Mordred

Well unfortunately wave-particle duality is an extremely repeatable experimental certainty. Trying to seperate one from the other is akin to separating energy vs mass. This has even been photographed to an extent. http://m.phys.org/news/2015-03-particle.html Belief is well and good, but unless you back your modelling with the mathematics and experimental evidence does very little good. So please feel free to show how your adapting Kalazu Klein coordinates to your viewpoint of a particle. How does Kalazu Klien provide the necessary degree of freedom to allow particles that don't interact with the weak force and how other particles do so. Please show how this interaction geometric dimension does so. (Mathematics) preferred. Now as your viewing a particle as merely pointlike. (Like a ball). It seems your viewpoint of what spin is also requires clarification. I would suggest looking at https://en.m.wikipedia.org/wiki/Stern-Gerlach_Experiment it should be obvious from this that spin does not mean the particle is spinning like a planet etc. Which from your post above in your gears analogy you appear to describe. For example ask yourself this fundamental questions. Why can electrons only have two spin states 1/2 and -1/2? If they were truly ball like point particles they should be able to have as many orientations as a ball. (Take a ball place two dots on opposite sides). How many orientations can you place those dots? (Magnetic poles). This is where the image of spinning point like particles breaks down. An electron is either spin up or spin down. Not spin 20 degrees etc. Another aspect is that it takes an electron or any other spin 1/2 particle 720 degrees rotation to return to its original quantum state. Can you replicate this with that ball? Lastly spin meaning angular momentum never changes for a Particle it never speeds up or slows down. It's an intrinsic property for a particle.

It seems to me from reading the above is that your visualization of particles are bullet like. This isn't correct. Particles are excitations in a field. The field itself can be zero or non zero. The excitation is a deviation from that field. The dimensions are mathematical descriptions of those deviations. This webpage has a decent description of the extra dimensions in regards to Kaluzu Klien. Key note it's the number of coordinates to describe a location. https://plus.maths.org/content/kaluza-klein-and-their-story-fifth-dimension Terms such as axis, poles to flip etc may be the cause of how I read the above.

Ooh boy, I got a bridge to sell you. Real cheap in Brooklyn. If I post it on Kijiji will you buy it? Point being don't believe everything on the web

No. Its explainable via physics and replicatable via physics. We have the ability to easily produce entangled particles. Don't take your understanding from pop media literature. There's more false hocus pocus in those write ups than reality.

You didn't catch the full correction on the first equation. Completely replace dv=pdf with DU=pdv. It's understandable your confused there. (For some dumb reason I typed f again Grr).{dumb spell check on phone} [latex]DU=pdV[/latex]. Here it should read as follows with the corrections. I will add a few details. First take the first law of thermodynamics. [latex]dU=dW=dQ[/latex] U is internal energy W =work. As we dont need heat transfer Q we write this as [latex]DW=Fdr=pdV[/latex] Which leads to [latex]dU=-pdV.[/latex]. Which is the first law of thermodynamics for an ideal gas. [latex]U=\rho V[/latex] [latex]\dot{U}=\dot{\rho}V+{\rho}\dot{V}=-p\dot{V}[/latex] [latex]V\propto r^3[/latex] [latex]\frac{\dot{V}}{V}=3\frac{\dot{r}}{r}[/latex] Which leads to [latex]\dot{\rho}=-3(\rho+p)\frac{\dot{r}}{r}[/latex] We will use the last formula for both radiation and matter. Assuming density of matter [latex]\rho=\frac{M}{\frac{4}{3}\pi r^3}[/latex] [latex]\rho=\frac{dp}{dr}\dot{r}=-3\rho \frac{\dot{r}}{r}[/latex] Using the above equation the pressure due to matter gives an Eos of Pressure=0. Which makes sense as matter doesn't exert a lot of kinetic energy/momentum. For radiation we will need some further formulas. Visualize a wavelength as a vibration on a string. [latex]L=\frac{N\lambda}{2}[/latex] As we're dealing with relativistic particles [latex]c=f\lambda=f\frac{2L}{N}[/latex] substitute [latex]f=\frac{n}{2L}c[/latex] into Plancks formula [latex]U=\hbar w=hf[/latex] [latex]U=\frac{Nhc}{2}\frac{1}{L}\propto V^{-\frac{1}{3}}[/latex] Using [latex]dU=-pdV[/latex] using [latex]p=-\frac{dU}{dV}=\frac{1}{3}\frac{U}{V}[/latex] As well as [latex]\rho=\frac{U}{V}[/latex] leads to [latex]p=1/3\rho[/latex] for ultra relativistic radiation. Those are examples of how the first law of thermodynamics fit within the equations of state. There is more intensive formulas involved. In particular the Bose-Einstein statistics and Fermi-Dirac statistics but the above serves as a good approximation. That should make more sense now again I apologize for the errors above and thanks again on the assistance in correcting. (You will note I added some missing details to assist) A further+1 for the last post. It was well thought out and polite. Thanks

