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If the observer is not in free-fall, the metric-tensor $g_{\mu,\nu}(s)$ at the observer's position, expressed in local coordinates around the observer, will not be $\eta_{\mu,\nu}$. Your first assumption about the path $(\gamma)$ is wrong. I guess what you are aiming at is the notion of the space of coordinates around a point, which is indeed a flat space ...


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When you say If something goes outside, then it will decrease inside! what you assume is exactly a conservation law. It may seem trivial, but it is not necessarily. Consider the population of a city, for example. At one point in time, you measure how many people are within the city borders; let's call this number $N_0$. Then, you observe all city ...


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When we say something is conserved or that there is a conservation law for a given thing, we mean that the quantity of it does not change. You neither lose nor gain any of that thing. More specifically, conservation can come in two flavours. Something can be globally conserved. This means that the total amount of that something in the universe does not ...


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It has a very simple yet important meaning.It simply means that the quantity that you are observing will always stay the same,even if that means that it gets transferred to another form or convert to another medium.You can not simply create more "stuff" of that quantity and you can not destroy it.It can not be created from nothing and it can not just be ...


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Let $M$ be your spacetime, a smooth manifold equipped with (pseudo) Riemannian metric (for example $\mathbb{R}^{(1,3)}$ for special relativity). The set of reference frames is the frame bundle over $M$, usually denoted $FM$. Explicitly a frame at point $p$ in $M$ can be viewed as an ordered orthonormal basis (with respect to the the inner product defined ...


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The kinetic term of the Lagrangian is proportional to $$g_{ij}v^iv^j$$ where the $v$s are the generalised velocities. Writing them as the time derivative of the generalised coordinates, i.e. $v^i\dot q^i$, taking the square root, and multiplying by a small time lapse $\epsilon$ you get $$\sqrt{g_{ij}\dot q^i\dot q^j}\epsilon,$$ which is a first order ...


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The name T-duality stands for Target-space duality, see e.g. this preprint.


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It comes from S matrix theory, long before quarks were imagined, S,T and U characterize the type of exchange in the Feynman diagrams entering the S matrix calculation, and they are called Mandelstam variables. s channel-------------------------- t channel------------------------u channel duality meant that the sums could be done either in S ...


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Yes. Two particles at a given position, one moving and the other at rest are having the same kinematic state. But dynamic state takes in the velocity. When you need to specify both position and velocity - it becomes kinetic state. After all kinematics + dynamics = Kinetics.


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A good question, you are right the frequency remains constant (unless you have Doppler effects due to relative movement, but that's not your question). For visible light, refraction properties are quite often in question and as such it make sense to speak in terms of wavelength. As you go even higher in "frequency", physicists start talking in keV and MeV ...


1

Yes. When you do stress testing of materials (for example, the Brazilian test of a disk shaped test object) you apply stress along a single axis (using for example an Instron machine). This is a good way to measure elastic properties of materials. On the other hand if you have a pressurized container (for example the hydraulics in your car brake system), ...


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One never pluralizes unit abbreviations. Your link goes to the BIPM, the body responsible for maintaining the definitions of the international system of units, and is authoritative. The folks at NIST agree and address most of your questions. I would say The pipe is 0.75 m long. or The pipe is 75 centimeters long. or even The pipe is ...


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cms and kgs are wrong. The SI units are abbreviations which are also used in the plural. You will write 2.6 m/s or 1 m/s, but say "2.6 meters per second" or "1 meter per second" respectively. Keep in mind the SI units are also used in tons of other languages that do not form the plural by attaching an -s. The units look the same in those languages. (e.g. ...


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I think what he's saying is that $$F_{net} = F_{nc} + \nabla U,$$ which is pretty standard. $f^a$ is your net force, which is the sum of your conservative and nonconservative forces. Conservative forces can be written as the gradient of some potential, which is where you get your $\nabla U$ from. $f^e,$ then, are your nonconservative forces.


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Of course they both give informations about the motion of bodies. The kinematic equations tell us simply what are the valors of the variables of the specific motion , that because kinematic studies only the variables of the motion and their changing. kinematic equations give us indications about : Velocities (the most simple and known equation of kinematic ...


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In the degenerate interiors of neutron stars, the equation of state is usually just density (and composition) dependent. You can express the pressure as a polytropic law of the form $P \propto \rho^\alpha$, where $\rho$ is the density. A stiff (or hard) equation of state is one where the pressure increases a lot for a given increase in density. Such a ...


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Can someone explain why the time-independent Schrödinger equation isn't an eom? The TISE is an eigenvalue equation due to applying separation of variables to the TDSE; it is an equation for the spatial function alone. Can someone explain in what sense exactly is the time-dependent Schrödinger equation an equation of motion? A Lagrangian ...


