Difference between revisions of "2034: Equations"
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:All quantum gravity equations
:All quantum gravity equations
:S<sub>g</sub> = (-1)/(2ε̄) i ð (̂ ξ<sub>0</sub> +̊ p<sub>ε</sub> ρ<sub>v</sub><sup>abc</sup> η<sub>0</sub> )̂ f<sub>a</sub><sup>
:S<sub>g</sub> = (-1)/(2ε̄) i ð (̂ ξ<sub>0</sub> +̊ p<sub>ε</sub> ρ<sub>v</sub><sup>abc</sup> η<sub>0</sub> )̂ f<sub>a</sub><sup></sup> λ(3̆) ψ(0<sub>a</sub>)
:All gauge theory equations
:All gauge theory equations
:H(t) + Ω + G⋅&
:H(t) + Ω + G⋅&; ... > 0 (Hubble model) ... = 0 (Flat sphere model) ... < 0 (Bright dark matter model)
:All cosmology equations
:All cosmology equations
Revision as of 11:37, 17 August 2018
Title text: All electromagnetic equations: The same as all fluid dynamics equations, but with the 8 and 23 replaced with the permittivity and permeability of free space, respectively.
| This explanation may be incomplete or incorrect: Created by an EQUATION - Please change this comment when editing this page. Do NOT delete this tag too soon.|
If you can address this issue, please edit the page! Thanks.
This comic gives a set of equations supposedly from different areas of mathematics and physics. To anyone not familiar with the field in question they look pretty similar to what you might find in research papers or on the relevant Wikipedia pages. To someone who knows even a little about the topic, they are clearly very wrong and only seem even worse the more you look at them.
|All kinematics equations||This equation literally states: "Energy equals a constant multiplied by time, plus half of density multiplied by speed multiplied by time squared". The first term here is hard to interpret: it could be correct if is a constant power applied to the system, but this symbol would more normally be used to denote an initial energy, in which case so multiplying by would be wrong. The second term looks similar to the traditional kinetic energy formula but with a density instead of the mass. This is then wrong without some accompanying volume term (on either side of the equation).|
|All number theory equations||Taken literally the equation says: "The nth K-number is equal to: for all i in 0 to infinity, for all pi in 0 to infinity; subtract pi from n, and multiply it with i minus e to the power of pi minus infinity". A twofold misconception can be seen here. The first is the reassignment of pi as a variable instead of the constant (3.14...). This might be a jab at how in number theory letters and numbers are used interchangeably, but where some letters are all of a sudden fixed constants. The second misconception is the use of infinity in the latter part of the formula. Naively this would signify that (with the reassigned pi values) the part in the power would range from minus infinity to zero. However, infinity is not a number and cannot be used as one without using a limit construct.|
|All fluid dynamic equations||This equation has superficial resemblance to portions of Maxwell's Equations, but just miscellaneous bits, some from the integral forms and some from the differential forms.|
|All quantum mechanic equations||This equation takes a state psi in the dimensions of x and y and equates it to an operator A performed on psi multiplied by the same operator performed on the tensor product of x and y. Seeing as the state psi is already the tensor product of the states x and y, this is equivalent to performing the same unknown operator twice on psi, and unless this operator is its own inverse such as a bit-flip or Hermitian operator, this equation is therefore incorrect.|
|All chemistry equations||A modification of the combustion of methane. The correct form is often taught and a good example problem but obviously there are more chemistry problems. is normally shorthand for activation energy, but in Randall's version it's jokingly used as a chemical ingredient and becomes , taking the hydrogen atom freed by the combustion equation shown. To deliver the punchline while maintaining proper stoichiometry, (which should be , since the oxygen keeps a free electron when it combines with a single hydrogen) is shown instead of . The proper methane combustion equation would be:|
|All quantum gravity equations||This is more similar to experessions which appear in Grand Unified Theory (GUT) than general quantum gravity. Unlike some of the other equations, this one has no interpretation which could make it mathematically correct. This is similar to the notations used to describe the symmetry group of a particular phenomena in terms of mathematical Lie Groups. A real example would be the Standard Model of particle physics which has symmetry according to . Here, and denote the special unitary and unitary groups respectively with the numbers indicating the dimension of the group. Loosely, the three terms correspond to the symmetries of the strong force, weak force and electromagnetism although the exact correspondence is muddied by symmetry breaking and the Higgs mechanism.