You know the funny part is you kept posting fails dimensional analysis with a 57 page book on dimensional analysis without reference to any specifics. Nor did you state why it fails dimensional analyses. However no matter there was some mistakes. First equation noted should have been [latex]dU=-pdf[/latex] I did make a mistake on this equation in forgetting an overdot. [latex]\rho=-3(\rho+p)\frac{\dot{r}}{r}[/latex] Should be [latex]\dot{\rho}=-3(\rho+p)\frac{\dot{r}}{r}[/latex] So how was this derived? [latex]dU=-\rho dV[/latex] [latex]U=\rho V[/latex] [latex]\dot{U}=\dot{\rho}V+{\rho}\dot{V}=-p\dot{V}[/latex] [latex]V\propto r^3[/latex] [latex]\frac{\dot{V}}{V}=3\frac{\dot{r}}{r}[/latex] Which leads to [latex]\dot{\rho}=-3(\rho+p)\frac{\dot{r}}{r}[/latex] If I choose to latex this as [latex]\rho=\frac{M}{4/3\pi r^3}[/latex] that's my choice not yours. Anyone can see it's the same as [latex]\rho=\frac{M}{\frac{4}{3}\pi r^3}[/latex] Missed a term [latex]\rho=\frac{dp}{dr}\dot{r}[/latex] and missed the minus sign [latex]\dot{r}=-3\rho \frac{\dot{r}}{r}[/latex] Last noted equation I missed a term. Comes from posting from a phone at 2am. [latex]c=f\lambda=f\frac{2L}{N}[/latex] Next time try exercising a little diplomacy. I don't mind mistakes pointed out in my latex or posted formulas. However you can keep the attitude about it at home. Thanks for pointing out the errors. Next try a little diplomacy. PS I'm sorry you have a problem with thermodynamic applications in Cosmology. However that is the way it is. Edit: seeing as you did find the errors I'll grant a +1

Maybe if you see the pv=nRt used in a point slide lecture note you will learn to listen. http://www.google.ca/url?sa=t&source=web&cd=2&rct=j&q=equation%20of%20state%20cosmology%20pv%3DnRt%20pdf.&ved=0ahUKEwjt3tGxnrzKAhXrn4MKHd8KC9QQFggbMAE&url=http%3A%2F%2Fwww.ir.isas.jaxa.jp%2F~cpp%2Fteaching%2Fcosmology%2Fdocuments%2Fcosmology01-05.pdf&usg=AFQjCNFB61v07XFKiEK2Oe9wYZmwX8d0xg&sig2=_7QjNO2IeKppzI6jnDMhBw "Fundamentals of Cosmology 5, the equations of state" page 7. By the way in case your not aware [latex]pv=nRt=nkt[/latex]. The latter being an adiabatic fluid.

