Measuring Frequency of Trans Planckian Blue Shift

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Consider a source of radiation that is emitting the radiation at the highest possible frequency inversely proportional to the Planck time interval as measured in the rest frame of the source.

What frequency would an an observer that is moving towards the source measure?
What frequency would an observer that is lower down in a gravitational well measure?

Do these sort of considerations mean we have to dismiss the idea of the Planck time interval as being the fundamental smallest time interval or equivalently the Planck frequency as being the highest possible frequency?
 
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We never had that idea in the first place.

The Planck length is only an approximate scale, at which gravity becomes as strong as the other forces. It's about 15 or 16 orders of magnitude beyond known physics, and purely hypothetical. The ideas that lead to it may well be wrong. Asking what happens at this scale in specific circumstances is meaningless, and not worth losing a nanosecond's sleep over.
 
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