are weight and entropy dimensions?

[36grit]

I've heard it said that there are four dimensions. Length, width, depth, and time. These are all things that we measure. They have dimensional properties. What about wieght? and temprature (or enropy as some say)?

[J.C.MacSwell]

I've heard it said that there are four dimensions. Length, width, depth, and time. These are all things that we measure. They have dimensional properties. What about wieght? and temprature (or enropy as some say)?

 

No they are not dimensions. They do have some properties that are based on dimensions.

Edited May 14, 2011 by J.C.MacSwell

[ajb]

You do not think of them as dimensions like you do for space-time. However, you can include things like temperature, energy, etc as dimensions in some configuration space.

[DrRocket]

You do not think of them as dimensions like you do for space-time. However, you can include things like temperature, energy, etc as dimensions in some configuration space.

 

Right.

 

That is exactly the way they are treated in classical rhermodynamics.

[mississippichem]

Right.

 

That is exactly the way they are treated in classical rhermodynamics.

 

Are you referring to a PVT surface..isotherms, adiabats and all that stuff?

[DrRocket]

Are you referring to a PVT surface..isotherms, adiabats and all that stuff?

 

state variables or "extensive and intensive properties" -- see for instance Chemical Thermodynamics by Kirkwood and Oppenheim (any book on classical thermodynamics will do).

 

Isotherms, adiabats, etc. are curves or surfaces in the state space.

[ajb]

That is exactly the way they are treated in classical rhermodynamics.

 

I doubt it is really appreciated that classical thermodynamics can be formulated in such geometric way. There are some nice links with differential forms and contact structures, I should know more about this than I really do!

[DrRocket]

I doubt it is really appreciated that classical thermodynamics can be formulated in such geometric way. There are some nice links with differential forms and contact structures, I should know more about this than I really do!

 

If I recall correctly (no guarantee) there are some old lecture notes from The University of Chicago that present classical theermodynamics from a geometric point of view.

[ajb]

If I recall correctly (no guarantee) there are some old lecture notes from The University of Chicago that present classical theermodynamics from a geometric point of view.

 

Cheers.

 

For those of you who don't know contact geometry is kind of the odd dimensional cousin of symplectic geometry. Symplectic geometry is found to be the mathematical framework of Hamiltonian mechanics, in short one can "encode" the Poisson brackets in a closed nondegenerate two form on the phase space. That is we have a Lie bracket on the phase space that satisfies the Leibniz rule over the product of functions. Note that not all Poisson brackets come from symplectic structures.

 

Related to contact geometry are Jacobi structures, which are like Poisson brackets apart from the Leibniz rule. We have instead

 

[math]\{f ,gh\} = \{f,g\}h + g \{f,h\}- \{f, 1\}gh[/math].

 

If [math]\{f,1 \}=0[/math] then we are back to a Poisson bracket.

 

 

In relation to the opening post, I expect (but have not thought too much about it) that you could include mass as a variable in the configuration space. You would then either have to worry about a conjugate variable and then end up with something like an extended phase space of position, momenta, mass, conjugate mass or end up with something more like a contact structure by just including mass. You may be able to then think in terms of Jacobi manifolds, I am not really sure.

 

 

As an aside, I have been working on a Grassmann odd generalisation of Jacobi manifolds to supermanifolds. Odd contact structures also appear, but I should call this work in progress as I have yet to explore this very far.

[36grit]

what is weight? We see things without it moving at the speed of light. Maybe weight is some kind of resistance to, "speed of light expansion", and collects in the back wash of time.

When we talk about a gravity time dialation are we saying that the gravitron field extending beyong the mass that houses it?

Perhaps mass bodies join together to conserve gravitron energy allowing some of the gravitrons to be freed up and exist beyond the mass body. I heard you'll actually weigh more standing next to the empire state building than you will a few feet away from it.

I know that gravity brings cosmic gas together and eventualy forms a star. but what came first, the the gas or the gravity field ? Can you have a gravity field drifting around in space without mass? Or do gravity fields radiate from mass? Could gravity crush other force fields into mass?

Is the gravitron itself a massless boson? with spin? Is there such a thing as anti gravity?

 

!

Moderator Note

Similar topics merged

Edited June 5, 2011 by swansont
modnote

[DevilSolution]

simply defined: a collective existence, weight is only called into play when comparisons are made and relativity deduced, i.e 1+1 holds the same space as 2+2 but 2+2 is denser ..... YO

 

circular motion is a confusing concept ^.^

Edited June 5, 2011 by DevilSolution

[Chad Sitzer]

Since weight and time are interrelated through relativity and notably time dilation could it not be argued that weight in some sense is at least part of the dimension of time. Heavier objects will experience the universe slower, aging relatively slower. High-velocity objects will attain grand masses and warp time.

