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7
votes
1answer
794 views

Counting degrees of freedom for gravitational waves as a gauge field

Sean Carroll has a new popularization about the Higgs, The Particle at the End of the Universe. Carroll is a relativist, and I enjoyed seeing how he presented the four forces of nature synoptically, ...
4
votes
1answer
163 views

How exactly are the degrees of freedom seen by a falling into a black hole observer related to the ones seen by a staying outside observer?

This is some kind of a follow up of this nicely to the point answer to a provocative (but nevertheless upvoted!) question, about the legitimacy of black hole physics. The answer mentions, that the ...
2
votes
1answer
238 views

A different proof for 6 degrees of freedom

I want a different proof of 6 degrees of freedom of a solid object made of $\ N$ particles. I am thinking along these lines: Definition of rigid body is $\ modulus[\vec{r_i}-\vec{r_j}]=constant \ ...
3
votes
1answer
230 views

Phase Space dimension of Lorenz Strange Attractor

It is often discussed in 3 spatial dimensions and the need for third dimension to prevent self intersection is mentioned. But shouldn't the phase space of the Lorenz system be 6 dimensional, i.e., the ...
1
vote
0answers
621 views

what's the difference between linear n-atom molecule and nonlinear n-atom molecule?

I am reading a material about the degree of freedom for linear n-atom molecule and nonlinear n-atom molecule. Here is my analysis for a diatomic molecule, if there are two atoms, we have to use 3 ...
1
vote
2answers
5k views

The number of degrees of freedom of a monatomic gas

Suppose that I have a monatomic gas sample consisting of $N$ atoms (e.g., $N$ argon atoms); thus there are no vibrations or rotations. How many degrees of freedom does the system have? Does the ...
3
votes
2answers
6k views

Modeling a two-mass, spring, damper system

I'm trying to model a system with two masses, two springs, two dampers, and one applied force using transfer functions. I'll then be inputting it into Simulink. The system looks like this but there ...
3
votes
1answer
309 views

Propagating degrees of freedom of graviton

What is the best way to see that the number of propagating degrees of freedom or gravitons in 3 dimensions is $0$ ? By graviton I mean the metric and NOT some topologically massive graviton that one ...
2
votes
1answer
331 views

Degrees of freedom in the infinite momentum frame

Lenny Susskind explains in this video at about 40min, as an extended object (for example a relativistic string) is boosted to the infinite momentum frame (sometimes called light cone frame), it has no ...
3
votes
2answers
180 views

Dark matter: degrees of freedom

I'm afraid this question could sound a little too vague. I don't even know if dark matter (DM) can be genuinely described by quantum field theory, or if quantum field theory should be somehow ...
8
votes
1answer
457 views

Clarification on “central charge equals number of degrees of freedom”

It's often stated that the central charge c of a CFT counts the degrees of freedom: it adds up when stacking different fields, decreases as you integrate out UV dof from one fixed point to another, ...
2
votes
2answers
2k views

degree of freedom of a rigid body 5 or 6?

I'm confused here. I have a three particle (rigid) system. What would be the degree of freedom? I found out five. 3 coordinates for center of mass and 2 for describing orientation. But we have only ...
4
votes
2answers
724 views

Counting degrees of freedom in presence of constraints

In a $N$ dimensional phase space if I have $M$ 1st class and $S$ 2nd class constraints, then I have $N-2M-S$ degrees of freedom in phase space. How can I calculate the degrees of freedom in ...
3
votes
3answers
935 views

Counting degrees of freedom of gauge bosons

Gauge bosons are represented by $A_{\mu}$, where $\mu = 0,1,2,3$. So in general there are 4 degrees of freedom. But in reality, a photon (gauge boson) has two degrees of freedom (two polarization ...
0
votes
1answer
117 views

Equipartition theorem for flowing gas

If an ideal gas is flowing with a velocity $v$, how is the equipartition theorem applied. Normally, we can say that $\frac{1}{2}mv_{x,rms}^2=\frac{1}{2}k_BT$. We can do the same thing for $v_y$ ...
5
votes
6answers
2k views

Degree of freedom paradox for a rigid body

Suppose we consider a rigid body, which has $N$ particles. Then the number of degrees of freedom is $3N - (\mbox{# of constraints})$. As the distance between any two points in a rigid body is fixed, ...
2
votes
1answer
411 views

Violations of Dulong-Petit rule as an upper limit to heat capacity

Does any known substance have a heat capacity at constant volume ($C_V$) per mole of atoms greater than $3k_B$ ~ 24.94 J/(mol K)? In order to count, the substance must actually be made of atoms, that ...
14
votes
1answer
2k views

What is the definition of how to count degrees of freedom?

This question resulted, rather as by-product, the discussion on how to count degrees of freedom (DOF). I extend that question here: Are necessary1 derivatives such as velocities counted as ...