Mordred

We will see if we can get you past the first chapter. Ie to understand the Hausddorff set itself. In particular the Haussdorf jump from infinity to zero I myself will be using Kevin Falconers textbook of which I have a hardcopy of entitled Fractal geometry.

As long as your prepared to understand the mathematics gladly but keep in mind its far more involved than you may realize.

Tell you what, let me know when you take the time to study the topic. Till then I have better things to do than try to teach someone unwilling to listen to what is actually involved in the theory. You don't even wish to properly understand the model your trying to push on others which is a complete waste of time.

Yes I know and its chalk full of problems that you won't understand so would be a waste of time explaining to you would you like me to list some of the more common paradoxes that arise from it? ie HdeV paradox?

Trust me I have studied fractal geometry there is no danger in that happening

No your expecting us to do your work for you instead of taking the time to study the ideas your trying to push on us without understanding the first thing that is involved in the theory.

This from someone that doesn't even understand the basics lecturing someone with a master degree in Cosmology and a Bachelors in particle physics lol. Do you have any idea how foolish that really sounds? Are you even aware that Haussdorff's method starts from infinity to zero? let alone a Libshchitz mapping vs a bi-Libschitz mapping entails? Please don't bore me with foolishness

Not really I first encountered this stuff years ago when it first started getting published. Your not the first to show me this stuff believe me Its far more complex than you realize. I study every theory I ever encounter, its why I am so versatile in different metrics

Yes I already read these articles Do you even know whats involved in the Hausdorff Dimension? as per equation 1 and 2 of the arxiv article? If you think that's easier to use your barking up the wrong tree lol http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Shah.pdf

I already explained to you why that won't work. It won't work with path integrals. We don't make physics complicated by choice the complications arise when you start adding degrees of freedom in multi particle systems. Using a function that is fixed for every location simply will not work when every coordinate has a different energy density. That is simple logic http://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide01.pdf here this is about as simple an intro as I can find on a quick search into the basics for field theory.

Well I just posted the distinction between propogators and operators above, this has nothing to do with microverses. Quite frankly your understanding of String theory is seriously lacking if you believe string theory solves infinity problems. There is far more of them in string theory than under GR. The more curves you involve the greater the number of infinities that will arise on Fourier transformations. If you have trouble with understand basic field theory then it will be impossible to detail String theory which involves extra fields with different dynamics that are all interconnected over the same finite space. Here is the thing to recognize every treatment is a plot on a graph...so every treatment can be treated as a Fourier transformation.

Because one cannot measure any action below the Planck constant. Which is also called a quanta of action, this is the distinction between a virtual vs a real particle ie the internal vs the external legs on a Feyman diagram

