A question on constants and dimensionless equations

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In summary, the conversation discusses a question about the equation 2\alpha \hbar = \pi^2 \mu_0 c, which is stated in a paper but the dimensions seem odd. The conversation also brings up the question of whether dimensionless objects are always constants.
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help1please
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Homework Statement



There is not really a problem, just a question which i am about to ask. The known data is

[tex]\alpha[/tex] the fine structure constant
[tex]\hbar[/tex] Plancks constant
[tex]c[/tex] the speed of light
[tex]\mu[/tex] permeability

Homework Equations



[tex]2\alpha \hbar = \pi^2 \mu_0 c[/tex]

The Attempt at a Solution



A paper I downloaded a while back, but can't actually link to states this equation

[tex]2\alpha \hbar = \pi^2 \mu_0 c[/tex]

in a derivation. It seemed a little odd, are the dimensions right? I noticed all the data in this equation are actually made up of constants. Is it wise to say that when you deal with dimensionless objects, they are always constants (for a separate question).
Thank you!
 
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  • #2
help1please said:

Homework Statement



Is it wise to say that when you deal with dimensionless objects, they are always constants (for a separate question).
Thank you!

No. For example, angles are dimensionless.
 

1. What are constants and dimensionless equations?

Constants are fixed numerical values that do not change in a given situation or experiment. Dimensionless equations are mathematical equations that do not have any units associated with them. They are used to describe relationships between different physical quantities.

2. Why are constants and dimensionless equations important in science?

Constants and dimensionless equations play a crucial role in science because they help us understand and describe the physical world in a more simplified and universal manner. They also allow us to make accurate and precise predictions and calculations.

3. How are constants and dimensionless equations used in scientific research?

Constants and dimensionless equations are used in scientific research in a variety of ways. They are often used to formulate theories and models, to design experiments, and to analyze data. They also help scientists to compare and relate different phenomena and systems.

4. Can constants and dimensionless equations change over time?

No, constants are fixed values that do not change with time. However, dimensionless equations can change if new information or data is discovered that alters our understanding of a particular phenomenon or system.

5. How do scientists determine the values of constants and create dimensionless equations?

The values of constants are determined through careful experimentation and observation. Dimensionless equations are created through mathematical analysis and manipulation of physical laws and principles.

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