Mordred

Lol excellent book I agree with that sentiment Another good book is Mathematical methods for Physicists by G. B. Arfken, H. J. Weber, and F. E. Harris.

17 gigabytes of pdfs lol also 125 textbooks in hardcover. Its amazing how much can be learned simply by studying different treatments for the same physics dynamics. Lol a side note one of the more humorous named models is Sir Roger Penrose "zig zag model" yes that is its offical name lmao. A little hint mo matter how complex looking any model appears. Always remember the basic definitions, units in SI and your classical formulas such as the one in this thread.

lol that's why I usually spend that time answering physics posts lol.

We can't get much detail from spectography, which only shows surface composition (how light interacts with elements). So our main data is from sampling. As mentioned the amount of collected samples is limited. Hence why drilling with probes is such a big deal. Other than that we can safely assume the asteroids will have compositions we find on Earth and other neighbors. After all the Earth according to theory arose from the same materials. Its safe to assume a certain percentage of your more valuable ores are contained in asteroids, though the heavier metal asteriods will tend to migrate towards the sun. Much like your more metal rich planets lie in the inner regions while the gas giants on the perimeter. So your more likely deposits of heavy metals will probably be your nearby asteriods. Although this doesn't mean those minerals cannot be on the outer regions, it will depend on the overall mass of the asteriod as to how it migrates. Yes if I guess correctly mining asteriods can be highly profitable. Probably enough to compensate the costs.(once the infrastructure is in place) (particularly as asteriods can have helium 3 which could potentially provide clean nuclear fusion. hope that helps Some papers suggest a source of platinum in asteroids for example http://web.mit.edu/12.000/www/m2016/finalwebsite/solutions/asteroids.html mentions many of the rarer minerals

was replying to this response

That is a a valid point, many read the science but hesitate to post there due to lack of knowledge or being worried that they will look foolish. As their comfort zone improves they become more active in the more scientific forums. There is no reeal way I know of in addressing this, as it breaks down to personal comfort zones. The best we as senior members can do is be as understanding and polite as possible. While providing a means to improve the understanding of a topic. Such as well written and informative articles etc. x posted with Beecee

Beecee gave a valid correction to your post. However LQC does have DM and the cosmological constant. Yes there is models that try to replace the two but when answering posts it is vital to make sure your responses are accurate and non misleading. Try not to take corrections personally, in many cases its not the models your referring to but how you are describing those models that needs improving. Use the opportunity to learn why you are being corrected. You will find that no one objects to spinfoam or quantum foam. Rather they are correcting how you are applying spinfoam in your descriptives. Accuracy is extremely important when replying to threads. For example LQC avoids the singularity issue by applying effective cutoffs called the IR and UV cutoff bounds. IR is your minima UV is the maxima. They avoid any infinities by using these cutoffs in their mathematics. However those same cutoffs allow the renormalization of spacetime. However as we cannot quantize gravity we still have renormalization problems. LQC doesn't provide an answer to this problem but is still working on it just as every other related theory is also doing. Fundamentally LQC is fully compatible with LCDM, with the exception that LCDM doesn't address how the universe started as it is no longer accurate prior to 10^-43 seconds. LQC doesn't address this problem either except for applying the cutoffs and having the bounce avoid the singularity issues due to infinities. In other words LQC doesn't solve the singularity issues it avoids them with renormalization cutoffs. Which is in essence the renormalization problem inherent in quantum field treatments. With the electromagnetic fields we know photons are discrete, we have yet to confirm this is true with spacetime itself. Every attempt to show that spacetime is lumpy (discrete) has shown it is smooth as in not discrete. ( a means to learn the cutoffs in QFT treatments is to study Observable operators and propogators which are not observable. To be observable requires a minima of a quanta of action. The effective maxima in QFT is the Planck temperature. https://en.wikipedia.org/wiki/Planck_temperature Relativity doesn't apply these cutoffs and won't until we solve the quantizing of spacetime issue. Though even if the cutoffs eventually get accepted as accurate relativity will still work as accurately. Within the range of cutoffs, that is the issue. Where do we establish the range where where a metric remains valid and when does it become invalid due to infinities. Spinfoam doesn't address this issue as a spinfoam uses operators in its renormalizations for each Hilbert space. In other words the external lines on a Feyman diagram. The internal lines being your virtual particles or fluctuations as opposed to an excitation. To get a better handle on this read http://www.scienceforums.net/topic/106004-useful-fundamental-formulas-of-qft/ I go into extensive detail on the operators vs propogators though I haven't done the path integrals for Feyman diagrams as of yet. (Still trying to figure out how to simplify)

