitational interaction. But at the high energies we are describing, where quantum gravity becomes important, the strength of gravitational interactions is comparable to that of the other forces gravity becomes strong and hence is important in particle interactions. Since the particle accelerators that are currently in existence (or that can even be dreamed up) probe energies that fall on a much smaller scale, gravity can be considered to be extremely weak at presently accessible energies.

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