Mordred

Ok it is obvious English isn't your primary language. However you have zero mathematics to explain your graphs. Secondly the term superposition refers to primarily probability wavefunctions under QED. A determined observable state is not a superposition state. Thirdly from what little I can determine from your rudimentary graphs your analysis is lacking in several details in terms of the magnetic moment. You should have an analysis from a detector in the x,y and z axis. Your analysis lacks the applicable range of possible orientations. My recommendation of applying the Maxwell equations still apply however I would like you to look into the stress energy momentum tensor for the electromagnetic field and its arrangement under geometry. You are correct that the electric field and the magnetic field is one and the same however those two fields are not symmetric. There is a 90 degree phase shift that must be accounted for. As well as the curl components. Your graphs are linear representations and do not satisfy the angular terms of the magnetic field. ! Moderator Note As I am now a participant in this thread I will no longer perform any moderator duties for this thread

All would be in a Bose condensate state ie thermal equilibrium but in that state they would have identical Compton wavelengths. They will still vibrate such as the harmonic oscillator. So they are never truly motionless regardless of how dense. Remember particles has no discernable volume. They aren't little corpuscular billiard balls of solid matter like. For example you can stack an infinite number of Bosons in the same space.

It was a proposed theory by Hoagland that was rejected by the scientific community. However the term hyperdimensional computing theory is widely used. https://en.m.wikipedia.org/wiki/Richard_C._Hoagland#Hyperdimensional_physics However I have seen the occasional string theory textbook use the term. Even as part of the title of the book.

From your question it sounds as you have a misunderstanding of what a dimension is under physics. A dimension is an independent variable or mathematical object. This is often also termed as an effective degree of freedom. For example the three spatial dimensions x, y,z can each change in value without changing the value of another coordinate. Time is given dimensionality if length through the ct interval gives a 4d. Higher dimensions such as string theory are topological in what is commonly called configuration space. The point like particle is given dimensionality of its path as described by its Langrangian.

This statement isn't entirely accurate. The FLRW metric is a GR solution of the weak field limit of GR. [math]g_{\mu\nu}= \eta_{\mu\nu}+h_{\mu\nu}[/math] The Schwartzchild metric is a common application of the strong field. The other common class of solutions being the vacuum solution. ( Though I do agree with your overall statements in your last post.) Edit should also note the energy momentum term being [math]T^{\mu\nu}=0[/math]

Correct I also have never seen any other symbol used. I learned instructional technique through the military. Visual aids was one of the numerous techniques taught as well as avoiding monotone speaking. An instructor that can verbally describe any lesson and sound enthusiastic about the subject helps to keep a student alert. The combination of the two plus interactive activity allows greater retention as it involves the numerous senses such as sight and sound etc. The demonstrations also goes along way to show the practical applications behind the physics lessons. This gives the student a greater awareness of how useful those lessons can be applied in everyday life. Another useful demonstration for gravity is to take a magnet placed on the ground or table. The a stick with two metal balls mounted with string at each end of the stick. Slowly lower the metal balls to the magnet and when the distance between the two metal balls begin to close in distance to each other. You then describe to the student the tidal force of gravity ( works well to describe how a centre of mass system affects freefall paths in parallel transport and how curvature affects parallel paths.). Lol I also often use a sink of water with semi bouyant particles of varying sizes to demonstrate density wave theorem for Spiral galaxies and the rings of Saturn. It greatly helps cut through some of the complex mathematics. It also makes the lessons more enjoyable for both student and instructor.

A tool to better help with the physics end of things is to use as many visual aids and simplified experiments as possible. For example Newton's laws becomes easy to visualize when you have a Newton spring scale. The more enjoyable a lesson is made through imaginative simple experiments the better the lesson sinks in. Something like GR would be trickier animations tend to help but a personal teaching aid I have used to help students understand the statement. [math] g_{\mu\nu}=\eta_{\mu\nu}+\h_{\mu\nu}[/latex] Was to take three clear sheets of plastic. Draw a Euclidean vector field on one sheet. Then draw a permutation such as a H+ gravity wave polarity on the second sheet then with the third sheet the resulting vector changes. Don't worry about exactness the idea is to get the generalized idea across.