Here perhaps this will help as it shows how QFT handles E=mc^2 (the full version) and shows the range of a force with the bosons mean lifetime m developing a list of fundamental formulas in QFT with a brief description of each to provide some stepping stones to a generalized understanding of QFT treatments and terminology. I invite others to assist in this project. This is an assist not a course. (please describe any new symbols and terms) QFT can be described as a coupling of SR and QM in the non relativistic regime. 1) Field :A field is a collection of values assigned to geometric coordinates. Those values can be of any nature and does not count as a substance or medium. 2) As we are dealing with QM we need the simple quantum harmonic oscillator 3) Particle: A field excitation Simple Harmonic Oscillator [math]\hat{H}=\hbar w(\hat{a}^\dagger\hat{a}+\frac{1}{2})[/math] the [math]\hat{a}^\dagger[/math] is the creation operator with [math]\hat{a}[/math] being the destruction operator. [math]\hat{H}[/math] is the Hamiltonian operator. The hat accent over each symbol identifies an operator. This formula is of key note as it is applicable to particle creation and annihilation. [math]\hbar[/math] is the Planck constant (also referred to as a quanta of action) more detail later. Heisenberg Uncertainty principle [math]\Delta\hat{x}\Delta\hat{p}\ge\frac{\hbar}{2}[/math] [math]\hat{x}[/math] is the position operator, [math]\hat{p}[/math] is the momentum operator. Their is also uncertainty between energy and time given by [math]\Delta E\Delta t\ge\frac{\hbar}{2}[/math] please note in the non relativistic regime time is a parameter not an operator. Physical observable's are operators. in order to be a physical observable you require a minima of a quanta of action defined by [math] E=\hbar w[/math] Another key detail from QM is the commutation relations [math][\hat{x}\hat{p}]=\hat{x}\hat{p}-\hat{p}\hat{x}=i\hbar[/math] Now in QM we are taught that the symbols [math]\varphi,\psi[/math] are wave-functions however in QFT we use these symbols to denote fields. Fields can create and destroy particles. As such we effectively upgrade these fields to the status of operators. Which must satisfy the commutation relations [math][\hat{x}\hat{p}]\rightarrow[\hat{\psi}(x,t),\hat{\pi}(y,t)]=i\hbar\delta(x-y)[/math] [math]\hat{\pi}(y,t)[/math] is another type of field that plays the role of momentum where x and y are two points in space. The above introduces the notion of causality. If two fields are spatially separated they cannot affect one another. Now with fields promoted to operators one wiill wonder what happen to the normal operators of QM. In QM position [math]\hat{x}[/math] is an operator with time as a parameter. However in QFT we demote position to a parameter. Momentum remains an operator. In QFT we often use lessons from classical mechanics to deal with fields in particular the Langrangian [math]L=T-V[/math] The Langrangian is important as it leaves the symmetries such as rotation invariant (same for all observers). The classical path taken by a particle is one that minimizes the action [math]S=\int Ldt[/math] the range of a force is dictated by the mass of the guage boson (force mediator) [math]\Delta E=mc^2[/math] along with the uncertainty principle to determine how long the particle can exist [math]\Delta t=\frac{\hbar}{\Delta E}=\frac{\hbar}{m_oc^2}[/math] please note we are using the rest mass (invariant mass) with c being the speed limit [math] velocity=\frac{distance}{time}\Rightarrow\Delta{x}=c\Delta t=\frac{c\hbar}{mc^2}=\frac{\hbar}{mc^2}[/math] from this relation one can see that if the invariant mass (rest mass) m=0 the range of the particle is infinite. Prime example gauge photons for the electromagnetic force. Lets return to [math]L=T-V[/math] where T is the kinetic energy of the particle moving though a potential V using just one dimension x. In the Euler-Langrange we get the following [math]\frac{d}{dt}\frac{\partial L}{\partial\dot{x}}-\frac{\partial L}{\partial x}=0[/math] the dot is differentiating time. Consider a particle of mass m with kinetic energy [math]T=\frac{1}{2}m\dot{x}^2[/math] traveling in one dimension x through potential [math]V(x)[/math] Step 1) Begin by writing down the Langrangian [math]L=\frac{1}{2}m\dot{x}^2-V{x}[/math] next is a derivative of L with respect to [math]\dot{x}[/math] we treat this as an independent variable for example [math]\frac{\partial}{\partial\dot{x}}(\dot{x})^2=2\dot{x}[/math] and [math]\frac{\partial}{\partial\dot{x}}V{x}=0[/math] applying this we get step 2) [math]\frac{\partial L}{\partial\dot{x}}=\frac{\partial}{\partial\dot{x}}[\frac{1}{2}m\dot{x}^2]=m\dot{x}[/math] which is just mass times velocity. (momentum term) step 3) derive the time derivative of this momentum term. [math]\frac{d}{dt}\frac{\partial L}{\partial\dot{x}}=\frac{d}{dt}m\dot{x}=\dot{m}\dot{x}+m\ddot{x}=m\ddot{x}[/math] we have mass times acceleration Step 4) Now differentiate L with respect to x [math]\frac{\partial L}{\partial x}[\frac{1}{2}m\dot{x}^2]-V(x)=-\frac{\partial V}{\partial x}[/math] Step 5) write the equation to describe the dynamical behavior of our system. [math]\frac{d}{dt}(\frac{\partial L}{\partial\dot{x}}-\frac{\partial L}{\partial x}=0[/math][math]\Rightarrow\frac{d}{dt}[/math][math](\frac{\partial L}{\partial\dot{x}})[/math][math]=\frac{\partial L}{\partial x}\Rightarrow m\ddot{x}=-\frac{\partial V}{\partial x}[/math] recall from classical physics [math]F=-\nabla V[/math] in 1 dimension this becomes [math]F=-\frac{\partial V}{\partial x}[/math] therefore [math]\frac{\partial L}{\partial x}=-\frac{\partial V}{\partial x}=F[/math] we have [math]m\ddot{x}-\frac{\partial V}{\partial x}=F[/math] What do you think were modelling??? it doesn't matter what treatment you use, how the vectors work under physics is fundamentally the same. I could describe relattivity via LQC or QFT or under the classical regime and the end result will be within good approximation. Do you know the first thing about how infinities arise on any exponental curve on a graph? surely you at least studied grade 4 mathematics?

