Mordred

Yes that's fine and thanks for letting us know. +1

LOL you know more than you realize. I often try to double check my statements just in case I make mistake, its one of the primary reasons why I often edit posts after my initial post.

In physics and mathematics a dimension is any independent variable. A coordinate axis qualifies as one can change a coordinate location such as x without affecting coordinate y. A string isn't some object but a convenient descriptive of waves. edit: I decided a little better clarity on string theory itself will be informative. The waves that string theory describes is specifically dealing with point-like particles of the standard model of particles. Spacetime itself if you use Virasoro algebra to describe the Lorentz group can have 26 dimensions. However dimensions as noted above is a math term described above. Here is the wiki link https://en.wikipedia.org/wiki/Virasoro_algebra

Oh man there's one I completely forgot about roflmao. Must have been over 20 years since I last seen this one referenced.

Here is one of the more modern experiments, where the two can be as closely investigated simultaneously as possible AFIAK. https://arxiv.org/abs/1205.4926 It is a variation of an experiment done by Wheeler to demonstrate the no hidden variable aspects. Details on this in the opening paragraphs. The pop media link also mentions that the measurement apparatus switches modes between particle or wave detection. so it isn't truly simultaneous just extremely close. This experiment however claims simultaneous photographing of the duality https://www.nature.com/articles/ncomms7407.pdf here is a pop media quick read https://phys.org/news/2015-03-particle.html

! Moderator Note No but I can I will consider that a request

I would like to add some details to the above. You are correct in the above in essence, however there is a more accurate way to think of the above that will help you better understand any field theory than just the spacetime field. First off a field in general is any assigned quantity/function etc assigned under (and this is important) a coordinate basis. In terms of quantity/function the three distinct types are scalar values or any function where the resultant is a scalar value, vector functions which have a magnitude or direction (including spinors) and tensor functions, which the previous aforementioned can also be tensors. (a rank zero tensor is scalar, rank 1 vector)., The spacetime metric 4d.. is a rank two tensor. However unless you get heavy into the math the important part is recognizing what defines a field. It is an abstract mathematical construct under a coordinate basis, however not specific to a chosen coordinate type...ie Schwartzchild, Kruskal, Euclid etc. (this is the basis of symmetry relations) for example any two identical vectors in magnitude and angle are symmetric objects at any coordinate. ( in this case identical). Now every coordinate is the assigned any of the above, either a scalar, vector or tensor field. In GR every coordinate is called an event. So really just think of spacetime curvature as a reflection of the values assigned at each coordinate. Now the literal definition of mass under all this is resistance to inertia change ( as per Newtons laws of inertia) in any and all field theories. Energy is just the ability to perform work, neither describe an object but they both describe specifically the field value at a given coordinate location. A large object will have numerous coordinates assigned to it. As they are also geometric objects ( can be described under a coordinate basis.) Now GR typically describes the worldlines, geodesics between two coordinates and the ratio of change between them. However this path can be curved. As mentioned mass/energy tells spacetime how to curve, so what does this mean... Well from the above we are probably measuring some set of vectors (ie falling object/ photon light path etc.) we could be using tangent vectors or other. Now in the 4D spacetime, time is treated as another coordinate axis. (key note time under GR is both coordinate time and proper time. ) The tau symbol [latex] \tau[/latex] being proper time https://en.wikipedia.org/wiki/Proper_time https://en.wikipedia.org/wiki/Coordinate_time as you can see from the links each event is described by coordinate time, now under SR this is the at rest frame described as Euclid as it follows Newton's laws of inertia to good approximation our everyday existence. The proper-time will follow either a curved or straight path. Its important to note that it is the proper-time that follows the geodesic line however at each coordinate (event/reference frame) the observer will observe a Euclidean geometry. It is when you compare two events/reference frames that a distinction becomes apparent. Hope this helps you take the next step into SR/GR or any field theory in general. Always keep in mind, spacetime curvature etc is a mathematical representation of change of a volume being measured or compared. Terms such as fabric/ manifold/fire bundles etc are simply descriptive assigned terms to help describe math relations between those field values.. LOL that list includes strings in string theory...ie the string is some waveform being described. Ratio of change between coordinate and proper time being an example of change occurring. Described as a geometry change.