Carrock you obviously have some difficulty seeing the ideal gas law relations involved. Might I suggest picking up a textbook.... In one of the other posts I posted you a few references. You obviously didn't read... Instead you choose to bounce through posts with a rather rude format. So I will respond in kind. 1) is not the term equation of state not a thermodynamic (statistical mechanic terminology? "In physics and thermodynamics, an equation of state is a relation between state variables.[1] More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions. It is a constitutive equation which " https://en.m.wikipedia.org/wiki/Equation_of_state Why do you think the terms "perfect fluid and ideal gas laws are used in Cosmology applications? They are after all classical statistical mechanic terminology So you explain why Cosmology involves equations of state without classical thermodynamic relations. Go on give it a whirl I could use a good laugh. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) I explained in that other thread that I often post pv=nRt as it's a simple thermodynamic relationships. I choose the simple form as many cannot comprehend the advanced forms. Personally what mathematical forms I choose to use is my choice provided its accurate. Instead of responding in the other thread my reply to you. You choose to attack a difference thread. PS there is nothing wrong with posting a previous post in another thread. It's a time saver so I don't have to do a bunch of latex I posted you numerous formulas showing the terms pressure and energy-density. Whenever you have ANY system with pressure you WILL have temperature. The More energetic or kinetic energy the particles has the greater it's energy density to pressure ratio This is basic physics. No matter how many references I've posted to you in the past you've ignored seeing the ideal gas law relations. So do your own search. Google "Ideal gas laws cosmology pdf" Then Google "thermodynamics cosmology pdf"

Oh my what a load of crud. Completely incorrect. I've read some usupported Doozies over the years, but this one takes the cake. You obviously didn't read my earlier post on what is spacetime. As GR does not describe it as some elastic substance. That is a common misconception based on an analogy. That statement alone proves to me beyond any doubt that your knowledge on GR is via multimedia literature. Your length contraction mechanism describing the ruler includes no details on the different observers which is a premise in relativity. I highly suggest studying the actual mathematics involved. Start with SR before advancing to GR. The last post isn't even close to being anywhere near an accurate description. Terms like tension in space etc etc is complete and utter garbage.

On the subject of the OP. Here is a future test on The equivalence principle being launched in Apr 2016. http://www.zmescience.com/science/physics/microscope-satellite-mass-equivallence-0423423/ In case it wasn't mentioned Gravity Probe B. http://m.smh.com.au/technology/sci-tech/nasa-confirms-einsteins-theory-of-relativity-20110505-1e9et.html

Ok that's roughly what I figured. Lets explain spacetime curvature. First let's set some ground rules. You cannot measure gravity, mass etc on an empty volume. Nor energy. You must have something to measure. space is nothing but volume, that happens to have the standard model particles residing in it. So a gravitational field is a field of particles that we measure the influence of gravity upon. Now we have to set a baseline. Well a good baseline is the average mass/energy density of the universe. Exact value isn't important. We will use the Schwartzchild metric which sets this value as zero to start. One final detail. Energy density of a collection of particles can cause pressure along with the particles kinetic energy. Now the Einstein field equations has something called the stress/energy/momentum tensor. You heard the expression "mass tells space how to curve , space tells mass how to move". Well there is a nice formula that explains this. [latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}[/latex] [latex]\rho[/latex] [latex]T^{\mu\nu}[/latex] is the stress tensor. The subscripts are coordinates. p is pressure [latex]\rho[/latex] is energy/mass density. https://en.m.wikipedia.org/wiki/Stress%E2%80%93energy_tensor So in the presense of mass there is an influence on the gravitational field. (Particles that reside in that locality). That influence gets greater the closer to the source of mass. voila spacetime curvature due to mass. Which is nothing more than the distribution curve measuring the influence of gravity upon the particles residing in a given volume. It was never meant to state that spacetime was it's own fabric or mysterious substance

Newtonian gravity isn't wrong in everyday situations. It just doesn't work well in curved spacetime. However in Euclidean space it's just as accurate. I'm still waiting on what you understand as curved spacetime. By the way every aspect of relativity has been tested. Though length contraction being the least. Afiak

I have to ask Bjarnes Do you fully understand what is meant by curved spacetime? Or is your visualization based upon the common misbelief that space has a fabric like substance that can be curved stretched etc. You would be amazed how few understand what spacetime curvature really represents. (Those same people are usually the ones that feel relativity is wrong). So please don't be insulted, just describe what you think spacetime curvature is describing.

This would be true only if there is no expansion/contraction. However at no point in the Universe history has it not been expanding. Different rates of expansion but expansion nonetheless.

Roflmao

No no no. A billion light years is a unit of distance. Not years. During this time the universe has been expanding so the distance of the light path will be GREATER than 13 billion years

It is published information in the Planck 2015 dataset. The other reason is any good textbook discusses redshift and it's influence upon redshift. Sachs Wolfe effect for example takes advantage of those influences to give us greater detail on expansion as well as the CMB. In Matt Roose "Introductory to Cosmology" the axis of evil" was explainable before the Planck dataset was released. In textbook terminology it's called dipole anisotropy. Matt Roose has a good chapter on it. Any major dataset published will include the calibration data. Most ppl that read it tend to ignore this info. Rather dry and boring I guess.

