# Plancks units and dimensions

#### faen

1. The problem statement, all variables and given/known data

1. What is the meaning of Planck’s units? Hint: Compare the strength of the 4 fundamental forces.

2. Calculate the Planck’s dimensions as a function of the SI units.

3. What are the dimensions of the human being in terms of Planck dimensions?

2. Relevant equations

Plancks's units defined in terms of the speed of light (c), the quantum of action (h/2pi), and the Newtonian gravitational constant G

strength of electromagnetic force $$\alpha = e/(hc/2pi)$$

strength of gravitational force is G

3. The attempt at a solution

1. I suppose the meaning of the planck units is that if they're set to unity while calculating a fundamental force (e.g. F=G*m*m/r^2), you wouldnt need a constant (such as G) to get the right number for force. However i cant figure out how im supposed to compare fundamental force strengths to show that.

2. The constants describing the planck units are already described in SI units. So i dont understand what im asked to do then.

3. This question i dont understand at all....

Thanks a lot to whoever helps.

#### nrqed

Homework Helper
Gold Member
1. The problem statement, all variables and given/known data

1. What is the meaning of Planck’s units? Hint: Compare the strength of the 4 fundamental forces.

2. Calculate the Planck’s dimensions as a function of the SI units.

3. What are the dimensions of the human being in terms of Planck dimensions?

2. Relevant equations

Plancks's units defined in terms of the speed of light (c), the quantum of action (h/2pi), and the Newtonian gravitational constant G

strength of electromagnetic force $$\alpha = e/(hc/2pi)$$

strength of gravitational force is G

3. The attempt at a solution

1. I suppose the meaning of the planck units is that if they're set to unity while calculating a fundamental force (e.g. F=G*m*m/r^2), you wouldnt need a constant (such as G) to get the right number for force. However i cant figure out how im supposed to compare fundamental force strengths to show that.

2. The constants describing the planck units are already described in SI units. So i dont understand what im asked to do then.

3. This question i dont understand at all....

Thanks a lot to whoever helps.

These constants can be combined in a unique way to give something that has the dimensions of a time (try it!). This is called the Planck time or if you want, "one unit of Planck time". The corresponding value can be given in seconds if you use the usual SI values for h bar, c and G.
You can then find what one Planck time is equal to in seconds.

The same thing for "Planck mass", "Planck length" and, if you want, "Planck energy" (which is simply the Planck mass times c^2)

Likewise

#### faen

So in order to write the planck units as a function of SI units, do i have to write the planck length in meters? Or should i just write all the SI units defining the planck length without calculating how they cancel eachother out?

In question 3, are they asking the average planck length and mass of a human being, or in which dimensions a human being exist in? English isnt my native language :P

#### nrqed

Homework Helper
Gold Member
I want to make sure that what I wrote is clear.

There is a unique way to combine c, $$\hbar$$ and G to get something that has the units of a length. This combination is of course independent of the units used for the three constants. This combination is defined to be one Planck unit of length.

So you will have

One Planck unit of length = expression in terms of c, $$\hbar$$ and G

(Of course, this is quite arbitrary because one could always multiply by any dimensionless constant such as $$\pi$$, 1/3 etc. But assuming that the dimensionless constant i snot huge or tiny, it would not change by very much the scale involved so we assume that the dimensionless constant is simply one.)

Now, if you plug in the values of c, $$\hbar$$ and G in SI units, you will obtain the value of the Planck length in meters. So you will have

One planck unit of length length = x meters

Once you have that, you can estimate the average height of a person in meters and then give the average height in Planck units of length

So in order to write the planck units as a function of SI units, do i have to write the planck length in meters? Or should i just write all the SI units defining the planck length without calculating how they cancel eachother out?

In question 3, are they asking the average planck length and mass of a human being, or in which dimensions a human being exist in? English isnt my native language :P

#### faen

Allrighty, got it. Thank you very much :-)

Just to be sure; to answer task 2 i have to just write down the planck length in meters, planck mass in kg etc? Hard for me to know what answer the teacher expects.

#### nrqed

Homework Helper
Gold Member
Allrighty, got it. Thank you very much :-)

Just to be sure; to answer task 2 i have to just write down the planck length in meters, planck mass in kg etc? Hard for me to know what answer the teacher expects.
yes, that's the way I interpret the question. One Planck unit of time is how many seconds, one Planck unit of mass is how many kg, etc...

You are welcome. Glad I could help.

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