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.
Highlights
Is There A Quantum and Minimum Length?One of the open questions in physics is whether there is a minimum length or not, and how to interpret such a thing precisely
The Planck length is considered by many physicists to be the minimum length
First we will turn to special relativity and the notion of the speed limit and how it leads to a trans-Planckian problem
Summary
One of the open questions in physics is whether there is a minimum length or not, and how to interpret such a thing precisely. Looking to the history behind this unit, in 1899, Max Planck first suggested the Planck length as a component of what he called the natural units (Planck, 1899, 1906). He assumed that there were three essential universal constants, namely the speed of light c, Newton’s gravitational constant G, and the Planck constant. Using only these three constants and dimensional analysis, he calculated what he thought were the fundamental length, time, mass, and temperature for matter. First we will turn to special relativity and the notion of the speed limit and how it leads to a trans-Planckian problem
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