Why are Planck units considered fundamental?

[Conn_coord]

Why are Planck units considered fundamental ?
After all, there is a square root in their expressions.
And the value of the Planck mass is 20 orders of magnitude greater than the average values of elementary particles.
$$ m_{pl}=\sqrt{\frac{1}{2\pi}\cdot \frac{hc}{G}}$$
The order of the value of mass in the famous Weinbergs formula corresponds to the mass of the proton and pion. But there is already a cube root.
S. Weinberg, Gravitation and Cosmology, John Wiley and Sons, New York, (1972)
pages 619-620
Equation 16.4.2
$$ m_{w}=\sqrt[3]{\frac{1}{4\pi^2}\cdot \frac{H_0\cdot h^2}{Gc}}$$
Obviously, the expressions above with elementary mass must contain it in the square and cube, respectively.
For example,
$$ m_{pl}^2=\frac{1}{2\pi}\cdot N_m \cdot m_0^2 $$
$$ m_{w}^3= \frac{1}{4\pi^2}\cdot N_m \cdot m_0^3 $$
$$where \qquad N_m=\frac{c^5}{2GhH_0^2}\approx 1.16\cdot 10^{121}$$
Please, tell me more formulas similar to the Planck and Weinberg formulas.

 

[Demystifier]

Fundamentality has nothing to do with absence or presence of the square root. If you think that a fundamental formula cannot have a square root, how about $i=\sqrt{-1}$?

 

[Conn_coord]

Maybe you're right.
But in my opinion i has nothing to do with reality.
It's more of a math trick.

And physical quantities have dimensions.
When we get kg^2, then this is the multiply of mass.

And in the case of the mass standard, we should get
$$ N_m\cdot m_0 = M \approx 10^{53}kg$$
https://en.wikipedia.org/wiki/Universe

$$2\pi\cdot m_{pl}^2= M\cdot m_0$$

 

[topsquark]

Maybe you're right.
But in my opinion i has nothing to do with reality.
It's more of a math trick.

And physical quantities have dimensions.
When we get kg^2, then this is the multiply of mass.

And in the case of the mass standard, we should get
$$ N_m\cdot m_0 = M \approx 10^{53}kg$$
https://en.wikipedia.org/wiki/Universe

$$2\pi\cdot m_{pl}^2= M\cdot m_0$$

Consider that the Planck expressions only use other constants. We may easily reverse this and express some of the other constants in terms of the Planck variables.

Also, many consider the Planck length to be the smallest possible length and the Planck mass to be the largest possible. IMHO, I do not agree with this as I've seen no theory that says this must be true. But many feel that way. That's another reason people call the Planck units fundamental.

-Dan

 

[Demystifier]

Also, many consider ... the Planck mass to be the largest possible.

I don't think that anybody considers it, Planck mass is about $10^{-5}$ grams.

 

[Dale]

Why are Planck units considered fundamental ?

Planck units are not considered fundamental. They are considered natural.

But in my opinion i has nothing to do with reality.
It's more of a math trick.

When the math trick accurately models reality then this opinion becomes rather suspect.

 

[hutchphd]

Or all of physics is a math trick. I think of Einstein's comment. Actually I think of Lord Buckley's commentary on "the Mighty Hip Einie" but that is a personal foible.

 

[fresh_42]

I think you should say goodbye to the request that our notation decides what is fundamental, natural, or universal.

Why are Planck units considered fundamental ?
After all, there is a square root in their expressions.

The ratio between a circle's diameter and circumference is an infinite number. It is quite natural I would say since it is constant in the entire universe, and for even many more reasons. However, it is only infinite because our number system relies on counting.

Two of the fundamental forces in nature are quadratic. They carry the fundamental property in their description. You cannot avoid roots if you want to calculate distances with them.

Everything with a complex number can also be phrased with real numbers. It is inconvenient, and terribly complicated when it comes to complex functions. Yet, nature is often best described by using them. Only because we cannot imagine imaginary numbers does not mean nature itself can't.

To the best of our knowledge, and checked in many dozens of experiments, the laws of nature are the same everywhere, be it in our labs or in the universe. What we see in the sky can be explained by what we do in the laboratory. A good reason to speak of universal laws.

Regarding the Planck units ...

Planck units are not considered fundamental. They are considered natural.

 

[Conn_coord]

There is no doubt that the mathematical apparatus is a very useful tool.

Maybe I'm wrong, but there is a big difference between fundamental units and natural units.
Not every natural unit is fundamental.
It is now accepted that the elementary charge is the fundamental unit.
The speed of light is the fundamental speed.
But if there are fundamental units of mass, length and time, they must be associated with fundamental physical constants.

