Mordred

Combination of both. Your three spatial dimensions are always included but under the global geometry. String theory under groups adds mathematical dimensions to separately define smaller volumes under transformations for different overlapping fields. In essence different embedded geometries each describing a different field dynamic. The key is symmetry transformations. For example Kaluzu-Klien has you relativity degrees of freedom. (ct,x,y,z) Now Kaluzu adds electromagnetic charge to the above. Making the above 5D. If you add the strong force you need a minimal 3 degrees of freedom to define the interactions of the quark family. So now we have 8. Now add the weak force for another 3. 11 dimensions. Under groups the above is SO(3)×SU(2)×U(1). This is the majority of the dimensions in String theory but not all

The above not exact isn't inaccurate enough to correct. Heuristically describing fields as creating space is commonly written in literature just keep in mind space is just the volume. As for the Entanglement information isn't exchanged faster than c. That is a pop media misnomer that I would prefer to help you understand under a new thread in QM forum as its a bit off topic on this thread. Yes string theory has 13 dimensions. (effective degrees of freedom), There is also embedded mathematical geometry states (local etc)

A little scattered, but one or two good questions in this. Don't think of one creating the other. In expansion the fields can affect volume change. You don't create space, as space has no substance that needs creating. By this referring to universe from nothing models describing the quantum process in the expansion of our universe from BB. Other than the caveat above (I never liked the term "space created" too misleading) for the reasons above. Ok this is s very important question. In physics a dimension is an independant value. By this I mean this variable etc can change without changing any other values. This is also called a "degree of freedom" Now in mathematical treatments it is preferable to reduce a system to the minimal number of degrees of freedom as possible. An example is "Hilbert space" which reduces the degrees of freedom to 2 dimensions. It does so in essence by charge vectors and symmetry groups. So for string theory ext the higher dimensions correspond to effective independant degrees of freedom a system has. Here is a classic example. A robot arm that only move up and down has 1 degree of freedom. It cannot move up without affecting the distance from the bottom. Now if that arm can move up/down and left/right. We have an additional degree of freedom. Now we can also spin that arm without affecting the other ranges of motion. So now spin is a degree of freedom that requires 2 dimensions to mathematically define. (angular momentum)

Whenever I sit down to write any article including the two in my signature I end up learning 😁. Site Articles (Articles written by PF and Site members) http://cosmology101.wikidot.com/redshift-and-expansion http://cosmology101.wikidot.com/universe-geometry The top article is my first attempt at writing site articles. Took me 6 months to finally complete. The second one went smoother only 2 and I find its better written. The trick is removing ambiguous sentences etc. Its amazing how simple it is to miss imply. (last one has a page two link at bottom of page) Edit: Lol though there was a huge debate on the Cosmological redshift and gravitational redshift on the viability of being treated one and the same. Listening to numerous Ph.D's arguing the pros cons was definetely a learning experience. Took P. Allen and I some effort to reword the article to allow the possibility of both. P.Allen and I took on sections of the first paper then blended in the two different writing styles. I learned a lot since writing the first so have been considering rewriting the first article.

That would be a useful project for me to help others. I may just do that

terms like empty or nothing doesn't really exist in physics. You have a volume, you can assign coordinates or events with a value even if the value is zero. So now it has a field within that volume. A common term used being vacuum. Which quite frankly is falling out of favor to the term "potential " Vacuum causes to much misunderstandings.

Thanks glad to help. The reason I can do that is that I spent years understanding field treatments. Prior to attempting to simplify it for others. For example I am still trying to improve my understanding of this 1 article after 5 years reading it over and over again and of course applying the mathematics "Fields" - A free lengthy technical training manual on classical and quantum fields https://arxiv.org/abs/hep-th/9912205

I knew you did but the opportunity to define local and global fields was presented. So I took advantage of it for other readers.

I have a personal definition of reality. Some may not agree with it but it works for me. Real can be defined as any measurable quantity or object that all observers can agree on. Invariant quantities. Variant quantities being examples of observer effects due to location etc. That is about as far as I ever go to define reality. I leave the more abstract arguments to others 😎

I misapplied that last statement you must have volume or area to have a geometry descibed as a field. Thanks for the catch Didn't realize I mistyped that last sentence. Bells locality to nonlocality is certainly defined under fields however. In order to understand those two terms you have to examine how local is defined as a field. (local) is always a boundary confined field. Local fields can be embedded onto our arbitrary global fields.

excellent

Simply put you cannot have a field if you have no volume. Or technically volume or area for 2d fields

Yes expansion is governed by fields. a field can be described as a distribution of any arbitrary values. So one cannot state volume causes fields. The volume simply defines the volume of whatever values the field is describing.

Yes but a further caveat fields can be smaller system states. ie the region of measurable influence. So the strong force from a single particle does not extend to infinity as per electromagnetic or gravity. In this sense we can confine the strong force from each particle by measurable "action" which under QFT is your operators describing system state wavefunctions under field treatments. This is where the distictions "local and global becomes defined

Understood on the cross post. Glad to help. (I did add an edit on above on x post)

Anytime you are able to assign more than one geometric location. (object, event, coordinate) You can treat any set of values to the coordinates under a field treatment. That is really the only requirenent to have a field. A field is any collection of values described via coordinate/geometry. Glad you enjoyed this thread by the way. Space is just volume, fields are not required to have space. However once you have volume you can describe that volume as a field. A field is an abstract device that abstract device allows us to "map" variations. The term spacetime is a field treatment. Its one describing changes with our 3d volume by adding time as a vector to track different rates of information exchange between coordinates or events.

