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A relatividade do irredutivel Espaço-Tempo

08.08.11

 

"Physicist Lee Smolin at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada, doesn't think so. He and a trio of colleagues are aiming to take relativity to a whole new level, and they have space-time in their sights. They say we need to forget about the home Einstein invented for us: we live instead in a place called phase space.

(...)

So what is phase space? It is a curious eight-dimensional world that merges our familiar four dimensions of space and time and a four-dimensional world called momentum space.

Momentum space isn't as alien as it first sounds. When you look at the world around you, says Smolin, you don't ever observe space or time - instead you see energy and momentum. When you look at your watch, for example, photons bounce off a surface and land on your retina. By detecting the energy and momentum of the photons, your brain reconstructs events in space and time.

The same is true of physics experiments. Inside particle smashers, physicists measure the energy and momentum of particles as they speed toward one another and collide, and the energy and momentum of the debris that comes flying out. Likewise, telescopes measure the energy and momentum of photons streaming in from the far reaches of the universe. "If you go by what we observe, we don't live in space-time," Smolin says. "We live in momentum space."

And just as space-time can be pictured as a coordinate system with time on one axis and space - its three dimensions condensed to one - on the other axis, the same is true of momentum space. In this case energy is on one axis and momentum - which, like space, has three components - is on the other.

Simple mathematical transformations exist to translate measurements in this momentum space into measurements in space-time, and the common wisdom is that momentum space is a mere mathematical tool. After all, Einstein showed that space-time is reality's true arena, in which the dramas of the cosmos are played out.

(...)

As far back as 1938, the German physicist Max Born noticed that several pivotal equations in quantum mechanics remain the same whether expressed in space-time coordinates or in momentum space coordinates. He wondered whether it might be possible to use this connection to unite the seemingly incompatible theories of general relativity, which deals with space-time, and quantum mechanics, whose particles have momentum and energy. Maybe it could provide the key to the long-sought theory of quantum gravity.

Born's idea that space-time and momentum space should be interchangeable - a theory now known as "Born reciprocity" - had a remarkable consequence: if space-time can be curved by the masses of stars and galaxies, as Einstein's theory showed, then it should be possible to curve momentum space too.

(...)

The quartet took the standard mathematical rules for translating between momentum space and space-time and applied them to a curved momentum space. What they discovered is shocking: observers living in a curved momentum space will no longer agree on measurements made in a unified space-time. That goes entirely against the grain of Einstein's relativity. He had shown that while space and time were relative, space-time was the same for everyone. For observers in a curved momentum space, however, even space-time is relative.

This mismatch between one observer's space-time measurements and another's grows with distance or over time, which means that while space-time in your immediate vicinity will always be sharply defined, objects and events in the far distance become fuzzier. "The further away you are and the more energy is involved, the larger the event seems to spread out in space-time," says Smolin.

For instance, if you are 10 billion light years from a supernova and the energy of its light is about 10 gigaelectronvolts, then your measurement of its location in space-time would differ from a local observer's by a light second. That may not sound like much, but it amounts to 300,000 kilometres. Neither of you would be wrong - it's just that locations in space-time are relative, a phenomenon the researchers have dubbed "relative locality".

Relative locality would deal a huge blow to our picture of reality. If space-time is no longer an invariant backdrop of the universe on which all observers can agree, in what sense can it be considered the true fabric of reality?

That is a question still to be wrestled with, but relative locality has its benefits, too. For one thing, it could shed light on a stubborn puzzle known as theblack hole information-loss paradox. In the 1970s, Stephen Hawking discovered that black holes radiate away their mass, eventually evaporating and disappearing altogether. That posed an intriguing question: what happens to all the stuff that fell into the black hole in the first place?

Relativity prevents anything that falls into a black hole from escaping, because it would have to travel faster than light to do so - a cosmic speed limit that is strictly enforced. But quantum mechanics enforces its own strict law: things, or more precisely the information that they contain, cannot simply vanish from reality. Black hole evaporation put physicists between a rock and a hard place.

According to Smolin, relative locality saves the day. Let's say you were patient enough to wait around while a black hole evaporated, a process that could take billions of years. Once it had vanished, you could ask what happened to, say, an elephant that once succumbed to its gravitational grip. But as you look back to the time at which you thought the elephant had fallen in, you would find that locations in space-time had grown so fuzzy and uncertain that there would be no way to tell whether the elephant actually fell into the black hole or narrowly missed it. The information-loss paradox dissolves.

(...)

Smolin's hunch is that we will find ourselves in a place where space-time and momentum space meet: an eight-dimensional phase space that represents all possible values of position, time, energy and momentum. In relativity, what one observer views as space, another views as time and vice versa, because ultimately they are two sides of a single coin - a unified space-time. Likewise, in Smolin's picture of quantum gravity, what one observer sees as space-time another sees as momentum space, and the two are unified in a higher-dimensional phase space that is absolute and invariant to all observers. With relativity bumped up another level, it will be goodbye to both space-time and momentum space, and hello phase space."


Daqui

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"It didn't feel so bad, until the Good Lord struck me down"

08.08.11

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