What is quantities: Definition and 207 Discussions

Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Mass, time, distance, heat, and angle are among the familiar examples of quantitative properties.
Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others function as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little.
Under the name of multitude comes what is discontinuous and discrete and divisible ultimately into indivisibles, such as: army, fleet, flock, government, company, party, people, mess (military), chorus, crowd, and number; all which are cases of collective nouns. Under the name of magnitude comes what is continuous and unified and divisible only into smaller divisibles, such as: matter, mass, energy, liquid, material—all cases of non-collective nouns.
Along with analyzing its nature and classification, the issues of quantity involve such closely related topics as dimensionality, equality, proportion, the measurements of quantities, the units of measurements, number and numbering systems, the types of numbers and their relations to each other as numerical ratios.

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  1. T

    A Save Time with CLASS Code: Neat Trick for Background Quantity Evolution

    Is there a neat way to "not" run the internal Boltzmann solver (for perturbations) in CLASS code and rather just solve for the background quantities? This way I can save the time otherwise spent in evaluating the perturbations and transfer functions. I am only interested in the time evolution of...
  2. P

    What Variables Must X̅ Have in Order to be Considered a Partial Molar Quantity?

    Hi everyone! It's about the following task. Partial molar quantities a) How are partial molar quantities defined in general? b) If X is an extensive state variable and X̅ is the associated partial variable, what types of variables must X̅ have? c) Is the chemical potential of component i in a...
  3. yucheng

    How do manufacturers determine the 'rated' quantities for motors?

    I'm confused with the term "rated". I checked this webpage though I am not confident about it's reliability. Context: Motor ratings etc. Does it mean maximum? Maximum in what regard? Heat produced/temperature? Is there a more reliable source on how manufacturers determine the 'rated'...
  4. L

    Conserved quantities via Poisson brackets

    Hi, Results from the previous task, which we may use I am unfortunately stuck with the following task Hi, I have first started to rewrite the Hamiltonian and the angular momentum from vector notation to scalar notation: $$H=\frac{1}{2m}\vec{p_1}^2+\frac{1}{2m}\vec{p_2}^2-\alpha|\vec{q_1}-...
  5. D

    I Equation which is related with the Lorentz invariant quantities

    Hi every one.How can i prove the below equation? And then that it's Lorentz invariant quantitude ? Thanks for your help
  6. Lotto

    B How to calculate measurement error by using other quantities?

    Let's say I have ##F=mg \tan \alpha## and want to calculate ##F##. I know ##m=(1.0 \pm 0.5)\,\mathrm{kg}## and ##\alpha=(20.5 \pm 0.5)° ##. How to calculate ##F=( 3.7 \pm ?)\,\mathrm N##? What is the general method of determining a measurement error in these cases?
  7. H

    B How and why can multiplication combine physical quantities?

    I am on a journey to not just understand how to manipulate physics equations but to understand why they work , and how they describe physical phenomena. I understand how division combines physical quantities. I have this much physical quantity 'per' this much physical quantity. It puts 2...
  8. Jenab2

    B Has there been no update to Allen's Astrophysical Quantities since 1999?

    I'm looking for a reference text for astronomy and astrophysics that provides astrophysical and cosmological data since Cox's 1999 update to CW Allen's Astrophysical Quantities. Among other reasons, I'm hoping for statistical data on confirmed exoplanets, which did not exist in 1999.
  9. Keith Koenig

    B Length, Time, and Velocity -- Which are fundamental quantities?

    We think of length and time as the first fundamental quantities and velocity as the first derived quantity but any two determine the third so we would be completely justified in defining velocity as a fundamental quantity and one of length or time as the other, with the remaining being the first...
  10. mcas

    Estimate the following quantities from a graph of the refractive index of NaCl

    a) I managed to obtain some results that are roughly around what is given in the answers. Because \varepsilon_{st} and \varepsilon_{\infty} are values of \varepsilon_{1}, I used this approximation: n\approx \frac{1}{\sqrt{2}} (\varepsilon_{1}+\sqrt{\varepsilon_{1}^2})^{1/2} -> \varepsilon_{1} =...
  11. D

    I Neglecting higher powers of small quantities in calculations

    Hi If x(t) is considered to be small so that higher powers ( greater than 2 ) can be neglected in a calculation does that also imply that the time derivative of x(t) can be considered small and powers greater than 2 be neglected ? Thanks
  12. DuckAmuck

    I Are permittivity and permeability quantities that can be predicted?

