Time dilation is a well-established phenomenon in physics that has been confirmed through numerous experiments and observations. It is a consequence of Einstein's theory of relativity, specifically the theory of special relativity. While "proven" is a strong word in science, the predictions of time dilation have been extensively tested and have consistently been found to be in agreement with experimental results.
The theory of special relativity states that the laws of physics are the same for all observers in uniform motion relative to each other. One of the consequences of this theory is that time can appear to run at different rates depending on the relative motion of observers. When an object is moving relative to an observer, time for that object will appear to pass more slowly compared to an object at rest relative to the observer.
This prediction of time dilation has been verified in various experiments and observations. One well-known example is the measurement of time dilation in particle accelerators. Fast-moving particles experience time dilation, which has been confirmed by comparing the lifetimes of unstable particles in motion and at rest. Additionally, experiments involving high-precision atomic clocks have also demonstrated time dilation effects.
Moreover, the Global Positioning System (GPS) relies on the principles of relativity to function accurately. The satellites in the GPS system are moving relative to observers on Earth's surface, and their clocks run slightly faster due to time dilation. If this relativistic effect were not taken into account, GPS calculations would accumulate significant errors.
Overall, the concept of time dilation is a well-established and confirmed aspect of physics, supported by a wealth of experimental evidence.