SR is a very special form of GR, ie under the Minkowskii ( Newton metric) it is one that requires constant velocity. No acceleration to maintain time symmetry any acceleration is a form of rapidity. This is all accounted for under GR as all frames are inertial. SR doesn't work well in field treatments because it doesn't account properly when you have curvature that causes rapidity. This is where the Principle of equivalence and the Principle of covariance comes into play under the kronecker delta vs the Levi Cevita connections. If you understood the math I posted the fundamental differences several posts back which neither one of you understood any of the involved equations. The full blown Einstein Field equations is where you see the fundamental differences in regards to how the stress tensor is involved in the zeroth, first and second order derivitaves. Zeroth order being the density, first order pressure, second order flux, 4th order vorticity. SR has far too many artifacts of the metric that is often misapplied beyond its range of applicability. You see far too may paradoxes from taking SR beyond its range of applicability. Google tidal forces, to better understand the Principle of general covariance as opposed to the Einstein elevator in regards to the principle of equivalence. Or a simple example take two falling particles, in the Einstein elevator those particles will maintain a parallel path as they drop (Euclid falt geometry detailed as the Newton approximation. However under the Principle of Covariance those paths will converge or diverge due to curvature. This is where your Schwartzchild metric if you want a reference see Master Geodesics. http://r.search.yahoo.com/_ylt=AwrBTvYycRtakm0A9JbrFAx.;_ylu=X3oDMTByOHZyb21tBGNvbG8DYmYxBHBvcwMxBHZ0aWQDBHNlYwNzcg--/RV=2/RE=1511776690/RO=10/RU=http%3a%2f%2fwww.physics.usyd.edu.au%2f~luke%2fresearch%2fmasters-geodesics.pdf/RK=2/RS=9wGlaQOcLTbwTfnsglPUeR.knyk-

No I haven't been taught the wrong way. GR 101 any field coordinate is influenced via the speed of information exchange with its neighboring location. The faster the particle moves the less time the field neighbor locality has time to affect the mean free path of said particle. In other words the entirety of a field never ever affects the particle simultaneously. So at every infinitisimal the particle number and species of every other particle within that specific locality will vary as the particle moves from A to B with a coupling constant limited by the speed of information exchange with its neighboring particles. This is precisely how time dilation and length contraction affects the mean flight time of said particle being modelled. It is not a global field influence but a simple application of the speed limit of information exchange with between particles within any given locality. This is where the mass term arises (resistance to inertia change) and how the coupling constants affect the mean free path of said particle along its flight trajectory. This is why the equations are time dependent at each locale. The greater the particle number density at each location, the greater number of particles that can influence that flight path.

In field treatments the function itself changes at every single coordinate. That is the literal definition of a field. It is an assigned function at every coordinate.

