Is There a Connection Between Planck Length and Planck Time in Relativity?

[roineust]

Is a single occurrence of light refraction in water, considered mathematically an addition of a dimension?

 

[Nugatory]

Is a single occurrence of light refraction in water, considered mathematically an addition of a dimension?

Whatever you mean to say here, it's coming across as nonsense. Try to formulate your question more clearly. If it's a new topic, start a new thread.

 

[PeroK]

Does a single occurrence of light refraction in water, considered mathematically an addition of a dimension?

"Dimension" in this context is the physical dimensions of length $L$, mass $M$ and time $T$. For example, velocity has dimensions of $LT^{-1}$,; force has dimensions of $MLT^{-2}$ and energy has dimensions of $ML^2T^{-2}$.

This is not to be confused with spatial and time dimensions.

Something like $\frac v c$, or $\frac {m_1}{m_2}$ which appears in a lot of mechanics problems, is dimensionless. This means also that these quantities are independent of the units. If the velocity is half the speed of light, then $\frac v c = \frac 1 2$ regardless of the units.

See:

https://en.wikipedia.org/wiki/Dimensional_analysis

 

[Thomas Sturm]

Maybe we could remove the arbitraryness of the original question regarding units by assuming a base measure of length as 1 Lightsecond = 299796 km = 1 Flash [f]. By using this base, the Planck-Length would become 0.53*10^-43 f. So why is it only roughly half the length that light could cover in 1 Planck-Time (1*10^-43 s)?
If you define your unit of length to only rely on your unit of time (which you can do since there is such a well defined, prominent speed...), then it becomes irrelevant what you mean by "1 Second" as well, the ratio still is roughly 2 Planck-Length = 1 Planck-Time. It might be "irrelevant" to ask why - but then, why's that?

 

[Ibix]

So why is it only roughly half the length that light could cover in 1 Planck-Time (1*10^-43 s)?

It isn't - your value for the Planck time is off by a factor of roughly two. The Planck time is 5.39×10^-44s, which is consistent with your Planck length in light seconds - as it must be by definition.

 

[Thomas Sturm]

"The Planck time is the time it would take a photon traveling at the speed of light to across a distance equal to the Planck length. " Is the, very sensible, answer to the original question, then. If I had just googled "planck time length" first...this was just such a "1st-post-idiocity" from me, it really made me laugh (and still smile as I type this, in a slightly embarrassed kind of way). Thank you Ibix.
"No. It just means that seconds are bigger than meters."
This just has to be the coolest answer, ever.