Of course, an expression missing an "=" sign, is difficult to interpret as an "equation", because equations normally express an "equality" of some kind. Nobody knows whether Randal refers to a horse here (equidae)
Randall's version clearly involves some similar groups although without the symbol it is hard to work out what might be happening. A term like has no current interpretation in mathematics, if anyone thinks otherwise and possibly has a solution to the quantum gravity problem they should probably get in touch with someone about that.
|All gauge theory equations||This equation looks broadly similar to the sorts of things which appear in gauge theory such as the equations which define Yang-Mills Theory. By the time physics has got this far in, people have normally run out of regular symbols making a lot of the equations look very daunting. The actual equations in this field rarely go far beyond the Greek alphabet though and no-one has yet to try putting hats on brackets. The appearance of many sub- and superscripts is normal (this links to the group theory origins of these equations) and for the layperson it can be impossible to determine which additions are labels on the symbols and which are indices for an Einstein Sum.
The left-hand side is the symbol for some action, in Yang-Mills theory this is actually used for a so-called "ghost action". On the right-hand side we have a large number of terms, most of which are hard to interpret without knowing Randall's thought processes (this is why real research papers should all label their equations thoroughly). The looks like a constant of proportionality which often appears in gauge theories. The factor of is not unusual as many of these equations use complex numbers. The symbol looks similar to a partial derivative symbol especially as the Dirac Equation uses a slashed version as a convenient shorthand.
The rest of the equation cannot be mathematically correct as the choice of indices used does not match that on the left-hand side (which has none). In particle physics subscripts (or superscripts) of greek letters (usually or ) indicate terms which transform nicely under Lorentz transformations (special relativity). Roman indices from the beginning of the alphabet relate to various gauge transformation propetries, the triple index seen on would likely come from some transformation (related to the strong nuclear force). Since has none of these (and is thus a scalar which remains constant under these operations), we would need the right-hand side to behave in the same way. Most of the indices which appear are unpaired and so will not result in a scalar making the equation very wrong. For those not familiar with this type of equation, it is a similar mistake messing up units and setting a distance equal to a mass.
|All cosmology equations||This is a parody of equations defining the Hubble Parameter although it looks like Randall has become bored and not bothered to finish his equation. Such equations usually have several terms representing the contributions of different substances to the energy-density of the Universe (matter, radiation, dark energy etc.). In this context could be Newton's constant and is something dark energy related although seeing them appear multiplied and on the same footing as is unusual (the dot is entirely unnecessary). Choosing to make a function of time and not of redshit is also unusual.
The second section looks like the inequalities used to show how what shape the Universe, based on the value of the curvature parameter . A value of 0 indicates a flat Universe (this more or less what we observe) whilst a positive /negative value indicates an open /closed curved Universe. Randall's choice of labels further makes fun of the field as both a flat sphere and bright dark matter are oxymoronic terms which would involve some rather strange model universes.
|All truly deep physics equations||is the Hamiltonian operator, which when applied to a system returns the total energy. In this context, U would usually be the potential energy. However, there is also a subscript 0 and a diacritic making indicating some other variable. Much of physics is based on Lagrangian and Hamiltonian mechanics. The Lagrangian is defined as with K being the kinetic energy and U the potential. Hamiltonian mechanics uses the equation . The Hamiltonian must be conserved so taking the time derivative and setting it equal to zero is a powerful tool. The principle of least action says allows most modern physics to be derived by setting the time derivative of the Lagrangian to zero.|
|This transcript is incomplete. Please help editing it! Thanks.|
- [Nine equations are listed and labeled as followed:]
- E = K0t + 1/2 pvt2
- All kinematics equations
- Kn = ∑i=0∞∑π=0∞(n-π)(i-eπ-∞)
- All number theory equations
- ∂/∂t ∇ ⋅ p = 8/23 (∯ ρ ds dt ⋅ ρ ∂/∂∇)
- All fluid dynamic equations
- |ψx,y〉 = A(ψ) A(|x〉⊗ |y〉)
- All quantum mechanic equations
- CH4 + OH + HEAT → H2O + CH2 + H2EAT
- All chemistry equations
- SU(2)U(1) × SU(U(2))
- All quantum gravity equations
- Sg = (-1)/(2ε̄) i ð (̂ ξ0 +̊ pε ρvabc η0 )̂ fa0 λ(3̆) ψ(0a)
- All gauge theory equations
- H(t) + Ω + G⋅Λ ... > 0 (Hubble model) ... = 0 (Flat sphere model) ... < 0 (Bright dark matter model)
- All cosmology equations
- Ĥ - u̧0 = 0
- All truly deep physics equations
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