Mordred

What causes time dilation requires years of heavy mathematics to fully understand. However here is a helpful starting point. What causes propogation delay of a signal in an electric circuit? As stated its a start point, however its applicable to other field interactions. You must first be absolutely clear on a few key definition. mass is resistance to inertia change.... kinetic energy ability to perform work due to momentum potential energy ability to perform work due to position. They may sound unrelated but believe me they are not. They are essential to understand how multiparticle fields interact and cause signal delays which is the essence of time dilation.

Too bad your understanding of many of the articles you claim back you up actually don't. This is often difficult to show as the proper details is under the math and not the written heuristic explanations that some of these articles use. The heuristic explanations are easily misinterpreted by many posters not just yourself and is a source of numerous misunderstood topics. More often than not posters when looking for support tend to look for key words or expressions that support their claim but never realize the mathematics of those articles describe something else entirely than their own interpretation.

Those extra dimensions are mathematical under definition ib string theory. A dimension is a variable that can change value without changing the value of any other variable. For 4d the 3 spatial and 1 time dimension this is usually the case. Now string theory looks at how other fields interact. They do so by looking specifically at the individual field potentials. This will overlap the volume above but in a smaller potential region depending on the range of each individual force. In order to do so one must add degrees of freedom (independent variables). In the first 4d example the fundamental string will reside there, this fundamental string gives rise to the other particles. They are not dimensions as per extra universes, but extra degrees of freedom of orbifolds and manifolds due to multi particle fields

You get down to it expansion or contraction is heavily related to the thermodynamic properties of each particle species. Of which we can sort their equations of state into fundamental groups. 1) matter only (can still cause expansion, depending on density compared to critical density). 2) Radiation ie photons, neutrinos etc (relativistic particles primarily) ie high kinetic term. 3) The Cosmological constant aka dark energy as a possible contributor. ( scalar field equation of state for this group) https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) The key components to an equation of state is the ratio of mass/energy density (kinetic terms) to pressure or potential energy. This is simplified to the [math] w=\frac{\rho[{p}[/math] see link.

Don't forget to preknife any cut lines, keeps to edges sharp with reduced splintering. You should try to fine tune joint fits with a chisel. Tight fits is best, though you will need to focus on keeping all joint cuts as square as possible. Ideally you should need to lightly tap in any joint fits without damaging wood surfaces. Most cutting blades are 1/8 th in thickness mark both sides of any blade cut where pieces can be salvaged and knife score all cut lines.

Well these are topics to address in another thread. Personally however much of what you described above I don't agree with though at one time I might have. That was back when I detested the usage of stochastics treatments. There is practicality behind QM but quite frankly for my physics interests QFT itself is a better tool. Try not to get too confused on which formulas involve probability and which ones that do not. Its not unusual to simply average a range of possible results such as the harmonic oscillator. Its a common technique even in classical physics.

What is adhok about applying a cutoff, there is always an established reasoning behind those cutoffs. For example it doesn't make much sense to define a particle that has energy levels too low to cause any observable or measurable effect. For that matter in order to be observable you must have some displacement hence operators as opposed to propogators. Though to fully understand an operator you must also define localization under LSZ which is a time ordered metric. Have you ever truly looked at the reasoning behind each type of cutoff or boundary condition? For example define when local action differs from non local effective action without applying a boundary to each of those two terms. Nothing arbitrary or adhok about having that requirement. Another good example being boundary conditions imposed by other field potentials. Primary example being the Dirichlet boundary condition to describe the temperature on a surface as opposed to the Neumann boundary condition which describes the flux of temperature beneath said surface. These boundaries aren't adhok. For example the Poission equations are elliptic so the Direchlet boundary condition is appropriate while the Neumann boundary condition applies to parabolic. In the above case a Green's function is defined not only with respect to an equation and its boundary conditions, but also with respect to a particular region. However more importantly the Greens function provides a limit between measurable "Observable" via ODE's to infinitisimal which are units so small they cannot be measured PDEs (partial differential equations) As far as probability or density functions go well a natural boundary is the set of Real. After all the sign doesn't matter for density. Negative probability via imaginary numbers doesn't particularly make sense either. (not to be confused with correlation functions. This applies to the limits of a domain. Infinity for example is not a number and cannot be manipluated algebraically. It only makes sense with an applied limit on a given function. Limits is a lengthy topic, ie limits of vertical and horizontal asymptotes, limits of the numerator and denominator, limit of quotient which all applies to graphs. I fail to see where you feel QM limits are adhok considering those same limits arise in differential calculus. Good example limit to the slope of a curve. Though under QM the slope is a discontinous wavefunction (discrete units) though thats not only form of discontinuos wavefunctions.

no it also keeps track of number density, not everything in QFT involves probability ie once you take a measurement. Obviously your missing the importance of the cutoffs with regards to fourier analysis. In particular the significance between operators and propogators in terms of the Feyman boundary conditions. However thats a lengthy topic in and of itself that is best left for another thread.