Site Articles (Articles written by PF and Site members) http://cosmology101.wikidot.com/redshift-and-expansion http://cosmology101.wikidot.com/universe-geometry Misconceptions (Useful articles to answer various Cosmology Misconceptions) 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 http://arxiv.org/abs/1304.4446 :"What we have leaned from Observational Cosmology." -A handy write up on observational cosmology in accordance with the LambdaCDM model. http://arxiv.org/abs/astro-ph/0310808 :"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe" Lineweaver and Davies these articles are fairly low level on math, of particular importance to this thread is the cosmological principle. This describes a uniform overall mass density, with no center, where expansion is roughly uniform. The two key terms to understand is homogeneous = no preferred location isotropic= no preferred direction. a BH is a central center of mass system so it is anistropic and inhomogeneous. It has a preferred location and direction. (the center of mass). Universe expansion is the opposite via the cosmological principle. The balloon analogy link above describes this.

Loop quantum cosmology is the more popular spinfoam model choice. In case anyone is interested. Its tricky to learn as one needs to understand QFT. For example spinfoams is a type of degree of freedom reduction. (taking complex systems and dynamics and mathematically reducing the number of required dimensions to describe the interactions).

glad to help and glad to see that your now looking at the problem correctly. +1 PS thanks for the link to the Lorentz paper I like to collect the older works for my personal archives

I certainly hope so as it is suppose to, the kinetic energy formula is a derivitative of f=ma. Tell me did you never notice that 1 joule of energy =1 Newton of force? Both force and energy involve the ability to perform work. Tell me did you even read the links I posted. If so why do they keep referring to Newtons three laws when discussing kinetic energy?

spin foam loop quantum gravity is one such model. "Introduction to loop quantum gravity and spin foam" https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/gr-qc/0409061&ved=0ahUKEwjl6NqaosHVAhUBU2MKHcubDkUQFggdMAA&usg=AFQjCNFQyCyhp4AAkygF3OyIWVyAk4tGHg So the statement you quoted is accurate their is such a theory not of his own making. Whether or not Handy was referring to this model is another question Not to play devils advocate here as the post in question does not describe what LQG entails lol. Particularly the hijack warning

The mistake I had was boosts as a scalar which is obviously wrong. A boost is a matrix so what you stated applies its the three vector that has the perdindicular component. http://www.physicspages.com/2011/06/22/lorentz-transformations-in-three-dimensions/ That was what I almost forgot

edit had to double check the boosts, which can be thought of as a rotation between space and time. will correct the above. Corrected I knew there was something I had to be careful on when we hit the 4d lol

Ah good ole vectors, There is a very neat trick to understanding SR and GR inherent in understanding vector calculus. That trick is to understand the differences between the dot product and the cross product of two vectors. This is also important to understand Lorentz boosts and rotations. All boosts use the dot product. All rotations use the cross product. This includes the hyperbolic trigonometric functions. Its also coincidentally the key to understanding the following. 1) orthogonality, when orthogonality of all planes of axis is preserved use Euclid trigonometry (at rest frame) Galilean relativity rules apply 2) acceleration=rapidity=rotation 3) righthand rule=covariant=lefthand=contravariant. (accleration and conservation of angular momentum) =rotational translations 4) kronecker delta is a dot product 5) Levi Cevita connection is a cross product. 6) principle of equivalence is a dot product though the knowing all dot products are scalars ie the dot product of two vectors is a scalar and the cross product of the same two vectors is a vector. Is of critical importance to understand the above aforementioned. here is a good look at cross product, the links on that page will get you to the dot product section. https://betterexplained.com/articles/cross-product/ its a handy site as it details the above in matrix form, however one must look at the specifics of the Lorentz boosts and rotations to with regard to relativity but the 3d dot product and cross product rules do apply in 4d but one has to study the commutations on the 4*4 matrixes. (the above is a preliminary before you step into 4d). The above naturally also applies to div and curl....flux, pressure,vorticity etc now an easy way to visualize hyperbolic trigonometry as per polar coordinates, take a rubber sheet draw a triangle upon said sheet. Write all all your trig functions that correspond to this sheet with the dot product rules. then take the sheet and fold it over a sphere, the vectors that make up the triangle are now curved not linear, so you now have different lengths on each vector. (cross product of hyperbolic trig functions, via the addition of a curvature term k.). In Lorentz the curvature term only applies to the ct,x coordinates. via the gamma factor Lorentz boost. The zeroth component is e=pc^2 your invariant speed of light. Now here is a neat trick to the above the Minkowskii metric preserves the inner dot product which when preserved also preserves orthogonality. However that is the MInkowskii tensor itself, when you undergo translations this will return a scalar value. examples, mass,energy, velocity, frequency, temperature, etc any scalar quantity. We do not need to add any dimensions to the dot product. However cross products such as angular momentum adds a vector perpendicular to vectors a and b so you need an additional dimension or degree of freedom. or dimension. PS note the matrix designations on the 3*3 matrix for cross product and dot products. All dot products (scalar values lie on the diagonal components.) this includes scalar value 0 as per conservation laws these curves are all hyperbolic. You can see the Hyperbolic vectors in this Kruskal diagram notice the curl of [latex]\phi[/latex] ? Now with the above, and as per the first image we can use the parallel transport of two vectors to determine our curvature. (in freefall under GR). The two vectors will converge on the center of mass giving loss of parallel transport,