    For example, can you predict the permittivity and permeability of a substance if you know what the atomic composition is? Is it a stat mech problem?
  13. dRic2

    I Discrete symmetries and conserved quantities

    Hi, please correct me if I use a wrong jargon. If I have discrete symmetries (like for example in a crystal lattice) can I find some conserved quantity ? For example crystal momentum is conserved up to a multiple of the reciprocal lattice constant and it is linked (I think) to the periodicity...
  14. K

    I Quantities in the Heisenberg Uncertainly Principle

    Hello, I am a Brazilian Physics student and would like to ask a question. Why are not all physical quantities related to each other by the degree of precision in the Heisenberg Uncertainty Principle? For example, why is it possible to determine the energy and position of a particle without its...
  15. F

    I Variant and Invariant Physical Quantities....

    Hello, In non-relativistic physics (where things move slower than the speed of light), the following physical quantities are invariant and variant (or relative) i.e. vary in value depending on the chosen frame of reference: Variant quantities: time ##t##, velocity ##v##, momentum ##p##...
  16. E

    B A question about quantities vs units in physical laws

    A quantity ##p## can be expressed as the product of a dimensionless number, ##\lambda_p##, and a unit, ##u_X##:$$p = \lambda_p u_X$$When we write the equation of a physical law, do the symbols represent the physical quantities ##p## or their dimensionless coefficients ##\lambda_p##? That is to...
  17. Arman777

    I Understanding Relation of Proper & Vector Quantities

    Let me define the letters before because they will be confusing: ##x##: 3-vector ##v##: 3-velocity ##a##: 3-acceleration ##X##: 4-vector ##U##: 4-velocity ##A##: 4-acceleration ##\alpha##: proper acceleration ##u##: proper velocity One can define the proper time as, $$d\tau = \sqrt{1 -...
  18. Replusz

    I Mathematical Truth of Physically Observable Quantities

    I assume this is true because using a passive coordinate transformation of the coordinate system should not effect how we measure something. I don't know if this is enough, hence if my original statement is just trivial, or if there is some deeper underlying thing lurking. Is the statement true...
  19. Z

    Calculation using 3 quantities: Shoveling snow to earn money

    Summary:: Hi, I am trying to solve the following: A person shovels driveways to earn money. She can shovel 12 driveways in 6 hours. She earns 18$ for each driveway.The person needs 360$ to buy a computer. How may hours does the person need to work? I am using unity method : 18$----6 hour 1...
  20. M

    I Conservation of Quantity: Noether's Theorem

    Hi, I have a question and I was hoping for some help. The reasoning goes something like this: There appears to be two fundamental types of coordinates x - space t - time and there appears to be three types of fundamental transformations - translations - rotations -...
  21. E

    B Manipulating quantities with natural units

    I'm only really just learning how natural units work so forgive me if this seems like a silly question. I was just wondering if someone could verify whether the following line of reasoning is valid (I will use joules instead of electron volts just so we can ignore the e conversion factor for...
  22. N

    Conserved quantities under the Lorentz boost

    In physics, a symmetry of the physical system is always associated with some conserved quantity. That physical laws are invariant under the observer’s displacement in position leads to conservation of momentum. Invariance under rotation leads to conservation of angular momentum, and under...
  23. S

    B Might all physical quantities be quantized?