HUP is the Heisenburg uncertainty principle. In the virtual argument its categorized as complementary uncertainty in this arxiv. There is a chart on how different measurements, physical laws have been in essence worded to support the VR reality hypothesis. One primary distinction surprise surprise is our universe arises from nothing according to this paper. Also a multiverse must exist for VR to be possible https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/0801.0337&ved=0ahUKEwj50bycvfzUAhXo44MKHUzSBrw4ChAWCCswAg&usg=AFQjCNGChmNY9GJ5GU0fshkAL-6NuE4BsQ As this is philosophy I am positive there is counter arguments to the arguments used in the paper

essentially correct thus far The only way to understand the strain changes between the two arms is under 3 dimensional analysis. Replace the charges I used above with position. (though keep in mind I didn't include the ct coordinate for relativity in the above) keeping it as simple as possible. The 4th order is the transverse traceless gauge. (The traceless is a particular type where [latex]h_{\mu\nu}=0[/latex] in the transverse direction. One where the effective degrees of freedom reduce to 2. (see spin above) hence plane waves. The above is needed to understand that only the (+2,-2) spins provide the degrees of freedom but that is a full lesson unto itself. Spin 2 being (+2,+1,0,-1,-2) mathematically (+1,0,-1) factor out. The +2 and -2 is your two independant polarization states. some literature will describe a GW wave with the following added relation. "a GW wave has no dipolar moment as it propogates." Dipole moment has spin statistics (+1,-1) Pauli matrixes (2d Hilbert space) Euclidean space is 3d, which modelled under 4d is the Minkowskii matrix [latex]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex] Scalar is spin 0. That what is meant by that statement. The effective degrees of freedom due to spin for a GW wave is (2,-2). Now my advise to everyone not previously familiar with the above. Reread any references you like on the Quadrupole section. Including references already posted on this thread. In particular the Ferrouri vs Carroll links. PS the use of "q" is represents any charged field. A charged field is anistropic. An uncharged field is homogenous and isotropic. So any field can represented in the above by field charge values at each coordinate. Using Pythagous we only require 3 charge points to describe the square relation above as under GR the transforms preserve pythagous. Anyways under reductions transverse traceless describes the two polarization as the required two independant polarizations. (The proofs require considerable understanding of GR to make sense of)

I don't know maybe this will help. Not many understand what is meant by monopole, dipolar or quadrupole. So lets show the difference as simple as possible. A monopole is a scalar quantity. (no vector component) First order tensor 1d. q or -q using charge. A dipole is a vector component represented by a line between two coordinates. {q}-------{-q} the two charges are seperated distance if displacement depends on mass and acceleration relations. This is a Second order tensor 2D (Pauli matrixes are examples. A quadrupole is a 3d 3rd order tensor {q}------{-q} |,,,,,,,,,,,,,,,,| |,,,,,,,,,,,,,,,,| {-q}----{q} The tensor form is [latex]\mathbf{q}=\begin{pmatrix}q_{xx}&q_{xy}&q_{xz}\\q_{xy}&q_{yy}&q_{yz}\\q_{xz}&q_{yz}&q_{zz}\end{pmatrix}[/latex]

Tar field interactions can exhibit medium like properties particularly with f=ma relations. A medium is a specific type of field. (a matter field). The LIGO detector is a matter field, The GW wave can be characterized as a force field. When force fields interact with matter fields you will get medium like properties and dynamics. However when 1 force field interacts with another force field. The (electromagnetic) the dynamics are not identical. F=ma becomes less useful as there is no rest mass term. Forget ether the only way to understand how the different fields interact is to study the equations of state. ( Or if you want a more challenging route. The coupling constants and how they apply to field interactions.) Matter fields resist changes in inertia more than force fields as matter fields are more strongly coupled. The lasers and arms represent two distinct field interactions with a GW wave interaction. 1) Arms = matter+force field interaction 2) Lasers=force +force field interaction. the invariant (rest) mass of each field is distinctive so when a force vector from another field acts upon it. The Displacement must not be equal as the mass is not identical. The M$M was looking for interaction described by 1 but instead showed interaction 2. (highly oversimplified heuristic view)

Yes the characteristic hurdle I see he needs to change is how strain works. Yet we have tons of experience both in physics and engineering measuring strain.

Nice paper, thanks for sharing

You must describe the changes in coordinate of all axis at precisely the same time. The changes are NOT IDENTICAL. . Done I'm finished with you

Stupid as it is your not able to apply that to spacetime. No offense but that is the most insanely stupid argument I have ever heard on a forum. You cannot describe spacetime changes without coordinates.

Your point does not apply under GR. period. By the way when you measure your using coordinates. So you setup a premise "You cannot measure without coordinates " equals true. But then how do you apply that to spacetime "metric"?