If the Planck length is the smallest unit of length that has any physical meaning then is it true to think that all the lengths are multiple of the Planck length?
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4Possible duplicate of Does the Planck scale imply that spacetime is discrete? – AccidentalFourierTransform Sep 30 '19 at 01:02
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As stated, this is just an algebra question, $\alpha = l / l_p$ where $l$ is any length, $l_p$ is the Planck length, and $\alpha$ is the multiplier that you mentioned. What do you really want to know? – Brick Sep 30 '19 at 01:05
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As "meter" is a unit of length in which if you measure me you will find me be of 1.80 meters but I was thinking if I can use plank length as unit of length and as plank length is smallest unit of length does that mean all length could be expressed as multiple of plank length? – Sep 30 '19 at 01:08
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2Planck is someone's name. It's capitalized, and it's spelled with a ck. – Sep 30 '19 at 01:25
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Also see https://physics.stackexchange.com/q/185939/123208 – PM 2Ring Sep 30 '19 at 02:13
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Yes, all lengths are multiples of the Planck length. All lengths are also multiples of the meter and the mile and the parsec. The Planck length is just another unit length and all lengths may be expressed as some multiple of any unit length.
The Planck scale is expected to be the scale at which quantum gravity is expected to become important. That does not mean that the universe is expected to be formed of Planck length pixels.
Dale
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6I’ll bet that the OP meant integer multiple. But they didn’t say that, so I agree with your answer. – G. Smith Sep 30 '19 at 01:36
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@G. Smith - that's what I thought after the first paragraph, which is in my opinion superfluous, but in the second paragraph he nevertheless answears the question correctly with "That does not mean that the universe is expected to be formed of Planck length pixels." – Yukterez Sep 30 '19 at 01:48
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1I wanted to explain both what the Planck length is (as an answer to the written question) and what the Planck length isn’t (as an answer to the intended question) – Dale Sep 30 '19 at 02:04