Mordred

Lol

Lol if you didn't understand or follow that article portion. Regardless of notation or otherwise. Then that portion definetely needs a major revamp and rethink.

Not quite, light takes roughly 326 light years to travel 100 Mpc. The changes in that time period is negligible compared to the age of the universe. So one can say roughly the same age. However when you take your measurements. You calculate the proper distance between two or more measurement points. Any time you take any measurements you must account for observer influences. [latex]d{s^2}=-{c^2}d{t^2}+a({t^2})d{r^2}+{S,k}{r^2}d\Omega^2[/latex] Here is the 4d Freidmann equation for distance measures. K is the curvature constant. a(t^2) is the scale factor which takes expansion at a point in time into account. http://en.m.wikipedia.org/wiki/Scale_factor_(cosmology) Note the scale factor also accounts for cosmological redshift. Any specific point in time will have the thermodynamic properties. The universe will be roughly the same temperature throughout. (Though the temperature variations isn't significant in 326 years, except in the early universe) You cannot directly see the same point in time throughout the universe. So you must calculate where objects will be at that point in time. I really wish I could post the charts from the lightcone calculator in my signature. However one can use that tool to see the changes in 326 years. For some reason this site doesn't like the latex the calc uses. You can refine the time period being calculated via the S_upper and S_lower values.

Sorry to me your not being very clear. Let's start with a basic question on photons. Lets assume a multibody problem. In compression are you referring to the waveforms? Or are you deferring to individual particles? Yes this is a trick question. Treat it as "how is a particle defined? Question How is this different from particle to particle interactions? Which analysis are you using? Either the transport of mass, energy or wave functions. (Other none OP transports aside). Forget trying to describe your model via a word salad. Use mathematics and specific interactions. Quite frankly if you want to convince anyone you need predictability. You can't have that without a proper math descriptive. Containing predictive levels of cause a leads to cause b. Does some of particle physics follow rotations similar to the geometry of spring dynamics ? Absolutely. Can you show those examples mathematically? Well I leave that in your hands. This far what I've read the answer is no. Feel free to correct me. I don't take insult. Lol do me and everyone else a fav. latex is far easier to read. http://www.scienceforums.net/topic/3751-quick-latex-tutorial/page-3#entry115211 pain in the butt I agree but highly recommended

Good methodology , being used to mnemonics I would of suggested a less obvious method.( lol I tend to think in terms of Boolean logic circuits) Yours is the better and more suited methodology. (I will leave this in your more than capable hands)

I incorporated some of the suggested changes. In the opening post. Please review. Any suggestions welcome including syntax and writing style. Don't worry I don't bite, I fully expect a site forum FAQ article to undergo numerous adjustments.