No details, Monte Carlo is used in a huge variety of applications its quite possible to use it in radiation applications but you need to provide a possible application and methodology of how to do so with regards to your OP. Describe how you would apply Monte Carlo to radiology and discuss the possible advantage or goal of doing so. After all there is already considerable aspects where this is already been examined here is one example https://www.crcpress.com/Monte-Carlo-Techniques-in-Radiation-Therapy/Seco-Verhaegen/p/book/9781138199903

The Cooper pairing is a good analogy in this case, the solutions that led to the spin2 statistics of GR is directly related to the spacetime curvature aspects if I recall the proofs correctly. Its often difficult to find those proofs. The spin 2 ties with the stress tensor which is rank 2. This will correspond to the effective degrees of freedom which in the Feymann diagrams will be reflected in the vertices. If I recall correctly under spin1 the longitudinal components can be eliminated through gauge transformations. However I will have to double check that.

Thanks as well to Beecee for the additional links also to Q-Reeuss for the additional link regarding Svidzinsky's papers. All of them have been helpful. I had already made the connection from reading the original paper of this thread that the vector gravity model would have spin 1 statistics. As opposed to the spin 2 of GR. As mentioned earlier in this thread vectors are rank 1 tensors which corresponds, also according to how the opening paper is presented the Graviton would need to follow the spin 1/2 rules being in his paper of the fermion family this would correspond to the SU(2) group under the Pauli matrixes. Fermions anticommute (antisymmetric) while bosons commute.(Symmetric) as per the Pauli exclusion principle. This will correspond the position and momentum operators of QM (QFT has different creation and annihilator operators) with which one being the field itself. Its easy to see that the challenges to a vector theory of gravity becoming fully validated as the more correct one will take a considerable amount of evidence. However be that as it may this is part of the scientific method to explore every possible method regardless of how remote until proven as not viable. The use of GW data is still in its early stages, it will take a considerable amount of time to develop well studied and fine tuned datasets. By fine tuned I mean well understood in terms of calibration issues, white-noise, false signals etc. The papers are all examining a limited dataset so there will be a period of contention as to how to account for all factors to get the most accurate readings. Alternative models actually enhance the rate this will develop as it places those datasets under a multitude of different examinations. One of the advantages of exploring all possibilities. Anyways all of Svidzinsky's papers are nowhere near conclusive enough with the available data to overturn GR at this time nor is it likely to occur too soon. The preponderance of proper examination process is lengthy, even with huge and long developed datasets, let alone a dataset with a limited duration such as GW measurement data. That being said its still enjoyable for me to examine a variation of a spin 1 field in this case applied to gravity. I have come across numerous variations of this over the years its part of the process.

Thanks for the additional articles, I figured there would be some results in terms of this model in regards to the measured GW waves. There always typically is papers and counter papers whenever you have any two competing theories where testable results come forth. In an earlier comment I made I had already noted that current datasets should already provide some of those tests. The issue will most likely take several years to resolve, in many cases the time it takes to prove or disprove a new theory can take several decades. I will read the additional articles after work. They also help confirm my understanding on the mathematic end. As previously mentioned the most thorough means to understand a theory is by direct study of its underlying math.

Thanks

I for one care little about the reputation system. I do thank you for sharing the article but give me the pleasure of examining it my own way. I have learned over 35 years of studying physics that one never understands a theory until he understands the mathematics of such. I don't ever follow the hype often accompanying a theory. Its far too distracting, when the real fun is actually studying it yourself in detail. How else can one truly understand the mind of the author who wrote it.

I will study the math directly from Svidzinsky's articles on my own thank you very much. Everything I have stated is implicit in his equations. I will use my own chosen methodology of researching his views and sharing my understanding of such. The equations are there... The words used to describe how a theory works in an interpretation of what can be mathematically supported. Far too often they distract from the inner workings of a theory and can lead to garden paths.

