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

[roineust]

This is probably repeating the same question, but i want to make sure it is:

I've watched the following 3 part video:


If we consider that g=h=c=1 and derive the meter, second and kg from them:

Does length contraction advance at the same rate as time dilation advances, as an object gets closer towards the speed of light?

Is the subject of arbitrariness now still what defines this question, as it was that defined it as originally expressed in this thread?

 

[Nugatory]

Does length contraction advance at the same rate as time dilation advances, as an object gets closer towards the speed of light?

Either I am misunderstanding your question or it was answered by @PeroK in post #8.

 

[roineust]

Either I am misunderstanding your question or it was answered by @PeroK in post #8.

How is it that an expression (gamma) that includes time and length in it, in the form of speed, is dimensionless?

 

[Dale]

How is it that an expression (gamma) that includes time and length in it, in the form of speed, is dimensionless?

You can easily work out the units for yourself.

 

[PeroK]

How is it that an expression (gamma) that includes time and length in it, in the form of speed, is dimensionless?

Because it only involves $v/c$ and that is dimensionless.

 

[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.