 

I feel we vastly overlook

Edited June 5, 2011 by Chad Sitzer

[Iggy]

arre weight and entropy dimensions?

 

I've heard it said that there are four dimensions. Length, width, depth, and time. These are all things that we measure. They have dimensional properties. What about wieght? and temprature (or enropy as some say)?

 

I may be a little (or a lot) off base here, but to me "dimensional properties" can mean something different and perhaps something rather worth getting into. In classical dimensional analysis a dimension is a fundamental physical property -- which is to say, it can't be defined as a combination of more fundamental properties and can't be measured as a combination of more fundamental units. The fundamental dimensions usually given are mass, length, time, electric charge, and temperature (although, electric charge and temperature aren't always allowed in the club).

 

A dimensionless quantity, on the other hand, is a value that doesn't change when the units used to measure the fundamental dimensions of the value change.

 

If I were to answer the OP, thermodynamic entropy has units of joules / kelvin or dimensionality of energy per temperature. Energy is mass • length² / time² so entropy all together would be,

 

[latex]\frac{M \times L^2}{T^2\times K}[/latex]

 

where M is mass, L is length, T is time, and K is temperature. But, temperature can be expressed as an energy, so entropy would be...

 

[latex]\frac{M \times L^2}{T^2 \times \frac{M \times L^2}{T^2}}[/latex]

 

and... yeah... that cancels, or I should say, it simplifies to 1. It is dimensionless, or at least can be expressed that way.

 

 

Weight has the same units and dimensionality as force which is Kilograms times meters per second squared, or M • L / T², so that will have dimensionality in the classical fundamental units.

[ajb]

what is weight?

 

Weight is the force on an object due to gravity.

 

Is the gravitron itself a massless boson? with spin? Is there such a thing as anti gravity?

 

In the context of quantum general relativity the graviton is massless and of spin-2. It is its own antiparticle, if that is what you mean by antigravity.

 

I may be a little (or a lot) off base here, but to me "dimensional properties" can mean something different and perhaps something rather worth getting into.

 

I do not think the that the initial question is about "units". Or at least I did not read it that way. But you are right, one has to not confuse these issues.

[Iggy]

I do not think the that the initial question is about "units". Or at least I did not read it that way. But you are right, one has to not confuse these issues.

Well... not units per se. Wikipedia's dimensional analysis page makes a good distinction of dimensions and units,

 

The dimensions of a physical quantity are associated with combinations of mass, length, time, electric charge, and temperature, represented by sans-serif symbols M, L, T, Q, and Θ, respectively, each raised to rational powers.

 

The term dimension is more abstract than scale unit: mass is a dimension, while kilograms are a scale unit (choice of standard) in the mass dimension.

 

Dimensional analysis -- Definition

The way I understand the OP -- it is essentially asking 'If length and time are measurable dimensions, what about these other things -- can they be considered dimensions too?' That is to say: What are the dimensions of weight and entropy... or are they dimensionless?

 

I would just answer that entropy can be dimensionless in mechanics so it would certainly not be a dimension like length or time. Weight has dimensionality (mass times length over time squared), but in case the OP meant 'mass' where it says 'weight'... yes... mass is often considered a base dimension just like length and time.

 

Here is a paper treating entropy's dimensionality in the same light:

 

Abstract:

 

One of entropy's puzzling aspects is its dimensions of energy/temperature. A review of thermodynamics and statistical mechanics leads to six conclusions: (1) Entropy's dimensions are linked to the definition of the Kelvin temperature scale. (2) Entropy can be defined to be dimensionless when temperature T is defined as an energy (dubbed tempergy). (3) Dimensionless entropy per particle typically is between 0 and ~80...

http://adsabs.harvard.edu/abs/1999AmJPh..67.1114L

 

Perhaps I'm not following what you meant by "units" or "confusing the issues" and perhaps I'm being a bit obscure with the OP's idea of "dimensional property"... quite likely.

 

[... edited for clarity... ]

Edited June 6, 2011 by Iggy

[ajb]

By "dimensional properties" I read "geometric properties" given the opening with the four dimensions of space-time.

 

I was wondering if the idea of dimensions ("units for physical measurables") in physics and dimensions as in spaces ("geometric" or "topological") would course some confusion to the unwary reader.

 

Dimensional analysis really just states that the laws of nature will not differ depending on the units employed. Dimension in this sense is more general than picking a scale. I think of a scale or unit as a representative of a dimension. Dimensions gives you the freedom to examine equations of physics without necessarily fixing a representative scale.

 

The standard dimensions (in this sense) are as you state are mass, length, time, electric charge, and temperature. However, I do not see why one would have to use these, though it is clear these are going to be very convenient for most physics questions. But that is another question.

 

I think 36grit needs to let us know if anything any of us has said helps him.

Edited June 6, 2011 by ajb