I agree with Swansont on needing the SI units to delve into the cosmological problem. You should also avoid normalized units. You need the higher precision to equate to the extremely small value of the cosmological constant.

Well your going to have to be clearer on which cosmological problem your addressing. The cosmological constant has several problems associated with it. The problem you have been working on in the past is the problem of why the observed values are so small. Much smaller than the 10^120 originally predicted value. The other problem is the Coincidence problem which amounts to "why now" do the DM and DE values seem so close. The latter related to the fine tuning problem. The first link doesn't address either of these two problems. The second link is the same paper just on a different site. Thise links does you no good for the first problem. It doesn't even attempt to address the problem described in the wiki link https://en.wikipedia.org/wiki/Cosmological_constant_problem

In the first article do you understand what a mathematical coincidence is ? Let's define that term. "A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation " now given that definition does the first article make more sense when the author keeps referring to the pure numbers and the coincidence between the pure numbers ? https://en.m.wikipedia.org/wiki/Mathematical_coincidence

Excellent you got it in a nutshell and your welcome. The old data I mentioned involved various calculations such as the mentioned age of the universe but also the values in the matter and radiation equality. The latter affects the timeline from matter to Lambda eras. Though in the latter the switch from matter dominant era which is a point of decelerating expansion. To the Lambda dominant era which would have accelerating expansion would be roughly when the universe was 7.3 Gyrs. This varies according to datasets I've seen it as low as 6.7 Gyrs in some datasets. Anyways glad to see you got the necessary answer one other side point is the Hubble parameter is only constant at a particular time. For example at redshift z=1100 It would be roughly 22,900 times greater than the roughly 70 km/sec/Mpc value today. In point of detail even though the Hubble parameter is decreasing the universe expansion is accelerating when looked at the overall radius. This is a couple of main factors of the non linearity of the scale factor. Using Stretch which is 1/a in the Lineweaver Davies notation the evolution of the Hubble parameter as a function of Z is. [math]H = H_0 \sqrt{\Omega_\Lambda + (1-\Omega) S^2 + \Omega_m S^3 (1+S/S_{eq})}[/math] However a more versatile form is [math]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/math]

Agreed most likely adds additional complexity. Might dig further into it though just to satisfy my curiosity.

The origin is Tamara Davies doctorate dissertation paper. https://arxiv.org/abs/astro-ph/0402278 Here is a link to a copy of it to fill in the details of those graphs. To me this actually explains a lot on the graph as were looking at much earlier datasets. At best we have the early WMAP dataset however more likely the COBE. A lot of development occurred since 2004 which the above graphs originated. For example equations. 2.3 to 2.9 are only good approximations in the small Z scales when the Hubble parameter is roughly linear. They do not work well beyond the Hubble horizon. Numerous corrections are needed and depend upon the evolution of the matter, radiation and Lambda evolution. This was a common problem at that era of cosmology. A good paper covering the latter is https://arxiv.org/abs/astro-ph/9905116 Distance measures in Cosmology. By Bunn and Hoggs Although it is slightly older paper it shows the knowledge of the era in how to apply cosmological redshift at greater distance. This is noted in the last link. You will see the equations used in the Tamara Davies paper discussed in the Bunn and Hogg paper. In essence the wordlines did not compensate for the matter, radiation and Lambda evolution accurately at higher redshift values.

Your application is incorrect neither of those documents tells you mass is divisible by (length multiplied by time). You need to study and pay attention to what each of those terms represent and how they are defined. Mass isn't associated with any geometric length nor time.

Well quite frankly it doesn't make sense to mp/(lp.tp^2). Let's start with the first two terms. How does it make sense to take Planck mass ( mass is resistance to inertia change) regardless of being a Planck unit in this case and divide that by a minimal Planck length ? Not to mention the Planck time unit. ? Time being a rate of change. Sorry but that simply doesn't make any applicable sense. PS I'm assuming your using the [math]\cdot[/math] for the multiply operand rather than the cross product. As I am aware your not familiar with inner and cross products in vector notation though that wouldn't make a difference in this case. The logic in either case escapes me. It makes zero sense to take mass and divide or even multiply by length even with time as part of the operation.