Lets put this into simple terms. Lets take the question , "what are the possible paths a particle will take to reach point B from A. try using a Mandelbrot function on this problem and every time you feed back the output of f(x) back into f(x) the number of possible paths will exponentially get discounted at each and every infinitesimal of the particle mean free path. That does us absolutely no good in regards to describing field kinematics via the Principle of least action. Which in essence provides a relation between the chosen path via the particles kinetic energy and the corresponding field potential. This field potential will vary at every infinitesimal location. So the path is never truly a straight line but is only approximately straight or curved. There is no way to make that work when it comes to any Geodesic equation of motion using the Mandelbrot set as it doesn't account for each and every field location in terms of the field potential at said coordinate. It doesn't take a mathematician to figure that one out.

Why would I use Mandelbrot sets when the Symmetry groups themselves do a beautiful job all on their own. There literally isn't very many cosmology applications that I cannot define and describe via SO(10) it encompasses all the standard model of particles including the Higgs. This has nothing to do with ideas from laymen etc that is one of the most common cop out excuses we hear all the time on these forums. In all honesty the only ideas that ever gain any form of advancement is when the mathematics is applied. No one including Einstein instantly developed a single equation. Those pop media eureka moments come after years of hard and diligent work.

So you expect others to do your work for you? What good would that do? Your the one pushing this idea of yours yet expect others to do your work in producing a model using the Mandelbrot sets. It doesn't work that way. I have my own research interests and models that I develop without any assistance from others. I have been working on Higgs field applications to the FRW metric for over 4 years now. Yet you expect to take the easy route?

Like I recommended earlier that will require you to open a separate thread to avoid forum rules violations on thread hijacking then I will gladly help you understand the Mandelbrot sets.

Which does no good unless you can apply the mathematics to all those images to show how to mathematically define and describe each image. Even under the Mandelbra sets. You have the mathematics that apply to simply the pixel coloration.

No I am teaching the proper method. Scalars, Vectors and spinors under symmetry... Simple That is what is involved in group theory and all that fancy notation Dubbelosix posted.

No it is not. Math is a lanquage with precision. Attempting to push your personal ideas is also a very bad move. You would be much better off if you study the math involved under physics before trying to push your personal conjectures. All your doing is providing misdirection and distractions that will mislead other serious posters who wish to properly learn physics. Quite frankly you would be better off studying some of the mathematical detail I have been posting including those references.

Polymath, you really shouldn't be giving advise on how physics works when you admit you don't understand the mathematics. That is like taking advise on surgery from a Carpenter.

OK I can see I have a bit of work cut out for me here. OK lets start with the problem of "Where does the energy come from". Well energy is simply a property that is defined by the ability to perform work. So it doesn't need to come from anywhere, it doesn't need to be created but simply emerges for various applications. Start with Potential energy: "In physics, potential energy is the energy possessed by an object because of its position relative to other objects" https://en.wikipedia.org/wiki/Potential_energy So by merely changing the position of one object compared to another I change the potential energy.... Kinetic energy: "In physics, the kinetic energy of an object is the energy that it possesses due to its motion" https://en.wikipedia.org/wiki/Kinetic_energy Now what about mass? Mass "is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied" https://en.wikipedia.org/wiki/Mass So looking at those statements Does energy need to exist in the first place or does it simply develop as field anisotropies develop via potential differences between two or more measurement points ? much like voltage in electrical circuits? Now as for the universe temperature. There is a very important relation between the density of particles in a given volume. This is simply the ideal gas laws in play. Yes pv=NRT. If you take x number of particles and compress them, the temperature will increase. To do otherwise would violate the laws of thermodynamics... In Cosmology applications the temperature follows a very interesting relation it is the inverse of the scale factor. [math]a=\frac{1}{T}[/math] that is a direct application of those ideal gas laws I just mentioned above. The question of the laws of physics becoming invalid in BH's depends on how one defines those laws of physics. In mathematical precision its when symmetry can no longer be applied. It would take a bit to fully describe that under math as it requires an understanding of various notations many aren't accustomed to but if you like I can readily post the mathematical descriptive.