Understanding Planck Length and Time in Relation to Spacetime and Acceleration

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DevonG
Planck length and Planck time are constants, correct?

If spacetime changes for an observer who accelerates to subluminal velocities, what happens to these units? If they're constant I'm guessing they can't be "stretched" or "squashed". So do they change in number for a given measurement (say, the length of a pencil at rest) as you accelerate?
 
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The length of an object, given in Planck units, can be different for different observers. Similar with a time span.
There is nothing wrong with that. It just means that "the length of X in Planck units in some arbitrary specific frame" has no special physical meaning.