that statement should have read a property of particles not mass lol oops. Missed that. I am working on this aspect, originally I had planned on including the metric and curvature tensor as defined in an arbitrary coordinate system of a point (test particle). The problem I've run into is simplifying the metric for the average reader. True, again the problem is keeping the article simple yet accurate. I agree more detail on the coordinate aspects of GR is needed for the article, which may be best to apply the Lorentz transformation from two examples from flat and in the Schwartchild metric. On the quantum foam aspects, it's looking like a link to a separate thread may be best. On note on the metric section here is what I have thus far and I'm reconsidering how to go about this section. GR matrix transformations In General Relativity the metric is seemingly complex. One must understand that GR is a coordinate system. When one describes bodies in motion such as planets and stars the metric of a sphere is useful. However at some point one must use an arbitrary coordinate metric. Recalling that GR has the time component as a coordinate as well. Coordinates in GR take the form (ct,x,y,z) this leads to a 4x4 matrix. For the moment we are ignoring everything but the exact specific real numbers the components of the metric take at a single point. Lets define a point as [math]x^\alpha[/math] and our new coordinate as [math]y^{\mu}[/math] these simple coordinates leads to [math]g_{\mu\nu}=g_{\alpha\beta}=\frac{dx^{\alpha}}{dy^{\mu}}\frac{dx^{\beta}}{dy^{\nu}}[/math] What exactly is a matrix. The wiki definition is useful. "In mathematics, a matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns that is treated in certain prescribed ways. The individual items in a matrix are called its elements or entries. " http://en.m.wikipedia.org/wiki/Matrix_(mathematics) One example is below. Which is a 4*4 matrix Note the numeric organization. [math] A_{m,n} =\begin{pmatrix}a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\\vdots & \vdots & \ddots & \vdots \\a_{m,1} & a_{m,2} & \cdots a_{m,n}\end{pmatrix}[/math] In GR it is common to replace m and n with [math]\mu[/math] and [math]\nu[/math] respectively. As one can see [math]\mu[/math] denotes the row and [math]\nu[/math] denotes the column. Both [math]\mu[/math] and [math]\nu[/math] are vectors. Matrix transformation examples can be found here http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fpure_ch9.pdf A more detailed 63 page article on matrix mathematics can be studied in this pdf. http://www.google.ca/url?sa=t&source=web&cd=1&ved=0CBsQFjAA&url=http%3A%2F%2Fwww.mheducation.ca%2Fcollege%2Folcsupport%2Fnicholson4%2Fnicholson4_sample_chap2.pdf&rct=j&q=matrix%20mathematics%20pdf&ei=WaBmVbjaCrDfsASK4YGwAQ&usg=AFQjCNFLoGWucTsDoKqVhBhrLWIaPeIHbw&sig2=P6W5USwrpu7eDNGAbRf4SQ. Einstein field equation Metric tensor In general relativity, the metric tensor below may loosely be thought of as a generalization of the gravitational potential familiar from Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as distance, volume, curvature, angle, future and past. [math]dx^2=(dx^0)^2+(dx^1)^2+(dx^3)^2[/math] [math]g_{\mu\nu}=\begin{pmatrix}g_{0,0}&g_{0,1}&g_{0,2}&g_{0,3}\\g_{1,0}&g_{1,1}&g_{1,2}&g_{1,3}\\g_{2,0}&g_{2,1}&g_{2,2}&g_{2,3}\\g_{3,0}&g_{3,1}&g_{3,2}&g_{3,3}\end{pmatrix}=\begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/math] Which corresponds to [math]\frac{dx^\alpha}{dy^{\mu}}=\frac{dx^\beta}{dy^{\nu}}=\begin{pmatrix}\frac{dx^0}{dy^0}&\frac{dx^1}{dy^0}&\frac{dx^2}{dy^0}&\frac{dx^3}{dy^0}\\\frac{dx^0}{dy^1}&\frac{dx^1}{dy^1}&\frac{dx^2}{dy^1}&\frac{dx^3}{dy^1}\\\frac{dx^0}{dy^2}&\frac{dx^1}{dy^2}&\frac{dx^2}{dy^2}&\frac{dx^3}{dy^2}\\\frac{dx^0}{dy^3}&\frac{dx^1}{dy^3}&\frac{dx^2}{dy^3}&\frac{dx^3}{dy^3}\end{pmatrix}[/math] The simplest transform is the Minkowskii metric, Euclidean space or flat space. This is denoted by [math]\eta[[/math] Flat space [math]\mathbb{R}^4 [/math] with Coordinates (t,x,y,z) or alternatively (ct,x,y,z) flat space is done in Cartesian coordinates. In this metric space time is defined as [math] ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/math] [math]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/math] In an effort to keep this article to a manageable length I will refer to the wiki article on Lorentz transformations and its connection to SR. http://en.m.wikipedia.org/wiki/Lorentz_transformation A free textbook (open source) can be found here http://www.lightandmatter.com/sr/ (For the Schwartzchild Metric I was thinking of using Kruskal Szekeres coordinates.) Though it may better to stick to the Schwartzchild Metric) and just link other coordinate systems of note.

All particle interactions contribute to temperature. ( This includes the strong, weak, gravitational and chemical potential) As well as pressure to energy density temperature relations. Though non relativistic matter has a negligible contribution. These can be found via the equations of state : http://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) What your describing in the electromagnet field can be modelled specifically under the electromagnetic stress energy tensor. (Includes relavistic) http://en.m.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor GR however (Einstein field equations) Accounts for any form of energy momentum. See stress energy tensor. http://en.m.wikipedia.org/wiki/Stress%E2%80%93energy_tensor The vacuum also can have scalar only influences on pressure/energy density relations. One notable example is the Higgs field. Another being the inflaton used in inflation. Both these examples are modelled via the scalar modelling equation (see that section under the First wiki link. These articles will fill in the blanks. http://arxiv.org/pdf/hep-th/0503203.pdf"Particle Physics and Inflationary Cosmology" by Andrei Linde http://www.wiese.itp.unibe.ch/lectures/universe.pdf:"Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis In GUT theories, there is a specific temperature where each force becomes indistinguishable from one another, or more accurately teach thermal equilibrium. In this state the system can also be modelled as a vacuum. Then you have the vacuum expectation value, which is related to the above. http://en.m.wikipedia.org/wiki/Vacuum_expectation_value

