What is Continuum: Definition and 142 Discussions

If we accept that there does indeed exist a set whose cardinality is between \aleph_0 and \aleph_1, what would such a set look like? I know that in ZM-C we can choose to either add the continuum hypotheses or not, but if we chose to negate it, that means that there definitely is a set greater...

If I am in my office and the space-time continuum is further bent, would I realize that time is passing slower or faster and why?PS: I am new to physics, so please provide a complete answer.

Homework Statement The continuum element shown in Figure (a) deforms to figure (b) I'm looking to find the positions after deformation (x coordinates) by expressing them in terms of E coordinates. Homework Equations The Attempt at a Solution x1 = E1 + E2 x2 = E1 + E2 x3 = E3 The...

Homework Statement I am studying my lecturer's notes and in this part he uses a delta potential to illustrate a simple example of Fermi's golden rule, that the rate of excitation is ##\propto t##. Homework Equations The Attempt at a Solution I've managed to get the bound states, by solving...

Freidel "Continuum Limit and Renormalization" ILQGS 1/4/14 http://relativity.phys.lsu.edu/ilqgs/ Tomorrow Laurent Freidel gives the online International LQG Seminar talk, the topic being "Continuum Limit and Renormalization". It might be helpful to look over a Freidel paper ahead of time...

Homework Statement I am self-studying this note and I am stuck in the derivation of the normal shear stress. I can't see how the relations (23) and (24) come about, i.e. I don't understand \tau'_{xx} = \frac{\tau_{xx}+\tau_{yy}}{2}+\tau_{yx} and \tau'_{yy} =...

Homework Statement Hi I can't follow the derivaton in this link. It is the following equality they have in the beginning, which I don't understand: \nabla \cdot u = \frac{1}{\rho}\frac{d\rho}{dt} Following the very first equation on the page, I believe it should be \nabla \cdot u =...

Looking for a quantum-based explanation as to why solids, when heated, emit radiation as a continuum, rather than discretely. Gas will emit discrete spectral lines when heated. Somone already suggested to me that there may be many random purtubations to the discrete energy levels in a heated...

Hello^^ (I'm new here) I want to know the mathematical tools i need to study continuum mechanics. It would be great if someone give me a link that contains video lectures. Thanks for help .

Does entanglement means that space-time is not a continuum after all?

Let's define a set (collection) \mathcal{C} by the following conditions. X\in\mathcal{C} iff all following conditions hold: 1: X\subset [0,1]. 2: X is closed. 3: If x\in X and x<1, then there exists x'\in X such that x<x'. 4: For all x\in X there exists a \delta_x >0 such that...

Hi, All: I have heard all these claims thrown around that the sex/gender* of a person is not "binary" , i.e., it is not necessarily either male or female, but instead that it is a continuum with male and female at the ends. Is there something to this? If so, how can one test this; are there...

Hello all, Background I've been playing with computer simulations quite a bit recently, and wrote one that crudely simulates the formation of star systems. My first version was a conventional many body simulation with about 300 small bodies; it actually tends to come up with convincing star...

Are there any textbooks on something like this, a self consistent treatment of classical electromagnetism (relavistic is fine too) where the field equations are solved alongside with the matter fields.

Let a displacement field be given by $$ u_1 = \frac{1}{4}(X_3 - X_2),\quad u_2 = \frac{1}{4}(X_1 - X_3),\quad u_3 = \frac{1}{4}(X_2 - X_1). $$...

Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=57592&stc=1&d=1365348538 I'm stuck at the second part, not really sure what to here to be honest. https://www.physicsforums.com/attachment.php?attachmentid=57590&stc=1&d=1365346819Homework Equations Usually the...

Is there a way to know one way or another? If smallest possible scale is Planck scale, does it mean that space-time is discrete where smallest possible step is Planck's length (PL) and smallest possible time is Planck's time (PT)? If I move my hand from point A to point B, say 1m exactly in...

It is said that the space time continuum gives rise to space and time. So, is space time continuum a mixture of space and time or something totally different from space and time? Plz elaborate as per current scientific understanding only. No out and out philosophy please?

Homework Statement What do you understand by the following terms; (i) principal stretch (ii) an anisotropic material (iii) a dilatant deformation, (iv) a Lagrangian description of a deformation, and (v) a pure deformation. Homework Equations Am just trying to find descriptions for...

I was wondering if anyone knows of a good book on the mathematical theory of continuum mechanics. I have looked online, and the only ones I can seem to find are like your average physics or applied mathematics book. I want something with rigorous theoretical formulation of the subject. It...

Hi all, I am trying to self-learn continuum mechanics, and I have a question regarding the development of the deformation gradient (which ultimately leads to green's deformation tensor). I have attached the specifics of the question in a attached photo. Ultimately, there comes a point...

Hi all, I'm currently trying to teach myself continuum mechanics (as I am enrolled in a course for which continuum mechanics is a pre requisite and have never taken such course) I have been reading a book by mase and mase "introduction to continuum mechanics for engineers" 2nd edition. I...

If someone were able to travel back in time and change an event in history which resulted in a divergent timeline from the one you came from would both timelines be part of the same space-time continuum? I suspected they could be because part of their timelines are shared and connected to...

What's being curved, when mass bends the "spacetime continuum?" Okay, I've read lots of books about Einstein's spacetime being curved by mass and all, but I've never read a really good hypothesis as to what, exactly, is being curved. You can't curved nothing (sounds like a double negative, but...

I have heard generally that it is possible to put different physical theories on a lattice and after renormalization get the same continuum theory. I mean, different lattice theories that lead to the same continuum theory. Is this true for, say, qcd, or other particle theories? Are there...

