The correct answer to whether this world would go on without us is :
(click to review http://theinnozablog.blogspot.com/2009/04/who-knows.html )
In Christianity, the Earth melts, but a new one is born. Since it needs no sun, figuratively speaking, - the eternal light of God and the Lamb (Lord Jesus Christ) having eliminated night, figure of speech - it's clearly a different planet than this one.
Since the late 19th Century, when, beginning with electrons, we got down to manipulating the most fundamental particles of the universe, human life has changed very fast. Alas, not for the better.
One measure of how fast is that, barely a century (100 years) ago - until Marconi's wireless and Edison's phonograph - all the music ever heard on Earth was live performance. Today, 2009 A.D., a tiny fraction of 1 percent is. The rest, i.e.,99 percent is electronically reproduced or broadcast, along with a trillion words and images each day. Welcome to Internet! Or be caught in the electronic-spider-web!
Those radiowaves don't die - like light, they travel on. Speak kind words today, for we have to swallow them one day. The human brain also emanates electric impulses at very low frequencies (8 Heartz): similar to, but far weaker than, the radio waves used to communicate with submarines.
Paranormalists, however, insist that our minds are transmitters that, with special effort, can focus like lasers to communicate across great distances, and even make more things happen. That may seem far-fetched, for some readers, though, but it's also a definition of prayer. A pray-er is a religious person who prays prayers for things to happen.
Experiment on yourself: think about these words and say to yourself or for somebody you know. Joy, natural, bliss, happy, laughter fun, cheerful, life's healthy, gleeful, delight, hearty, simple, deliciously tasty, dreamy, variety, heavenly bliss, refreshing, pleasure, goodness, enjoy, carefree, smile, friendly, celestial peaceful.
The emanation from our brains, like radio waves, must also keep going - where? Space is now described as an expanding bubble, but that architecture is still a theory. Reality is when the time-dimension and space-dimension merged as one. Along its great mysterious interstellar curvatures, perhaps it's not unreasonable to think that our thought waves might eventually find their way back here.
Or even that one day - long after we're gone, unbearably lonely for the beautiful world from which we so foolishly banished ourselves - we, or our memories, might surf home aboard a cosmic electromagnetic wave to haunt our beloved Earth. Welcome Home again, the second time !
Like a gap in the forest when a giant tree falls, new growth will rush in. Gradually, the asphalt jungle will give way to a real one.
The pockets of wild palm nut trees deep in the Amazon, or of the durian* fruit trees in virgin forest of Borneo, or of tea trees in Burma's jungles, aren't accidents. Once, humans were there too. The wilderness swallowed them and their memory, but its shape still bears their echo. As will Garden of Eden in Jerusalem, East of Eden.
(more details from http://www.propheticrevelation.net/hcity1.htm )
*durian= a tropical fruit with torny shell envelopes the fragrant creamy taste fibrous meat.