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

[Axuality]

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?

 

[Bob_for_short]

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.

 

[Axuality]

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)?

 

[Bob_for_short]

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

 

[Axuality]

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)?

 

[Fredrik]

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.

 

[Naty1]

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...

 

[Axuality]

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.