What's the difference between analytical and continuum mechanics?

Homework Statement A large cylindrical tank of radius R is full of water to a height h(t). This drains under gravity out of the bottom of the tank through a small hole of radius r. The acceleration due to gravity is g. The pressure of the air can be assumed to be the same at the top and at...

I have never had an advanced classical mechanics class, only elementary level treatments using mostly Newtonian approaches, on very simple mechanical systems. I'm interested in learning about continuum mechanics, having in mind the applications in the applied field of seismology, which studies...

Continuum approximation of fluid mechanics (& relativistic fluids) I have a few 'foundational' questions on fluid mechanics which I haven't been able to find quick answers to, any help would be appreciated. At the start of any course on fluids, one is told of the continuum hypothesis...

Homework Statement http://img683.imageshack.us/img683/7060/selection001l.png Homework Equations \epsilon^{pl} = \epsilon - \epsilon^{el} \epsilon^{pl} = \epsilon - \frac{\bar{\sigma}}{E} r = \frac{\epsilon_w}{\epsilon_t}The Attempt at a Solution I'm stuck trying to calculate \bar{\sigma}...

Continuum Mechanics Books - help please Hi all.. Im almost done with this course in the current semester .. just academically .. I really haven't ' felt ' this subject .. haven't truly understood it ..so I'm re reading it these vacations . I need a v good book .. please suggest the best...

Homework Statement The components of stress in the x_i reference Cartesian system at a point of interested have been determined to be: \left[\begin{array}{ccc} 500 & 0 & 300 \\ 0 & 700 & 0 \\ 300 & 0 & -100 \end{array}\right] \mathrm{MPa} Determine the principal values and directions of...

I've looked at a few Physics programs and none seem to cover any time of fluids or continuum mechanics in general. It seems to be a very relevant subject to cover but it's only slightly addressed in one of the lower level classes. In these classes they usually only going over Bernoulli's...

Homework Statement http://imageshack.us/photo/my-images/513/selection027.png" http://imageshack.us/photo/my-images/513/selection027.png Homework Equations E_{ij}=\frac{1}{2} \left( \frac{\partial{u_i}}{\partial{X_j}} \frac{\partial{u_j}}{\partial{X_i}} - \delta_{ij}\right)...

Will taking a course is continuum mechanics give me the same background as in classical mechanics or would I need to take both separately? Can anyone explain the difference if there is one between classical mechanic vs continuum mechanics in simple nontechnical terms.

Hello, I'm not sure if this is the right place to ask about Continuum Mechanics or if the right place would be the engineering forums, but since Continuum Mechanics is a branch of Classical Mechanics, I thought it might be the place. My question is about Stress. Why does the stresses on...

Homework Statement see attachment. Homework Equations Navier Stokes continuity equation: The Attempt at a Solution So what I tried to do was to use the above equation to see if it equals zero. del(rho)/del(t)=del(xyz-t)/del(t) =-1 then to make the deriving easier...

http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true Above reference describes the history of the continuum hypothesis. Among the items of interest is the development of axiom systems in which the continuum hypothesis is true.

Hello, I have problem with understanding the concept of energy of deformed body. As far as I know, Clapeyron's theorem states that elastic energy of deformed body is half the work done by external forces; this are surface and body forces which deform the body. Then, I wonder, where has...

Usually in statistical physics, when your system has a large number N of particles, you take the continuum limit -- you let N\rightarrow\infty, and convert sums to integrals (with an appropriate normalization factor). My understanding is that as a finite number tends to infinity, the infinity...

Homework Statement This is not so much a homework problem but a part of a project I'm working on. So in just a few words; what I have (at time t=0) is a discrete state (half simple harmonic oscillator) connected to a wire with continuous states. These states are coupled by a complex...

I consider an array of lattice points and construct a vector at each lattice points. How to convert this discrete system into a continuum one by using the Taylor series expansion by considering the lattice distance say \lambda? thanks in well advance?

Please explain how the Continuum Idealization allows us to treat properties as point functions and to assume that properties vary continually in space no jump continuity? Thanks

Suppose we assume that the Continuum Hypothesis is false. Then there must be a subset of the real numbers that has the cardinality of Aleph 1. What is an example of such a subset?

how easy does it become to learn general relativity after a good course in continuum mechanics?

First off, hi everyone! This is my first post because I just found these forums (by Googling "Physics forums" in hopes of finding a good forum to ask science questions, specifically physics!). Anyway, I received a text message from a friend who is a teacher in grade school and was not sure how...

Hello! I read somewhere about intro to continuum mechanics. There was a vector \vec{\mu} and displacement vector \delta\vec{\mu}. As vector \vec{\mu} move, it will get new position \vec{\mu}'=\vec{\mu}+\delta\vec{\mu} \vec{\mu}'=\vec{\mu}+\frac{\partial\vec{\mu}}{\partial x_i}\delta...

Hi I'm looking for a good, in depth book on continuum mechanics and classic gauge theory. Can you suggest something? What I know about the subject is the chapter in Goldstein's classical mechanics.

I can do Calculus reasonably well in the context of multi-variables and simple undergraduate problems, but its all algebraic, I don't have a geometric understanding of how it is that the solving happens. Fortunately, with the Lagrangian method, I can appresciate at least qualitatively how one...

So i seem to have run into a problem. I found a way to accurately measure white light pulses but i still need some help doing the math. The information i have is: 1) wavelength vs time graphs [of the white light] 2) Material - using 2 fused silica prisms to compress the white light The math...