 

[fresh_42]

There is no doubt that the mathematical apparatus is a very useful tool.

Maybe I'm wrong, but there is a big difference between fundamental units and natural units.

This is quibbling. There is no such thing as a fundamental unit. Except, we defined some as fundamental in order to simplify their worldwide usage. They are called SI units.

Before you use properties like natural or fundamental you ought to define them! Believe it or not, all three properties natural, fundamental, and universal are defined in mathematics. It is a bit more complicated in physics. What are your definitions? Without them, it remains quibbling.

Not every natural unit is fundamental.
It is now accepted that ...

... by whom, where, what ...

the elementary charge is the fundamental unit.

I'd say it is a minimal quantity. Its minimality allows us to call it a fundamental unit.

The speed of light is the fundamental speed.

I'd say it is a maximal speed. Its maximality allows us to call it a fundamental unit.

But if there are fundamental units of mass, length and time, they must be associated with fundamental physical constants.

Again. You are juggling words. You can take this as a definition of a fundamental unit and argue that mass, length, and time don't allow a fundamental unit. But this would all be philosophy à la Wittgenstein.

What is your point? Do you want to teach physicists another use of language? Do you wonder what a fundamental mass would be?

 

[Conn_coord]

Please, tell me more formulas similar to the Planck and Weinberg formulas.

 

[Dale]

Maybe I'm wrong, but there is a big difference between fundamental units and natural units.

I have never heard of "fundamental units" before your post. I have only heard of natural units, of which Planck units are merely one example of many.

 

[PeterDonis]

Why are Planck units considered fundamental ?

Who says they are? Do you have a reference?

 

[PeterDonis]

Please, tell me more formulas similar to the Planck and Weinberg formulas.

This is way too vague and open-ended.

 

[vanhees71]

I'd say, "natural units" are such units that are defined on what are "fundamental constants of nature", which of course depends on our current knowledge of physics.

The current definition of the SI units is almost a system of "natural units" in this sense but not completely since for the definition of the second as unit of time, we still don't use a fundamental constant but a constant based on a specific atom, i.e., $\Delta \nu_{\text{Cs}}$ of the hyperfine transition of Cs-133 atoms. Other than that all the 6 physical base units of the SI is based on the definition of fundamental constants, although of course all these definitions also depend on the definition of the second.

 

[Conn_coord]

What is your point? Do you want to teach physicists another use of language?

No way, I'm just bad at English :)

Do you wonder what a fundamental mass would be?

There is a funny formulas
$$m_0 = \frac{H_0\cdot h}{c^2} \approx 1.6\cdot 10^{-68}kg$$
$$r_0 = \frac{G\cdot H_0\cdot h}{c^4} \approx 1.2\cdot 10^{-95}m$$
$$t_0 = \frac{G\cdot H_0\cdot h}{c^5} \approx 4.0\cdot 10^{-104}s$$
These quantities are more like fundamental then Planck`s
Multiplying them by N_m we get the global characteristics of the Universe.

 

[dextercioby]

Who is H_0? And your last comment (who is N_m?) is a mere speculation, which is not permitted here.

 

[Conn_coord]

Who is H_0? And your last comment (who is N_m?) is a mere speculation, which is not permitted here.

H₀ - Hubble constant
$$N_m = \frac{c^5}{H_0^2Gh} \approx 1.16\cdot 10^{121}$$
$$N_m = \frac {5}{4\pi}\cdot \frac{2}{\alpha} \cdot e^{\frac{2}{\alpha}}$$
α - fine structure constant

 

[Nugatory]

H0 - Hubble constant

Which is not a constant…

 

[Conn_coord]

Which is not a constant…

I think so too.
N_m is not a constant, but the main counter.
After all, the Universe is expanding, global characteristics are changing (size and age).
But what about the mass ?
Could it be that the mass of the Universe has been increasing from zero to the present day?
With speed m₀/t₀= 10³⁵kg/s.

 

[Demystifier]

I think the answer is 42, so that we can close this thread.

 

[Conn_coord]

I think the answer is 42, so that we can close this thread.

Sorry, I know I broke the rules.
It's just a pity that there is no place to discuss the issue

 

[DrClaude]

This is numerology. Thread closed.

 

[PeterDonis]

It's just a pity that there is no place to discuss the issue

To add a final note: If there is no place you can find that allows you to discuss some issue, you should reconsider whether the issue is actually worth discussing.