    Please take a look at my first thought experiment: You have 2 coins to place on the table. The distance between them may be between 0 (inclusive) and 1 meter (exclusive). So if you want to store the number 15 you simply set the distance to 0,15m. You can later read the information by measuring...
  24. A

    I Variation of geometrical quantities under infinitesimal deformation

    This question is about 2-d surfaces embedded inR3It's easy to find information on how the metric tensor changes when $$x_{\mu}\rightarrow x_{\mu}+\varepsilon\xi(x)$$ So, what about the variation of the second fundamental form, the Gauss and the mean curvature? how they change? I found some...
  25. Q

    Understand Logic of Wald & Zoupas' Expression on Conserved Quantities

    Wald and Zoupas discussed the general definition of ``conserved quantities" in a diffeomorphism invariant theory in this work. In Section IV, they gave one expression (33) in the linked article. I cannot really understand the logic of this expression. Would you please help me with this?
  26. S

    B Are trigonometric ratios physical quantities?

    I already know the fact that angles are physical quantities, but sin, cos of some angles are quantities? Quantities are those things, which can be quantified, are sin, cos, tan be quantified through measurement, if yes then other mathematical functions should also be categorised as physical...
  27. C

    MHB Understanding Unit Cancellation in Physics Equations

    here's the question: a = b/e b = 1 kg m-1 e = 1 kg m-2 what is a? including units I assume it's to do with cancelling out the units when you divide but I really don't know what the answer is
  28. Zahid Iftikhar

    I Inertial Frames: Constant Quantities?

    My question is about some physical quantities which two observers in two respective inertial frames will find the same. I wonder are there any such quantities? Some books say force, speed of light etc are constants for both the observers. Please guide me on this. Regards.
  29. H

    A Do thermal quantities change in quantum phase transition?

    Such as, Chern insulator, normal insulator, topological insulator, do they have any discontinuous change in thermal quantities? Do they have order parameters?
  30. BookWei

    I Examples of invariant quantities

    In SR, we know that ##\vec E \cdot \vec B## and ##E^{2}-B^{2}## are invariant. Although I can prove those two invariant physical quantities mathematically, I do not know how to find at least one example to demonstrate that ##\vec E \cdot \vec B## and ##E^{2}-B^{2}## are invariant. Many thanks!
  31. E

    Which quantities are not the same for this capacitor setup?

    Homework Statement Two parallel-plate capacitors with the same plate separation but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is: A. potential difference...
  32. Clara Chung

    Energy question, what are the quantities conserved?

    Homework Statement Homework EquationsThe Attempt at a Solution I don't know how to do the last part. What are the additional conservation laws? I don't think momentum is conserved because there is force acting on the particle. I don't think angular momentum is conserved too because there is a...
  33. Clara Chung

    Momentum question -- What quantities are conserved in an elastic collision....

    Homework Statement Homework EquationsThe Attempt at a Solution How do I calculate part d? I know that (m2-m1)v0 = m2v2+m1v1 where v0 = root (2gh), v1 and v2 are the new velocity of the masses (m2+m1)v02 = m2v22 + m1v12 I also know that v2-v1=2v0 but how do I separate the KE of mass 2?
  34. Toby_phys

    Using Noether's Theorem to get conserved quantities

    Homework Statement N point particles of mass mα, α = 1,...,N move in their mutual gravitational field. Write down the Lagrangian for this system. Use Noether’s theorem to derive six constants of motion for the system, none of which is the energy Homework Equations Noethers Theorem: If a...
  35. I

    Operation with tensor quantities in quantum field theory

    I would like to know where one may operate with tensor quantities in quantum field theory: Minkowski tensors, spinors, effective lagrangians (for example sigma models or models with four quark interaction), gamma matrices, Grassmann algebra, Lie algebra, fermion determinants and et cetera. I...
  36. O

    A Classical field models with infinite conserved quantities

    Couldn't really fit the precise question in the title due to the character limit. I want to know what are some sufficient conditions for a model in classical field theory to possesses infinitely many conserved quantities. The sine-Gordon and KdV equations are examples of such systems. Now...
  37. T