First seperate the pathways into series and parallel paths. Then apply the series and parralel capacitance addition equations to each pathway circuit. Add the resultance together for the total capacitance. Series. [latex]c_t=\frac {1}{c_1}+\frac{1}{c_2}...[/latex] Parallel [latex]c_t=c_1+c_2...[/latex]

Quantum foam is also a mathematical descriptive. When you get into the details. I think it may be best to place that under the QM forum. Then provide a link to each article. Still deciding on that. Atm the curvature and stress energy tensors is giving me headaches trying to simplify them.

I just finished writing a FAQ on "What is space time made of " http://www.scienceforums.net/topic/89395-what-is-space-made-of/#entry869949 You might want to read it as treating space time as some form of fabric, medium etc is a common misconception. Thanks to pop media articles primarily.

FAQ article development, feel free to ask questions or make suggestions. (I'm still working on the Einstein field equation section. Probably keep that portion seperate to minimize length) This question is amongst one of the most commonly asked questions in relativity. Numerous articles both in pop media and peer reviewed articles refer to terms such as space time fabric, space time curvature. This leads the new learners with a common misconception that space has some mysterious fabric or material like property. To answer this properly we need to describe a few principles. A) gravity influences mass B) energy is a property of particles, or physical configurations such as feilds. Energy does not exist on its own. C) space is defined as a volume only. That volume contains the standard model particles and feilds. It is not something form of ether. In GR space is mapped in an arbitrary coordinate system. Without the time component the coordinates are in 3d. D) spacetime is any metric that includes the time component as a vector. This is the 4th dimension, in GR the time component is treated in coordinate form. E) General relativity is a coordinate system metric. This coordinate system makes use of manifolds. Which is a topological space that is resembles Euclidean space at beach point. For example a Euclidean space (flat space), can undergo a homeomorphism to curved space via relativistic effects such as inertia and mass to an observer. The rubber sheet example is one such homeomorphism. http://theory.uwinnipeg.ca/users/gabor/black_holes/slide5.html A good YouTube video is http://m.youtube.com/watch?v=MTY1Kje0yLg Keep in mind the rubber sheet analogy is just that. An analogy, it was never intended to state that space time is a materialistic fabric or ether. A classical example of a homeomorphism is the coordinate change from Cartesian coordinates (Euclidean flat space) to polar coordinates. (Curved, spherical geometry) https://www.mathsisfun.com/polar-cartesian-coordinates.html http://en.m.wikipedia.org/wiki/Manifold http://en.m.wikipedia.org/wiki/Homeomorphic Now with those in mind, we find that spacetime curvature is a geometric coordinate relation of how the strength of gravity influences the particles that reside in the volume of space. In short it is a geometric description of how gravity influences particles not the volume of space. The terms fabric, curvature, sretches are misleading. They are analogies used to explain the change in geometric relations. 2) How is space time created? The volume of space simply increases, space itself is just volume filled with the standard model particles.

Have you thought about the portion where I specified a downward as opposed to lateral pull on the table cloth. Why would the previous method make the trick easier to perform? The answer has something to do with friction. Specifically static friction.

Your welcome.

If measurement and observations are found that disagree with the Cosmological principle then yes it would need to be dropped. Thus far all the best datasets and measurements still find the principle accurate. These datasets are not limitted to WMAP and Planck, those two are merely the more popularly known. Correct. This is the value also provided in numerous textbooks as well. Afaik cosmology papers are still currently using this value. The metrics of the BB model accounts for the aspects of time vs distance. There is several different types of time used in cosmology. Cosmic, conformal and proper time. There is also different categories of distance measure. Proper conformal and commoving distance. Think of it this way. At any specific moment in time. The average universe density and thus rate of expansion is uniform. So at any moment of time. The Cosmological principle applies. The FLRW metrics accounts for this via the scale factor. It is a good point to raise in regards to time. One of the articles provided by Brian Powell that I included goes into this detail.

