Mordred

The same degrees of freedom still exist. What your describing is the changes within the electromagnetic degrees of freedom. Not the number of degrees of freedom.

No how QED handles fields is based upon the gauge boson (exchange particle for electromagnetic force). This is the photon, but the photon itself has no charge itself it merely exchanges the charge from one charged particle to another. An electromagnetic field is comprised of a virtual (off shell ) photon at every point in space, first you set a baseline value for that field (zero or non zero). Then introduce your influence (charged particles). The photon being the mediator boson transfers the charge from one particle to the other on that field. But in itself the photon causes no direct influence upon the field ( other than its role as the mediator boson)

To expand on Swansorts reply, there is no hard and fast cross over point. Every equation in physics is a reasonable approximation. For every day applications on Earth Newtons laws are of a high enough degree of accuracy that we don't need GR nor SR. Until you get closer to Mercury Keplers laws are accurate to match observational evidence. While GR is more accurate, Newtonian math works fine. For example do you need to know the rate of time at your head is different than at your feet when you won't notice the effect over a thousand years? GR and SR doesn't ignore Newtonian physics such as centrifugal acceleration. Rather it modifies the observer coordinate changes. an oversimplified way of thinking of this is Newton assumed time was a constant. SR doesn't. Without time dilation effects spacetime is just space as time isn't used as a vector coordinate. This is what is termed Euclidean coordinates (geometrically it's equivalent to Cartesian coordinates, visualize a flat map.) When you add the time component as not being constant but light being constant to all observers. The geometry of the coordinates of the map must change, (length contraction). The map becomes curved like a globe (polar coordinates). For the Euclidean to polar coordinate rules Google Lorentz transformations. If you use a Lorentz factor calculator and play with the numbers, you can a better feel for when you may wish to use GR or Newton. ( This is what I did when I first started learning GR) Now the reason I asked you to start this thread, from a previous thread you asked a question on geodesics and acceleration. Geodesics are specifically falling objects or objects in freefall. Think of it this way if your a rocket or object that generates its own acceleration you can choose whatever path you want. However a freefall object must follow the spacetime curvature geodesic. I find myself posting these metrics repeatedly, but if one can follow them the important transformation rules from Euclidean to polar coordinates are detailed. (Newtonian to spacetime curvature Lorentz transformation. First two postulates. 1) the results of movement in different frames must be identical 2) light travels by a constant speed c in a vacuum in all frames. Consider 2 linear axes x (moving with constant velocity and [latex]\acute{x}[/latex] (at rest) with x moving in constant velocity v in the positive [latex]\acute{x}[/latex] direction. Time increments measured as a coordinate as dt and [latex]d\acute{t}[/latex] using two identical clocks. Neither [latex]dt,d\acute{t}[/latex] or [latex]dx,d\acute{x}[/latex] are invariant. They do not obey postulate 1. A linear transformation between primed and unprimed coordinates above in space time ds between two events is [latex]ds^2=c^2t^2=c^2dt-dx^2=c^2\acute{t}^2-d\acute{x}^2[/latex] Invoking speed of light postulate 2. [latex]d\acute{x}=\gamma(dx-vdt), cd\acute{t}=\gamma cdt-\frac{dx}{c}[/latex] Where [latex]\gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[/latex] Time dilation dt=proper time ds=line element since [latex]d\acute{t}^2=dt^2[/latex] is invariant. an observer at rest records consecutive clock ticks seperated by space time interval [latex]dt=d\acute{t}[/latex] she receives clock ticks from the x direction separated by the time interval dt and the space interval dx=vdt. [latex]dt=d\acute{t}^2=\sqrt{dt^2-\frac{dx^2}{c^2}}=\sqrt{1-(\frac{v}{c})^2}dt[/latex] so the two inertial coordinate systems are related by the lorentz transformation [latex]dt=\frac{d\acute{t}}{\sqrt{1-(\frac{v}{c})^2}}=\gamma d\acute{t}[/latex] So the time interval dt is longer than interval [latex]d\acute{t}[/latex] transformation rules. Here is relativity of simultaneaty coordinate transformation in Lorentz. [latex]\acute{t}=\frac{t-vx/c^2}{\sqrt{1-v^2/c^2}}[/latex] [latex]\acute{x}=\frac{x-vt}{\sqrt{1-v^2/c^2}}[/latex] [latex]\acute{y}=y[/latex] [latex]\acute{z}=z[/latex]

While it's good your looking at the math I'm not confident your looking at the history of how these formulas came into effect. some of the changes you've made I can't see working out to observational evidence but that's tricky to determine due to the incomplete sections. Seems to me your modifying equations without studying the physics behind them. For example earlier this thread I posted a couple of links on recent tests of the gravitational constant. Which fine tuned the value to an extremely high degree. I need to ask how much do you understand on relativity which the FLRW metric derives from ? The reason I ask is there is some concerns I have that the equations you posted will alter the light paths from a near critically flat universe to one that I can't even describe as being homogeneous and isotropic. (Despite the fact your using equations that require a homogeneous and isotropic distribution)