I really don't know how your getting your numbers particularly on the powers. No cosmological equation I have ever encountered gives [math] c^7[/math] for example. I highly recommend step back and refresh your memory on the relevant cosmological constant equations. It looks to me as your following the wrong garden path on key relations but I cannot discern where the error is arising from.

This will help you better understand those above spacetime diagrams they look to be very similar to the ones produced by Lineweaver and Davies. The other factor you must also remember is the radius change of the observable universe. This gives the illusion of a curved worldine. However the worldline itself is close to flat. The volume changes are incorporated into these diagrams. Hope this helps https://arxiv.org/abs/astro-ph/0310808 One of the main problems with these diagrams at higher z scales is that the time period between z=10 and Z=1100 is that the time period between that change is rather miniscule due to the non linearity of the Z scale. So it is incredibly difficult to show this on graph.

Hubble distance is the distance light would travel without expansion. So it should be a distance corresponding to universe age. I will try and locate a more up to date graph for you when I get off work. There is a graph by Lineweaver and Davies with a good solid explanation. It is still an older dataset however it is far more accurate than this one. Unfortunately the cosmocalc in my signature is still down it used to be able to produce these graphs.

This graph doesn't look very accurate the redshift scale is nonlinear so that may be throwing me off. For example the CMB lies around z=1100. The Hubble horizon should be closer than the particle horizon. At z=1100 you should have a recession speed of 3.2 c. Judging from the site descriptives and the graph this looks like a graph from an older dataset. Recession speed should not fall off. It's calculated by [math] v_{recessive}H_0 D[/math]

Good point just a side note I've often wondered if the Frenet Serett equations used in R^3 would apply to R^4. However that's just a side note curiosity lol.

This link is earlier in this thread. Unruh came up with an interesting solution. Just thought I would post here for you Joigus. https://arxiv.org/pdf/1703.00543.pdf

Let's take an example. Take two stars at some distance apart Now surround those stars with a uniform mass/energy density. The pressure is uniform so there is no pressure gradient. On all sides of those stars equal pressure is exerted. So no net force exists to give the star movement into a particular direction. Yet the stars do seperate due to expansion. The cosmological constant affects the uniform distribution contributing to added volume. Yet it does not exert a force or pressure term.

Nope the cosmological constant has no gravitational force or Coulomb force term. A force is a vector it has a magnitude and direction. The cosmological constant is a scalar quantity. It's value only has a magnitude. This is one critical detail you have to learn to seperate. The two types of fields will have different dynamics.

Ok start with Newton first law of inertia. Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This describes a freefall condition. It also describes a state where you have either constant velocity or at rest. Now the Lorenz transforms describes the relativistic affects under a constant velocity. See here this link saves me typing the transformation rules. https://en.m.wikipedia.org/wiki/Lorentz_transformation Now any change in velocity or direction involves acceleration. In the Lorentz transforms this is described as rapidity. It will involve a scew symmetry of the Lorentz transforms such as a rotation or boost. Proper acceleration (the acceleration 'felt' by the object being accelerated) is the rate of change of rapidity. https://en.m.wikipedia.org/wiki/Rapidity A straight line geodesic doesn't involve acceleration. Objects that experience no force including psuedoforces move at constant velocity. This isn't a curved spacetime. A curved spacetime describes the particle path when you involve acceleration. Hence curved spacetimes are assymetric. A flat spacetime under constant velocity is symmetric under a 180 degree rotation of the momentum vector. Example a car moves 180 km/hour in the x axis direction. If the car maintains the same velocity in the minus x direction. You have a symmetric relation where the only difference is the change in the plus or minus x direction. When you involve acceleration you now have a curved geodesic or worldwide. (Curved spacetime ). A curved path must involve acceleration as you have direction changes at the minimal.

The Observer in the QM sense means any measurement or interaction. It isn't related to free will. When you measure a superposition wavefunction you have determined the state and the probability function collapses. This wiki link covers this in some detail. https://en.m.wikipedia.org/wiki/Observer_effect_(physics)