Hot answers tagged physical-constants
41
Dear Michael, first of all, the question you are asking is very important and you may master it completely.
Dimensionful constants are those that have units - like $c, \hbar, G$, or even $k_{\rm Boltzmann}$ or $\epsilon_0$ in SI. The units - such as meter; kilogram; second; Ampere; kelvin - have been chosen partially arbitrarily. They're results of random ...
36
To formalize dushya's comment as an answer:
Since the kilogram is an arbitrary, man-made unit, the actual numerical value of the proton mass in kilograms is meaningless (i.e. it's as good as its value in pounds, ounces, stones, solar masses, $\textrm{MT}/c^2$, etc.). The true fundamental constants of nature are dimensionless: they have the same value in ...
18
Yes, Avogadro's constant is a redundant artifact from the era in the history of chemistry in which people didn't know how many atoms there were in a macroscopic amount of a material and it is indeed legitimate to set Avogadro's constant equal to one and abandon the awkward obsolete unit "mole" along the way. This $N_A=1$ is equivalent to
$$ 1\,\,{\rm mole} = ...
16
There was a proposal in 2006 trying to define NA as an exact number[1,2]:
$$ N_A^* = 84\;446\;888^3 = 6.022\;141\;410\;704\;090\;840\;990\;72 \times 10^{23} $$
the problem? This value is incorrect, as the currently most accurate result is[3]
$$ N_A = 6.022\;140\;84(18) \times 10^{23} $$
i.e. $N_A^*$ is now 3 s.d. away from $N_A$. As I have commented, if ...
14
$G$ is just a constant of proportionality to get the units right (so that when $m_1$ and $m_2$ are in kilograms and $r$ is in meters you get a force in Newtons rather than wingdingalings or something really weird). Indeed cosmologists like to work in a system of units where $G = c = 1 \text{ (dimensionless)}$, and particle physicists like to work in units ...
11
The problem is that you want your unit definitions to be realizable - so specifying "1 mol is long number molecules, 1 gram is 1/12 of the mass of one mol of $C_{12}$" is nice for your thought process, but as long as there is no practical way to count molecules at such scales to a precision of better than $10^{-9}$ (which I think is the precision of the ...
10
This does allow you to make a prediction--- the significance of the match tells you approximately the number of attempts you have made to get such a coincidence. The ratio of the mass of a proton to a mass of a steel cylinder in Paris was determined by the psychology of some French revolutionaries.
But from the accuracy you get, one can be 99.99% sure that ...
10
The infinitesimal length interval between two events in spacetime $ds$ is defined by
$$ds^2=c^2 dt^2 - dx^2 - dy^2 - dz^2$$
The creature is dimensionally consistent, because time is multiplied with a speed. You can think of $(t,x,y,z)$ as the four coordinates of spacetime $(x^0,x^1,x^2,x^3)$ and $c$ appears naturally in the equations. However, the usual ...
9
One should separate the question into two parts, the first of which is philosophical, and the second physics. The philosophical question is resolved by understanding that there are "constants" which are just those that set the system of units, and these are constant for the simple reason that they define our conventional units.
The unit-defining constants ...
9
Your guess is correct. After electroweak symmetry breaking, the coupling constant for the residual $U(1)_\textrm{EM}$ gauge group can be written as a function of the couplings of the broken $SU(2)_L \times U(1)_\textrm{Y}$ gauge groups:
$$
\alpha = \frac{1}{4\pi}\frac{g^2 g\prime^2}{g^2+g\prime^2} = \frac{e^2}{4\pi}
$$
These couplings, however, are running ...
8
Only dimensionless quantities are important. They are just pure numbers and there can't be any ambiguity about their value. This is not so with dimensionful quantities. E.g. if I tell you my speed $v$ relative to you is $0.5\, \rm speedons$ that doesn't give you much information as I have a freedom to define my $\rm speedon$ units any way I want. Only way I ...
8
You've seen the speed of light quoted as roughly $3*10^8\, \text{m/s}$, so the speed of light is very fast compared to one meter and one second. This is roughly a human walking speed, so your question could be interpreted as asking why light is few hundred million times faster than a walking speed.
The speed people walk is rather anthropocentric, though. ...
7
There is no proof that fundamental constants are constant. Indeed I've seen claims that string theory allows varying constants, though I've also seen comments (I think Lubos Motl blogged on this a while back) that such arguments are wrong.
There are lots and lots of publications measuring fundamental constants and review articles of such measurements. ...
7
Your last couple of comments, about units, are incredibly important. It only makes sense to compare two things if they have compatible units. So, to use your example, it doesn't really make sense to talk about the size of Planck's constant relative to the electron charge, but it does make sense to talk about the mass of the muon relative to the mass of the ...
7
The formula is obtained by dimensional analysis. Up to a constant dimensionless factor, the given expression is the only one of dimension length that one can make of the fundamental constants $\hbar$, $c$, and $G$.