Not quite, geodesics are for free fall. The subject for more detail is the equivalence principle https://en.m.wikipedia.org/wiki/Equivalence_principle If you want I recommend a new thread and I'll help you out with it if you need. Though it will have to wait till I land lol. (Not supposed to have cell phones going on flights hehe)

I'm going to reward a +1 to that response. Time dilation is a tricky subject to accept.

the short answer is no you can't puncture spacetime as it isnt a fabric. The OP can refer to the 'What is space" pinned topic on top. So other than showing the stress/momentum elements to the stress momentum tenser I'd say were done

This equation specifically described how energy density/pressure influence the stress energy momentum equation that tells space how to curve. I'll dig up some of the momentum transforms later on after my flight. Correct

Its the stress energy/momentum tensor that tells space how to curve. In the Minkowskii form the usual equation to describe this is [latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex]

not bad you have the concept. A better terminology would be the acceleration is an acceleration of the seperation distance, not the rate of expansion per Mpc. the universe will expand without DE, just to be clear the DE is needed to expalin why the rate between galaxies or Observable universe radius isnt slowing down. we can measure a relative velocity faster than c above the Hubble horizon which is c* age of the universe. Yuo already know recesive velocity is only an apparent but not real velocity. well done. +1

actually I gave you the formulas to understand DDE, including the steps. That was the discussion on redshift conversions. Every step you need to calculate DDE (Newtonian sense) from Luminosity is covered in this thread. On PR the only step missing is Mie scattering. As far as the hydrodynamic and magnetosphere I'm still working on a way to properly cover those and simplify at the same time. Granted I'm assuming you know angular momentum, vs orbits of you don't I'd advise a different thread. I can't teach all the physics involved. That's an unreasonable expectation. I can provide direction.

Not in argument with this reply but its handy for me to note in order to dig up the right metrics to show you... by the way option B is more agreed upon currently afiak. So this is one model for seperation to address eventually. At one time it as felt the density increased right up to the protostar. However later views and research now support magnetosphere seperation. How early this occurs will take some research. The other factor is heat convection.

Were talking of nebula in the sense of plasma within a galaxy, for example the Orion Nebula is only 1.35 light years from Earth. I is a star forming region. "The Orion Nebula is an example of a stellar nursery where new stars are being born. Observations of the nebula have revealed approximately 700 stars in various stages of formation within the nebula." https://en.wikipedia.org/wiki/Orion_Nebula that should answer your questions. Stars can and do form in any nebula with sufficient density provided some mechanism causes over densities to form. A common occurance is nearby supernova shockwaves.

Okay well the excel sheet is handy to get the feeling for the numbers. It doesn't particularly lead to understanding what those numbers mean. Nevertheless, as a lot of your posts are directly related to T Taurie stage. I would like to know what view you have on the accretion disk itself. A) the accretion disk increases in density right up to the protostar? B) or are you looking at a seperation via magnetosphere accretion theory.? The reason I ask this is for the luminosity functions. Now I assume your aware the inner accretion disk has a higher angular velocity than the outer disk. Also the mass density and temperature will follow a gradient. Ie no open regions. (Unless you count case b.) So taking that into consideration "How would you apply DDE ?" As Luminosity has a mass to luminosity relation https://en.m.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation It also has luminosity to wavelength relations that depend upon its spectral index. If the mass density follows a curve then the luminosity will as well (assuming same spectral index) If you think about this how can you apply the Poynting vector or DDE metrics without determining the nebula dynamics?

When asked what your goal was your response was Now how to you plan to accomplish this without understanding the metrics involved describing the accretion disk? here is a list of some of the formulas involved. https://astro.uni-bonn.de/~astolte/StarFormation/Lecture2012_PMS.pdf how many of these do you understand?

Then explain what your trying to accomplish. You kept pushing DDE, Poynting vectors etc throughout this thread. What does that have to do with how the Sun formed?

"Nebulae are often star-forming regions, such as in the "Pillars of Creation" in the Eagle Nebula. In these regions the formations of gas, dust, and other materials "clump" together to form larger masses, which attract further matter, and eventually will become massive enough to form stars. " https://en.m.wikipedia.org/wiki/Nebula Now ask yourself what caused a nebulae to collapse".? They can be balanced in distribution so never collapse. Leading theory with evidence support of iron 60 I believe it was (which can only be formed in super nova events) is a nearby super nova is the cause

You need to model a nebula in order to form a star/Sun. A) nebula density B) average density C) material type ie hydrogen, lithium deuterium etc. D) average blackbody temperature of nebula E) condensed anisotropy development F) Jeans equations (hydrodynamic) G) along with f cause of collapse H) isothermal sphere distribution of mass to protoplanetary disk. (Hydrodynamics) However right now you need to know the basic physics. We covered blackbody to redshift. We haven't gotten into shell theorem, Keplers laws in particular elliptical orbits Then we need hydrodynamic approximations (which involves mass/energy to temperature/pressure relations). star formation involves a lot of relations and knowledge.

