dof

user116211

Feb 21, 2016 11:05

@ACuriousMind: Can I ask you about degrees of freedom?

ACuriousMind

I think you can

user116211

AFAIK, DOF are the independent parameters that determine the physical state of the system.

ACuriousMind

@Danu What "trouble" do the other programs have? If the sampling rate is too low to let the oscillation look like the oscillation it is (i.e. it just looks like a jagged line), I think you can usually increase the sampling rate somewhere

user116211

A single particle has 6 DOF 3 position coordinates and 3 velocity coordinates, right?

ACuriousMind

@user36790 Jep

user507974

Feb 21, 2016 11:09

@user36790 its better to think of it as 3 position and 3 momentum but yea

ACuriousMind

@user507974 That's just the difference between Lagrangian and Hamiltonian viewpoint, I'm not sure one is "better"

Danu

Ohhhh one can use gnuplot work as the backend for TikZ :D

@ACuriousMind Hah

Have you tried plotting a sin(1/x)?

user116211

But why are the DOF of gas molecules described differently?

ACuriousMind

@Danu No, since I don't have it installed here

@user36790 What do you mean?

user507974

@ACuriousMind personally i prefer lagrangain perspective but if you talk say its position and velocity then people naturally want to ask why isnt acceleration another dof

Danu

Feb 21, 2016 11:11

Well, TikZ doesn't manage :P

user116211

@ACuriousMind DOF of gas molecules are described by translational, rotational, vibrational coordinates.

ACuriousMind

@user507974 Well, because the equation of motion is second order - so you need only position and its first derivative.

@user36790 Yes, so?

user507974

@user36790 is this a diatomic gas?

and ideal or non-ideal

ACuriousMind

A molecule is not a point particle, so it has DOF that the point particle hasn't

user116211

@ACuriousMind Firstly I read DOF is position and velocity coordinates and then there I read translational, rotational, vibrational. Aren't they different?

ACuriousMind

Feb 21, 2016 11:13

@user36790 You said it yourself: "DOF are the independent parameters that determine the physical state of the system."

user507974

@user36790 are you familiar with eigenvalues and eigenvectors?

user116211

@user507974 yup.

ACuriousMind

For a molecule, just giving the position and velocity of its center of mass is not enough to determine the state, since it can also rotate, and vibrate

For a point particle, giving position and velocity is enough since it can't do anything but move

user116211

@ACuriousMind so, in classical mechanics, we read about particles only?

user507974

@user36790 the collection of eigenvectors for a system at its fundamental level is the most natural way to describe a system, in the case you described there would be positional and velocity dependent terms, but then that still doesnt span the full vector space

ACuriousMind

Feb 21, 2016 11:15

@user36790 No, why would you think so? Rotational dynamics are certainly a part of classical mechanics.

user116211

@ACuriousMind when it comes to molecules, we require transla.., right?

user507974

so if we have a diatomic molecule whizzing around and we can describe its translational information what are we missing to give a full description of it

i guess that ended up being rhetorical...

to simplify lets say one atom is heavy and thus is the COM

we need to figure out how to describe the relative position of the other atom

Secret

ljkhttps://youtu.be/RjbKYNcmFUw

Hmm...

user507974

and to do that you need a few pieces of information right, namely these are?

user116211

@ACuriousMind: So far I read Statistical meechanics, the macrostate is defined by the distribution $\rho(q_1,q_2,q_3\ldots p_1,p_2,p_3\ldots)$. So, they were talking of particles only?

user507974

Feb 21, 2016 11:20

@Secret had a friend send me this one a bit ago

that being said the friend of mine in question is basically a stick in the mud about all energy sources that arent NIF or thorium so i wasnt surprised

TheGhostOfPerdition

@user36790 Which book are u referring for statistical mechanics,? I'm self studying too

user116211

@TheGhostOfPerdition Reif's Fundamentals of Statistical and Thermal Physics.

ACuriousMind

@user36790 Yes and no. Mostly you should indeed imagine an ideal, monoatomic gas for that. But you can also describe a molecule by just giving the $q_i,p_i$ for each of its atoms. The reason one usually doesn't do this is that those $q_i,p_i$ are not unrelated, since the molecule can't just fly apart - there are constraints and forces between them than make the whole description ugly, so it is better to rephrase them in terms of the "true" d.o.f.

user116211

Also, there is Baby Reif: Berkeley Vol 5; it is different from the former.

TheGhostOfPerdition

@user36790 is it good to study thermodynamics before studying SM?

Thanks

ACuriousMind

Feb 21, 2016 11:24

So, whether or not "they were talking of particles only" depends on whether or not a specific form of the Hamiltonian is assumed, and whether or not the system is assumed to be unconstrained

user116211

@TheGhostOfPerdition everything is good, I suppose ;)

skull petrol

Traditionally thermo comes first.

TheGhostOfPerdition

I'm not really sure how it is usually taught in colleges

user116211

@TheGhostOfPerdition I'm a self-studying student; I at-least got acclimatised to thermo first as it is in our course; std xi. Also in JEE.

skull petrol

Learning thermodynamics first will help you a lot in physical chemistry :)

Secret

Feb 21, 2016 11:33

>It is generally argued that Aharonov–Bohm effect illustrates the physicality of electromagnetic potentials, Φ and A, in quantum mechanics. Classically it was possible to argue that only the electromagnetic fields are physical, while the electromagnetic potentials are purely mathematical constructs, that due to gauge freedom aren't even unique for a given electromagnetic field.

However, Vaidman has challenged this interpretation by showing that the AB effect can be explained without the use of potentials so long as one gives a full quantum mechanical treatment to the source charges that pr…

user116211

@ACuriousMind Oh! So, if I want to take them in consideration, would the Hamiltonian change?

Secret

We know that electromagnetic fields are bookeeping devices, but at the same time in first year physics, we ca actually measure the electromagnetic field with a meter (but we cannot for the potentials).

So does that mean bookeeping devices can sometimes be physically detectable. How to reconcile these two pieces of information?

ACuriousMind

@Secret How do you "measure" an electric field? All you can do is observe some "charged" particles doing some dance. I believe Daniel's point is that it's already a step toward "metaphor" or "bookkeeping devices" to say that observing charged particles do something is equivalent to "measuring an electric field".

@user36790 Yes, the Hamiltonian in terms of the $q,p$ of the individual atoms looks different than that of the "true" d.o.f. of the molecule (in principle, the latter can be obtained from the former, of course)

Secret

@ Acuriousmind I see, thinking about it, if I recalled correctly the meter reading is just current, so basically the only thing we can conclude is "there is something that causes the current" and does not really conclude to us that it is an electromagnetic field

So ultimately is all forms of detection of a physical quantity indirect, in that we can only infer its presence but not actually detect it directly?

ACuriousMind

@Secret For that to be answerable you have to say what "directly" means. At the end of the day, all you're doing is inferring things about the outside world based on your sensory input anyway. You could be a brain in a jar for all you know. (You might notice I don't think it's meaningful to talk about "real" and "unreal" or "direct" and "indirect" in this manner)

user116211

Feb 21, 2016 11:46

@ACuriousMind "true" dof means?

user116211

Translational, rotational......

ACuriousMind

@user36790 The translational/rotational/vibrational ones you usually use for molecules

user116211

@ACuriousMind Got it!

The h Bar

Participants