I rarely look at magazines with regards to physics, when I spend time on physics for light reading I typically hunt down a thesis paper on a given topic then immerse myself in the math. Researching any of it as I go along... lol. So sorry on not being able to help in that regard. However the Feymann lectures is a good blend as an aid to both the math with decent explanations though not a magazine... http://www.feynmanlectures.caltech.edu/

Well I now have a decent grasp of what he is doing in this paper. In essence he has taken GR spacetime geometry and broken down the action of that field into two separate fields field's. The Minkowskii field [latex] \eta_{\mu\nu}[/latex] with witch he has changed the dummy indices to ik. Nothing wrong with that they are dummy indices. His metric is done in covariant terms. He keeps the Minkowskii field Euclidean flat and overlaps it with a curved 4 vector field ([latex]A_k[/latex] that describes the multi particle motion. Naturally when you do this you require the transformation between them which can then and is described as another field. [latex](f_{ik})[/latex].Which is the the metric replacement for GR's metric tensor [latex]g_{\mu\nu}[/latex] The action of the field [latex] A_k[/latex] follows the principle of least action. However the particle motion does not follow the geodesics of the background geometry [latex] \eta_{ik}[/latex] which can readily be considered a preferred frame of reference as it is the most invariant reference. From my point of view... however be that as it may.. Instead of the particle following the metric tensor [latex]g_{\mu\nu}[/latex] as per GR his particles follow a metric independent path. The one performs a transform to correlate the differences between the metric and the particle motion. The [latex]A_k[/latex] 4 vector forms the (I usually call it the permutation tensor) [latex]h_{ik}[/latex] The singularity issues I am still working through however if my understanding is correct could amount to a similar technique used in LQC (Though LQC uses a wicks rotation) that of the advantage that anytime two lines cross ([latex] \eta_{ik}[/latex] and [latex] A_k[/latex] cross they form finite and determinable points of reference. Hence closing the group set to one of finite points only viable. This has an advantage on renormalization as finite sets are renomalizable by nature. Hence a commonly used methodology in applying an effective cut-off prior to singularity conditions. He doesn't have event horizons as he keeps the photon particle energy constant at the EH in so far as his redshift doesn't suggest the particle loses energy due to redshift but preserves its energy. This in turn has the consequence that the Chandrasekhar limit doesn't apply the same. However occurs at 35M. He has numerous solutions of GR and his theory as to numerous different situations where the two do not match and several that do. I can foresee another point of contention in that in this model the particle is not a field excitation from what I have discerned which can conflict from the QFT view. However only time will tell lmao side note he still follows the Einstein summation rules for the covariant and contravariant terms (as indicated by the indices).

! Moderator Note I believe we all prefer this in a more appropriate lounge joking aside lol. I now wonder if its red and shiny via a chemical reaction or other ? lmao

With regards to your quote, I've had plenty of thoughts on the [latex]A_k[/latex] vector field. Which as you mentioned would be a rank 1 tensor. I'm still going through his math with regards to his weak field approximation. The [latex]F_{ik}[/latex] replacement to [latex]g_{\mu\nu}[/latex] isn't a problem as its straight substitution. Where I am having difficulties is the structure of the [latex] h_{ik}[/latex] tensors with regards to the [latex] A_k[/latex] vector. Though its highly likely I may be overthinking the problem lmao its a bad habit of mine. Anyways to answer a previous question he has the particle velocity as a function of time and is utilizing the scalar quantities V and G to generate the new vector field from the Euclid field. However he is still using the spacetime coordinate system of the Minkowskii metric. Anyways the mathematics doesn't stray as far from GR as one might be inclined to believe from the descriptives. In many ways it amounts to whether or not one can reduce the GR rank 2 tensor to deal specifically with the permutations to the Euclid background to a rank 1 vector/tensor field from what I have determined thus far

I've run across some theoretical calc's for the BB GW waves but will have to dig them up. Hopefully I can locate them again located a paper by Kip Thorne see section 9.1 https://arxiv.org/pdf/gr-qc/9506086.pdf whether or not LISA will b able to detect the primordial GW waves according to Kip Thorne will depend on whether the event will generate a frequency band of [latex] 10^{-14} [/latex] however according to that same paper the odds aren't great as according to his research on the CMB (references in that paper) the frequency band could be as low as [latex] 10^{-18}[/latex] It would be impossible for LIGO to detect them or any other ground based detector however LISA has an extremely remote chance judging from this paper.

