5770 and 13,000,000,000 is a big difference!
I am looking for a good explanation to the difference opinion of the age of the universe. Please help me out!
As an observant astrophysicist (pun intended; I'm actually a theorist), I get this question a lot. Personally, most answers I have heard seem rather contrived and do little justice to either the science or the Torah. The study of physics and the study of Torah are both wonderful pursuits of a "higher truth," but they consist of very different methods and really speak different languages. I am highly skeptical of any that claim proof of a theory in one field based on evidence from the other.
But to answer your question more directly, I view the issue as a classic example of the Torah "speaking in the language of man," a concept found throughout Rabbinic literature. We know the Torah was given to a rag-tag collection of ignorant slaves less than two months after fleeing for their lives, and having only the simplest knowledge of their own history, much less "science." How should the Torah begin? "In the beginning, 13.7 billion years ago, the scalar inflation field expanded by 47 orders of magnitude, then began cooling adiabatically into a quark-gluon plasma"?? Even to the most secular scholar, the Torah is a brilliant study in human nature and emotion. To understand it, we must read it in its own language, not ours. As many medieval commentators point out, the purpose of Genesis is to teach us moral lessons, and at most, political history, not science.
The Seder Olam Rabbah added up all of the generations in the Torah and those in the rest of Biblical history to determine how many years had passed since the Creation of Adam. By that reckoning, 5770 years have now elapsed since that Creation. Genesis 1 describes Six Days between the initial Creation of "the Heavens and the Earth" and the Creation of Adam. If you add six days to 5770 years, you get an elapsed time from the Creation of the Universe to now of 5770 years.
Many different and unrelated scientific inquiries have produced evidence consistent with the Earth and the Universe being orders of magnitude older than 5770 years. In The Challenge of Creation, Chapter Nine: "Evidence for an Ancient Universe," R' Natan Slifkin accessibly summarizes some of the these methods, including analysis of fossils, tree rings, and geological features.
To your point, he describes the evidence for a Universe age on the order of 10 billion years that comes from telescope observations of galaxies that are 10 billion light-years away. The presence of light from a source that far away implies that the light had been travelling for 10 billion years before it reached us, which implies that the galaxy it came from and the Universe containing it are at least that old.
A great deal of ink has been spilled trying to deal with this apparent disagreement between Scriptural and scientific evidence. The following few chapters of The Challenge of Creation describe a number of approaches to this issue as well as the author's approach.
When science says "the world is 13,000,000,000 years old", they are not saying "I was there. I have a video. I KNOW". They say "based on the evidence that I have, and based on the laws of nature that I observe, the world could have been created like this.
Or maybe not. Maybe there are other scientific laws involved that we just don't know about. We don't know everything yet, and it's possible all of our theories wouldn't work under different conditions. Remember, in the Rambam's time, everyone was convinced that the science of his day was absolutely true, to the extent that we had to "show" how we agree to science.
Or one can add, even if you say that from the Big Bang on everything was natural, the original yesh mi-ayin, the something from nothing, must have been supernatural. If creation is supernatural, there is no reason to stop the supernatural involment by the Big Bang, why not extend it to the end of creation. It says that when Hashem created the world, it was created fully formed. Meaning, Adam was an adult. If he would come to a doctor and ask "how old am I?" the doctor would say "middle aged". Was he or not?
In other words, it's not a scientific question, as it deals with "did Hashem perform this miracle or that miracle".
Many would answer: "Ahh... But it's a much smaller miracle for Hashem to create a "Big Bang" than create a world. Why make miracles bigger than they are?"
The answer to that this is not a scientific argument. Why Hashem makes a bigger miracle instead of a smaller isn't a scientific question. Maybe philosophical, but not scientific.
So in the end, there is no scientific evidence of the age of the universe. Philosophically one may find it hard to believe why Hashem would create the world looking old, but there are no questions based on science.
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There are a number of answers to this question:
Rabbi Aryeh Kaplan has shown that the tradition of the age of the world is not a simple subject.
Let's stick to Jewish sources only and ignore any other source.
We have two dating systems.
Now, according to the gemorah, option 1 will not tell us the age of the world. It will only tell how long humanity as descendand from Adam has been around. The gemorah tells us that we can not know or study what came before, what is above, what is below, and what will come in the future. As far back as we can know, is how long we as people knowing Gd have been around, and that is all we are allowed to know.
However, the gemorah says that some people, teacher to student can teach each other otherwise, and we have many cryptic statements in the Gemorah regarding the age of the world. One such statement is that the world was created 974 generation before the giving of the Torah. (Or 947 generations before Adam was created) Depending on if you use a generation as defined between Adam and Noach, or between Noach's son's and Avraham, or between Avraham and Moshe, you will get a different calculation on how many years the world existed before Adam. (anywhere from 18,940 years to 177,089 years)
According to another view of the Kabbalists and Ramban:
Rabbi Aryeh Kaplan expounds this further based on the writings of Rabbi Isaac of Acco.
The concept of the world being some 6,000 years old comes from Christianity, and Priests. These sentiments, for some reason unknown by anybody, have been adopted by modern day Charedim as the 'Torah True' view... despite the fact that nobody has ever suggested that the world is only 6,000 years old until some Christian priest decided to make that claim despite the scientific findings of Darwin and early Paelontology. The Tiferes Yisroel wrote:
In 1857 Philip Henry Gosse (A Non Jew who had no Jewish sources) was the first person to ever suggest that the world was close to 6,000 years old! He made this suggestion in his book Omphalos: an Attempt to Untie the Geological Knot. And now, that Christian book, is somehow touted as 'Torah!' You'd have to ignore at least 6 Gemoras, half the rishonim, a few achronim and your own eyes to say the world is less than 10,000 years old!
To summarize: A debate exists regarding the age of the world, because it is something which we can not know, and are instructed that it is not worth knowing. Despite this, we have many different Agadatas which give us a large variety of options for the age of the world. On top of that, we have a strong influence from Christian scholars convincing certain sects of Judaism, that a literal reading of both Seder Olam and the chumash is the only true answer to the question (despite the Torah Sh'baal peh which tells us otherwise!)
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