Quantization of Length: Can You Achieve Every Length Between 1" and 2"?

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Discussion Overview

The discussion revolves around the concept of quantization of length, particularly in the context of stretching a rubber band from 1" to 2". Participants explore whether every possible length between these two points can be achieved, considering implications from quantum mechanics (QM) and the nature of physical states.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that during the stretching of a rubber band, not all lengths between 1" and 2" can be achieved due to quantization effects.
  • Others argue that in quantum mechanics, only stationary states are quantized, allowing for non-stationary, transient states where intermediary lengths are possible.
  • One participant suggests that while length is not quantized in current theories, there may be implications in a quantum theory of gravity.
  • Another point raised is that the positions of the particles making up the rubber band are not perfectly defined, leading to a "smeared out" effect that complicates achieving a specific length.
  • A later reply connects the concept of uncertainty in quantum mechanics to the idea of quantization of length, suggesting that lengths do not exist until defined, thus implying a form of quantization is necessitated by uncertainty.

Areas of Agreement / Disagreement

Participants express differing views on whether quantization of length exists and how it relates to the stretching of the rubber band. There is no consensus, as some argue for the possibility of all lengths being achievable while others emphasize limitations imposed by quantum mechanics and uncertainty.

Contextual Notes

Participants note that the discussion is limited by the current understanding of quantum mechanics and the definitions of length, with unresolved implications regarding the relationship between uncertainty and quantization.

Axuality
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Do I understand this?-if I stretch a rubber band from a 1" length to a 2" length...

If I stretch a rubber band from a 1" length to a 2" length, is it true that it was not all possible lengths between 1" and 2" sometime during the stretch?

In other words, at some level, quantization enters in and makes it impossible to achieve every possible length between one and two inches?
 
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Axuality said:
If I stretch a rubber band from a 1" length to a 2" length, is it true that it was not all possible lengths between 1" and 2" sometime during the stretch?

In other words, at some level, quantization enters in and makes it impossible to achieve every possible length between one and two inches?

No. In QM only stationary sates are quantized so there are non stationary, transient states (described with superpositions of stationary ones with changing coefficients) when intermediary positions are possible.
 


Bob_for_short said:
No. In QM only stationary sates are quantized so there are non stationary, transient states (described with superpositions of stationary ones with changing coefficients) when intermediary positions are possible.

Thank you. And then am I to understand that I couldn't have STOPPED the rubber band at any length I so choose, (in other words at one of those transient states)?
 


The length is never quantized in QM so any length is possible. On a quantum level it will just fluctuate a little bit.
 


Bob_for_short said:
No. In QM only stationary sates are quantized so there are non stationary, transient states (described with superpositions of stationary ones with changing coefficients) when intermediary positions are possible.

Thank you. And then am I to understand that I couldn't have STOPPED the rubber band at any length I so choose, (in other words at one of those transient states)?
 


There's no quantization of length in the current theories, but there might be in a quantum theory of gravity. There is however another problem that will make it impossible to give your rubber band exactly the length you want it to have. None of its component particles has a position that's perfectly well defined. Their positions are always "smeared out" over some small region.
 


I was about to post the same points as Fredrik ...In addition, Leonard Susskind in THE BLACK HOLE WAR claims such energy states ARE quantized, but for all practical purposes appear continuous on macroscopic scales...He also mentions the Braginsky standard quantum limit which reflects the optimal (but limited) accuracy of submicroscopic measurements...
 


Fredrik said:
There's no quantization of length in the current theories, but there might be in a quantum theory of gravity. There is however another problem that will make it impossible to give your rubber band exactly the length you want it to have. None of its component particles has a position that's perfectly well defined. Their positions are always "smeared out" over some small region.

It appears evident that the smearing out of which you speak, explained by the Uncertainty Principle, is the mother of quantization of length. Due to the uncertainty, no length actually exists until it is defined(specified). Until all possible lengths are defined(unreasonable), then in the only reasonable definition of terms, all lengths do NOT exist yet. Hence quantization of length is actually necessitated and supported by the second problem you mention, uncertainty.

It is only natural of course that Uncertainty and quantization are related in this way.
 

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