Initial redshift will give us an estimated distance. Keep in mind both those articles I wrote several years back. Let's take that star example again. If Say that star was moving away from us extremely fast. One would think it's further away than what it really is. If it was moving toward you at the same speed you would think it's closer than it really is. (Based solely upon redshift measurement) I'm almost hesitant to answer this part given you tendency to get distracted. Yes you will measure different redshift to a certain degree at various points. Those variations are due to other redshift interference. (NO THIS IS NOT BIG NEWS). Any physicist working on the data knows what type of influences can be involved. So they will take other data to filter out those influences. Remember the Planck 2012 Right hemisphere "axis of evil". Where one axis appears hotter than the other.? That was simply due to not having enough filter to compensate for Earths movement. Calibration on the Planck data is published in their papers including the calibration settings. Several of their papers deals just with their calibration.

You can't rely on just redshift. Let's say I want to measure a star. First I know hydrogen gas a specific spectrum on the Rayleigh scale. So from this I can estimate the frequency of the emitter. Good so far now let's follow the light path from that star to Earth. First question to answer, is that light path a straight line? Surprisingly enough due to universe geometry influence the path can be curved. Just as spacetime curvature can alter the path of a light Ray. So we must compensate for this change. (Distance change in light path) 2) did the light path enter a gravity well? This causes gravitational redshift/blueshift. 3) what's is the stars movement compared to our. (Doppler shift) You cannot from measure alone distinquish cosmological redshift, from gravitational redshift or Doppler shift. You require further details and measurements to seperate how much each has influence upon your light Ray. For these reasons distance measurements requires mountains of data to fine tune them. They require multiple methods. Parallax being one of them. Here these will help. Site Articles (Articles written by PF and Site members) http://cosmology101.wikidot.com/redshift-and-expansion http://cosmology101.wikidot.com/universe-geometry

David you really need to grasp a few concepts. First redshift is only calculatable if you know the emitter frequency. (For this we note the Rayleigh scale on specific elements) Secondly there is several types of redshift. (Cosmological, gravitational, Doppler). Thirdly we must filter out our own environment influences ( galaxy, solar system and planetary movement). Local radiation etc. It took years of expiremental research to correlate the average redshift in the CMB. It took years of experimental research to develop the redshift formula. (Previously it was hypothesized as "tired light" or alternatively referred to as "spectral shift" As mentioned you cannot separate theory and evidence. Evidence is a fundamental part of a working theory This has more to do with how early can galaxies form than the CMB itself.

No they don't band the evidence to support theory. If evidence shows up that proves the theory wrong they rethink the theory. This has happened to me several times lol. I develop a hypothesis, work on the math. Look for evidence and experimental data. If I find data that conflicts I try to explain it with my hypothesis. If I cannot then I know something is wrong. So I try to figure out how wrong my hypothesis is. (Note at no time did I consider the above a working theory). One of the steps to test a theory is a diligent effort to prove that theory wrong. Otherwise you will never develop a strong long lasting theory.

Correct couldn't have explained it better myself

Yeah I am familiar with that thread. I'll take the word of professional peer review articles over a forum discussion any day. Particularly since Pioneer anomoly has been discussed to death in other forums I'm also a member of. A forum is a learning and teaching aid. One doesn't change a theory via a forum. You would need to publish in a peer review to hope to do that (Anyways this is off topic). Do you have further questions on measuring satellite distance,?

Just to note if you plan on tackling relativity. You better have conclusive experimental evidence. I saw the thread that was locked. For lack of such. The Pioneer anomoly for example was figured out to be caused by anisotropic radiation loss due to the crafts own heat. You can get the paper in the reference on this page. https://en.m.wikipedia.org/wiki/Pioneer_anomaly Just a side note forums are battered with posters that assume something is wrong, believe they have the solution but can't even do the mathematical side of the theory they are fighting against.

No matter how confident we are in any theory the scientific method always considers some error. No theory is ever claimed 100%. So we continue to improve our confidence in a theory.