For further info Google Keplers laws. Unfortunately we cannot define one formula. http://en.m.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion Key note on center of mass.

@Tar I read sometime ago one of your posts in regards to deviding a ball into 12 equally geometric shapes. Excellent work on that subject. You obviously have a strong interest in geometry. The reason for mentioning this involves a method of style in posting responses.( lol diaper bags don't quite cut it) Many readers don't study previous posts. When you reference a subject try to include supporting articles and previous posts. One cannot think of every possibility or thought process of every individual. When you step into the try and teach mode, do some supporting research. Supply articles with metric examples. In this case geometry based articles are particularly handy. Side note teach non personal mathematics and models. Those should properly remain seperate threads. Just some word of advise to all responders to posts. (Also be patient, knowledge has many directions and forms) PS I posted the above also for other regular forum members. Always try to supply study guidance and material (It has nothing to do with looking like a genius, it's about supplying teaching aids and direction) Now this post is synonymous of the mobius strip. http://en.m.wikipedia.org/wiki/M%C3%B6bius_strip However the posts by the OP may be better suited by other complex geometry shapes. Some examples here https://www.google.ca/url?sa=t&source=web&cd=9&ved=0CDYQFjAI&url=http%3A%2F%2Fwww.maths.ed.ac.uk%2F~aar%2Fsurgery%2Fzeeman.pdf&rct=j&q=mobius%20strip%20mathenatics%20pdf&ei=bFRpVYbRHIilgwSc6IH4CQ&usg=AFQjCNGVCp3NzO1ajnFEx8PkDtxD6DzVZQ&sig2=JJemu3wWcoDLkF1n9FPxNA

In my spare time I will be writing a series of useful articles to help answer common questions. As these are being designed for forum reference I feel strongly on cooperative review. Here is the first. Please look over and feel free to make suggestions. Any solid contributions will be accorded credit at the end of the final product. (Key note all articles MUST comply with textbook descriptives, they are being designed as teaching aids) [latex]\textbf{The Cosmological principle}[/latex] is defined as "at sufficiently large scales, the universe appears as homogeneous and isotropic." [latex]\underline{Homogenous}[/latex] is oft defined as " no preferred location" [latex]\underline{Isotropic}[/latex] is oft defined as "no preferred direction" Obviously at smaller localized scales we can see numerous examples of systems that are inhomogeneous and anisotropic (planets, stars galaxies and large scale structures). However if you increase the radius of measurements sufficient enough those non uniform regions essentially become negligible or more accurately averages out. A good analogy is look at the surface of a lake. At small scales you can discern waves and ripples. As you increase in height or distance from the lake those non uniform regions become a uniform appearing surface. The cosmological principle works the same way. The scale commonly used is 100 Mpc mega parsecs. Speed of light in a vacuum: [latex]c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}[/latex] The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometers (19.2 trillion miles). In astronomical terms, it is equal to 3.26 light-years, and in scientific terms it is equal to 3.09×1013 kilometers The cosmological principle has an added reward in that complex systems can be modelled as good approximations with far less complicated mathematics. However it should be noted that if measurements and observations disagree with the cosmological principle those metrics become invalid. We're lucky though as the body of evidence fully support the cosmological principle. A commonly referred to example being the CMB. Cosmic microwave background. Although the temperature images look chaotic, the difference in temperature of the blue regions and red regions are roughly 1/1000 of a degree. Certainly supports the cosmological principle. The cosmological principle is of importance in telling us that the Universe did not have an origin point nor is the result of an explosion. This is of primary importance in regards to expansion and inflation. Lets detail this a bit further. Take any number of points, three or more. As the volume of space increases, the same ratio of change will occur between any two points and the angles between those points also do not change. This mathematically is only possible via a uniform change regardless of location. A good analogy is the balloon analogy or the raisin bread analogy. http://www.phinds.com/balloonanalogy/: A thorough write up on the balloon analogy used to describe expansion http://tangentspace.info/docs/horizon.pdf:Inflation and the Cosmological Horizon by Brian Powell The other consequence of the cosmological principle is that the universe cannot have a rotation. All rotating bodies have a center of rotation and rotation imparts a preferred direction.

