Imagine I have a device that can stop time for the person who holds it (similar to Bernard's Watch). This device works in a very specific way - it creates a bubble around the user (just large enough to hold the user) in which time flows much faster than in the rest of the universe. The difference is very high but it is finite (say 100,000 times faster). This means that if the person holding the device experience times at "normal speed" the rest of the world outside the bubble appears to him to be drastically slowed down, almost (but not quite) to a standstill. In contrast, anyone outside the bubble looking in would see everything inside the bubble happening at lightning fast speed (almost instantaneously).
The border between this bubble of faster time and the rest of the universe is not infinitely thin - there is a boundary (say a few centimetres thick) where the speed of time changes gradually from one to the other.
My question is what side effects would this bubble cause? For example: any sounds from the outside would sound quieter and deeper, as the wavelengths are "stretched out" at the boundary. Similarly looking out of the bubble the outside world would appear darker and redder, as light is red-shifted. In fact with enough time dilation you would be able to see x-rays with your naked eyes. I'm also positing that waves such as light and sound would also bend at the boundary, as if they had struck a lense, so the outside world would appear distorted. Moving object such as bullets would also be deflected slightly (if they struck at an angle).
Are there any other interesting effects that could arise? What would happen if you walked up to another person, as they crossed the bubble's boundary? Is there anything cool you could do with this device?
For extra credit: would this violate any physically laws in any way e.g. conservation of energy? Show your working!