Wormhole Metric...... How is this screwed up.

[Mordred]

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.

Edited November 27, 2017 by Mordred

[SuperPolymath]

9 minutes ago, Mordred said:

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.

There is no way to make that work when it comes to any Geodesic equation of motion. It doesn't take a mathematician to figure that one out.

The mandelbrot set, infinite as it may be, was used for making more precise finite measurements  Even for something as close to particle physics as the electrical pathways in telephone cables across an entire grid.

You don't work fractal geometry but I've cited three articles that show how this is done for particle physics

[Mordred]

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.

Edited November 27, 2017 by Mordred

[SuperPolymath]

You don't think it's possible that's you've been taught the wrong way? That the standard is not really all that accurate to the way things really are? It's actually more probable than not, in Einstein's time math was not having it's limits tested by fractals - so all the math we use for modern physics isn't even close to representing nature under the Planck length, where it becomes more necessary as quantum gravity is being explored

Fractal cosmology is a minority approach. I'd seriously consider learning more about it for your personal research

Edited November 27, 2017 by SuperPolymath

[Mordred]

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.

Edited November 27, 2017 by Mordred

[SuperPolymath]

26 minutes ago, Mordred said:

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.

Okay, now how does this pertain to fractal geometry, specifically non-static quantum gravity waves seen in scale relativity, which isn't so much GR as SR

Moreover,SR beyond the speed of light

Because that's what's really going on down in the "quantum" world you know. It's puppet is 4 fundamental interactions, not the other way around. & this is actually supported by observation

[Mordred]

 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-

[SuperPolymath]

8 minutes ago, Mordred said:

 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

 

Field treatments need to be held accountable to the physical world, not the other way around. And if the physical world has infinite motion of infinitely tiny bodies (particle waves, the energy that energy releases) infinitely beyond the Planck length & time, where lorentz transformations need to he used for SR in quantum gravitational interactions, than you could be doing all of this wrong. This really aught to be looked at, QM really really needs to be reconsidered.

Edited November 27, 2017 by SuperPolymath

[Mordred]

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]

Just now, SuperPolymath said:

Field treatments need to be held accountable to the physical world, not the other around. And if the physical world has infinite motion of infinitely tiny infinitely beyond the Planck length & time, where lorentz transformations need to he used for SR in quantum gravitational interactions, than you could be doing all of this wrong. This really aught to be looked at, QM really really needs to be reconsidered.

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?

[SuperPolymath]

12 minutes ago, Mordred said:

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

H^=ℏw(a^†a^+12)

the a^† is the creation operator with a^ being the destruction operator. H^ 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. ℏ is the Planck constant (also referred to as a quanta of action) more detail later.

 

Heisenberg Uncertainty principle

Δx^Δp^≥ℏ2

 

x^ is the position operator, p^ is the momentum operator. Their is also uncertainty between energy and time given by

 

ΔEΔt≥ℏ2 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

 

E=ℏw

 

Another key detail from QM is the commutation relations

 

[x^p^]=x^p^−p^x^=iℏ

 

Now in QM we are taught that the symbols φ,ψ 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

 

[x^p^]→[ψ^(x,t),π^(y,t)]=iℏδ(x−y)

π^(y,t) 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 x^ 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

 

L=T−V

 

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

 

S=∫Ldt

 

the range of a force is dictated by the mass of the guage boson (force mediator)

ΔE=mc2 along with the uncertainty principle to determine how long the particle can exist

Δt=ℏΔE=ℏmoc2 please note we are using the rest mass (invariant mass) with c being the speed limit

 

velocity=distancetime⇒Δx=cΔt=cℏmc2=ℏmc2

 

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 L=T−V 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

 

ddt∂L∂x˙−∂L∂x=0 the dot is differentiating time.

 

Consider a particle of mass m with kinetic energy T=12mx˙2 traveling in one dimension x through potential V(x)

 

Step 1) Begin by writing down the Langrangian

 

L=12mx˙2−Vx

 

next is a derivative of L with respect to x˙ we treat this as an independent variable for example ∂∂x˙(x˙)2=2x˙ and ∂∂x˙Vx=0 applying this we get

 

step 2)

∂L∂x˙=∂∂x˙[12mx˙2]=mx˙

 

which is just mass times velocity. (momentum term)

 

step 3) derive the time derivative of this momentum term.

 

ddt∂L∂x˙=ddtmx˙=m˙x˙+mx¨=mx¨ we have mass times acceleration

 

Step 4) Now differentiate L with respect to x

 

∂L∂x[12mx˙2]−V(x)=−∂V∂x

 

Step 5) write the equation to describe the dynamical behavior of our system.

 

ddt(∂L∂x˙−∂L∂x=0 ⇒ddt (∂L∂x˙) =∂L∂x⇒mx¨=−∂V∂x

 

recall from classical physics F=−∇V in 1 dimension this becomes F=−∂V∂x therefore ∂L∂x=−∂V∂x=F we have mx¨−∂V∂x=F

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?

I think we're miscommunicating here. I'm saying that no field theory was designed for interactions beneath the Planck length. Becaus

[Mordred]

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

Edited November 27, 2017 by Mordred

[SuperPolymath]

5 minutes ago, Mordred said:

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

I know, & yet might thread is talking about particles as euphemisms for microverses in hypertime made out of tiny bodies in accelerated SR motion, more of the same. The only thing like that mathematically was the madbelbrot set. This would indeed require math to define, but certainly not anything that's used for the standard model.

Say there's a possibility, & there is one, that this is how the universe is, that Zeno's paradox isn't a paradox but a truth, even the smallest possibility is worth investigating

 

Edited November 27, 2017 by SuperPolymath

[Mordred]

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.

 

 

Edited November 27, 2017 by Mordred

[SuperPolymath]

2 minutes ago, Mordred said:

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.

 

That's exactly it, we could really be overcomplicating things with conventional equations like these, something totally different would need to be utilized in defining a microverse theory. Something more like fractal geometry

[Mordred]

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.

[SuperPolymath]

12 minutes ago, Mordred said:

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

There are other ways than what you're familiar with, ie field theory, string theory, etc that are better geared towards my potential microverse theory

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3866471/

http://www.scirp.org/journal/PaperDownload.aspx?paperID=72482

https://arxiv.org/pdf/hep-th/0007224

[Mordred]

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

 

Edited November 27, 2017 by Mordred

[SuperPolymath]

7 minutes ago, Mordred said:

 

7 minutes ago, Mordred said:

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

 

 

Than why would those physicists bother making said equations??

I looked at the dates of those articles. This stuff is newer, a LOT newer than what you've used in this thread.

[Mordred]

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

Edited November 27, 2017 by Mordred

[SuperPolymath]

So even though I don't work in the field you do, I obviously stumbled on to something with my ideas. What these articles as late as 2014 are touching on is related to what I've been trying to explain. So either I'm prescient, or I've looked into more than you think when I made that thread because that's exactly what they're resorting to

[Mordred]

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

Edited November 27, 2017 by Mordred

[SuperPolymath]

8 minutes ago, Mordred said:

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?

Which is exactly why I'd like you, vmedvil to stop brushing this off and take more time exploring these alternatives. Im reading you won't because I'm "not credible" but vmedvil actually shares more of my sentiments, especially regarding black holes

[Mordred]

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.

[SuperPolymath]

2 minutes ago, Mordred said:

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.

I'm not expecting anyone to do anything. I hope non-steady state model, the big bang singularity theory, action at a distance, & the Planck length get discredited for the advance of science. All I can do is throw in my two cents, thank you for at least looking at my ideas

[Mordred]

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