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Rescaling time in differential equations

It is the non-dimensionalization of the last two differential equations. Assuming $g$ as the acceleration due to gravity ($\text{m}/\text{s}^2$) and $l$ as the length (m), $\sqrt{l/g}$ has the ...
Pustam Raut's user avatar
3 votes
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Rescaling time in differential equations

It's an usual procedure in deriving non-dimensional equations, from the dimensional ones: angles have no physical dimensions, they wanted a "scaled" (non-dimensional) time as well. You just ...
basics's user avatar
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5 votes

What are natural units?

You already live in a world where natural units apply. The speed of light is exactly $1$ light-year/year, or equivalently $1$ light-second/second. Or approximately $1$ foot/nanosecond. This is useful ...
mmesser314's user avatar
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1 vote

Why are Critical Exponents simple non-integer powers?

In two dimensions, we know from conformal field theory that many critical exponents are rational numbers. In three or higher dimensions it is not known whether this remains so. In particular, in ...
mike stone's user avatar
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Convert Coulomb's law in CGS units to SI units

Coulomb's law gives the force between two charges. This force is proportional to each of the two charges, and inversely proportional to the square of the distance between them. So, we will have some ...
Riley Scott Jacob's user avatar
2 votes
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The Principle of Homogeneity of dimensions states that you can add,subtract quantities with same dimensions but we cannot add a constant with an angle

Dimensional homogeneity principle should be interpreted like so,- that you can't compare or equate two quantities if they have different dimensions (like distance to speed). If they have same ...
Agnius Vasiliauskas's user avatar
2 votes

What are dimensions and how are they defined?

Dimensions of physical quantities are not related to spacetime dimensions. Dimensions of physical quantities tell us how a given quantity depends on different units of measurement. Dimensions of ...
Níckolas Alves's user avatar
3 votes

Is invariance under rescaling of the Lagrangian lost during quantization?

$\hbar$ introduces a scale with dimensions of action that means that a symmetry that rescales the action by an overall constant is no longer a symmetry in quantum theory. One way to see this is from ...
Andrew's user avatar
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5 votes

Is invariance under rescaling of the Lagrangian lost during quantization?

Commutator $[\phi,H] = \phi H - H\phi$ does not involve division by or differentiation by momentum, so it scales with $H$, and thus with $\lambda$. This is in contrast to $\{\phi,H\}$, which involves ...
Ján Lalinský's user avatar
3 votes

Is invariance under rescaling of the Lagrangian lost during quantization?

Your final equations show that you just need a redefinition of $\hbar$ and scaling of $\hat \Pi$. It basically means that $\phi$ will have different amounts of quantum behavior, and the classical ...
Jos Bergervoet's user avatar
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Is there a true one-dimensional object?

‘1D’ is a mathematical abstraction. There are no ‘true’ physical embodiments of mathematical abstractions.
my2cts's user avatar
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4 votes

Is there a true one-dimensional object?

Actually, if you think about it, there isn't anything that's 3 dimensional either. Any physical object is made of atoms. The frontier of such object is undefined (since atoms & electrons do move ...
xryl669's user avatar
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4 votes

Is there a true one-dimensional object?

It really depends on what you mean by "object". There are mathematical objects of 1 (geometrical) dimension, like curves. Also, there are mathematical objects of 0D, like points, of 2D, like ...
Steeven's user avatar
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4 votes

Is there a true one-dimensional object?

Ideal mathematical objects only exist in human imagination, not in the real world. It sometimes happens that a particular mathematical object is a useful (if imperfect) model for something in reality.
John Doty's user avatar
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12 votes

Is there a true one-dimensional object?

While other answers have pointed out that there is no 1D or 2D “physical object” in the real world, you could make the argument that they do exist depending on what you mean by "object". If ...
Jbag1212's user avatar
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4 votes

Is there a true one-dimensional object?

In reality there's no 1D objects, nor 2D objects, everything has width, height and depth. Even molecules, atoms and electrons (...
Agnius Vasiliauskas's user avatar
27 votes
Accepted

Is there a true one-dimensional object?

As far as we know, there are no one-dimensional objects in the real world. A one dimensional object (an object that has length but no width or height) is a mathematical abstraction. Having said that, ...
gandalf61's user avatar
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2 votes

Is there a true one-dimensional object?

Well, a simple example of a one-dimensional object is a string (consider it infinitely thin). This string might be deformed and curved as much as you want. Interestingly enough, you can join together ...
Gabriel Ybarra Marcaida's user avatar
1 vote

Dimensions of constants

Pure numbers are dimensionless, but numbers that measure things usually are not. A length can be $12$ inches or $1$ foot. Units matter here. If you say the length is $12$ or $1$, you don't know how ...
mmesser314's user avatar
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Dimensions of constants

dimension of constant such as speed of light (C)=M0L1T-1. dimension of planks constant=[ML2T-1]. dimension of number such as 1,2,3,4......etc have no dimesion
sumit's user avatar
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3 votes

Dimensions of constants

Take for example the gravitational constant. Expressed in SI units it is: $$G=6.674\cdot 10^{-11}\frac{\text{m}^3}{\text{kg}\cdot\text{s}^2}$$ You can also express this constant in imperial units. You ...
Thomas Fritsch's user avatar
1 vote

Fundamental and derived physical quantities

A base unit of measurement, or fundamental unit, is adopted for a base quantity within a conventionally chosen subset of physical quantities, such as the SI base units: meter, kilogram, second, ampere,...
cconsta1's user avatar
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