Questions involving the laws which are scale invariant, i.e. that apply to different scales equally. Also laws that involve exponential behavior, expressed in terms of certain magnitudes to the power of certain exponents.

learn more… | top users | synonyms

0
votes
3answers
408 views

How to distinguish between the spectrum of an atom in motion and the one of a scaled atom?

Galaxies are moving dragged by the space expansion. When atoms are in motion the doppler effect will shift the spectra of the emitted photons. The proton-to-electron mass ratio, $\frac{m_e}{m_p}$ ...
5
votes
5answers
963 views

Are the physical laws scale-dependent?

If you read the article "More Is Different", by P.W. Anderson (Science, 4 August 1972), you will find a deep question: are the physical laws dependent of the size of the system under study? As an ...
10
votes
2answers
3k views

Why are smaller animals stronger than larger ones, when considered relative to their body weight?

I am interested in why many small animals such as ants can lift many times their own weight, yet we don't see any large animals capable of such a feat. It has been suggested to me that this is due to ...
8
votes
2answers
7k views

How can an an ant lift 50 times its own weight and pull 30 times its weight?

According to many sites like this one, an ant can apparently lift 50 times its own weight and pull 30 times its weight. Is it true? Can it be proved using physics? Though most sites agree that an ...
2
votes
2answers
346 views

Scale invariance symmetry as a simple argument in an electrostatics problem

In the comments to this post, it was hinted that proving that the force acting on a charge at a vertical distance from a uniformly charged plane is independent of that distance can be done by ...
17
votes
6answers
15k views

Google interview riddle and scaling arguments

I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result. The riddle goes as follows: "imagine you are shrunk to the size of a coin (i....
9
votes
2answers
2k views

How does the period of an hourglass depend on the grain size?

Suppose I have an hourglass that takes 1 full hour on average to drain. The grains of sand are, say, $1 \pm 0.1\ {\rm mm}$ in diameter. If I replace this with very finely-grained sand $0.1 \pm 0.01\ ...
9
votes
4answers
1k views

Are we big or small?

How does the size of humans compare to the size of other objects in the universe? Are we among the relatively large or the relatively small things? My very preliminary research suggests that the ...
2
votes
2answers
2k views

Characteristic length, characteristic time and complexity of the process

Different physical processed (starting from elementary particles or even below to the universe itself) have different length scales $L$ and different characteristic times $T$. Larger processed tend to ...
3
votes
1answer
444 views

Using Wien's Law to show spectral distruibution function of one temperature represents all temperatures

This is a exercise question from Quantum Mechanic textbook by Bransden: Using Wien's Law to show that if the spectral distribution function of black body radiation, $\rho(\lambda,T)$ is known at ...
2
votes
3answers
186 views

Why are log scales so common?

I am currently reading a very nice book on scales in physics. There is a discussion on the different physical scales which are based on the effect of the corresponding phenomena, the given examples ...
1
vote
2answers
222 views

Amount of material required for a pressure tank

I read the answer for the question Why is a hot air balloon “stiff”? and thought something sounded ridiculous. My engineering requirement is that the walls be strong enough. Here $T$ will be the ...