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The proper constructions resembling quantum mechanic's formalism does exist in classical mechanics, but it goes a bit beyond lagrangian formalism. In classical mechanics, you can represent a system by a phase space with points corresponding to states of the system. Now, functions over that phase space form a symplectic Lie algebra together with the Poisson ...


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Hadrons are strongly interacting particles, and at the elementary particle level are studied by Quantum Chromodynamics within the standard model. Before the standard model became standard, hadrons were studied experimentally and a multitude of resonances were found in meson meson or meson proton interactions. These were studied theoretically using particle ...


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related: http://math.stackexchange.com/q/160882/224026 see also: http://en.wikipedia.org/wiki/Metric_tensor: " From the coordinate-independent point of view, a metric tensor is defined to be a nondegenerate symmetric bilinear form on each tangent space that varies smoothly from point to point. "


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1- A degenerate matrix is a matrix whose rank is smaller thank its dimension. 2- A singular (non-invertible) matrix is one who has a vanishing determinant. Equivalence of the two : A matrix whose rank is smaller than it's dimension when diagonalized will have at least one zero eigenvalue, and consequently a vanishing determinant.


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If $\text{det } g = 0$, then $\text{ker } g \neq \{\vec{0}\}$, ie there is some vector $X \in \text{ker } g$, such that $g(X,\ast) $ gives zero 1-form, so $g(X,Y)=0 $ for any $Y$.


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ATLAS has no experiment-wide definition of "fiducial", it basically means sensitive to signal. The definition is confusing because, unlike most experiments, ATLAS (and CMS, D0, CDF, etc) doesn't just define the physical area where the experiment is sensitive, they also define collision properties. This means the definition of fiducial isn't limited to the ...


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At present for physics research, a phenomenologist is a theoretical physicist who is well grounded in the current physical theories and at the same time understands the data and can create detailed theoretical models that can predict the behavior of future experiments. In this context, phenomenology is the study of the way current theories fit the data and ...


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This presentation (NB: PDF) has a "jargon" page that states, Fiducial (Webster's): Taken as a standard of reference Founded on faith or trust Having a nature to be trusted Fiducial Volume (Particle Physics): The volume used to make physics measurements The volume where the detector is assumed to be well understood With the ...


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In some detector experiments, The response at the periphery of the detector is poorly understood. The majority of background events interact in the periphery of the detector. The periphery of the detector is the final shielding. Some parts of the detector may be broken. In such cases, results from such parts of the detector are ignored. The results are ...


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Have a look at this http://journals.aps.org/prc/abstract/10.1103/PhysRevC.52.380 The effective masses and the screening masses of hadrons at finite temperature and density for the quantum hadrodynamics two (QHD-II) model have been investigated under the one-loop approximation. The nucleon-nucleon interaction through pion, sigma, omega, and rho mesons ...


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See the following examples: $\rho_1 = \frac{1}{2}(|00\rangle + |11\rangle)(\langle 00| + \langle 11|)$ is a maximally entangled state. $\rho_2 = \frac{1}{2} (|0\rangle \langle 0| + |1\rangle \langle 1|)$ is a maximally mixed state. The difference is not related with "maximally". Your question can be changed to : What's the difference ...


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For those curious I was able to find an answer. IT stands for Isomeric Transition. A metastable state emits a photon to decay to a lower energy List of decay modes: http://ie.lbl.gov/education/decmode.html


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Suppose we have two Hilbert spaces $\mathcal{H}_A$ and $\mathcal{H}_B$. A quantum state on $\mathcal{H}_A$ is a normalized, positive trace-class operator $\rho\in\mathcal{S}_1(\mathcal{H}_A)$. If $\mathcal{H}_A$ is finite dimensinal (i.e. $\mathbb{C}^n$), then a quantum state is just a positive semi-definite matrix with unit trace on this Hilbert space. ...


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When the state space for a system can be expressed as a tensor product of the state spaces of individual components of the system, an entangled state is one that can't be expressed as a tensor product of states of those individual components. Thus an entangled state is a particular type of (pure, i.e. non-mixed) state. A mixed state, by contrast, is a ...


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If you are talking about rigid bodies like billiard balls or asteroids one has a definition of a body: In physics, a rigid body is an idealization of a solid body in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it.(Wikipedia) ...


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There is no general definition of a body for physics, as in everyday speech where one has to qualify further either by context or content. A body of water, means a bulk ensemble of water molecules and further analysis depends on the context. Two colliding bodies could be billiard balls or asteroids. It is a blanket term that needs further attributes if ...


