Infinities in renormalizable theories arise due to the divergent nature of certain calculations, such as loop diagrams. They are typically defined as mathematical expressions that become infinite when certain parameters (such as energy or momentum) approach certain values. In order to measure infinities, physicists use a process called renormalization, which involves subtracting out the infinite terms and replacing them with finite ones.
Handling infinities is crucial in order to obtain meaningful and accurate predictions from renormalizable theories. If left unaddressed, infinities can lead to nonsensical results and render the theory useless. By handling infinities, physicists are able to make precise calculations and predictions that can be tested experimentally.
There are several techniques used by physicists to handle infinities in renormalizable theories. One common method is dimensional regularization, which involves introducing a small parameter (called epsilon) that allows for the cancellation of infinities in the final result. Another method is zeta function regularization, which involves replacing the divergent sums in the calculations with finite values using the Riemann zeta function.
While physicists have developed various techniques to handle infinities in renormalizable theories, there are still limitations to these methods. For example, some calculations may still result in infinite values even after applying renormalization. In these cases, physicists may resort to approximations or make simplifying assumptions in order to obtain finite results.
It is unlikely that infinities can ever be completely eliminated in renormalizable theories. This is because they are inherent to the mathematical framework used to describe physical phenomena, and as our understanding of the universe evolves, new theories and calculations may also introduce new types of infinities. However, through the use of renormalization techniques, physicists are able to effectively handle and minimize the impact of infinities in their calculations.