lets expand on this to highlight the significants of this. All rotations use the vector calculus of the cross product. All linear translations use the dot product of vector calculus. Those tensors you mentioned allow us to keep track of the vector algebra. A nice little chart on this link is extremely useful to understand how tensors work (You will be amazed how simple it is). A dot product is two vectors on the same plane and returns a scalar quantity. A cross product is those same two vectors but includes a vector perpendicular to both. ie as per angular momentum (torque). http://tutorial.math.lamar.edu/Classes/CalcII/CrossProduct.aspx Please note the dot product on you 3 by 3 matrix is always on the diagonal, the cross products fill the other slots. The site explains it well. One lesson I've learned over the years on various forums. A large number of posters tend to reject what they don't understand. More often than not once they understand what they rejected. More often than not they then accept it. I'm hoping once you see how useful vector calculus is including tensors this may be the case.

The error correction messages are of more exacting detail than the previous software as well. Now the error messages provide a direction in the error string involved in more complex latex forms.

Interesting reading thanks for sharing, these papers will help my current modelling.

Yep its taking objects and using Newtonian scales to measure the force when the object collides with a plate as one exsmple. There is a test you can perform at home. In Industrial tests one example is smashing cars against a force plate. Done every single day lol.

Here Pay attention to this key element in Kinetic energy. The kinetic energy of a moving object is equal to the work required to bring it from rest to a velocity. So average velocity is useless to us. You want to calculate how much work the bullet delivers to the wall it hits. You need the amount of work if takes to move an object from rest to the velocity at the time of impact.

I guess you didn't understand about syntax. It isn't the sites fault when you write ke=mom+va where you intention for va is average velocity. The correct mathematical syntax is ke=p+v_a the subscript allows one to seperate different identical variables. This avoids the confusion I had when I first read your post as va means velocity times acceleration. Had you properly written your mathematical expressions correctly in the first place, I would not have mentioned Dimensional analysis. That is your error not the sites nor mine. Swansont already informed you that there is no linear components in an angular momentum system where the conservation of angular momentum is defined. Your formula will not work on angular systems. The fundamental mistake you've made however is that your not paying attention to how kinetic energy is defined. ke= net force*displacement

So your going to rewrite physics and mathematics just because your too lazy to learn. Got it Thanks for wasting our time

Lol +1 on that glanced at it at work

Yes we are talking about probability distributions as a function. The two detectors are your observers, Though there is single detector variations I believe on Bells. All observers interact, all interactions cause interference. This is the measurement problem of the HUP. Though the HUP is also a fundamental that exists even if measurements are not being taken. One can correlate if measurements taken on Alice detector affect measurements taken on B detector by comparing the statistical trends between detector A and B. If a correlation exists then the two data tables will have in essence constructive probability (positive) trends. Hence strongly correlated, A has a strong correlation with B. If the trends are opposite ie as one rises the other decreases this is still a correlation but a negative one or more accurately A has an inverse dependance on B and vise versa. IF the two datasets have no symmetry in their trends, ie one trend stays constant while the other changes then you have no correlation. There is no dependancy between A and B In Bells we are seeing if these trends exist that could be attributed to a hidden variable dependancy but one must also look for trends in a time dependant manner. ( After all we want the time dependancy ) (the above is a bit of an oversimplification), The point being correlation functions do not identify cause, it identifies the trends in datasets, graphs etc, it tests if one dataset has any dependancy on another dataset. Those trend comparions form your correlation probability functions with polarity angles. As we are also testing if their is a dependancy on distance between the two detector results. so the time dependancy and angles is of crucial importance. Bells is a particular application of statistical dependency, The essence of Bell’s theorem is that the function P(a| b) has distinctly different dependences on the relative angle between the analyzers for a local hidden variable description and for quantum mechanics. PS side note we already have one dependency but it a dependency of a past interaction. The time of entanglement and the conservation of spin when the two entangled particles are first created. (This however is a seperate correlation function than the hidden variable correlation function, ) Though different functions may be related.

That does clarify your approach, thanks for that. Well understanding how statistical mechanics is applied to the correlation function in Bell's is useful in seeing how it is applied to the two detectors. Truthfully a solid route of study is precisely how correlation functions are defined under statistical mechanics then under QM/QFT applications. The Pearson correlation function I mentioned earlier is useful to understand how they operate. At least for approximately linear correlations. Obviously understanding the above applies to any type of correlation function