# Are Special Relativity and quantized spacetime in contradiction?

**URL:** <https://boards.straightdope.com/t/are-special-relativity-and-quantized-spacetime-in-contradiction/809717>\
**Category:** Factual Questions\
**Created:** [February 28, 2018, 1:47am UTC](https://boards.straightdope.com/t/are-special-relativity-and-quantized-spacetime-in-contradiction/809717 "2018-02-28T01:47:05Z")\
**Posts on this page:** 4\
**Page:** 2

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [March 3, 2018, 2:44am UTC](https://boards.straightdope.com/t/are-special-relativity-and-quantized-spacetime-in-contradiction/809717/21 "2018-03-03T02:44:13Z")

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The textbook example would be the energy levels of the hydrogen atom. An electron in a hydrogen atom can have an energy of -13.6 electron volts, or -3.4 eV, or -1.51 eV, or -0.85 eV, and so on, but not any energy in between (the general formula is -13.6 eV/n^2, where n is any integer).

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**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\
**Post date:** [March 3, 2018, 3:08am UTC](https://boards.straightdope.com/t/are-special-relativity-and-quantized-spacetime-in-contradiction/809717/22 "2018-03-03T03:08:26Z")

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> [@"\[wikipedia](#):
>
> ([Planck units - Wikipedia](http://en.wikipedia.org/wiki/Planck_length#Theoretical_significance))"]The Planck length is believed to be the shortest meaningful length, the limiting distance below which the very notions of space and length cease to exist. Any attempt to investigate the possible existence of shorter distances, by performing higher-energy collisions, would inevitably result in black hole production. Higher-energy collisions, rather than splitting matter into finer pieces, would simply produce bigger black holes.

So, yes, distance and time in spacetime do seem to be based on integer values – but the integers are not very big. The Planck length is more that 24[sub]10[/sub] orders of magnitude smaller than the ångström unit.

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [March 3, 2018, 3:23am UTC](https://boards.straightdope.com/t/are-special-relativity-and-quantized-spacetime-in-contradiction/809717/23 "2018-03-03T03:23:05Z")

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It’s widely believed to be the shortest meaningful length, but there’s no real basis for that wide belief. Physicists wouldn’t be surprised if it turns out to be true, but we’d be even less surprised if it turns out not to be. It’s just that, if there is a smallest meaningful length, we don’t have any better guesses for what it might be… but there’s nothing that says that it has to be something that we would guess.

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**Author:** ![Qadgop\_the\_Mercotan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/qadgop_the_mercotan/32/83_2.png) [@Qadgop\_the\_Mercotan](https://boards.straightdope.com/u/Qadgop_the_Mercotan)\
**Post date:** [March 3, 2018, 4:15pm UTC](https://boards.straightdope.com/t/are-special-relativity-and-quantized-spacetime-in-contradiction/809717/24 "2018-03-03T16:15:39Z")

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> [@Chronos](#):
>
> But **Qadgop** , you’ll lose all that tasty neutronium if you just let it go collapsing into black holes willy-nilly.

Cynthia thinks I should cut back on my neutronium consumption anyway.

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