Which type of friction? Which is the greater? Lets keep this to linear relationships for the time being. Until you have a clear understanding on the linear relationships of force and friction. We don't need added complexity. (Answering this should answer why a swift, uniform jerk on the tablecloth is needed and why you get a momentary movement of the plates at the initial point at the beginning of the jerk.) Side note if you plan on practicing this trick use oil cloth. Have maximum two feet over hang. Use heavier smooth objects. Do not pull towards you but rapidly pull down on the table cloth.(why will this make a difference?) Helps to use a long stick initially wrap the cloth around the stick for a uniform pull.

The reason I mentioned coefficient of friction is to help you realize the following scenario. Which will be easier to make that trick work ? A) a tablecloth made of smooth plastic B) a table cloth made of a rough course thread? You have two types of friction with three coefficients of friction. The table material. The table cloth material The object on top of the table. Each of the above also has its own mass. Work with the formulas for static and kinetic friction of each object Work with the amount of force needed to move each object in terms of first static friction, then kinetic friction. Key note if you move the table cloth slow the objects will land on the floor. But if you move the table cloth with enough instantaneous velocity the objects remain on the table. Figure out how the above questions relate to the two rates. (I recall posting a table of various coefficient of friction per material type listings)

Not necessarily, think of the 45 GeV as more of a jet channel. This particular jet has cropped up in the search for the 125 GeV Higgs boson in some papers. However I've also seen the 45 GeV transverse energy In papers involving neutralinos , dileptons and higglets. In and of itself I would consider it as detection channel or calibration method to detect other particles rather than a detection of a 45 GeV particle which it isn't. Remember the measured energy of a particle depends on the observer. A key note is that transverse energy is essentially measurements of the transverse wave. Recall that the electromagnetic force Carrier is the photon. http://en.m.wikipedia.org/wiki/Transverse_wave More accurately the 45 GeV is a signal in a transverse angle, how it is measured at other angles will have different energy signatures. The combination of the various channels or jets is used to isolate the properties of the particle in question. This particular channel and 45 FeB signal is often mentioned in searches for the 125 GeV Higgs, neurtralinos, dileptons and higglets in various papers. Without reading the full paper you referenced I cannot tell which one he suggests. Here I found this in a thesis paper http://lss.fnal.gov/archive/thesis/2000/fermilab-thesis-2015-02.shtml It describes the process in extreme detail. Here is the opening paragraph. "Neutral weakly interacting particles, such as neutrinos, escape from typical collider detectors without producing any direct response in the detector elements. The presence of such particles must be inferred from the imbalance of total momentum. The vector momentum imbalance in the plane perpendicular to the beam direction is particularly useful in pp and pp colliders, and ¯ is known as missing transverse momentum, here denoted ~E/T. Its magnitude is called missing transverse energy, and is denoted E/T. Missing transverse energy is one of the most important observables for discriminating leptonic decays of W bosons and top quarks from background events which do not contain neutrinos, such as multijet and DrellYan events. It is also an important variable in searches for new weakly interacting, long-lived particles. Many beyond-the-standard-model scenarios, includ- ing supersymmetry, predict events with large E/T. The reconstruction of ~E/T is very sensitive to particle momentum mismeasurements, particle misidentification, detector malfunctions, parti- cles impinging on poorly instrumented regions of the detector, cosmic-ray particles, and beam- halo particles, which may result in artificial E/T."

One way to look at at is particle decays that miss the detectors. Or rather the detectors cannot pick up. Here is how this paper describes it. "Neutral weakly interacting particles, such as neutrinos, escape from typical collider detectors without producing any direct response in the detector elements. The presence of such particles must be inferred from the imbalance of total momentum. The vector momentum imbalance in the plane perpendicular to the beam direction is particularly useful in pp and pp colliders, and ¯ is known as missing transverse momentum, " http://arxiv.org/abs/1106.5048

Lol how would they stack in boson particles. An infinite number of bosons can occupy the same space.

In all honesty carbon filters are great for most gases. On liability issues you need to seek professional chemical/gas filtration companies. I recommend asking other companies and similar industries for advice and direction. Any forums advise is meaningless in a court regardless of how diligent. Seek professional, reputable and accredited help. Reputable third party companies is a highly valuable resource.

Oh we can joke about Hubbles constant as its only constant in space, not in time.