yeah that would be challenging to keep low lol

Funny how there are formulas in QFT that literally calculates the particle number density. So I don't see how it loses track of them. The Bose Einsten and Fermi Dirac statistics is used to calculate the number density of a particle species from the blackbody temperature. in QFT you use the Number operator given by [math]N=\int\frac{d^3p}{2\pi)^3}a^\dagger_\vec{p} a_\vec{p}[/math] where [math]a^\dagger, a [/math] are the creation and annihilation operators. Several important cutoffs in QFT is the IR, UV and LSZ cutoffs to prevent infinities. The Lehmann-Symanzik-Zimmermann formula is used on the scattering amplitudes. In particular its application to path integrals. [math]|\vec{p}\rangle[/math] is the particle, however its described via its momentum eugenstate, The LSZ and QFT use the Klien Gordon as opposed to the Schrodinger equation which provides the second order of the space and time deriviatives [math]-\hbar^2\frac{\partial^2}{\partial^2}\psi(\mathbb{x},t)=(-\hbar^2c^2\nabla^2+m^2c^4)\psi(\mathbb{x},t)[/math] The LSZ formula is extensive in its time ordered path integrals as you approach infinity in particular when you account for the number of vertex external lines on tree level diagrams. (lengthy topic of its own). However the cutoffs provides the bounds. (little sidenote when the operators above commute your describing a boson field, when anticommute its a fermionic field) ie via Pauli (another lengthy topic on how that works with above)

Each space represents a different graph or plot. These different spaces can occupy different dynamics being described in the identical volume. In String theory which employs QM these different spaces more often than not describe different potentials of interactions within a compact potential region. For example if you have a spacetime volume, you first describe the spacetime geometry, then you can describe the potential variations due to say the electromagnetic field at some finite portion of the above region, or the strong force etc. The fundamental goal of string theory is to start with a fundamental string (waveform) that all other particles arise from. Each particle also has a wavefunction (several actually each describing different particle properties). The fundamental string is usually considered to be the graviton spin 2 but not always...Don't confuse this with thinking that gravity causes all other particles lol. It is a unification state of thermal equilibrium where all particles become indistinguishable (thermal equilibrium) commonly called supergravity which later on different forces decouple from. Ie electroweak symmetry breaking. ( this gives rise to different strings in the same volume) much like a waveform has harmonics.Think of an irregular waveform that cannot be described by a single sinisoidal equation. The irregularities can be broken down into the harmonic sinusoidal waveforms that make up the standing wave. Some waveforms from different fields ie electromagnetic causes interference with other waveforms ie strong force, weak force etc. So a reading of a multiparticle field has numerous interferences within itself. Each of these interferences and interactions forms the individual strings and spaces used to model each individual string (waveform) of the same overall fundamental string (spacetime region)

Dang I only have a 1912 physics textbook lol

No problem anytime

Yes the overal topology is flat but one must have care on what the term flat vs curve means in this context. Its not flat as per a shape but flat as to how the universal field densities affect the worldlines of light paths. Curvature causes parallel light paths to either converge or diverge. A flat field geometry maintains parallel paths. This is how it applies within our observable portion. Yes but one has to be careful here the infall of matter into LSS formation aids expansion as it concentrates matter into smaller regions while reducing the overall global density. So a matter only universe can expand due to this evolution as the global density decreases gravity on a global scale lessens. While at the locality of an LSS strengthens. Yes the mass density of an LSS region is much higher than the average. A side note the cutoff boundary of an LSS is when the mass density becomes less than 100 times the critical density of the universe. It is the local strength of gravity that prevents global expansion via the cosmological constant from affecting within the LSS structure. The coupling strength of an LSS overpowers the Lambda term locally. So yes an LSS is in essence decoupled from expansion.