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I don't have an "official" distinction, but one difference is that statistical mechanics is used for systems with a very large number of particles, and is only concerned with quantities which are averaged over the whole ensemble. Many-body theory deals with smaller systems, and attempts to treat all the particles in the system, within some approximation. ...


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ok, you know that plucking a guitar string makes it vibrate. It vibrates up and down, up and down, again and again in the same pattern until friction stops it. a guitar string can emit different harmonics, but these are just higher or lower notes moving in the same regular pattern Harmonic motion is a term used to describe the same idea, of a process ...


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My take on this is that an experiment requires a manipulation of nature such as to produce a minimum set of conditions necessary to approximate a given phenomenon. Often this means a simplification of the natural case. Experiments may therefore involve a reduction in the complexity of a natural phenomenon in order to render it's workings more evident. The ...


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I have heard it called the spin tensor or spin matrix.


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These are the generators of Lorentz transformations, see Peskin and Schroeder, pg. 41. $S^{ij}$ are rotation generators, and $S^{0i}$ are the boost generators.


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According to page 291 of Brian Cowan's Topics in Statistical Mechanics, a relation of the form $$ U=U(S,V,N) $$ is referred to as the "fundamental relation" for the system. That is, internal energy (or more generally, a thermodynamic potential) expressed as a function of entropy $S$, volume $V$, and particle number $N$. Note that a relation of this form ...


1

I believe you have the basic ideas correct. The binding energy is the energy required to create Z separate protons and N=A-Z separate neutrons from a (A,Z) nucleus in its ground state. Another way to think about it is binding energy is the mass energy which is missing from a nucleus compared to the mass energy of the individual nucleons. When talking ...


1

I think Terran is as good a word as any, as is Geo. Thinking of terms where Solar or Lunar are used. Solar Gravity, Lunar Gravity, Terran Gravity, or Earth's Gravity. Solar Magnetic Field, Lunar Magnetic Field (which, I'm not sure there is one), Earth's Magnetic Field or Geo-Magnetic Field is also used. Earth's, Geo or Terran are the best 3 options I ...


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Technically this question is off topic and would belong in an astronomy SE, but the answers you probably are seeking are terrestrial or terran depending on whether it is a person or an object. Terran has been sorta scooped up by the Starcraft community though so terrestrial is used in almost all cases to my knowledge.


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Waves is one common way in which nature expresses the flow of energy through space and time. A pulse is just a special type of wave - a solitary wave. And solitary waves that dissipate a minor amount of energy into the medium, have low dispersion, and are able to maintain their shape over distance are called 'solitons'. A vortex ring is a good and ...


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Based on Einstein's assertion: All our well-substantiated space-time propositions amount to the determination of space-time coincidences {such as} encounters between two or more material points. the notion "reference frame" should likewise be expressed in terms of (requirements on) "material points" and "space-time coincidences" in which they did, ...


1

In the equation $y=\textrm{sin}(\omega t+ \phi)$ $\omega$ is the angular frequency of the oscillator, and $\phi$ is the phase angle. Let's start with the most basic version of this equation, and then build back up to the most general case. If we set $\omega=1$ and $\phi=0$ then we are left with $y=\textrm{sin}(t)$ which in the basic sine function. If we ...


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If you remember transformation of functions, $\omega$ would stretch the sine function in the x-axis, and $\phi$ would transform (or move) the sine function along the x-axis. With that in mind, the phase is how far along the sine function is in one period. In phase is when two sine functions have the same phase and period and so have the same peaks and ...


1

Since the graph of sin function is identical to that of a sin wave, I know why the sine function is used in the wave equation The $y=\sin(\omega t)$ part that you mention you are familiar with, starts at (0,0). That is, at time $t=0$ the sine is $y=\sin(\omega 0)=0$. The only thing a phase angle does is to shift the starting point. If a phase angle is ...


0

So based on this, what's really a reference frame? In pre-relativistic mechanics, reference frame is a system of points whose mutual distances are assumed constant - a rigid body. For measurements of position on Earth, the reference frame is often Earth's body, assumed to be rigid. For measurements of position in space, Earth's body could be used. ...


-1

It would help to read this section of Galilean Invariance as this reconciles it nicely with more intuitive notions of relative frames of reference. Two observers moving at different speeds (or help us all accelerations), would not agree on the simultaneity of some events. This represents a shift in relative time due to motion, which is why you see a $vt$ ...


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The most direct and beautiful answer to this important question has been provided by Taylor and Wheeler in their famous book "Spacetime Physics". If you google "spacetime physics wheeler frame of reference" for images, you will be led to a picture of space divided regularly into a 3-dimensional grid pattern. The crucial thing though is that at each grid ...



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