Actually I wanted to write this article on 2015. Before completing the articles i tried to add more information on it so I googled some beliefs about gotra system. And I found one article , which claimed that gotra system does not violate modern theory of genetics. According to that article,  Y-chromosome of male get transferred only to son, so  gotra system is scientific.  It took me five more year to study and build confidence to complete this article.  

What is Gotra system.

According to Hindu belief, every person  belongs to a lineage of particular Rishi ( Hindu apostle ). Every lineages are given  a particular Gotra, Generally name of that particular Rishi, and it is strictly prohibited to get married within same gotra system.  Such gotra are unique for a particular family name, but sometime two or more than two family names can have same gotra. And if gotra is not found,  they can use a gotra "kashyap". Since Gotra is based on family name, father and son share same gotra but daughter will use gotra of her husband after marriage.  So, we can see, gotra is based on the male lineages. 


Is is good to marry with a person sharing same gotra
People believe that it is amoral  to marry with a person with same gotra. And as I mentioned in the beginning,  some people are trying to justify gotra system from scientific points of view. Their claim is y-chromosome is always transferred to male lineages only without a single audeltration. This statement is very true and it helps anthropologists to study about lineages and even some scientists can use them to find interrelationships between homo sapiens and other species too. But, from the point of view of marriage , it is totally useless.
Even your siblings will not have y chromosome
since y-chromosomes, is transferred only to male children, female siblings will not have the y-chromsome. If marriage within same gotra is formidable because of the Y-chromosome, brothers and sisters are eligible to marry, on the basis of gotra system. 


But there are other chromosomes too 
It has been found scientifically that, whenever a person produces a gamet a minor mutation occurs. If you are unknown about mutation, it is sudden change in chromosomes which creates some defects in your body. If  marriage is done  with own siblings,  both gametes will share same mutation of your parents ad well; resulting more mutation and there is high chances of having abnormal offspring. But If marriage is done with a person who doesn't share same genetic history,  there will be  mutation iwhichn different genes, which can be cancelled by another normal gene, so possible abnormalities are minimized . So it is better to avoid a person with chose genetic history.
So what about gotra.
A child gets half genes from father and half from mother.  Again if child produces another child , the new child will have only half genes,  from his each parents so he/she will have only 25% genes from grandparents. It will decrease in similar trend and after ten or fifteen generations,  there will be negligible portions of the ancestors gene. To be more specific,  after fifteen generation,  the gene will be depleted to 0.0030517578 percent. Let's take another example from maternal branch.  Generally maternal branches are forgotten after four or five generations. But in five generation, still there will be 3.125 present gene. If genetic theory is taken into consideration,  it is wise to marry with a person who share less portion of gene. But gotra system does just the opposite.
So so you still believe in gotra system?