A quick question concerning constants and planck units

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Discussion Overview

The discussion revolves around the relationships between various physical constants using Planck units, including the exploration of calculations involving Planck length, time, energy, temperature, and their connection to constants like the speed of light and the Boltzmann constant. Participants share their findings and experiences while engaging with these concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that dividing Planck length by Planck time yields the speed of light, prompting curiosity about other potential relationships among constants using Planck units.
  • Another participant provides specific values for Planck energy and Planck temperature, demonstrating that their division results in the expected value for the Boltzmann constant, suggesting that the relationships are designed to yield such results.
  • A participant acknowledges a calculation error regarding the Boltzmann constant, attributing the discrepancy to a mistake in handling the powers of ten.
  • There is a discussion about the design of Planck units, with one participant emphasizing that these constants are defined to equal 1 in Planck units, likening it to the definition of the calorie in terms of heat capacity.
  • A participant expresses surprise at the exactness of the speed of light as a defined constant, indicating a learning experience regarding the definitions of physical units.

Areas of Agreement / Disagreement

Participants generally agree on the relationships between the constants as defined by Planck units, but there is a recognition of individual calculation errors and misunderstandings that lead to different interpretations of the results. No consensus on the exploration of more complex constants is reached.

Contextual Notes

Participants acknowledge the importance of careful handling of units and powers in calculations, indicating potential limitations in understanding or applying these concepts correctly.

Who May Find This Useful

Individuals interested in the relationships between physical constants, the use of Planck units, and those exploring foundational concepts in physics may find this discussion beneficial.

FysixFox
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Recently I have taken an interest in physical constants (and, through it, an interest in SI units and the upcoming redefinition of the kilogram). I actually have a list of almost all of them now, standard uncertainties included. After a bit, I decided to have a bit of fun messing around with the constants just to see what popped out.

Upon dividing Planck length by Planck time, I was surprised and intrigued to discover that the answer is the speed of light. I then began to wonder if there could possibly be other relations like this that, using Planck units, give such constants. Planck energy times Planck time gave me the reduced Planck constant, 1.0545717×10-34 J×s. Planck length cubed divided by the product of Planck mass and Planck time squared gave me the gravitational constant, 6.67384×10-11.

But oddly, upon dividing Planck energy by Planck temperature in an attempt to arrive at the Boltzmann constant, I hit a... strange roadblock. The Boltzmann constant DID technically come out the other side... but it came out 1064 times larger than it should have. Instead of 1.38065×10-23, I was getting 1.38065×1041. Why is this?
 
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You must've made a silly mistake.
Planck energy: EP = 1.9561 × 109 J
Planck Temperature :TP = 1.416 8 × 1032 K

EP/TP = 1.9561 × 109/1.416 8 × 1032 J/K = 1.38 × 10-23 as expected. By the way, this is not surprising at all. Planck's units are carefully defined with that exact property in mind. It is that way by design.
 
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dauto said:
You must've made a silly mistake.
Planck energy: EP = 1.9561 × 109 J
Planck Temperature :TP = 1.416 8 × 1032 K

EP/TP = 1.9561 × 109/1.416 8 × 1032 J/K = 1.38 × 10-23 as expected. By the way, this is not surprising at all. Planck's units are carefully defined with that exact property in mind. It is that way by design.

Ah! I see! It seems that the × 1032 part of the denominator migrated to the numerator somehow, likely an error on my part rather than the calculator's. Silly me. :-p

And interesting that the constants would come out like that. It kind of makes me wonder if some of the more complex constants could also be created using Planck's units in some manner. I'll continue to mess around with these constants for a while longer.

Thanks!
 
FysixFox said:
Ah! I see! It seems that the × 1032 part of the denominator migrated to the numerator somehow, likely an error on my part rather than the calculator's. Silly me. :-p

And interesting that the constants would come out like that. It kind of makes me wonder if some of the more complex constants could also be created using Planck's units in some manner. I'll continue to mess around with these constants for a while longer.

Thanks!

As I said, the constants come out like that by design. Planck length, mass, time ,etc were chosen with that very property in mind. What that means is that all these constants are equal to 1 (exactly, by definition) in Planck units. To be surprised or amazed by that is equivalent to being surprised that the heat capacity of water is 1 cal/(g.°C). The unit calorie was defined that way.
 
dauto said:
As I said, the constants come out like that by design. Planck length, mass, time ,etc were chosen with that very property in mind. What that means is that all these constants are equal to 1 (exactly, by definition) in Planck units. To be surprised or amazed by that is equivalent to being surprised that the heat capacity of water is 1 cal/(g.°C). The unit calorie was defined that way.


I'm kind of a noob at this whole physics thing, I was surprised that the definition of the meter is why the speed of light is an exact number instead of an estimate. :P
 

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