No thats not what I stated at all. You've probably seen the expression " spacetime tells mass how to move, mass tells spacetime how to curve". Spacetime is any metric where time is treated as a dimension. Space is simply the volume. Whether space can exist apart from spacetime is a seperate topic deserving of its own thread. If spacetime requires a mass distribution to cause curvature how can it have no mass ? The quoted section doesn't make much sense considering the the following formulas (not including critical density The acceleration equation is given as [latex]\frac{\ddot{a}}{a}=-\frac{4\pi G\rho}{3c^2}(\rho c^2+3p)[/latex] This leads to [latex]H^2=\frac{\dot{a}}{a}=\frac{8\pi G\rho}{3c^2}-\frac{kc^2p}{R_c^2a^2}[/latex] The evolution of matter, radiation and lambda and how it affects expansion can be seen here [latex]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/latex] These formulas all involve mass terms in the matter, radiation and Lambda density terms. (trying to answer two posts at once) Anyways it is the mass densities of each contributor that defines the rate of expansion. So the quoted section doesn't make much sense. The reason why they don't cause an inherent direction to expansion to LSS and galaxies is those same contributors have a uniform distribution surrounding the LSS and Galaxies. So in essence via f=ma no structure facing has a greater force than any other facing. The uniform distribution doesn't support a stronger force upon any facing to impart inertia. Instead the metric volume itself expands. Not to mention the greater than c expansion rate is due to a specific formula [math] v=H_0d[/math] the greater the distance the greater the recessive velocity. (its an apparent not a true inertial velocity that depends on the observers distance). Local to any observer location the rate is identical within the first Mpc roughly 70 km/sec/Mpc. Being the value of time (now) in the past ie at CMB its roughly 22990 times that value. One can calculate that via the last equation. You can see the column here that applies that equation. The row where S =1.00 and a equals 1.00 is today the last column is rate today the 1090 row is surface of last scattering in the H/H_0 column. We chose to use Gly instead of Mpc as many posters better relate to lightyears as opposed to parsecs [math]{\small\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}[/math] [math]{\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&H/Ho \\ \hline 0.001&1090.000&0.000373&0.000628&45.331596&0.041589&0.056714&22915.263\\ \hline 0.002&608.566&0.000979&0.001594&44.853035&0.073703&0.100794&9032.833\\ \hline 0.003&339.773&0.002496&0.003956&44.183524&0.130038&0.178562&3639.803\\ \hline 0.005&189.701&0.006228&0.009680&43.263304&0.228060&0.314971&1487.678\\ \hline 0.009&105.913&0.015309&0.023478&42.012463&0.396668&0.552333&613.344\\ \hline 0.017&59.133&0.037266&0.056657&40.323472&0.681908&0.960718&254.163\\ \hline 0.030&33.015&0.090158&0.136321&38.051665&1.152552&1.651928&105.633\\ \hline 0.054&18.433&0.217283&0.327417&35.002842&1.898930&2.793361&43.981\\ \hline 0.097&10.291&0.522342&0.785104&30.917756&3.004225&4.606237&18.342\\ \hline 0.174&5.746&1.252327&1.874042&25.458852&4.430801&7.300157&7.684\\ \hline 0.312&3.208&2.977691&4.373615&18.247534&5.688090&10.827382&3.292\\ \hline 0.558&1.791&6.817286&9.184553&9.242569&5.160286&14.365254&1.568\\ \hline 1.000&1.000&13.787206&14.399932&0.000000&0.000000&16.472274&1.000\\ \hline 1.791&0.558&22.979870&16.668843&6.932899&12.417487&17.112278&0.864\\ \hline 2.961&0.338&31.510659&17.154169&10.671781&31.602098&17.220415&0.839\\ \hline 4.896&0.204&40.170941&17.267296&12.969607&63.498868&17.267296&0.834\\ \hline 8.095&0.124&48.860612&17.292739&14.364429&116.275356&17.292739&0.833\\ \hline 13.383&0.075&57.557046&17.298283&15.208769&203.541746&17.298283&0.832\\ \hline 22.127&0.045&66.254768&17.299620&15.719539&347.823873&17.299620&0.832\\ \hline 36.583&0.027&74.952986&17.299815&16.028491&586.370846&17.299815&0.832\\ \hline 60.484&0.017&83.651102&17.299968&16.215356&980.768127&17.299968&0.832\\ \hline 100.000&0.010&92.349407&17.299900&16.328381&1632.838131&17.299900&0.832\\ \hline \end{array}}[/math]

The dimensionless scale factor " a" or the Hubble parameter. Both vary at different points of the expansion history. The reason is quite lengthy to explain but as expansion occurs the density of radiation and matter changes as well but at different ratios. Expansion is a thermodynamic process, as the matter, and radiation density varies while the cosmological constant stays constant each affects expansion though during different eras in our expansion history one has been more dominant than the other. The sequence is radiation, matter then Lambda dominant eras. (inflation is a radiation dominant phase)

How about 5 out 10 massĺess particles are also limitted to c. Though they equal c lol. Also spacetime curvature requires a mass density distribution even though spacetime itself is just a volume where time is treated with dimensionality of length. After all mass tells spacetime how to curve. Probably the more accurate answer is expansion does not involve kinematic motion. As the universe is roughly uniform in mass distribution there is no net force in any direction to cause a directional motion via f=ma. Though unfortunately that tends to confuse some laymen lol.

excellent point

Yeah true enough over a long enough duration taking measurements lol good catch

Ever try to explain all the complexities to the public ? It is a very complex topic. At some point physicists must describe these complexities in terms people can relate to. A good example is the rubber sheet analogy of spacetime curvature. Its simply used to convey the basic concepts

I see nothing to incorrect in the last its accurate as far as the last post goes. However different parts of your body will age at different rates lol. Its simply too insignificant to worry about

No because once again there is different reference frames and therefore different rates involved.

If you were to have an atomic clock sitting next to you the clock and you are still in different reference frames

I lost count lol

Time is a measure of rate of change or duration it is a property of whatever process is being examined.