I liked your last post Studiot nice simplification

Simple fact is that ground based antennas will never be sensitive below 1 hertz due to seismic interference largely. Space antennas are free from this constraint and can achieve much lower frequencies [latex] 10^-4[/latex] to [latex] 10^-1[/latex]. Sensitivity involves how an antenna resonates with a frequencies amplitude. The other factor involved is noise levels. (signal to noise ratio). Some of those we have already mentioned. Now that being said LISA will be more sensitive at lower frequencies however will lose sensitivity at larger frequencies. As I previously mentioned the arm length is one of the criteria. This is part of the response to a given signal. For example the dimensionless amplitude h of a GW wave upon a (I will use a Michelson and Morley detector (most common example in documentation ad textbooks)is given by [latex] h=2\frac{\delta L}{L}[/latex] which is also the amount of strain. The path length difference between the two arms then becomes [latex]\delta L=2(\delta L_1- \delta L_2)[/latex] or shortly [latex] h=\frac{\delta L}{L}[/latex]then there is the incident angel and what percentage of the waveform is occurring. This means the latter formula is further modified by [latex] h=\frac{\delta L}{L}=h sinc(\frac{2\pi L}{\lambda})[/latex] you can find these formulas in numerous articles discussing LIGO or LISA detectors. However I will save you the trouble and simply post the reference I used to write this particular post. see chapter 4 of how LISA calculates its sensitivity. The above formulas are from that chapter....They are largely the same in any laser interferometer article... https://lisa.nasa.gov/archive2011/Documentation/sts_1.04.pdf

Well regardless of your opinion I see little value in his article. I formed my own opinion of it via my own reading and study of his article. I am already familiar with the GW plotter site. As far as sensitivity goes I can literally get you papers that also state that LISA would be more sensitive. One of those papers contains the original formula I provided. The paper itself is specific to a lecture on GW waves and contained that rough [latex] 10^10[/latex] back of the envelope calculation. Here is NASA'a quick rundown on its precision. "These signals are extremely small and require a very sensitive instrument to detect. For example, LISA aims to measure relative shifts in position that are less than the diameter of a helium nucleus over a distance of a million miles, or in technical terms: a strain of 1 part in 1020 at frequencies of about a millihertz. " https://lisa.nasa.gov/ In essence it follows precisely what I am stating. The detector will be able to detect a change many orders more fine that LIGO will. This isn't a mistake. Simple logic should tell you that if the signal strength is many orders weaker it will take a more sensitive detector to pick up that signal. A simple analogy is that if you have two digital multimeters and look at the specifications. The multimeter that that measure a microvolt will be more sensitive than one that can only pick up the Millivolts range. But hey if you wish to buy that low grade DMM feel free lol. Its also a simple logic that a signal with a stronger radiated power will be easier to detect....the second formula directly correlates to that radiated energy. Obviously you will not grasp the relation between frequency and the energy of the signal.

yes however rapidity includes acceleration change. The acceleration change from constant velocity for the travelling twin will generate a hyperbolic rotation on the spacetime diagram. side note once you accelerate you are following a different geodesics. I won't go into great detail on how this rotation is shown on the Minkowskii tensor but simply state that the tensor undergoes a rotation.

There is a simplified example showing the Minkowskii spacetime diagrams with a brief example of the Hyperbola involved. See the hyperbola in invariance and on https://owlcation.com/stem/Minkowski-Diagram a little side not the twin paradox with the turnaround twin would generate a similar hyperbola the plot would look much like c^2/C^4 if you run through the twin paradox calcs see 2d plot. The point of the acceleration change in direction lead to the rotation on that plot https://www.wolframalpha.com/input/?i=plot+c^2%2FG^4 edit :{later correction to last post } -oops I made a mistake to that plot had the powers inverted...the space and time coordinates would fall on the hyperbola [latex] x^2-c^2\tau^2=\frac{c^4}{g^2}[/latex] Lewis Ryder has how this is derived from the 4 momentum, If requested I can latex in his solution from the Minkowskii line element [latex] ds^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/latex]

Well I for one cannot fathom how his 85% dark matter, 15% baryonic matter, universe doesn't instantly collapse at time of the BB. His negative energy gravity doesn't account for the detail that gravity is a vector that leads towards mass. I don't really buy his longitudinal component of gravity as being the source of DE. Particularly since the amount of DM and baryonic matter has an equation of state of w=0. He uses the argument that the gravitons generate positive pressure to give an equivalent radiation pressure term as the FLRW metric however in this case this pressure would reduce as the universe expands. I won't get into the significant differences his matter % would have on the CMB temperatures...