I think that the majority of the evidence we now have from a diverse range of independent investigations make it a 'sure thing' that something like a Big Bang did happen. There are technical quibbles about age discrepancies and expansion rates, but I would be very surprised if these were not ironed out in a decade or so after we got better data, and more of it, to look at. I would be excited if a real show stopper could be found that forced us to reconsider whether Big Bang theory is correct, but there are simply too many things that the Standard Model explains and successfully predicts. The observations that suggest an age problem between the universe and the oldest stars are technically very difficult, and for the expansion, you need many more than just 5 or 10 galaxies upon which to base an age estimate. We will have to wait and see how the Hubble Space Telescope measurements of galaxy distances will continue to advance as the distances to many more galaxies are measured.
Personally, I have always had trouble with the word 'believe'. It has been used in pretty sloppy ways over the centuries. People 'believe' in flying saucers, the magical properties of certain numbers, ghosts and astrology. On the other hand, it is not the business of science to create new belief systems. We are trying to determine how the physical world actually works and this has nothing to do with whether you believe it to work one way or the other. I do not 'believe' in Big Bang theory any more than I 'believe' in special relativity, the constancy of the speed of light, quantum theory or Newton's law of gravity. I do not see these features of the physical world as matters of belief. They either represent the world as we see it to the limits of our present ability to measure and test, or they do not. Today, all of these physical theories and laws that we have codified seem to be corroborated by our experimental and observational evidence. So far as I am concerned, they are not matters of 'belief' but matters of fact, until such time in the future when new observations say otherwise.
Any new theory must, however, explain everything that the older theory did, include the 'new data', and THEN make predictions about new phenomena that were not covered by the older theory. Scientists are not interested in clever explanations like some cheap science fiction story filled with bogus terminology. We are only interested in how well a theory accounts for specific observations that can be used to test its viability.
Copyright 1997 Dr. Sten Odenwald
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