Discussions about the physical significance of the Planck length have no experimental (and too little theoretical) support, so that your second ...
7
Using fundamental physical constants try to construct expression which unit is legth.
So using dimensional analysis, we have a data of: $G = m^3 \cdot kg^{-1} \cdot s^{-2}$, $c = m \cdot s^{-1}$ and $\hbar = J \cdot s = kg \cdot m^2 \cdot s^{-1}$.
Than we are to construct length $l = m$ in the following way:
$$l = G^a c^b \hbar^d = m^{3a + b+d} \cdot ...
7
The expression $(\hbar G/c^3)^{1/2}$ is the unique product of powers of $\hbar, G,c$, three most universal dimensionful constants, that has the unit of length. Because the constants $\hbar, G,c$ describe the fundamental processes of quantum mechanics, gravity, and special relativity, respectively, the length scale obtained in this way expresses the typical ...
7
SPEED OF LIGHT:
This is a very interesting question. Going through the foundations of electromagnetism and the theory that led to Maxwell’s equations, there is an interesting element that can grab your attention. You can see that the speed of light is not as abstract and mysterious as it appears to be, but only if you look from a different perspective.
I ...
6
Another thing that would be changed by a varying fine structure constant would be that it would alter almost every electromagnetically mediated phenomenon. All of the spectra of atoms would change. What would also change would be the temperature at which atoms can no longer hold onto their electrons, since the strength of attraction between electrons and ...
6
CODATA is a group that compares and combines all the most accurate experimental measurements of fundamental constants to give recommendations for best-guess values that should be used.
They periodically update their values as new experiments are done.
You are seeing that some wikipedia pages use old (not-updated) CODATA recommendations, while others have ...
6
The IAU General Assembly 2012 finished a few days ago. Assuming resolution B2 (PDF) was passed, the astronomical unit has been frozen and the following values are exact by definition
$$
1\mathrm{a} = 365.25\mathrm{d} = 365.25 \cdot 86\,400\mathrm{s} = 31\,557\,600\mathrm{s}
\\
1\mathrm{ly} = 299\,792\,458 \mathrm{\frac ms} \cdot 1\mathrm{a} = ...
6
1) The best answer here might be a little of both. This kind of question gets at the notion of what time is. You can define a system of measuring time by using light. The time between events is then the distance that light would travel in the duration between those events. Then by definition, the speed of light is $1$ and dimensionless, as we measure time ...
5
The three constants you give illustrate the arbitrariness of units. The magnetic constant
$$K_m = 10^{-7} {N\over A^2}$$
serves to define the Ampere. The definiton of the Ampere implied by this (defined) constant is that the force between two long wires carrying one Ampere of current at a separation of 1 meter is 10^{-7} Newtons per unit length. If you ...
5
This is more of a philosophical question. There is no way to actually prove something, see the Münchhausen Trilemma. The best we can do in science is coherence, that the theory fits the observation. Varying "constants" on other planets or near the black hole simply don't fit the data. Furthermore science is evolving and subject to change. If one day the ...
5
Expanding on what Vladimir said: the thing that is changing with energy is $e$ (the others are not constants so much as conversion factors between length and time, time and energy, etc.). The reason the charge can vary is that the vacuum is not entirely empty. Sloppily speaking, near a charge, the electric field interacts with virtual (electron/positron) ...
5
Basically, you are proposing to redefine the kilogram, and your approach has been proposed and recently (in october 2010) abandoned ( http://en.wikipedia.org/wiki/Kilogram#Carbon-12 ).
I think the reason why the Watt-balance approach has been preferred for the future definition of the kilogramme was mainly technological : it is more precise and would allow ...
5
no, I am afraid you have not discovered a physically relevant relation until you prove what is the relation between the series and the terms defining the theory in the UV (such as $g_{3}$ at some scale $\mu$, $m_{u,d}$, electromagnetic corrections...). I would be much more impressed if you could get at the same time a similar formula for the neutron mass ...
5
You write a paper and send it to a reputable journal.
Then the reviewers have a go at it. Unless the editor rejects it on his or her own discretion.
If your paper is not based on solid physics and written in a language compatible with physics as we know it your odds are very, very bad.
I've submit it in to a physics conference [...]
Be aware that ...
5
The Planck length doesn't have any shape because it is not a curve of any sort; it is a constant equal to $\ell_P =\sqrt{\hbar G/c^3}\sim 1.6\times 10^{-35}\,{\rm meters}$. This constant may be chosen as a natural and convenient (in the research of quantum gravity) unit of the length of anything, e.g. curves. But curves that are as short as one Planck length ...
4
Basically, there's no reason why we couldn't redefine the mole as as simple integer number of atoms or molecules. In fact, as other users have mentioned, there's a lot of people who'd like to do that.
On the other hand, that's not how chemists actually use the mole in practice. You simply can't count 6×10^23 atoms or molecules, nor do you need to. What is ...
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