I have no problem with that, nor did I state there isn't an influence. We showed that there is. However our goal is to model a nebulae. One isn't going to do that particle by particle. My suggestion is to start looking into metrics that will teach you how to model multiparticle systems. Then we can incorporate Poynting vector and possibly DDE into those metrics. That's the little trick with modelling. A model may or may not be correct and most can be improved. The techniques of those models can be used in adapting to a new model. We can continue doing the single particle influences now if you choose or later. Doesn't matter to me. I'm just here to help. Eventually though you Will need to learn hydrodynamics to accomplish what your after. http://blogs.hsc.edu/sciencejournal/files/2014/03/Chaudhry.pdf http://arxiv.org/abs/1008.2973 A particular direction is accretion theory.

Assuming an average movement of the dust is about the best you can do realistically. For example now that your more aware of the calculations involved. Ask yourself "How much difference can 0.00395 nm wavelength have on a dust particles movement" One joules/m^3 is equal to 6.24×10^18 eV One joule is equal to one Newton. so assuming 100% transfer to a 1 metre cubed body (unrealistic) 0.00395 nm corresponds to 3.1388*10^5 eV not even a Newton. a dust particle wouldn't get a full m^3 of that energy. It would only recieve a miniscule fraction from DDE. That's assuming 100% absorbtion. amazing what happens when you crunch the numbers. Poynting Robertson metric uses mie scattering, and luminosity. The above was the DDE effect itself. Even if we run through the calcs for Poynting Roberston. I think you will find the primary contribution to how planets develop will be more due to what's involved in density waves via Nebulae theory. DDE and Poynting vector would be minor players to the hydrodynamic influence. They may have influence but it's small comparatively. For your modelling, now that you have a better understanding I think you'll agree that a focus on understanding the influence of density waves may be your most applicable step towards your model. This is one of the reasons the astronomy textbooks cover density waves when explaining nebulae theory in particular when covering planetary formation. (The handy part of density wave hydrodynamics is that it's a multiparticle metric) it treats the dust in the same manner as an ideal gas. So the techniques and formulas used there will be extremely handy to model your multi particle system. I'm positive you'll agree it would be nearly impossible to model a nebulae particle by particle. So you will need the hydrodynamic metrics.

[latex]5.9958*10^{14}[/latex] Hz Close enough lol. My fault on that formula typed the wrong relation halfway through lol I fixed it. [latex]v=\frac{c}{\lambda}[/latex] Ok now you know the relations. After you calculate the DDE for a static observer, (handy for a reference). If the observer is moving toward or away from you will need to do vector addition. To calc the new redshift/blueshift. Now this far it's easy. What if the object is moving left or right? For that step we need a difference formula. I want you to look at transverse Doppler effect this entire page is important to understand. https://en.m.wikipedia.org/wiki/Relativistic_Doppler_effect Next work out the orbit of a dust particle, (remember it will probably be moving in the directory of the Suns rotation) Also probably elliptical. You now have the tools to model build DDE on dust. Keep in mind at a certain radius from the Sun DDE won't matter as it will get the energy from both sides of the Sun. Hope that helps, play around with the relations, practice conversions, then build you new skills into the full metric The blackbody temperature and these conversions will help gather data from datasets you may have but just had the wrong data type for your skill upon first reading. This will open up a larger volume of useful data.

[latex]f=\frac{c}{\lambda}[/latex] [latex]e=\frac{ch}{\lambda}[/latex]

You can for the purpose of learning choose rounded off values. At the moment were more interested in the steps themselves. Very good, remember to learn latex you can quote a post with a formula so do that on my post (it will help learn the rules and syntax) Here is some useful relations. [latex]\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}[/latex] Remember baby steps we will modify this formula for dust later. [latex]f=\frac{c+v_r}{c+v_s}f_o[/latex] c=velocity of waves in a medium Vr is the velocity measured by the source using the sources own proper-time clock(positive if moving toward the source vs is the velocity measured by the receiver using the sources own proper-time clock(positive if moving away from the receiver)

This one will work to start with. We will need to adapt this one later. Those values will work were just training on how to model build atm

yes in the case of the spectrum of our sun. and yes correct. now take the suns diameter calculate the radius and roatation speed to calculate the blueshift on one side then redshift on the other. Redo the above calc at 5800 k. when you do that you just calculated DDE influence from our sun today. post what values your going to use for rotation velocity, diameter and temp. first do a static observer. Don't worry this will get more complex as we go.