Abstract

In gravity theory, there is a well-known trans-Planckian problem, which is that general relativity theory leads
to a shorter than Planck length and shorter than Planck time in relation to so-called black holes. However, there has been little focus on the fact that special relativity also leads to a trans-Planckian problem, something we will demonstrate here. According to special relativity, an object with mass must move slower than light, but special relativity has no limits on how close to the speed of light something with mass can move. This leads to a scenario where objects can undergo so much length contraction that they will become shorter than the Planck length as measured from another frame, and we can also have shorter time intervals than the Planck time.
The trans-Planckian problem is easily solved by a small modification that assumes Haug’s maximum velocity for matter is the ultimate speed limit for something with mass. This speed limit depends on the Planck length, which can be measured without any knowledge of Newton’s gravitational constant or the Planck constant.

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