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

In summary, the Planck length and the Planck time are simply units of measurement, and the numbers -35 and -43 are arbitrary in the sense that they are a result of defining what a meter and a second are. There is no specific reason for these numbers to be chosen other than convenience. Time dilation and length contraction can be calculated using the same gamma factor, and they are both observed to happen on the same scale. The relevance of an object moving at close to the speed of light is seen in relativistic aberration, which has been well measured and understood. Astrophysicists use theories that modify Newtonian dynamics rather than General Relativity dynamics to explain dark matter, and this choice may be due to the complexity of understanding experiments
  • #36
Is a single occurrence of light refraction in water, considered mathematically an addition of a dimension?
 
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  • #37
roineust said:
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.
 
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  • #38
roineust said:
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
 
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  • #39
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?
 
  • #40
Thomas Sturm said:
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.
 
  • #41
"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.
 
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