    Prove v^ has all of a vector's quantities

    Homework Statement Hi Given the linear velocity formula: v* v^ = r*ω(-sinθi^ + cosθj^) i^, j^, v^ - unit vectors I'm to prove that v^ has direction, turn and magnitude Magnitude: |v^| = sqrt((-sinθ)^2 + (cosθ)^2) = 1 (as is also stated in unit vector's definition) Direction and turn...
  38. S

    I Conserved Quantities in GR: Explained

    Hello! I am reading about spherical geometry and for a static system and based on the metric, ##p_0## and ##p_\phi## are constant of motion. I am not sure I understand in which sense are they constant? The energy of a particle measured by an observer depends on the metric (so on its position) in...
  39. P

    Conserved quantities Lagrangian

    Homework Statement Hi, I'm doing the double pendulum problem in free space and I've noticed that I get two different conserved values depending on how I define my angles. Obviously, this should not be the case, so I'm wondering where I've gone wrong. Homework EquationsThe Attempt at a Solution...
  40. N

    B Must two quantities have the same dimensions

    Must two quantities have the same dimensions if you are using one quantity as an exponent in raising other to a power? What is the dimension ( or dimensionless) of '2' in mv2/r ?( v is raised to the second power)
  41. M

    I Two Conserved Quantities Along Geodesic

    Hi Everyone! I have done three years in my undergrad in physics/math and this summer I'm doing a research project in general relativity. I generally use a computer to do my GR computations, but there is a proof that I want to do by hand and I've been having some trouble. I want to show that...
  42. binbagsss

    General Relativity geodesics, killing vector, conserved quantities

    Homework Statement Homework EquationsThe Attempt at a Solution [/B] Let ##k^u## denote the KVF. We have that along a geodesic ##K=k^uV_u## is constant , where ##V^u ## is the tangent vector to some affinely parameterised geodesic. ##k^u=\delta^u_i## , ##V^u=(\dot{t},\vec{\dot{x}})## so...
  43. I

    I What did Newton mean by "Ghosts of Departed Quantities"

    "Ghosts of Departed Quantities" And a host of ones own deity?
  44. E

    Verify that the sum of three quantities x, y, z

    Homework Statement Verify that the sum of three quantities x, y, z, whose product is a constant k, is maximum when these three quantities are equal. Homework Equations w = x + y + z k = x * y * z The Attempt at a Solution Assuming that my understanding of the question is correct i.e. that we...
  45. binbagsss

    GR conditions conserved quantities AdS s-t; t-l geodesic

    Homework Statement Question attached Homework Equations The Attempt at a Solution part a) ##ds^2=\frac{R^2}{z^2}(-dt^2+dy^2+dx^2+dz^2)## part b) it is clear there is a conserved quantity associated with ##t,y,x## From Euler-Lagrange equations ## \dot{t}=k ## , k a constant ; similar for...
  46. PrathameshR

    B Canonically conjugate quantities

    In a lecture on introductory quantum mechanics the teacher said that Heisenberg uncertainty principle is applicable only to canonically conjugate physical quantities. What are these quantities?
  47. T

    B How are initial radioactive isotope quantities assumed?

    I'm stuck on this idea. How are initial radioactive isotope quantities assumed in radiometric dating? There are current abundances for all isotopes, but wouldn't these abundances have been different in the past (much higher)? I honestly can't grasp how radioactive isotopes with short half lives...
  48. Caio Graco

    Quantities without unit of measure

    Homework Statement Quantities without unit of measure are: A) Necessarily scalar B) Necessarily vector C) Can be scalar or vector D) They are neither scalar nor vector Justify your answer!Homework Equations No equations The Attempt at a Solution For example, the refractive index of a medium...
  49. E

    Conserved quantities in the Korteweg-de Vries equation

    Homework Statement Consider the Kortweg-de Vires Equation in the form $$\frac{\partial \psi}{\partial t}+\frac{\partial^3 \psi}{\partial x^3}+6\psi\frac{\partial \psi}{\partial x}=0$$ Find the relation between the coefficients ##c## and ##d## , such that the following quantity is conserved...