What does it mean to model an object?

[susskind99]

I'm trying to come up with a good definition for model:

X is modeled means x exists at time 1 and point 1 and has direction y, then it will exist at time 2 and point 2.

Of course there are different types of modeling, for example, sometimes particles decay into other particles.

Let me know if you have any better ideas about how to improve my definition.

 

[Jolb]

X is modeled means X corresponds, in at least some respects, with some simpler object Y. We can then use Y to gain insight into those aspects of X that correspond to Y.

Modeling is the art of finding analogous structures and using them to deduce things about the structure of interest. Physical models are mathematical (I know of no exceptions in use in physics), whereas architectural models are scaled drawings. Even the elementary-school science lab "model" of a "sun" connected to pivoting "planets" is a model we learn from (see picture below).

PS: I will always remember the chemistry majors at my undergrad university toting around bags of connectable stick and ball toys to build little "models" of molecules. PPS: I can't resist posting a picture. Can you believe they actually use these to educate undergrads?

 

[susskind99]

PS: I will always remember the chemistry majors at my undergrad university toting around bags of connectable stick and ball toys to build little "models" of molecules. PPS: I can't resist posting a picture. Can you believe they actually use these to educate undergrads?

Yea, I guess those toys of molecules are a bit of a waste of time. I certainly never bothered with them back when I taught myself chem.

I guess what I want to know is what does it mean to model motion.

 

[SteamKing]

Well, there is rectilinear motion, circular motion, motion under the influence of a gravitational field, motion which is retarded by resistance, simple harmonic motion (damped and undamped), ...

All of these types of motion are modeled using sets of equations which predict the position of an object as a function of time.

 

[susskind99]

All of these types of motion are modeled using sets of equations which predict the position of an object as a function of time.

Wouldn't it be more accurate to say "as a function of time and vector"?

 

[SteamKing]

Not necessarily. What does "as a function of time and vector" mean?

 

[Jolb]

I think what you are getting at is the idea of "initial conditions" in dynamical theories. Dynamical models in physics need two ingredients to make a prediction:
1) the laws of the theory, which are usually partial differential equations (e.g., F=ma, Lagrange's equations/Hamilton's equations, Schrödinger's equation, Einstein Field Equations, etc.) and
2) the initial conditions of the system

If you were trying to predict the motion of a classical particle, then you would need Newton's laws together with the initial state of the particle (position and momentum vectors) in order to get an equation that tells you the position vector of the particle as a function of time. As another example, to model the time it takes an electron to tunnel through an insulating barrier, we would not only need the Schrödinger equation but also the initial quantum state of the particle, which is not a simple vector but rather a wavefunction.

Then again there are physical models which are not dynamical. Thermodynamics, for example, almost always takes the "thermodynamic limit" which assumes things are always in equilibrium--the time dimension does not matter in the theory, which only concerns itself with "Thermodynamic Variables" like temperature, pressure, entropy, etc. Take for example PV=NkT, the ideal gas equation of state. This is a very useful model but doesn't have any sort of time variable indicating time dependence.

 

[CWatters]

I guess what I want to know is what does it mean to model motion.

To write equations that describe the motion of the object.