Working in different units

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In summary, the conversation discusses the use of non-standard units for physical constants such as the speed of light, Planck's constant, and Boltzmann constant. The possibility of using these units to calculate other physical constants, such as Newton's Gravitational Constant, is explored, but it is determined that these units alone are not enough to form a complete system. The concept of Planck units, which do form a complete set, is also mentioned. Ultimately, the issue is resolved.
  • #1
shanu_bhaiya
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Homework Statement



Is there any standard method known to work with units in which speed of light (c), Planck's constant (h), Boltzmann constant (kb) are given by:

c=1
h=2*pi (i.e. h_cross=1)
kb=1

For example, how can we calculate Newton's Gravitational Constant (G) in these units. If there's any systematic method for this please help.

Homework Equations



n/a

The Attempt at a Solution



Basically, I tried to calculate the G by expressing G in terms of c, h and kb, but I have not been able to do so.
 
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  • #2
Those units alone will not be enough to completely define the units of the gravitational constant though they can go some way toward it. It can be shown that you need 7 base units in order to have a complete system i.e. one in which any quantity can be expressed as a combination of base units. (in SI these are m, s, kg, A, mol, K, candela)

the three units you propose could be expressed in SI as m.s^-1, kg.m^3.s^-2 and kg.m^3.s^-2.K^-1
These on their own do not form a complete set, however they can easily be used to express measurements of energy and some other measures.
These three units alone would not be suitable for measuring, for instance length, as there is no combination of these units that leaves only metres in the answer.

In terms of the constant G with units m^3.kg^-1.s^-2 you could get close by expressing it in terms of: c^6.hbar^-1.s^2 or c^4.hbar^-1.m^-2 but that is the simplest you could achieve as m and s cannot be expressed separately by these units alone.

Introucing an additional unit of Planck length L would allow you to express G in terms of these units as G = 123456789x c^4.hbar^-1.l^-2 (123456789 is an example number, you'd have to work it out yourself)

EDIT: the system of Planck units is well established and does for a complete set: http://en.wikipedia.org/wiki/Planck_units
note there is no 7th Planck unit since it takes mols as being a single atom and in SI and other system mols is just a defined multiplier
 
  • #3
thanks david... matter got resolved
 

1. What are the benefits of working in different units as a scientist?

Working in different units allows a scientist to gain a broader perspective and understanding of their field. It also helps to develop diverse skills and techniques, as well as build a larger network of colleagues and collaborators.

2. How can working in different units enhance my research and career opportunities?

By working in different units, a scientist can gain exposure to different research methods and approaches, which can lead to new ideas and collaborations. This can also help to make a scientist more versatile and attractive to potential employers.

3. What challenges may arise from working in different units?

One potential challenge of working in different units is the need to adapt to different work cultures and environments. This may require strong communication and interpersonal skills, as well as the ability to be flexible and open to new ideas.

4. How can I successfully navigate working in different units?

To successfully navigate working in different units, it is important to establish clear communication with colleagues and supervisors, be open to learning and trying new things, and maintain a positive and professional attitude. It may also be helpful to seek guidance and support from mentors or colleagues who have experience in working in different units.

5. How can I incorporate my experiences from working in different units into my work?

As a scientist, you can incorporate your experiences from working in different units by incorporating new techniques or approaches into your research, collaborating with colleagues from different units, and applying the skills and knowledge gained to advance your career. Additionally, reflecting on your experiences and what you have learned can help shape and improve your future work.

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